EDUC 566 Jan13 1
University of Southern California
Rossier School of Education
Course Syllabus
EDUC 566 - Teaching Mathematics and Science
January 2013
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INTRODUCTION AND PURPOSE
From a cultural-historical perspective mathematics and science were not considered separate
disciplines and those who investigated the natural world were called natural philosophers. Perhaps the
acronym STEM - Science, Technology, Engineering and Mathematics – is an attempt to re-integrate
these disciplines into a more holistic approach to the teaching and learning about our natural world.
The philosophical underpinnings of this course are rooted in the cultural-historical viewpoint and
brought to life by challenging students to solve real-world problems through constructive activity and
modeling processes.
Model-based reasoning and inquiry are the heart and soul of what scientists, engineers, and
mathematicians do and therefore a natural means of integrating the STEM disciplines. For instance, we
challenge teacher candidates to create a model of a vehicle collision for a movie stunt company. Using
a ‘toy’ kit made by the K’nex Education Company student teams construct vehicles and drawings of
the vehicles, conduct performance investigations, create tables and graphs of their performance
characteristics, form diagrams of the collision, and present their complex model to their colleagues.
Such a process emulates the actual practices of the STEM community. We firmly believe that unless
our teacher candidates themselves experience this process first hand it is unlikely that they will engage
their own students in these critical dimensions of STEM practices.
COURSE OBJECTIVES
Candidates will develop:
an understanding of and flexible application of learning theories to the learning of elementary
mathematics and science.
general instructional strategies and those specific to mathematics and science.
learning experiences in which mathematics and science is related to and integrated with
students’ interests, community concerns, and societal issues.
balanced assessment practices.
a systematic approach based on learning theory to the analysis and design of curricula.
an attitude of inquiry toward one’s practice (lessons as experiments) through individual and
collaborative study, discussion, assessment, analysis, and classroom –based research and
practice.
self-efficacy, craftsmanship, collegiality, and flexibility in addressing problems of practice in
the classroom, school, and community.
EDUC 566 Jan13 2
SUMMATIVE COURSE ASSESSMENT
The Content Area Task – Science. In this assessment you will provide an overview of
important features of your classroom context that influence your instructional decisions. Your response
will provide evidence of: 1) your knowledge of students; and 2) your ability to identify and summarize
important factors related to students’ science learning and the school environment.
Use the learning cycle lesson plan format provided (see Appendix B and week 10 of the
syllabus for details). The plan should include the following information: student academic content
standards, ELD standards (if applicable), learning objectives, formal and informal assessments,
instructional strategies and learning tasks, and resources and materials.
Given the description of students that you provided, how do your choices of instructional
strategies, materials, technology, and the sequence of learning tasks reflect students’ backgrounds,
developmental levels, interests, and needs? Be specific about how your knowledge of these students
informed the lesson plans, such as the choice of text or materials used in lessons, how groups were
formed or structured, using student learning or experiences (in or out of school) as a resource, or
structuring new or deeper learning to take advantage of specific student strengths. (TPEs 4,6,7,8,9).
CTC STANDARDS
Standard Unit I or R Description Assessment
Standard 4
Relationships
Between Theory
and Practice
1, 2 Introduced Candidates examine
Feuerstein’s Theory of
Cognitive Modifiability and
its relationship to human
learning; instruction, and
student attitudes and
conduct.
Describe what you see as the
important concepts in this
article(s). Elaborate on why
you think so. How do you
view its connection to your
classroom practice?
Describe the relationship
between the article(s) and
what you have learned about
learning theories.
Candidates write a reflection paper in
week 1 and 2 (5 pages double spaced),
answering the following prompts:
Standard 5
Standard 6
Pedagogy and
Reflective Practice
3-10 Introduced Candidates evaluate
instructional alternatives,
articulate the pedagogical
reasons for instructional
decisions,
and reflect on their teaching
practices.
Candidates respond in writing and
verbally to prompts requiring them to
evaluate instructional strategies
presented from text, video, and
classroom observations.
Standard 7A
Standard 8A(a)
Pedagogical
Preparation for
Mathematics
3-10 Introduced As part of 566, candidates
learn specific teaching
strategies that are effective
in supporting them to teach
the state-adopted academic
content standards for
students in mathematics (K-
8).
Based on classroom observations, text,
and video resources candidates present
written and verbal analysis of a variety
effective instructional strategies
designed to:
develop students’
understanding of mathematical
computations, concepts, and
symbols; solve common
problems,
EDUC 566 Jan13 3
apply solutions to novel
problems,
help students understand
different mathematical topics
and make connections among
them,
solve real-world problems
using mathematical reasoning
and concrete, verbal, symbolic,
and graphic representations,
and
foster positive attitudes toward
mathematics, and encourage
student curiosity, flexibility,
and persistence in solving
mathematical problems.
Standard 8A(b)
Pedagogical
Preparation for
Science
3-10 Introduced As part of 566 candidates
learn specific teaching
strategies that are effective
in supporting them to teach
the state-adopted academic
content standards for
students in science (K-8).
They understand and
demonstrate through lesson
planning how to balance the
focus of instruction between
science information,
concepts, and investigations.
Their explanations,
demonstrations, and class
activities serve to illustrate
science concepts and
principles, scientific
investigation, and
experimentation. Candidates
emphasize the importance of
accuracy, precision, and
estimation.
Based on classroom observations, text,
and video resources candidates present
written and verbal analysis of a variety
effective instructional strategies
designed to balance the focus of
instruction between science information,
concepts, and investigations,
Candidates create an integrated math
and science lesson based on the
learning cycle. The lesson should
include mathematics standards in
addition to science standards. Use the
5e learning cycle model to design the
lessons. In your 5e lesson plan respond
to the specific bulleted items listed in
the description of the learning cycle. In
weeks 7 and 10 you will submit
modified drafts of components of the
final project thereby giving the
instructors an opportunity to critique
your progress.
Standard 13
Standard 14.2
Learning to Teach
through supervised
fieldwork
3-10 Introduced As part of 566, candidates,
demonstrate a fundamental
ability to teach in the major
domains of the Teaching
Performance Expectations.
Candidates create an integrated math
and science lesson based on the learning
cycle. The lesson should include
mathematics standards in addition to
science standards. Use the 5e learning
cycle model to design the lessons. In
your 5e lesson plan respond to the
specific bulleted items listed in the
description of the learning cycle. In
weeks 7 and 10 you will submit
modified drafts of components of the
final project thereby giving the
instructors an opportunity to critique
your progress.
Standard 14.5
Learning to Teach
through supervised
fieldwork
3-10 Introduced As part of 566 each
candidate observes,
discusses, reflects on and
participates lesson planning
Candidates create and analyze lesson
plans, analyze classroom observations
and videos of effective teaching as well
as videos of their teaching and videos of
EDUC 566 Jan13 4
and reflection and teaches
individual students and
groups of students before
being given daily
responsibility for whole-
class instruction.
Prior to or during the
program each candidate
observes and participates in
two or more K-12
classrooms, including
classrooms in hard-to-staff
and/or underperforming
schools.
their fellow classmates’ teaching events.
Candidates create and analyze lesson
plans, analyze classroom observations
and videos of effective teaching as well
as videos of their teaching and videos of
their fellow classmates’ teaching events.
Standard 14.6
Learning to Teach
through supervised
fieldwork
1 M As part of 566, each
candidate must have
satisfied the basic skills and
subject matter requirements.
All candidates must pass the multiple
subject CSET.
TEACHER PERFORMANCE EXPECTATIONS (TPEs)
TPE Unit I or
R
Description Assessment
TPE 1: Making
Subject Matter
Comprehensibl
e to Students
2-10 I Candidates demonstrate the ability
to teach the state adopted academic
content standards for students in
science and mathematics.
Candidates create an integrated math and science
lesson based on the learning cycle. The lesson
should include mathematics standards in addition
to science standards. Use the 5e learning cycle
model to design the lessons. In your 5e lesson plan
respond to the specific bulleted items listed in the
description of the learning cycle. In weeks 7 and 10
you will submit modified drafts of components of
the final project thereby giving the instructors an
opportunity to critique your progress.
TPE 3
Interpretation
and Use of
Assessments
9 I Candidates understand the
purposes and uses of different
types of diagnostic instruments,
including
entry level, progress-monitoring
and summative assessments.
Candidates access their state’s department of
education website and find a few released test
items used by their state to determine annual yearly
progress (AYP) as required by NCLB. Using
NCTM’s, Standard 3 Worthwhile Mathematical
Tasks for characteristics of good problem-based
assessment items, candidates analyze one of the
released problems using the seven criteria listed.
Then, if necessary, candidates try to improve the
item so that it becomes a problem-based
assessment that would be useful in the classroom.
TPE 4: Making
Content
Accessible
2-10 I Candidates incorporate specific
strategies, teaching/instructional
activities, procedures and
experiences that address state-
adopted academic content
standards for students in order to
provide a balanced and
comprehensive curriculum.
Candidates create an integrated math and science
lesson based on the learning cycle. The lesson
should include mathematics standards in addition
to science standards. Use the 5e learning cycle
model to design the lessons. In your 5e lesson plan
respond to the specific bulleted items listed in the
description of the learning cycle. In weeks 7 and 10
you will submit modified drafts of components of
the final project thereby giving the instructors an
opportunity to critique your progress.
TPE 5: Student
Engagement
2-10 I Candidates clearly communicate
instructional objectives to students.
They ensure the active and
Candidates create an integrated math and science
lesson based on the learning cycle. The lesson
should include mathematics standards in addition
EDUC 566 Jan13 5
equitable participation of all
students.
to science standards. Use the 5e learning cycle
model to design the lessons. In your 5e lesson plan
respond to the specific bulleted items listed in the
description of the learning cycle. In weeks 7 and 10
you will submit modified drafts of components of
the final project thereby giving the instructors an
opportunity to critique your progress.
TPE 6A:
Developmental
ly Appropriate
Teaching
Practices
Grades K-3
2-10 I Candidates create a structured day
with opportunities in mathematics
and science for movement. They
design math/science activities that
suit the attention span of young
learners. Their instructional
activities connect with the
children’s immediate world; draw
on key content from more than one
subject area; and include hands-on
experiences and manipulatives that
help students learn.
Candidates respond in writing and verbally to
prompts requiring them to evaluate instructional
strategies presented from text, video, and
classroom observations specific to K-3 students.
TPE 6B:
Developmental
ly Appropriate
Teaching
Practices
Grades 4-8
2-10 I Candidates design math/science
learning activities to extend
students’ concrete thinking and
foster abstract reasoning and
problem-solving skills. They help
students develop learning
strategies specific to math/science
to cope with increasingly
challenging academic curriculum.
They assist students, as needed, in
developing and practicing
strategies for managing time and
completing assignments.
Candidates develop students’
skills for working in groups to
maximize learning.
Candidates respond in writing and verbally to
prompts requiring them to evaluate instructional
strategies presented from text, video, and
classroom observations specific to 4-8 students.
TPE 7:
Teaching
English
Learners
2-10 I Candidates know and apply
pedagogical theories, principles
and practices for the development
of academic language,
comprehension, and knowledge in
the subjects of the core curriculum.
They use systematic instructional
strategies, including
contextualizing key concepts, to
make grade-appropriate or
advanced curriculum content
comprehensible to English
learners.
Candidates create an integrated math and science
lesson based on the learning cycle. The lesson
should include mathematics standards in addition
to science standards. Use the 5e learning cycle
model to design the lessons. In your 5e lesson plan
respond to the specific bulleted items listed in the
description of the learning cycle. In weeks 7 and 10
you will submit modified drafts of components of
the final project thereby giving the instructors an
opportunity to critique your progress.
TPE 8:
Learning about
Students
2-10 I Candidates draw upon an
understanding of patterns of child
and adolescent development to
understand their students. Using
formal and informal methods, they
assess students’ prior mastery of
academic language abilities,
math/science content knowledge,
and skills, and maximize learning
opportunities for all students.
Through interpersonal interactions,
they learn about students’
math/science abilities,
Candidates create an integrated math and science
lesson based on the learning cycle. The lesson
should include mathematics standards in addition
to science standards. Use the 5e learning cycle
model to design the lessons. In your 5e lesson plan
respond to the specific bulleted items listed in the
description of the learning cycle. In weeks 7 and 10
you will submit modified drafts of components of
the final project thereby giving the instructors an
opportunity to critique your progress.
EDUC 566 Jan13 6
ideas, interests and aspirations.
TPE 9:
Instructional
Planning
2-10 I Candidates plan instruction that is
comprehensive in relation to the
subject matter to be taught and in
accordance with state-adopted
academic content standards for
students.
They establish clear long-term and
short-term goals for student
learning, based on state and local
standards for student achievement
as well as on students’ current
levels of achievement. They use
explicit teaching methods such as
direct instruction and inquiry to
help students meet or exceed grade
level expectations. They plan how
to explain content clearly and
make abstract concepts concrete
and meaningful.
Candidates create an integrated math and science
lesson based on the learning cycle. The lesson
should include mathematics standards in addition
to science standards. Use the 5e learning cycle
model to design the lessons. In your 5e lesson plan
respond to the specific bulleted items listed in the
description of the learning cycle. In weeks 7 and 10
you will submit modified drafts of components of
the final project thereby giving the instructors an
opportunity to critique your progress.
By addressing these Teacher Performance Expectations, this course assists you in preparing for the
Teacher Performance Assessment (TPA) at the conclusion of this program. Completion of the TPA is
required in order to be recommended for a credential from the University of Southern California.
COURSE REQUIREMENTS
1. Annenberg videos – In weeks 2, 4, 6, 8, and 10 you will view the assigned Annenberg video and
respond in writing to the prompts. Be prepared to discuss your written responses with your forum
group. These assignments are worth 5 points each, total of 25 points. Each of the five assignments
are found in Appendix E.
2. Reading Responses – Weeks 1, 2, and 8.
Read the assigned articles the week before they are to be discussed. Upload the responses
24 hours before Class Time to the appropriate on-line page before Class Time. A one-point
deduction will be incurred if the responses are late.
Write a reflection paper (2-3 pages double spaced) on the assigned article(s). Address the
following prompts:
a. Describe what you see as the important concepts in this article(s). Elaborate on why
you think so.
b. How do you view its connection to your classroom practice?
c. Describe the relationship between the article(s) and what you have studied regarding
learning theories.
d. Include citations.
3. Mathematics and Science Textbook Responses – Weeks 3 through 9
Read the chapter(s) and respond to the prompts for the chapter the week BEFORE they are
to be discussed. Upload the responses 24 hours before Class Time to the appropriate on-line
page before Class Time. A one-point deduction will be incurred if the responses are late.
EDUC 566 Jan13 7
Responses must be written using Word software so that the responses may be copied and
pasted to the Note Pods that will be used during Class Time. These responses to prompts
are to be completed prior to the week that the textbook assignment will be discussed in
class. Your responses will be used during Class Time in break out groups and whole class
discussions. Your instructor may require you to attach all or part of your paper to the Notes
Pod during group or whole-class instruction.
4. Class Time Requirements
Participation: We are encouraging you to use multimedia tools to create the most effective
learning environments for your classroom including this class. We expect you to be
connected through a computer/monitor, video camera, and audio connection. This makes
you eligible to earn maximum point value for the class time work. If you are connected by
audio only, you are not eligible for the maximum point value assigned during class time.
Each student will be required to copy and paste all or parts of homework assignments
during class time. Students are also required to examine text, image, audio, and video
information from the instructor and other students during class time. Instructors will award
points during class time for text, image, audio, and video contributions. Students who do
not meet these requirements will be deducted points during class time. Instructors will
notify students who are deducted points through the private chat option while on line. We
are aware that Internet and phone networks can be unpredictable and out of your control. In
our experience, these type of interruptions are not frequent, but when they do occur,
students will not be held accountable for such events.
5. IMAP CD Assignments – Weeks 2, 4, 6, 7, and 9.
Watch the prompt for each video labeled “To Consider Before Viewing the Video Clip”
and write out answers to the questions.
View the interactions and respond in writing to the prompts labeled “Reflection Questions
For Teachers.” Sometimes there is only one prompt labeled “for teachers”
Upload the responses 24 hours before Class Time to the appropriate on-line page before
Class Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Microsoft Word software so that the responses can be
copied and pasted to Note Pods that will be used during Class Time. These responses are to
be completed prior to the week that the CD assignment will be discussed in class. Your
responses will be used during Class Time in breakout groups and whole class discussions.
Your instructor may require you to attach all or part of your responses to the Notes Pod
during group or whole-class discussions. All videos will be found in Phillip, R., Cabral, C.,
& Schapelle, B. (2005). Searchable IMAP video collection; Children’s mathematical
thinking clips. San Diego, CA: Center for Research in Mathematics and Science Education,
San Diego State University.
IMAP CD-ROM: Integrating Mathematics and Pedagogy to Illustrate Children's Reasoning San
Diego State University Foundation Randy Philipp, San Diego State University
ISBN-10: 0131198548
ISBN-13: 9780131198548
Publisher: Allyn & Bacon
Copyright: 2005
Format: CD-ROM Only
EDUC 566 Jan13 8
6. Model-Based Inquiry Project, Weeks 2, 3, 4, 6, and 10.
For this project you will need to purchase the Forces, Energy, and Motion kit from K’Nex
Industries, Inc. Toll free number 1-888-ABC-KNEX. P.O. Box 700 Hatfield, PA 19440-
0700. The kit can be purchased online at www.knexeducation.com.
For each K’Nex lesson you will conduct the investigation and respond in writing to the
embedded questions and prompts.
During the Class Time discussions you will present and discuss your findings.
7. Lesson Design Project – Weeks 5, 7, and 10
Create a science lesson(s) based on the learning cycle. Use the 5E Learning Cycle Model
(see Appendix B; The K’Nex Forces, Energy, and Motion kit; and websites for descriptions
and examples of the learning cycle to design the lessons.
In weeks 5 and 7 you will submit first drafts of components of the final project thereby
giving the instructors an opportunity to critique your progress. For the final lessons due
Week 10 you will address the PACT Context for Learning and Science Content Task
components. In week 10 up to 10 points will be awarded based on the Planning Making
Content Accessible rubric.
Mathematics misconceptions resources
http://www.ericdigests.org/pre-9213/hispanic.htm
http://www.counton.org/resources/misconceptions/
http://www.svsu.edu/mathsci-center/uploads/math/gmmisconcept.htm
Science misconception lists
http://www.amasci.com/miscon/opphys.html
http://www.newyorkscienceteacher.com/sci/miscon/index.php
http://www.huntel.net/rsweetland/science/misconceptions/
http://scienceinquirer.wikispaces.com/misconception
http://www.emints.org/ethemes/resources/S00001766.shtml
http://www.svsu.edu/mathsci-center/uploads/science/gsmiscon.htm
http://www.digital-recordings.com/publ/pubscie.html
Learning Cycle websites
http://www.coe.ilstu.edu/scienceed/lorsbach/257lrcy.htm
http://www.learnnc.org/lp/pages/663
http://faculty.mwsu.edu/west/maryann.coe/coe/inquire/inquiry.htm
http://www.the-aps.org/education/lot/lotunits.htm
http://www.bioedonline.org/slides/slide01.cfm?q=learning+cycle+models
http://findarticles.com/p/articles/mi_hb6515/is_3_20/ai_n29459091
http://www.thefreelibrary.com/ASTE+invited+article:+why+the+learning+cycle%3F-
a0184150730
Examples of teacher created learning cycles – free for 10 days.
http://www.lessonplanet.com/search?keywords=learning+cycle&rating=3
All of the requirements for this course are described below. The MAT program adheres to the Carnegie
standard for course workload. The expected weekly “class time” or contact hours for a course of this
length and credit value is 3 hours 10 minutes. The expected weekly “out of class” workload for this
course is approximately 6 hours 20 minutes. The following provides a description of all of the Class
EDUC 566 Jan13 9
Time activities and Out-of-Class assignments that are required for this course.
Class Time Class Time and/or contact hours weekly: The class meets once a week for 2 hours. For on-line
students, in order to receive full credit for class time, you must be present via video and
teleconferencing. Class time and participation is worth 10% of the overall course grade.
GRADE DISTRIBUTION TABLE
A 100-95% B+ 89-86% C+ 79-76 % D+ 69-66% F 59-0%
A- 94-90% B 85-83% C 75-73% D 65-63%
B- 82-80% C- 72-70% D- 62-60%
DISTANCE LEARNING
This course is offered both on-line and on campus; the activities, expectations and requirements are
identical between the two versions. The on-line course is conducted through a combination of real time
and asynchronous modules, just as the on-campus version is conducted with some in-class and out-of-
class sessions. About 70% of the course will occur asynchronously. All candidates will be required to
complete assignments on-line, in the field and independently along with completing related reading
assignments. The time needed to complete all assignments fulfills course unit time requirements.
By this point in the program, candidates' level of technical competence should include basic
knowledge of the Internet. They should have an account on, at least, one site that allows people to
interact with one another (e.g. Facebook, MySpace, Skype, etc.). Basic tasks will include posting
attachments, opening and posting discussion forums and uploading assignments including video clips
(the mechanics of this will be taught). As in past courses, candidates will need to be able to video
record their interactions with candidates (which may be accomplished through the use of a portable
micro video camera) and upload edited versions (time limited) of their work. In addition, to complete
assignments and access course documents, candidates should have some familiarity with Microsoft
Word, Power Point, Excel, and basic Internet surfing.
Candidates will have ongoing access to the instructor and fellow classmates throughout the course.
Through the Course Wall, e-mails, course calendars, and Forums, the instructor will maintain ongoing
communication with candidates. These tools also provide candidates with a variety of ways to contact
the instructor, share their ideas, comments and questions through private and public means. In addition,
candidates will be made aware of real-time opportunities to engage in discussions with the instructor
and their fellow classmates. The Course Wall provides a place for the instructor to share new
information and new postings. Due dates will automatically appear both on a student’s homepage and
in their calendar.
E-mail and chat will be the primary forms of immediate communication with the instructor. E-mail
will be checked on a daily basis during the weekdays and will be responded to within 48 hours. The
course calendar provides candidates with assignment due dates and notification of scheduled office
hours for all faculty members teaching this course. Candidates may attend office hours with any
instructor; however, if a student has a specific question about assignments or coursework, it is
preferable to attend office hours with your instructor of record.
The Forum provides candidates a place to post questions, comments, or concerns regarding readings
and assignments at any time during the duration of the course. In addition to weekly Class Time
sessions, the Forum is the primary location for candidates to communicate their learning with one
another. It will be open at all times for postings and reactions.
EDUC 566 Jan13 10
All required materials will be prepared and posted prior to the start of the course, but an instructor may
add additional optional material at any point. All links and attachments will be checked weekly for
updates.
In the Event of Technical Breakdowns
Candidates may submit assignments to the instructor via e-mail by the posted due date. Remember to
back up your work frequently, post papers on the LMS (Learning Management System) or in
Blackboard once completed, load files onto a power drive, and keep a hard copy of papers/projects.
Standards of Appropriate Online Behavior:
The protocols defined by the USC Student Conduct Code must be upheld in all online classes.
Candidates are not allowed to post inappropriate material, SPAM to the class, use offensive language
or online flaming. For more information, please visit:
< http://www.usc.edu/student-affairs/SJACS/ >
ACADEMIC ACCOMMODATIONS
The University of Southern California is committed to full compliance with the Rehabilitation Act
(Section 504) and the Americans with Disabilities Act (ADA). As part of the implementation of this
law, the university will continue to provide reasonable accommodation for academically qualified
candidates with disabilities so that they can participate fully in the university’s educational programs
and activities. Although USC is not required by law to change the “fundamental nature or essential
curricular components of its programs in order to accommodate the needs of disabled candidates,” the
university will provide reasonable academic accommodation. It is the specific responsibility of the
university administration and all faculty serving in a teaching capacity to ensure the university’s
compliance with this policy.
Any student requesting academic accommodations based on a disability is required to register with
Disability Services and Programs (DSP) each semester. A letter of verification for approved
accommodations can be obtained from DSP. Please be sure the letter is delivered to me as early in the
semester as possible. DSP is located in STU 301 and is open 8:30 a.m. - 5:00 p.m., Monday through
Friday. The phone number for DSP is (213) 740-7766.
ACADEMIC INTEGRITY
The University’s Student Conduct Code articulates violations that are most common and readily
identifiable. Conduct violating university community standards that is not specifically mentioned
still may be subject to disciplinary action. General principles of academic honesty include and
incorporate the concept of respect for the intellectual property of others, the expectation that
individual work will be submitted unless otherwise allowed by an instructor, and the obligations
both to protect one’s own academic work from misuse by others as well as to avoid using another’s
work as one’s own. All candidates are expected to understand and abide by these principles.
Sanctions for violations of the university Student Conduct Code are assessed appropriately for the
cited violation. Sanctions will be considered in light of candidates’ entire conduct records at the
university and will be designed to hold candidates accountable for their actions and the resulting or
potential consequences of such actions, to promote the educational well-being of candidates and to
protect the educational environment of the university and the safety of its community.
EDUC 566 Jan13 11
All academic integrity violations will result in an academic consequence. Failure to comply with
the terms of any imposed sanctions may be considered an additional violation.
Scampus, the USC student guidebook contains the Student Conduct Code and information on
Academic Integrity. It is the student’s responsibility to be familiar with and abide by these
guidelines, which are found at:
http://web-app.usc.edu/scampus/
A summary of behaviors violating University standards can be also found at:
http://web-app.usc.edu/scampus/1100-behavior-violating-university-standards-and-appropriate-
sanctions/
INCOMPLETES
IN – incomplete (work not completed because of documented illness or some other emergency
occurring after the eighth week of the semester; arrangements for the IN and its removal should be
initiated by the student and agreed to by the instructor prior to the final exam); IX – lapsed incomplete.
Conditions for Removing a Grade of Incomplete - If an IN is assigned as the student’s grade, the
instructor will fill out the Incomplete (IN) Completion form which will specify to the student and to
the department the work remaining to be done, the procedures for its completion, the grade in the
course to date and the weight to be assigned to the work remaining to be done when computing the
final grade. A student may remove the IN by completing only the portion of required work not finished
as a result of documented illness or emergency occurring after the eighth week of the semester.
Previously graded work may not be repeated for credit. It is not possible to remove an IN by re-
registering for the course, even within the designated time.
Time Limit for Removal of an Incomplete - One calendar year is allowed to remove an IN.
Individual academic units may have more stringent policies regarding these time limits. If the IN is not
removed within the designated time, the course is considered “lapsed,” the grade is changed to an “IX”
and it will be calculated into the grade point average as 0 points. Courses offered on a Credit/No Credit
basis or taken on a Pass/No Pass basis for which a mark of Incomplete is assigned will be lapsed with a
mark of NC or NP and will not be calculated into the grade point average.
EDUC 566 Jan13 12
COURSE AND ASSIGNMENT OVERVIEW
EDUC 566 Jan13 13
Week
and
Unit
No.
HW Assignments Due
Date
Points
1 Read the Feuerstein article pgs 50-75. 8 points awarded before class
time.
Write a reflection paper (2 pages double spaced), answering the
following prompts:
1. Based on the most important concepts in this article describe how
you will use them as part of your instructional practices (at least one
page).
2. Describe the relationship between the article(s) and what you have
learned about learning theories.
3. Create a graphic organizer that depicts the important ideas in the
article.
Describe your experiences as a learner of mathematics and science - 2
points to be awarded during Class Time.
Include recollections from elementary, middle, high school, and
college experiences. Equally important, describe informal learning
experiences that are related to science and mathematics.
24 hours
before
class
time
10
points
total
2 Read the Feuerstein article pgs 75-100. 8 points awarded before class
time.
Write a reflection paper (2 pages double spaced), answering the
following prompts:
1. Based on the most important concepts in this article describe how
you will use them as part of your instructional practices (at least one
page).
2. Describe the relationship between the article and what you have
learned about learning theories.
3. Create a graphic organizer that depicts the important ideas in the
article.
IMAP video 1. 2 points awarded during class time.
Video Clip 1. View the interactions on video clip 1. Read the prompt
labeled “To Consider Before Viewing the Video Clip” and write out
answers to Reflection Questions 1, 1a, 1b, 1c, 2,3,4,5a, and 5c For
Teachers.
Annenberg Video – Problem Solving. View the Problem Solving
video and respond in writing to one question from each group. Be
prepared to discuss your written responses with your forum group. 5
points.
Conduct the K’nex Vehicle Gravity Design Competition found in
Appendix C.
You should complete the activities through the second vehicle design.
The completed competition will be due in week three.
24 hours
before
class
time
15
points
total
EDUC 566 Jan13 14
3 Read Van de Walle Ch. 9 Developing Meanings for Operations 145-
166 (21 pp.). Create 6 comparison problems a follows: Difference
unknown, larger unknown, smaller unknown, product unknown, set
size unknown, and multiplier unknown. 2 points awarded before class
time.
Read Lawson Ch 1. Respond to question 1 p 21. 4 points awarded
before class time.
Conduct the K’nex Vehicle Gravity Design Competition found in
Appendix C. 4 points to be awarded during Class Time.
You should complete all of the activities.
24 hours
before
class
time
10
points
total
4 Van de Walle Ch 10 – 20 pgs. 2 points awarded before class time. HW
Activity 10.18: Patterns in the Nines facts. P. 179. Describe the
patterns you found and identify the cognitive functions used in pattern
identification.
Lawson Ch. 3. How Students Think. – 20 pgs. Answer question 2, pg
59. 3 points awarded before class time. Read Lawson Chapter Lawson
Ch. 3. How Students Think. – 20 pgs.
Answer question 2, pg 59.
Administer Puzzle 2 pg. 44 to three students: How High Will
the Water Rise? Give the Puzzle to one student at a time so that
he or she can explain his or her answers and reasoning. Record
students’ responses and classify the answers and explanations
into developmental levels.
3 points awarded before class time.
IMAP Video 3 - 2 points to be awarded during Class Time.
Read the prompt labeled “To Consider Before Viewing the Video
Clip” and write out answers to the questions.
View the interactions on video clip 3 and respond in writing to
prompts 4b and 5 in the section “Reflection Questions For Teachers.”
Annenberg video
Workshop 1. Astronomy: Eliciting Student Ideas
(http://www.learner.org/resources/series29.html) –. Be prepared to
discuss your written responses with your forum group. 5 points.
Model-Based Inquiry – Invent an egg protection device. 3 points
awarded during class time.
24 hours
before
class
time
15
points
total
5 Lawson Ch 6. Inquiry Instruction, 13 pgs.
Lawson Ch. 7. Planning for Inquiry. 16 pages.
Learning cycle lesson plan – first draft. Create a science lesson based
on the learning cycle. Use the 5e learning cycle model to design the
lesson. In your 5e lesson plan respond to the specific bulleted items
24 hours
before
class
time
10
points
total
EDUC 566 Jan13 15
listed in the description of the learning cycle. 8 points awarded before
class time.
Van de Walle Ch 12 - 27 pgs. Ch 12 Developing Strategies for Whole-
Number Computation 213-239 (26 pp). 2 points. Activity “Pause and
Reflect” p. 234. Identify the cognitive functions you used to solve the
problems.
6 Van de Walle Ch 14 – 32 pgs. Ch 14 Algebraic Thinking:
Generalizations, Patterns, and Functions pp. 254-286.
HW Activity 14.3, p 258: What Do You Know about the Shapes? 2
points awarded before class time. Create another problem and identify
the cognitive functions you used to solve the problem you created.
Ch 14 Activity 14.9 Conjecture Creation. Challenge your students to
make up conjectures on their own after you have modeled the process.
Describe in writing the model(s) you created and how the students
responded. 4 points before class time.
IMAP Video 13. Read the prompt labeled “To Consider Before
Viewing the Video Clip” and write out answers to the questions.
View the interactions on video clip 13 and respond in writing to the
prompts labeled “Reflection Questions For Teachers.” 2 points
awarded during class time.
Annenberg Video – Workshop 2. Biology: Why Are Some Ideas So
Difficult?
Focuses on the need for conceptual understanding and examines the
scope of student ideas by exploring the central idea of photosynthesis;
that the substance of plants comes mostly from the air.5 points.
Collides Investigation. Use knowledge from your K’nex experiences
to create a model of a two vehicle collision. 2 points awarded during
class time.
24 hours
before
class
time
15
points
total
7 Learning Cycle Lesson Plan revised draft. 4 points awarded before
class time.
Van de Walle Ch 18 – 21 pgs. Respond in writing to Pause and Reflect
prompts on pages 351 and 364. 4 points awarded during class time.
IMAP video 15. 2 points awarded during class time. Read the prompt
labeled “To Consider Before Viewing the Video Clip” and write out
answers to the questions.
View the interactions on Video Clip 15 and respond in writing to the
prompts labeled “Reflection Questions For Teachers.”
24 hours
before
class
time
10
points
total
EDUC 566 Jan13 16
8 Read Schmittau, J. 2003. Cultural historical theory and mathematics
education (pp. 225-245). 6 points awarded before class time. Write a
reflection paper, about three pages double spaced, answering the
following prompts:
1. Describe what you see as the important concepts in this article(s).
Elaborate on why you think so.
2. How do you view its connection to your classroom practice? This
section should be about two-thirds of the paper.
Peters & Stout Science in Elementary Education Ch 4 - 35 pgs. 2
points awarded during class time. Create a concept map for the big
idea in your learning cycle lesson (pg 81,82)
Annenberg Video – Workshop 5. Vision: Can We Believe Our
Own Eyes? (90 min.)
Explores the origins of student ideas to find out whether experience
equals learning. Shows how experience can work for or against
learning because students can disbelieve concepts that they have
“learned.”Be prepared to discuss your written responses with your
Forum group. 5 points.
24 hours
before
class
time
13
points
total
9
Access your state’s department of education website and find a few
released test items used by your state to determine annual yearly
progress (AYP) as required by NCLB. For the released items, first
decided if they are good problem-based assessments that help you find
out about students understanding of the concepts involved. In Van de
Walle see Appendix B, Standard 3 Worthwhile Mathematical Tasks
for characteristics of good problem-based assessment items and
analyze one of the released problems using the seven criteria listed.
Then, if necessary, try to improve the item so that it becomes a
problem-based assessment that would be useful in the classroom. 6
points awarded before class time.
Read Van de Walle Chapter 16. Ch 16 Developing Strategies for
Fraction Computation 309-327 (19 pp). HW Activity 16.1 First
Estimates p. 311. 2 points awarded during class time. Randomly
estimate and write 10 addition or subtraction fraction problems each
on 10 index cards on 1 side. Quickly look at each card for no more
than 5 seconds and write on the back if it is more or less than 1.
Upon completion, explain why you made your decisions.
IMAP video 17. 2 points awarded during class time. Watch video clip
17 – Sharing of story-problem solutions. Read the prompt labeled “To
Consider Before Viewing the Video Clip” and write out answers to the
questions. View the interactions on video clip 17 and respond in
24 hours
before
class
time
10
points
total
EDUC 566 Jan13 17
writing to the prompts labeled “Reflection Questions For Teachers.”
10 PACT event – Content Area Task in Science 10 points
Annenberg video – Following Children’s Ideas in Mathematics. View
the Following Children’s Ideas in Mathematics video and respond in
writing to the prompt: describe what you learned about the long-term
development of students’ mathematical thinking.
Be prepared to discuss your written responses with your forum group.
5 points.
Tug-Of-War – 2 points awarded during class time. Your task is to
design a vehicle that will win a tug-o-war against any other vehicle.
24 hours
before
class
time
17
points
total
EDUC 566 Jan13 18
UNIT 1 – Week 1
The Theory of Mediated Learning Experience
LEARNING OBJECTIVES
Introduce participants to Reuven Feuerstein’s theory of Structural Cognitive Modifiability
through Mediated Learning Experience (MLE). MLE is the engine that drives cognitive
modifiability and develops an individual’s cognitive functions.
Analyze mathematics and science standards using Bloom’s Taxonomy.
READER - TEXT BOOK ASSIGNMENTS
Feuerstein, R., Falik, L., & Rand, Y. (2006). Chapter 3 The Theory of Mediated Learning Experience
pgs 55-95. Jerusalem, ICELP Publications.
1. Reading Response - 8 points. Upload 24 hours before Class Time. A one-point deduction will be
incurred if the responses are late.
Read the Feuerstein article.
Based on the most important concepts in this article describe how you will use them as part of
your instructional practices (at least one page).
Describe the relationship between the article(s) and what you have learned about learning
theories.
Create a graphic organizer that depicts the important ideas in the article.
2. Describe your experiences as a learner of mathematics and science - 2 points to be awarded
during Class Time. Upload 24 hours before Class Time. A one-point deduction will be incurred if
the responses are late.
Include recollections from elementary, middle, high school, and college experiences. Equally
important, describe informal learning experiences that are related to science and mathematics.
3. Class Time – 2 points to be awarded during Class Time.
UNIT 2 – Week 2
Applying the Theory of Mediated Learning Experience
LEARNING OBJECTIVES
Apply Mediated Learning Experience’s universal criteria, situational parameters, and cognitive
functions to the teaching and learning of mathematics and science.
Introduce elements of model-based inquiry and reasoning.
Analyze mathematics and science standards using Bloom’s Taxonomy and cognitive functions.
Analyze student thinking about addition.
Understand model-based reasoning and inquiry by invent a model of energy.
READER - TEXT BOOK ASSIGNMENTS
Read the Feuerstein article pgs 75-100. 8 points awarded before class time.
EDUC 566 Jan13 19
1. Reading Response. Upload 24 hours before Class Time. A one-point deduction will be incurred if
the responses are late.
Read the Feuerstein article pgs 75-100. 8 points awarded before class time.
Based on the most important concepts in this article describe how you will use them as part of
your instructional practices (at least one page).
Describe the relationship between the article(s) and what you have learned about learning
theories.
Create a graphic organizer that depicts the important ideas in the article.
2. IMAP CD Assignment. Upload 24 hours before Class Time. A one-point deduction will be
incurred if the responses are late. 2 points to be awarded during Class Time.
Watch video clip: Children solve a missing addend problem.
Video clip 1. View the interactions on video clip 1. Read the prompt labeled “To Consider
Before Viewing the Video Clip” and write out answers to Reflection Questions 1, 1a, 1b, 1c, 2,
3, 4, 5a and 5c For Teachers.
Upload the responses to the appropriate online page before Class Time. A one-point deduction
will be incurred if the responses are late. Responses must be written using Microsoft Word
software so that the responses can be copied and pasted to Note Pods that will be used during
Class Time. These responses are to be completed prior to the week that the CD assignment will
be discussed in class. Your responses will be used during Class Time in break out groups and
whole class discussions. Your instructor may require you to attach all or part of your responses
to the Notes Pod during group or whole-class discussions.
3. Conduct the K’nex Vehicle Gravity Design Competition found in Appendix C. Upload 24
hours before Class Time A one-point deduction will be incurred if the responses are late. 2 points
to be awarded during Class Time.
You should complete the activities through the second vehicle design. The completed
competition will be due in week three.
4. Class Time 3. 2 points to be awarded for IMAP assignment along with discussion.
5. Annenberg Video – Problem Solving. View the Problem Solving video and respond in writing to
one question from each group. Be prepared to discuss your written responses with your forum
group. 5 points.
UNIT 3 - – Week 3
Nature of Science
LEARNING OBJECTIVES
Understand the development of number ideas and meaning for number operations.
Understand the nature of science.
Identify and apply MLE-based strategies for engaging students in the learning of mathematics
and science concepts.
Identify, understand, and apply components of model-based reasoning and inquiry.
EDUC 566 Jan13 20
READER - TEXT BOOK ASSIGNMENTS –
1. Textbook Assignment - 6 points. Upload 24 hours before Class Time. A one-point deduction will
be incurred if the responses are late.
Read Van de Walle Chapter 9 and respond to the prompts below for the chapters BEFORE
week 3. Responses must be written using Microsoft Word software so that the responses can
be copied and pasted to Note Pods that will be used during Class Time. Your responses will be
used during Class Time in break out groups and whole class discussions. Your instructor may
require you to attach all or part of your paper to the Notes Pod during group or whole-class
instruction.
Chapter 9 - Developing Meanings for Operations 145-166 (21 pp.). Create 6 comparison
problems a follows: Difference unknown, larger unknown, smaller unknown, product
unknown, set size unknown, and multiplier unknown. 2 points awarded before class time.
Read Lawson Chapter 1: Educational Goals and the Nature of Scientific. Respond to question 1
p 21. 4 points awarded before class time.
2. Conduct the K’nex Vehicle Gravity Design Competition found in Appendix C. 4 points to be
awarded during Class Time. Upload 24 hours before Class Time.
You should complete all of the activities and responded to all of the questions and prompts. Be
prepared to show your vehicle on the video camera and discuss this investigation.
3. Class Time - 4 points awarded during Class Time for K’Nex Vehicle Gravity Design
Competition.
Conduct the K’nex Vehicle Gravity Design Competition found in Appendix C. 4 points to be
awarded during Class Time. You should complete all of the activities.
Unit 4 – Week 4
Patterns of Thinking By Scientists And By Adolescents
LEARNNG OBJECTIVES
Analyze classroom interactions based on MLE universal criteria and situational parameters.
Understand how to help children master the basic facts and develop place value concepts.
Understand patterns of thinking by scientists and by adolescents.
Model the design-redesign engineering concept and apply it to a real world problem.
READER – TEXTBOOK ASSIGNMENTS
1. Textbook Assignments – 5 points for the two assignments. Upload 24 hours before Class Time. A
one-point deduction will be incurred if the responses are late. Responses must be written using
Word software so that the responses can be copied and pasted to Note Pods that will be used during
Class Time. Your responses will be used during Class Time in break out groups and whole class
discussions. Your instructor may require you to attach all or part of your paper to the Notes Pod
during group or whole-class instruction.
Read Van de Walle Chapter 10 Helping Children Master the Basic Facts 167-186 (20 pp.). HW
Activity 10.18: Patterns in the Nines facts. P. 179. Describe the patterns you found and identify
the cognitive functions used in pattern identification. 2 points.
Read Lawson Chapter Lawson Ch. 3. How Students Think. – 20 pgs.
o Answer question 2, pg 59.
o Administer Puzzle 2 pg. 44, How High Will the Water Rise?, to three students. Give the
Puzzle to one student at a time so that he or she can explain his or her answers and
EDUC 566 Jan13 21
reasoning. Record students’ responses and classify the answers and explanations into
developmental levels.
o 3 points awarded before class time.
2. IMAP CD Assignment – 2 points to be awarded during Class Time
Watch video clip 3 – Gretchen and subtraction. Read the prompt labeled “To Consider Before
Viewing the Video Clip” and write out answers to the questions.
View the interactions on video clip 3 and respond in writing to prompts 4b and 5 in the section
“Reflection Questions For Teachers.”
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. These responses are to be completed prior to
the week that the CD assignment and will be discussed in class. Your responses will be used
during Class Time in break out groups and whole class discussions. Your instructor may
require you to attach all or part of your responses to the Notes Pod during group or whole-class
discussions.
3. Invent an egg protection device. Details in Appendix C. 3 points awarded during class time.
4. Class Time – 5 points to be awarded during Class Time for the IMAP video responses and K’nex
Egg-citing design competition.
5. Annenberg Video - Workshop 1. Astronomy: Eliciting Student Ideas.
(http://www.learner.org/resources/series29.html ). Click on the icon titled VoD for the
assigned workshop.
Introduces constructivism by examining student beliefs on what causes the seasons and their
explanations for the phases of the moon.
See appendix E for the required responses to the video. Be prepared to discuss your written
responses with your forum group. 5 points.
Unit 5 – Week 5
The Learning Cycle
LEARNING OBJECTIVES
Analyze classroom interactions based on MLE.
Identify the elements of the learning cycle.
Understand how to help students develop strategies for whole-number computation.
READER – TEXTBOOK ASSIGNMENTS
1. Textbook Assignments. Lawson Ch 6. Inquiry Instruction, 13 pgs. Lawson Ch. 7. Planning for
Inquiry. 16 pages.
4. Learning cycle lesson plan – first draft. Create an integrated math and science lesson based on
the learning cycle. The lesson should include mathematics standards in addition to science
standards. Use the 5e learning cycle model to design the lesson. Use the 5e learning cycle
model (see Appendix B; The K’Nex Forces, Energy, and Motion kit; and websites for
descriptions and examples of the learning cycle) to design the lessons. In your 5e lesson plan
EDUC 566 Jan13 22
respond to the specific bulleted items listed in the description of the learning cycle. In weeks 7
and 10 you will submit modified drafts of components of the final project thereby giving the
instructors an opportunity to critique your progress. 8 points awarded before class time. Upload
24 hours before Class Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. Your responses will be used during Class
Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your paper to the Notes Pod during group or whole-class instruction.
Ch 12 Developing Strategies for Whole-Number Computation 213-239 (26 pp). 2 points
awarded during class time.
Activity “Pause and Reflect” p. 234. Identify the cognitive function you used.
Class Time. 2 points to be awarded during Class Time for Van de Walle text assignment.
Unit 6 – Week 6
Algebraic Thinking
LEARNING OBJECTIVES
Analyze classroom interactions based on MLE.
Examine in detail how algebraic thinking can be developed starting in elementary school
through mathematics and science.
Identify the components of algebraic thinking and how they can be applied to the learning of
mathematics and science.
Identify, understand, and apply components of model-based reasoning and inquiry.
READER – TEXTBOOK ASSIGNMENTS
1. Textbook Assignments – 6 points. Upload 24 hours before Class Time. A one-point deduction
will be incurred if the responses are late.
Read Van de Walle chapter 14 and respond to the prompts below for the chapters BEFORE
week 6.
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late. Responses must be
written using Word software so that the responses can be copied and pasted to Note Pods that
will be used during Class Time. Your responses will be used during Class Time in break out
groups and whole class discussions. Your instructor may require you to attach all or part of
your paper to the Notes Pod during group or whole-class instruction.
Ch 14 Algebraic Thinking: Generalizations, Patterns, and Functions pp. 254-286
HW Activity 14.3, p 258: What Do You Know about the Shapes? 2 points.
Create another problem and identify the cognitive functions you used to solve the problem you
created.
Ch 14 Activity 14.9 Conjecture Creation. Challenge your students to make up conjectures on
their own after you have modeled the process. Describe in writing the model(s) you created and
how the students responded. 4 points.
2. IMAP CD Assignment – 2 points to be awarded during Class Time.
Watch video clip 13 – Procedural vs. Conceptual Teaching.
EDUC 566 Jan13 23
Read the prompt labeled “To Consider Before Viewing the Video Clip” and write out answers
to the questions.
View the interactions on video clip 13 and respond in writing to the prompts labeled
“Reflection Questions For Teachers.”
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. These responses are to be completed prior to
the week that the CD assignment will be discussed in class. Your responses will be used during
Class Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your responses to the Notes Pod during group or whole-class discussions.
3. Collides – 2 points to be awarded during Class Time. Upload 24 hours before Class Time. A one-
point deduction will be incurred if the responses are late.
Use knowledge from your K’nex experiences to create a model of a two vehicle collision.
See appendix C for details. Include algebraic expressions in your model.
4. Class Time – 4 points to be awarded for the IMAP video responses and Collides model.
5. Annenberg Video – Workshop 2. Biology: Why Are Some Ideas So Difficult? (90 min.) Focuses on the need for conceptual understanding and examines the scope of student ideas by exploring the central idea of photosynthesis, that the substance of plants comes mostly from the air.
See appendix E for the required responses to the video. Be prepared to discuss your written
responses with your forum group. 5 points.
Unit 7 – Week 7
Analyzing Student Thinking
LEARNNG OBJECTIVES
Understand student thinking by analyzing students’ written responses to cognitively demanding
tasks.
Understand and apply proportional reasoning.
Identify, understand, and apply components of model-based reasoning and inquiry.
READER – TEXTBOOK ASSIGNMENTS
1. Learning Cycle Lesson Plan. 4 points. Upload before class time.
Based on comments and suggestions from the first draft submitted in week 5, modify and
improve your lesson.
2. Textbook Assignments – 4 points awarded during class time. Upload the responses 24 hours
before Class Time to the appropriate on-line page before Class Time. A one-point deduction will
be incurred if the responses are late
Read Van de Walle Chapter 18 and respond to the prompts below for the chapters BEFORE
week 7. 2 points awarded during class time.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. Your responses will be used during Class
EDUC 566 Jan13 24
Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your paper to the Notes Pod during group or whole-class instruction.
Ch. 18 Proportional Reasoning pgs 348-369. Respond in writing to Pause and Reflect prompts
on pages 351 and 364.
3. IMAP CD Assignment. 2 points to be awarded during Class Time.
Watch video clip 15 – Felisha Adding Fractions.
Read the prompt labeled “To Consider Before Viewing the Video Clip” and write out answers
to the questions.
View the interactions on Video Clip 15 and respond in writing to the prompts labeled
“Reflection Questions For Teachers.”
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. These responses are to be completed prior to
the week that the CD assignment will be discussed in class. Your responses will be used during
Class Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your responses to the Notes Pod during group or whole-class discussions.
4. Class Time – 6 points - 4 points to be awarded for Van de Walle, and 2 points for the IMAP video
responses.
Unit 8 – Week 8
Mathematics and Science Reform
LEARNING OBJECTIVES
Identify, understand, and apply components of model-based reasoning and inquiry.
Explore the mathematics and science reform process in the United States. The contribution that
the cultural-historical process described by Vygotsky to the reform process is examined in the
article written by Jean Schmittau. Application of the cultural-historic process will require
significant changes in the ways teachers view the teaching of mathematics and science and
changes in their own understanding of fundamental concepts such as multiplication.
Identify and describe the different views on the reform process in mathematics and science in
the United States.
Identify components of the PACT process.
READER – TEXTBOOK ASSIGNMENTS
1. Reading Response – Read Schmittau, J. 2003. Cultural historical theory and mathematics
education.(pp. 225-245). In A. Kozulin, B. Gindis, S. Miller, & V. Ageyev (Eds.). Vygostky’s
educational theory in cultural context. Cambridge. UK: Cambridge University Press. 6 points.
Upload 24 hours before Class Time. A one-point deduction will be incurred if the responses are
late.
Write a reflection paper, three pages double spaced, answering the following prompts:
Describe what you see as the important concepts in this article(s). Elaborate on why you think
so.
EDUC 566 Jan13 25
How do you view its connection to your classroom practice? This section should be about two-
thirds of the paper.
2. Textbook Assignment – Read Chapter 4 Peters & Stout Science in Elementary Education and
respond to the following prompt BEFORE week 8. Chapter 4 Peters & Stout Science in Elementary
Education. Create a concept map for the big idea in your learning cycle lesson (pg 81,82). 2 points
to be awarded during Class Time.
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. Your responses will be used during Class
Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your paper to the Notes Pod during group or whole-class instruction.
3. Class Time – 2 points to be awarded the Peters & Stout assignment.
4. Annenberg Video – For week 8 go to the Annenberg Private Universe Project in Science website
by entering this URL in your browser: http://www.learner.org/resources/series29.html
Click on the icon titled VoD for Workshop 5. Vision: Can We Believe Our Own Eyes?
Explores the origins of student ideas to find out whether experience equals learning. Shows how
experience can work for or against learning because students can disbelieve concepts that they have
“learned.”
See appendix E for the required responses. Be prepared to discuss your written responses with
your forum group. 5 points.
Unit 9 – Week 9
Assessing Student Progress
LEARNING OBJECTIVE
Analyzing effective means of assessing student progress.
READER – TEXTBOOK ASSIGNMENTS
1. Textbook Assignment. 6 points awarded before class time.
Access your state’s department of education website and find a few released test items used by
your state to determine annual yearly progress (AYP) as required by NCLB. For the released
items, first decide if they are good problem-based assessments that help you find out about
students understanding of the concepts involved. In Van de Walle see Appendix B, Standard 3
Worthwhile Mathematical Tasks for characteristics of good problem-based assessment items
and analyze one of the released problems using the seven criteria listed. Then, if necessary, try
to improve the item so that it becomes a problem-based assessment that would be useful in the
classroom.
Read Van de Walle Chapter 16 and respond to the prompts below for the chapters BEFORE
Week 9. 2 points awarded during class time. Developing Strategies for Fraction Computation
309-327 (19 pp).
HW Activity 16.1 First Estimates p. 311. 2 points awarded during class time.
EDUC 566 Jan13 26
Randomly estimate and write 10 addition or subtraction fraction problems each on 10 index
cards on 1 side. Quickly look at each card for no more than 5 seconds and write on the back
if it is more or less than 1. Upon completion, explain why you made your decisions.
Upload the responses 24 hours before Class Time to the appropriate on-line page before
Class Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and
pasted to Note Pods that will be used during Class Time.
Your responses will be used during Class Time in break out groups and whole class
discussions.
Your instructor may require you to attach all or part of your paper to the Notes Pod during
group or whole-class instruction.
2. IMAP CD Assignment – 2 points to be awarded during Class Time.
Watch video clip 17 – Sharing of story-problem solutions.
Read the prompt labeled “To Consider Before Viewing the Video Clip” and write out answers
to the questions.
View the interactions on video clip 17 and respond in writing to the prompts labeled
“Reflection Questions For Teachers.”
Upload the responses 24 hours before Class Time to the appropriate on-line page before Class
Time. A one-point deduction will be incurred if the responses are late.
Responses must be written using Word software so that the responses can be copied and pasted
to Note Pods that will be used during Class Time. These responses are to be completed prior to
the week that the CD assignment will be discussed in class. Your responses will be used during
Class Time in break out groups and whole class discussions. Your instructor may require you to
attach all or part of your responses to the Notes Pod during group or whole-class discussions.
3. Class Time – 4 points to be awarded for IMAP CD responses, Van de Walle text assignment.
UNIT 10 – Week 10
Context for Learning and Science Content Task
LEARNING OBJECTIVES
Create a learning event that includes the PACT requirements described below. 10 pts.
1. Annenberg video – Following Children’s Ideas in Mathematics. View the Following Children’s
Ideas in Mathematics video and respond in writing to the prompt: describe what you learned about
the long-term development of students’ mathematical thinking. Be prepared to discuss your written
responses with your forum group. 5 points.
2. Conduct the Tug-of-War Competition described below. 2 points to be awarded during Class
Time. Upload the responses 24 hours before Class Time to the appropriate on-line page before
Class Time. A one-point deduction will be incurred if the responses are late.
Your task is to design a vehicle that will win a tug-o-war against any other vehicle. Each
participant will build a vehicle that they think will beat the competition. Each pair of competitors
will take a picture of their vehicle and send it to their competitor. The competitor will then build
this vehicle from the picture. Verbal or written instructions should be included with the pictures so
each competitor can build the vehicle as intended. Each participant will then conduct the tug-o-war
EDUC 566 Jan13 27
with their own vehicle and the vehicle they built based on their competitors picture and other
information
3. PACT: Context for Learning and Science Content Area Task. 10 points. Upload 24 hours
before Class Time. A one-point deduction will be incurred if the responses are late.
EDUC 566 Jan13 28
Context for Learning
Purpose
The Context for Learning evidence provides a brief overview of important features of your classroom
context that influence your instructional decisions. Your response will provide evidence of: 1) your
knowledge of students; and 2) your ability to identify and summarize important factors related to
students’ science learning and the school environment. You’ll be referring to your description of
students and the teaching context in your responses to the Content Area Task in Elementary
Science.
Overview
If you teach science to more than one class of students, focus on only one class.
Identify learning objectives for both the curriculum content and the development of academic
language related to that content.
Provide descriptive information about the instructional context and instructional resources.
Describe important features of the class that will affect your instructional decisions.
What Do I Need to Do?
Complete the Context for Learning Form. The form is located after the prompts for the
Context Commentary.
Respond to each of the prompts in the Context Commentary.
Context Commentary
Write a commentary of 3-5 single-spaced pages (including prompts) that addresses the following
prompts. You can address each prompt separately, through a holistic essay, or a combination of both,
as long as all prompts are addressed.
1. Briefly describe the following about the context in which the learning segment would be
taught:
a. Type of school/program, (e.g., elementary/middle school, themed magnet, or charter
school)
b. Kind of class (e.g., third grade self-contained, sixth grade core math/science) and
organization of subject in school (e.g., departmentalized, interdisciplinary teams)
c. Degree of ability grouping or tracking, if any
2. Describe your class with respect to the features listed below. Focus on key factors that
influence your planning and teaching of this learning segment. Be sure to describe what your
students can do as well as what they are still learning to do.
a. Academic development
Consider students’ prior knowledge, key skills, developmental levels, and other special
educational needs. (TPE 8)
b. Language development
Consider aspects of language proficiency in relation to the oral and written English required
to participate in classroom learning and assessment tasks. Describe the range in vocabulary
EDUC 566 Jan13 29
and levels of complexity of language use within your entire class. When describing the
proficiency of your English learners, describe what your English learners can and cannot
yet do in relation to the language demands of tasks in the learning segment. (TPEs 7, 8)
c. Social development
Consider factors such as the students’ ability and experience in expressing themselves in
constructive ways, negotiating and solving problems, and getting along with others. (TPE 8)
d. Family and community contexts
Consider key factors such as cultural context, knowledge acquired outside of school, socio-
economic background, access to technology, and home/community resources.
3. Describe any district, school, or cooperating teacher requirements or expectations that might
impact your planning or delivery of instruction, such as required curricula, pacing, use of
specific instructional strategies, or standardized tests.
EDUC 566 Jan13 30
Context for Learning Form
Provide the requested context information for the class selected for this task. This form is designed to be completed electronically. The blank space does not represent the space needed. Use as much
space as you need.
About the subject area/course
1. How much time is devoted each day to specific instruction in science in the class which is the focus
of this task? ______________________________________________
About the students in the class
2. How many students are in the class you are documenting? _____
3. How many students in the class are: English learners ____
Redesignated English Learners _____ Proficient English speakers ____?
4. Please complete the following table about your
English Learners’ latest CELDT scores (if available):
# of Students at Each CELDT Level in Different Modalities
Score Level Listening Speaking Reading Writing Overall
Beginning
Early
Intermediate
Intermediate
Early Advanced
Advanced
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5. How many students have Individualized Education Plans (IEPs) or 504 plans? _____
6. How many students participate in a Gifted and Talented Education (GATE) program? _____
About the school curriculum and resources
7. Describe any specialized features of the classroom setting, e.g., bilingual, Structured English
Immersion, team taught with a special education teacher.
8. If there is a particular textbook or instructional program used for science instruction, what is it? (If
a textbook, please provide the name, publisher, and date of publication.)
9. What other major resources are typically used for science instruction in this class?
Content Area Task-Science
Be sure to address the learning of curriculum content and related academic language.
To identify standards, please list the standard number, followed by the text of the standard. If only a
portion of a standard is being addressed, then only list the relevant part(s).
Use the preferred lesson plan format in your program or the optional lesson plan format provided. The
plan should include at least the following information: student academic content standards, ELD
standards (if applicable), learning objectives, formal and informal assessments, instructional strategies
and learning tasks, and resources and materials
1. Given the description of students that you provided in Task 1.Context for Learning, how do your
choices of instructional strategies, materials, technology, and the sequence of learning tasks reflect
students’ backgrounds, developmental levels, interests, and needs? Be specific about how your
knowledge of these students informed the lesson plans, such as the choice of text or materials used
in lessons, how groups were formed or structured, using student learning or experiences (in or out
of school) as a resource, or structuring new or deeper learning to take advantage of specific student
strengths. (TPEs 4,6,7,8,9)
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PLANNING MAKING CONTENT ACCESSIBLE
ES2: How do the plans make the curriculum accessible to the students in the
class? (TPEs 1,4,5,6,7,8,9)
Level 1 Level 2 Level 3 Level 4
Plans refer to students’
experiential
backgrounds1, interests,
or prior learning2 that
have little or no
relationship to the
learning segment’s
standards/objectives. OR
There are significant
content inaccuracies in
plans that will lead to
student
misunderstandings.
Plans draw on students’
experiential
backgrounds, interests,
or prior learning to help
students reach the
learning segment’s
standards/objectives.
Plans for the
implementation of
learning tasks include
support3 to help
students who often
struggle with the
content.
Plans draw on students’
prior learning as well as
experiential backgrounds
or interests to help
students reach the
learning segment’s
standards/objectives.
Plans for learning tasks
include scaffolding or
other structured forms
of support4 to provide
access to grade-level standards/objectives.
All components of
Level 3 plus:
Plans include well-
integrated instructional
strategies that are
tailored to address
a variety of
specific student
learning needs.
1 Cultural, linguistic, social, economic
2 In or out of school
3 Such as strategic groupings of students; circulating to monitor student understanding during independent or group work;
checking on particular students. 4 Such as multiple ways of representing content; concrete models; modeling strategies of scientific inquiry; providing
graphic organizers, rubrics, or sample work.
EDUC 566 Jan13 33
Appendix A
MLE classroom observation notes template
Universal
Criteria Strategies Evidence
Intentionality-
Reciprocity
Cognitively demanding tasks implemented, lesson
types vary (project-based, games, procedural, etc.)
Rules and procedures negotiated with students
Interventions – reinforcement, recognition, balanced
with negative consequences.
Relationships with high need students developed,
e.g. Passive, aggressive, attention problems.
Non-verbal behavioral cues established
Meaning Importance of subject matter conveyed including the
processes of learning.
Energy and enthusiasm for teaching and learning are
clearly demonstrated.
Transcendence Lessons connected to previous and future learning.
Process questions balanced with fact based
questions.
Teacher models the process of generalizing and asks
students to generalize from specific instances to the
underlying rule
Prompts students’ need to seek and find complex
relationships by providing analogies, models, and
representations.
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Cycle of Inquiry for Mathematical and Scientific Problem Solving Using Cognitive Functions
Engaging: Approaching and Connecting to Problems
Cognitive Function Teacher definition Evidence
Defining (Understanding)
the problem
Recognizing that something has to be done
and figuring what to do by forming
relationships between the various sources
of information in the problem; devising a
plan; and implementing the plan.
Activating prior knowledge Searching through past experiences in order
to make associations between aspects of the
problem and similar aspects of past
experiences with similar problems.
Analyzing Breaking a problem into its parts and
figuring how the parts are connected or
related to one another; determining which
parts are relevant and which are irrelevant;
and identifying missing parts or
information.
Visualizing Generation of a symbolic, figural, or
pictorial representation of a verbal
stimulus.
Paraphrasing through
rereading
Rewriting, rewording, or restating in your
own words the problem you have just read,
seen, or heard.
Systematic exploration and
planning
Exploring the problem in an organized and
orderly manner, representing the problem
in multiple ways, and constructing a logical
plan to solve the problem.
Comparing Looking for similarities and differences
between two or more objects, events, or
situations in the problem.
EDUC 566 Jan13 35
Exploring: Discovering relationships and patterns; employing tools; explaining possible solution paths, concepts and strategies while
problem solving; manipulating problem elements and representations.
Cognitive Function Teacher definition Evidence
Analogical reasoning Thinking about, representing, and exploring
the problem and ways to solve it based on
analogs, models, and examples from prior
experience.
Modeling Designing a representation of a system with
interactive parts and with representations of
those interactions. Designing models can be
performed with the use of conceptual,
physical, mathematical, and computation
models, or combinations of these.
Forming relationships Making connections between
representations, objects, events, or
situations in the problem.
Forming functional
relationships
Making connections between two or more
things that are changing their values in the
problem in such a way that the changes are
related or are working together in an
interdependent way.
Hypothetical thinking
(Using inductive and
deductive thinking)
If …. Then… thinking. Making a
conjecture (or educated guess) about the
solution to the problem, and searching for
the logical evidence to support the claim or
deny it.
Providing logical evidence -
falsifying
Giving and explaining details, clues, and
proof that connect together and make sense
for supporting a tentative solution to the
problem.
Conserving Constancy Identifying and describing what stays the
same in terms of an attribute, concept or
relationship within the problem while some
other things are changing.
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Explaining, Elaborating, and Validating: Determining whether a solution is complete and moving beyond a particular problem by
generalizing to other situations
Cognitive Function Teacher definition Evidence
Evaluating Determining the reasonableness of the
solution in the context of the original
problem.
Inductive thinking Taking aspects from various details that
seem to form a pattern, categorizing them
into general relationships of attributes
and/or behaviors, and organizing the results
to form a general rule, principle, formula,
recipe, or guide that can be applied to solve
similar problems.
Deductive thinking Applying the newly found solution, general
rule, principle, or formula to a novel
problem, situation, or a set of details.
EDUC 566 Jan13 37
Appendix B
The Learning Cycle Model of Instruction
The learning cycle is a research-supported, constructivist instructional model based on how humans learn. From a constructivist
perspective, learning can be perceived as a conceptual transformation: “The learning theory that emerges from Piaget’s work can be
summarized by saying that cognitive change and learning a specific direction take place when a scheme, instead of producing the expected
result, leads to a perturbation, and perturbation, in turn, to an accommodation that maintains or reestablishes equilibrium.” (von
Glasserfeld, 1995, p.68). The learning cycle is useful in science and mathematics for organizing curricula at the unit and daily lesson plan
level.
The Five Phases of the Learning Cycle
1. Engagement
In the first phase the teachers develops a ‘hook’ or context to capture the student’s attention. A hook or context provides motivation
that develops anticipation and induces curiosity and suspense. Selected tasks should be cognitively demanding (see criteria for cognitively
demanding tasks). Examples include:
Hands-on
Scenario – real world or teacher created
Demonstrations – discrepant or ill-structured events
Simulations and games
Observe: plants growing; animal behavior; phenomena depicted on video
Use a set of materials to solve a given problem
Minimize or maximize something
Identify an unknown
Field trips
The activities of this phase make connections to past and future activities. The connections depend on the learning task and may be
conceptual or procedural. Successful engagement results in students being puzzled and actively motivated in the learning activity.
Planning for the engagement and exploration phase
What are your mathematical/scientific goals/standards for the lesson (i.e., what is it that you want students to know and understand
about mathematics/science as a result of this lesson)?
EDUC 566 Jan13 38
In what ways does the task build on student’s previous knowledge? What definitions, concepts, or ideas do students need to know
in order to begin to work on the task?
What are all the ways the task can be solved?
Which of these methods do you think your students will use?
What misconceptions might students have?
What errors might students make?
What are your expectations for students as they work on and complete this task?
What resources or tools will students have to use in their work?
How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work
individually or in small groups/pairs? Will students be partnered in a specific way? If so in what way?
How will students record and report their work?
How will you introduce students to the activity so as not to reduce the demands of the task?
What will you hear that lets you know students understand the task?
2. Exploration
Exploration activities are designed so that during class students have common, concrete experiences that begin building concepts,
processes, and skills. In Piagetian terms, engagement brings about disequilibrium while exploration initiates the process of equilibration.
The aim of exploration activities is to establish experiences that a teacher can use later to formally introduce a concept, process, or skill.
As a result of their mental and physical involvement in the exploration activity, students establish relationships, observe and identify
patterns, identify variables, and pose questions. The teacher guides the students as they explore, suggesting strategies to use and monitors
levels of frustration.
Teacher actions during exploration include the function of stimulating students’ mathematical and scientific constructions via the
introduction of new mathematical/scientific ideas into a classroom conversation (Lobato, et al. 2005). These actions may include:
1. Describing a new concept.
2. Summarizing student work in a manner that inserts new information into the conversation.
3. Providing information that students need in order to test their ideas or generate a counterexample.
4. Asking students what they think of a new strategy or idea (perhaps from a “hypothetical” student).
5. Presenting a counterexample that the teacher has not seen any students introduce and thinks no one will.
6. Engaging in Socratic questioning in an effort to introduce a new concept.
7. Presenting a new representation.
EDUC 566 Jan13 39
As students are working independently or in small groups:
What questions will you ask to focus their thinking?
What will you see or hear that lets you know how students are thinking about the mathematical/scientific ideas?
What questions will you ask to assess students understanding of key mathematical/scientific ideas, problem solving strategies, or the
representations?
What questions will you ask to advance student’ understanding of the mathematical/scientific ideas?
What questions will you ask to encourage student to share their thinking with others or to assess their understanding of their peer’s
ideas?
How will you ensure that students remain engaged in the task?
What will you do if a student does not know how to begin to solve the task?
What will you do if a student finishes the task almost immediately and becomes bored and disruptive?
What will you do if students focus on non-mathematical aspects of the activity (e.g. spend most of their time making a beautiful poster
of their work)?
3. Explanation
The process of explanation provides the students and teacher with a common use of terms relative to the learning task. The teacher
directs student attention to specific aspects of the engagement and exploration activities. Students are asked to give their explanation of
what occurred (or attempt to answer the guiding question). The teacher introduces a mathematical or scientific explanation in a direct and
formal manner. Explanations are ways of listing, labeling, and ordering the exploratory experiences. The teacher should base the initial part
of this phase on students’ explanations and clearly connect the explanations to experience in the engagement and exploration phases. The
explanation phase can be teacher-, textbook- or technology-directed. Teachers commonly use oral explanations, but there are other
strategies, such as reading, video, film, and educational courseware. This phase continues the process of cognitive construction and
provides scientific and mathematical words for explanations. In the end, students should be able to explain exploratory experiences using
common mathematical /scientific terms.
How will you orchestrate the class discussion so that you accomplish your mathematical/scientific goals? Specifically:
Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?
In what ways will the order in which solutions are presented help develop students understanding of the mathematical/scientific ideas
that are the focus of your lesson?
What specific questions will you ask so that students will:
make sense of the mathematical/scientific ideas that you want them to learn?
expand on, debate, and question the solutions being shared?
make connections between the different strategies that are presented?
look for patterns?
EDUC 566 Jan13 40
begin to form generalizations?
What will you see or hear that lets you know that students in the class understand the mathematical/scientific ideas that you intended for
them to learn?
4. Elaboration
Once students begin developing an explanation of their learning tasks, it is important to involve students in further experiences that
extend or clarify the concepts, processes, or skills. In some cases students may still have misconceptions or they may only understand a
concept or procedure in terms of the exploratory experience. Elaboration activities provide further time and experience that contribute to
learning.
5. Evaluation
Students need feedback on their progress and this can occur informally or formally. Informal assessment (formative) occurs from
the beginning of the teaching sequence whereas formal assessment is best done after the elaboration phase.
As you write the specifics for each phase in the “What the teacher/student does,” estimate the time it will require and place the estimate
under the name of each phase.
Learning Cycle – generalized lesson format
Phase Purpose What the teacher does What the student does
Engage
(time)
To elicit students’
interest in the
concept(s).
1. Creates interest.
2. Generates curiosity.
3. Raises questions.
4. Identifies what the
students know about the
topic.
5. Gives a general
introduction about what the
student will be studying.
1. Asks questions, such as: Why
did this happen? What do I
already know about this? What
can I find out about this? How do
I approach this task?
2. Shows interest in the topic.
Explore
(time)
1. Provides experiences
needed for
understanding.
2. Stimulates inquiry.
3. Provides students
1. Encourages students to
work together without
direct instruction from the
teacher.
2. Observes and listens to
1. Thinks freely, but within the
limits of the activity
2. Uses previously acquired
strategies (or develops new ones),
skills, and concepts to find
EDUC 566 Jan13 41
with the opportunity to
make their own
discoveries and to figure
things out for
themselves.
4. Reveals students’
ideas and thoughts.
5. Sets the stage for
more structured
activities.
students as they interact.
3. Asks probing questions
to redirect students’
investigations when
necessary.
4. Initiates introduction of
mathematical/scientific
concepts when necessary:
Description of a new
concept which can include
an idea, the meaning
associated with a
mathematical symbol, why
something works, an
image, a relationship, or
connections among ideas
or representation;
summarizing student work
in a manner that inserts
new information into the
conversation; provide
information that students
need in order to test their
ideas or generate a
counterexample; ask
students what they think of
a new strategy or idea,
perhaps from a
hypothetical student;
present a counterexample
that the teacher has not
seen any students introduce
and thinks no one will;
engage in Socratic
questioning in an effort to
solutions
3. Forms new predictions and
hypotheses
4. Tests predictions, conjectures,
and hypotheses
5. Tries alternatives and
discusses them with others
6. Records observations and
ideas
7. Suspends judgment
EDUC 566 Jan13 42
introduce a new concept;
present a new
representation.
5. Elicits responses to
initiation of concepts.
6. Proves time for students
to puzzle through
problems.
7. Acts as a
consultant/coach for
students.
Explain
(time)
1. Introduce new
concepts, ideas, skills,
relationships, solutions,
and explanations.
2. Verify or validate
students’ ideas,
discoveries, solutions.
3. Challenge students’
alternative concepts.
1. Encourages students to
explain concepts and
definitions in their own
words
2. Asks for justification
(evidence) and clarification
from students
3. Uses students’ previous
experiences as the basis for
explaining concepts
4. Formally provides
definitions, explanations,
and new labels
1. Explains possible solutions or
answers to others.
2. Listens critically to another
students’ explanations offered by
the teacher.
3. Refers to previous activities.
4. Uses recorded observations in
scientific/mathematical
explanations.
Elaborate
(time)
1. Correct students’
misunderstandings.
2. Broaden and deepen
students’
understandings.
3. Provide the
opportunity for students
to practice the new ideas
1. Expects students to use
formal definitions and
explanations.
2. Encourages students to
apply the concepts and
skills in new situations and
tasks.
3. Reminds students of
1. Applies new labels,
definitions, explanations, and
skills to new, but similar,
situations.
2. Uses previous information to
ask questions, propose answers,
make decisions, create and solve
similar problems, design
EDUC 566 Jan13 43
and skills so they
develop the feeling of
being competent.
4. Promote
generalization and
transfer of learning.
alternative explanations
and probes them.
4. Refers students to data
and evidence and asks:
What do you already
know? Why do you
think…?
experiments.
3. Draws reasonable conclusions
from evidence
4. Records observations and
explanations.
5. Checks for understanding
among peers.
Evaluate
(time)
1. Assess students’
level of conceptual,
procedural and problem
solving understanding.
1. Observes students as
they apply new concepts
and skills
2. Assesses students’
knowledge and/or skills
3. Looks for evidence that
students have changed
their thinking or behaviors
4. Allows students to
assess their own learning
and group-process skills
5. Asks open-ended
questions, such as: Why do
you think…? What
evidence do you have?
What do you know about?
How would you explain?
1. Answers open-ended questions
by using observations, evidence,
and previously accepted
explanations.
2. Demonstrates an
understanding or knowledge of
the concept or skill.
3. Evaluates his or her own
progress and knowledge.
4. Asks related questions that
would encourage future
investigations.
Use the following format for your Learning Cycle lesson in weeks 5, 7, and 10. Respond to all of the bulleted prompts in the column
“What the Teacher does”. Fill in what you expect the student will do cognitively (use the cognitive functions found in appendix D) in the
column “What the student does.”
EDUC 566 Jan13 44
5E Time
Frame
What the
teacher does
What the
student does Prompts
En
ga
ge
As students are working independently or in small groups:
In what ways does the task build on student’s previous knowledge? What definitions, concepts, or ideas do students need to know in order to begin
to work on the task?
What are your mathematical/scientific goals/standards for the lesson (i.e., what is it that you want students to know and understand about
mathematics/science as a result of this lesson)?
What are all the ways the task can be solved?
Which of these methods do you think your students will use?
What misconceptions might students have?
What errors might students make?
What are your expectations for students as they work on and complete this task?
What resources or tools will students have to use in their work?
How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work individually or in small
groups/pairs? Will students be partnered in a specific way? If so in what way?
How will students record and report their work?
How will you introduce students to the activity so as not to reduce the demands of the task?
What will you hear that lets you know students understand the task?
Ex
plo
re
As students are working independently or in small groups:
What questions will you ask to focus their thinking?
What will you see or hear that lets you know how students are thinking about the mathematical/scientific ideas?
What questions will you ask to assess students understanding of key mathematical/scientific ideas, problem solving strategies, or the representations?
What questions will you ask to advance student’ understanding of the mathematical/scientific ideas?
What questions will you ask to encourage student to share their thinking with others or to assess their understanding of their peer’s ideas?
How will you ensure that students remain engaged in the task?
What will you do if a student does not know how to begin to solve the task?
What will you do if a student finishes the task almost immediately and becomes bored and disruptive?
What will you do if students focus on non-mathematical aspects of the activity (e.g. spend most of their time making a beautiful poster of their work)?
Ex
pla
in
How will you orchestrate the class discussion so that you accomplish your mathematical/scientific goals? Specifically:
Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?
In what ways will the order in which solutions are presented help develop students understanding of the mathematical/scientific ideas that are the focus
of your lesson?
What specific questions will you ask so that students will:
make sense of the mathematical/scientific ideas that you want them to learn? expand on, debate, and question the solutions being shared?
make connections between the different strategies that are presented?
look for patterns? begin to form generalizations?
What will you see or hear that lets you know that students understand the mathematical/scientific ideas that you intended for them to learn?
Ela
bo
rate [No prompts]
Ev
alu
ate [No prompts]
EDUC 566 Jan13 45
Learning Cycle Lesson Scoring Rubric
1 or
1-2
2 or
3-4
3 or
5-6
or
7-8
Learning cycle
lesson All phases of the
LC are not
clearly elaborated
based on
descriptions
provided in the
template.
A significant
prompts in each
phase of the
learning cycle are
clearly addressed.
Only a few
cognitive
functions for
each phase of the
LC are identified.
Most are not
clearly applied to
students’ learning
of the
math/science
concepts.
All phases of the
LC are clearly
elaborated based
on descriptions
provided in the
template.
A significant
number of
prompts in each
phase of the
learning cycle are
not clearly
addressed.
Only a few
cognitive
functions for
each phase of the
LC are identified.
Most are not
clearly applied to
students’ learning
of the
math/science
concepts.
All phases of the
LC are clearly
elaborated based
on descriptions
provided in the
template.
Most, but not all,
prompts in each
phase of the
learning cycle are
clearly addressed.
Cognitive
functions for
each phase of the
LC are identified
but not clearly
applied to
students’ learning
of the
math/science
concepts.
All phases of the
LC are clearly
elaborated based
on descriptions
provided in the
template.
All prompts in
each phase of the
learning cycle are
clearly addressed
based on
descriptions
provided in the
template.
Cognitive
functions for
each phase of the
LC are identified
and applied to
students’ learning
of the
math/science
concepts.
EDUC 566 Jan13 46
Appendix C
K’nex Vehicle Gravity Design Competition
The Scenario
The National Automobile Association is looking for engineering teams to design, construct, and test
gravity powered vehicles that can travel in a straight line for six meters from the end of an 18 inch high
ramp.
Contest procedures and rules
1. Open up your kit and investigate all of the components.
2. Create a ramp for your vehicle that is 12 inches high at one end. The ramp can be as long as
you want but the vehicle release point must be no more than 12 inches above the floor.
3. Design and test your first vehicle. Your first vehicle may not travel the full six meters from the
end of the ramp.
4. Draw a sketch of this first vehicle, no matter how far it traveled.
5. The sketches must use lines and geometric shapes that represent the actual structural pieces that
the vehicle was built from. The sketches should also include the actual number and names for
the pieces.
6. The design sketches must show a top and a side view projection.
7. The sketches must be smaller scaled down versions of the vehicle that will be built.
8. The vehicle must travel 6 meters in a straight line from the end of an 18 inch high launching
ramp.
9. After you design, test, and sketch the first vehicle, you will redesign the vehicle a second and
third time. For the second and third redesign include a new top and side sketch of the modified
vehicle along with the number of each of the different pieces that were used.
Engage
Vehicle Design 1 – make a top view and side view sketch of your first vehicle no matter how far it
traveled down your 12 inch high ramp. The sketches must use lines, circles, and other geometric
shapes that represent the actual structural pieces that the vehicle will be built from.
Top View
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Side View
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Explore
Vehicle 1
1. Based on your sketch, make a table listing the names and the number of each of the K’Nex
pieces that you used to build your first vehicle.
After you build your first vehicle, you will release it from the top of the 12 inch high ramp.
Why is it important that you always release your vehicle from the top of the ramp?
What do you think the variables are so far in this investigation?
What are the values of the variables?
2. Let your vehicle roll down from the top of the ramp without pushing it.
3. Estimate how much of the six meters it traveled. Express this estimate as a percent. For
instance, if it traveled about half of the six meters then it went 50% of the way. Or, if it went
about one-fourth of the way then it went 25% of the way. Express this distance as a decimal
and a fraction. Record these values in Table 1.
4. Measure the distance in meters it travels from the bottom of the ramp until it stops. Record this
value in Table 1.
5. Make three trials with your vehicle and record your data in the chart below.
Why should you conduct three trials with your vehicle and not just one trial?
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When the vehicle stops, describe how you are going to measure the distance the vehicle
traveled. Think about the front and back of the vehicle when you write out your procedure.
Describe how you are going to determine whether or not the vehicle has traveled in a straight
line before you measure the distance. How straight does the line have to be before you measure
the distance?
TABLE 1 Original
Vehicle Design
Trial 1 Trial 2 Trial 3 Average
Estimated
distance
traveled as a
percent
Estimated
distance
traveled as a
decimal
Estimated
distance
traveled as a
fraction
Actual distance
traveled in
meters
How close was
your estimate
as a percent
compared to the
actual value?
Express this
comparison as a
percent.
Are there any new variables in this investigation?
If so, what are they?
What do you think the relationship is between the variables you have identified so far?
Distance Vehicle Travels in Meters
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Vehicle 2
Vehicle Design 2 – make a top view and side view sketch of your second vehicle.
Top View
Side view
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Vehicle 2
1. Based on your sketch, make a table listing the names and the number of each of the K’Nex
pieces that you will use to build your second vehicle.
What do you think the variables are so far in this investigation?
2. Let your vehicle roll down from the top of the ramp without pushing it. Measure the distance it
travels from the bottom of the ramp.
3. Estimate how much of the six meters it traveled. Express this estimate as a percent. For
instance, if it traveled about half of the six meters then it went 50% of the way. Or, if it went
about one-fourth of the way then it went 25% of the way. Express this distance as a decimal
and a fraction. Record these values in Table 2.
4. Measure the distance in meters it travels from the bottom of the ramp until it stops. Record this
value in Table 2.
Make three trials with your vehicle and record your data in the chart below.
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TABLE 2
Vehicle 2
Trial 1 Trial 2 Trial 3 Average
Estimated
distance
traveled as a
percent
Estimated
distance
traveled as a
decimal
Estimated
distance
traveled as a
fraction
Actual distance
traveled in
meters
How close was
your estimate
as a percent and
the actual
value?
1. Did vehicle 2 outperform vehicle 1? Why or why not?
2. Are there any new variables in this investigation? If so, what are they?
3. What do you think the relationship is between the variables you have identified so far?
Distance Vehicle Travels in Meters
entimeters
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Vehicle 3 Vehicle Design 3 – make a top view and side view sketch of your third vehicle.
Top View
Side view
1. Based on your sketch, make a table listing the names and the number of each of the K’Nex
pieces that you will use to build your third vehicle.
EDUC 566 Jan13 54
What do you think the variables are so far in this investigation?
2. Let your vehicle roll down from the top of the ramp without pushing it. Measure the distance it
travels from the bottom of the ramp.
3. Make three trials with your vehicle and record your data in the chart below.
TABLE 3
Vehicle 3
Trial 1 Trial 2 Trial 3 Average
Estimated
distance
traveled as a
percent
Estimated
distance
traveled as a
decimal
Estimated
distance
traveled as a
fraction
Actual distance
traveled in
meters
How close was
your estimate
as a percent and
the actual
value?
1. Did vehicle 3 outperform vehicle 1 and 2? Why or why not?
Distance Vehicle Travels in Meters
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2. Are there any new variables in this investigation? If so, what are they?
3. What do you think the relationship is between the variables you have identified so far?
Summary of data
Design Type Trial 1 Trial 2 Trial 3 Average
Original vehicle
Second vehicle
Third vehicle
Explain
Look at the data table and describe any patterns that you notice.
What do you think caused the pattern that you noticed?
Make a sketch of the gravity design system that your team has been investigating. Identify critical parts
of this system. This is a model of the gravity design challenge that you have been working on. Be
prepared to explain your model and your investigation to the rest of the class.
Egg-citing Design
The Scenario
Automobile laws in California require all passengers to wear a seat belt. Many cars now have safety
features called air cushions. What is the purpose of these safety devices?
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The Challenge
As a member of the automotive engineering team you have been assigned the responsibility of
improving the overall safety of the company’s cars. You and your team believe that the current
restraint system of the vehicles needs to be revised, especially since the testing procedures have been
upgraded and more sensitive raw eggs will be used instead of the standard electronic dummy.
The Constraints
1. Each engineer must submit a detailed diagram of their car.
2. Each engineer must submit a procedure for testing their safety system.
3. During the investigation phase engineers will use imitation eggs.
4. Raw eggs, in plastic bags, will be used for the final test.
The Rules
1. All ramps will be 120 centimeters long and must be maintained at a ramp height of 18 inches.
The lower end of the ramp will be butted against a wall.
2. Detailed sketches must accompany each final report. The terms potential and kinetic energy
must be used in the explanation of how the safety system functions. Kinetic and potential
energy are described in the teachers guide found in the kit.
3. During final testing all eggs must be housed inside a plastic bag.
4. Evaluating and rating of the safety system after the final test run is as follows:
Excellent – The shell is not cracked and the yolk is unbroken.
Fair – The shell cracked but the yolk is unbroken.
Unacceptable – The shell cracked and the yolk is broken.
All engineers must prepare a final report that details the safety features implemented, how the testing
was conducted, and the results of this testing. Reports must also include additional safety
recommendations that might be considered.
“Collides” You are the stunt coordinator for the new movie “Collides”. In the movie one of the scenes requires
three types of cars to participate in a chase and a subsequent collision. The cars should have different
sources of energy and travel at different speeds. The producer has given you the following conditions
for the collision:
EDUC 566 Jan13 57
1. The cars must be built from the K’nex kit - Force, Energy and Motion.
2. Two cars are involved in a chase, going the same direction on the same street.
3. Another car is traveling on a different street from the two cars in the chase.
4. The lead car in the chase will make it through the intersection without a collision.
5. The following car in the chase and the car traveling on the other street will collide.
6. The collision takes place at the intersection of the two streets.
7. The minimum distance of the lead chase car and the collision car from the intersection is 120
meters.
Your task is to provide the producer with a model of the collision.
Components of the models that will evaluated for the winning production company.
1. A scale model to depict your collision.
2. Diagrams, graphs, tables, equations, and written explanations to describe the cars’ movements.
3. A video of the actual collision scene along with a formal presentation of the model.
Standards: Algebra I: 5.0, 6.0, 9.0, 15.0
Vehicle Tug-O-War
Your task is to design a vehicle that will win a tug-o-war against any other vehicle. We will use a
playoff elimination system to determine the winner. Each participant will build a vehicle that they
think will beat the competition. Each pair of competitors will take a picture of their vehicle and send it
to their competitor. The competitor will then build this vehicle from the picture. Verbal or written
instructions should be included with the pictures so each competitor can build the vehicle as intended.
Each participant will then conduct the tug-o-war with their own vehicle and the vehicle they built
based on their competitors picture and other information
EDUC 566 Jan13 58
Appendix D
Cognitive Functions – The Prerequisites of Learning*
Input phase – collecting the information
Description of
cognitive
strength
Definition Examples of prompts and questions to ask to
develop the cognitive functions
Description of cognitive weakness and
examples
1. Clear and
focused
perception
Focused perception; use all
senses to perceive all data
correctly and clearly. Keep
your focus on one spot.
What do you see?
What is here?
Have you perceived everything?
Where do you have to look?
Blurred and sweeping perception. Not
knowing where to start looking, look at
everything as a whole.
Look very quickly here and there.
2. Searching
systematically
Collect the data step by step in
a systematic way so that
nothing is lost and nothing is
done twice.
We are going to look step by step. One by one. In what
order? Let’s start here, on the left at the top, then from
left to right, then the second row, etc.
Look up a word in a dictionary, a place on a map,
check that all words are correctly spelled.
Counting one by one.
Unplanned, impulsive, and unsystematic
behavior.
Criss-cross perception, here-there-
everywhere without rhyme or reason.
Counting the same things twice.
3. Labeling Enrich vocabulary to describe
objects, events and
experiences precisely.
Describe the objects according to their characteristics
and definition.
What are the characteristics? In what way do they
differ? In shape, distance, color, number, size,
direction?
How can we call a four-sided closed figure with equal
sides, but no equal angles?
Lack of, or impaired receptive verbal tools
that affect discrimination (e.g. objects,
events, relationships, etc. do not have
appropriate labels).
Because of lack of correct names to describe
objects, events and relations, with their main
features, they are not adequately observed;
the child does not see a difference e.g.
between a rectangle and a square, it’s the
same for him.
4. Spatial
reasoning
Use concepts to indicate place,
direction, position and
orientation in relation to each
other or to a frame. Be able to
use spatial concepts.
How are things related to each other? Parallel, at a right
angle, central, in the middle of…?
Where is this? (e.g. top-left; bottom-middle; next to…;
left of…; in front of; etc.
In what direction are they running: towards…; coming
from left to right, east to west, north to south?
Lack of, or impaired, spatial orientation, the
lack of stable systems of reference impairs
the establishment of topological and
Euclidean organization of space.
Problems with left/right discrimination.
Problems with map reading.
Problems with drawing simple objects,
especially their 3-D relationships.
Problems with describing where you are and
EDUC 566 Jan13 59
where you want to go.
5. Temporal
reasoning
Use the correct concepts to
describe time and sequence.
Look for data which give you
indication of the sequence of
things and the ordering in
time.
How do you know what comes first and thereafter?
Lack of, or impaired, temporal concepts.
Problems with planning – starting on time.
6. Conserving
constancy
Be attentive that some
characteristics of an object or
a relationship change while
others remain the same.
What changes and what stays the same?
Which characteristics change?
If a square is rotated, does it remain a square?
If gasoline costs $2.00 per gallon how much will you
pay for 5 gallons?
Lack of, or impaired, conservation of
constancies (size, shape, quantity,
orientation) across variation in the factors.
Using additive thinking when
multiplicative thinking is required.
7. Being precise Being attentive to details
when it is important to do so. Have you noticed the details?
Are these two objects really the same height?
Lack of, or deficient need for, precision and
accuracy in data gathering.
Not noticing the place of the comma in a
number.
Not being precise in measuring lengths,
weights, etc.
8. Using more
than one source
of information at
once.
Take into account more
characteristics at the same
time (height, length, width,
number, shape, etc. Feel the
need to collect information
from different sources.
Have you been complete in gathering the data?
Where can you find information on what to do?
How many ways are we being presented with
information on what to do?
Lack of capacity for considering two or
more sources of information at once, this is
reflected in dealing with data in a piecemeal
fashion rather than as a unit of organized
facts.
Dealing with data in a piecemeal fashion
rather than as an organized unit, e.g. with a
school task – text, drawings, numbers
indicating order, tables, maps, index,
dictionary.
9. Activating
Prior Knowledge
Remembering and retrieving
relevant information from
memory.
Where have you seen or heard of this before?
Does this look or sound familiar? Why?
Lack of or deficient need for retrieving
relevant knowledge from long-term memory
in order to make connections among
characteristics of something currently being
considered or a problem to be solved.
10. Analyzing Identifying a structure,
process, concept, object, etc.
as a whole or unit and the
parts or elements the make up
the whole.
What are the parts of this thing?
How are the parts related to one another and to the
whole?
What are the steps of this process or procedure? Are
they in order? Why is this order important?
Impaired or deficient propensity for
breaking material, structures, or processes
into its parts and determining how the parts
relate to one another and to an overall
structure or purpose.
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Elaboration phase - processing the gathered information
Description of
cognitive
strength
Definition Examples of prompts and questions to ask to
develop the cognitive functions
Description of cognitive weakness and
examples
1. Defining the
problem
Recognizing the problem and
being able to define it. What’s the problem here?
What do we have to do?
Is there a problem?
What is it?
Does it fit? Is everything all right? Is it correct?
Inadequacy in the perception of the
existence and definition of an actual
problem.
There is little or no awareness that
something doesn’t fit, or it is not right.
Difficulty in getting started because there is
a lack in knowing what to do.
2. Selecting
relevant
information
In a multitude of information,
select the information which
you need to solve the problem
and neglect/eliminated the
rest.
What information do you need to solve the problem?
What do you not need to solve this problem?
What is a key word in this task?
What is the important information and what is not
important information for solving this problem?
Inability to select relevant vs. non-relevant
cues in defining a problem.
Difficulty in finding key words in a reading
passage, and in forming a summary.
Difficulty in selecting the information
which is needed to solve a word problem.
3. Comparing Developing the need to
compare things, to look a
similarities and differences
with other things and events.
In what way are they same? Different?
Expand the repertoire of criteria to compare.
How should we compare these things, by size, color,
shape, quantity, etc.?
What does ‘greater than/less than’ mean?
What does ‘n times as much’ mean?
Let’s look at the first as, what are the words to the left,
now let’s look at the second as, what are the words on
the right of this as?
Prepositional relations compared – eight divided by
four compared to eight into four.
Lack of spontaneous comparative behavior
or limitation of its application by a restricted
need system.
Compare on the basis of only one arbitrary
criterion.
Compare on the basis of non-relevant
criteria.
Lack of spontaneous comparison with prior
knowledge.
Difficulty in identifying the lack of
correspondence between mathematical
symbols and the words they represent (e.g.
if the expression eight divided by 2 is
translated word-for-word in the order in
which it is written, the resulting
mathematical expression 82 would be
incorrect .
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4. Broadening
your mental field
Have an overview, take into
account as many factors as
possible. Effective memory
capacity. Analogous to
computer with a large hard
disk and a fast retrieval speed.
We are confronted here with a mass of data. Can’t we
put them into order? Can’t we recognize groups? What
things could belong together? On what basis?
How can we memorize better?
Writing down key words.
Making a schema, a table, a matrix.
Keeping an agenda.
Have a system of visual retrieval (post-it-notes),
writing in the margins.
Narrowness of the mental field.
Forget things easily.
Deal with things as pieces one by one,
rather than in units or chunks.
Not able to process two things at the same
time.
When you learn something new, you forget
the previous learning(s).
5. Forming
relationships,
making
connections
Put things in relation to each
other.
Cause – effect relations.
Means – ends relations.
Have you seen something similar before?
How are these connected?
Is A the cause of B, or does B cause A? Why?
Episodic grasp of reality.
Dealing with events and objects as if there is
no connection between them, in an episodic
way.
6. Need to pursue
logical evidence
Have a need to justify the
answer and be able say why
choose a certain solution.
Spontaneously search for date
to justify a statement.
How do you know this? How do you know whether
your answer is correct?
Why is it correct? Why not?
Explain your answer.
Lack of, or impaired, need for pursuing
logical evidence.
Giving an answer but not knowing why the
answer is right or wrong.
The student accepts statements without
critically examining them.
Beliefs are either unexamined and
unjustified or justified by their
correspondence with the beliefs of an
authority figure, such as a teacher or parent.
7. Internalizing
and representing
information
Composing a mental image of
the information. Visualizing
and mentally representing
information in different ways.
Make a mental picture of the information.
Visualizing the information in more than one way.
Lack of, or impaired interiorization.
8. Hypothetical
deductive –
predictive
thinking
If … then thinking. Represent
mentally what could possibly
happen, if… Inference: draw a
conclusion; one thing follows
from another.
What do you think could happen?
What do you predict will happen?
What could the possible solutions be?
What can you infer from this statement?
What can you conclude from this?
Lack of, or impaired, inferential-
hypothetical thinking.
Limited capacity to come up with
possibilities.
9. Developing
strategies to test
hypotheses
Check a hypothesis mentally:
what could be the effect of an
event. Find means to check
and confirm a hypothesis.
If a possibility is thought of,
look for data which confirms
or refutes it.
Shall we look for a strategy to check it?
Let’s compare with the model, analyze the model’s
characteristics, make a drawing, schema, write down
the steps, look for more data; use additional reliable
sources of information like encyclopedias, use a
calculator after making the operations mentally; use the
reverse operation.
Lack of, or impaired, strategies for
hypothesis testing.
Have a need to check solutions in a concrete
rather than a mental way.
Have no need to check at all.
Difficulty in representing possible effects.
EDUC 566 Jan13 62
10. Selecting a
frame of
reference,
structure, or
framework for
problem solving
Choose a framework in which
a solution can be found. Where shall we look for a solution?
What operation should we do here: is this a
multiplication problem or an addition problem? Is this a
problem of classification?
Do we need a science text or dictionary? Shall we got
to the library or ask an expert?
Lack of, or impaired ability to define the
framework necessary for problem solving
behavior.
Have no idea where to start looking.
Have no idea which operation to choose.
11. Planning
systematically
Represent the steps toward a
solution one by one. What are the steps we have to take in order to arrive at
our goal?
What are you going to do first? And then? And then?
Lack of, or impaired, planning behavior.
Start working in an unsystematic way.
12. Categorizing Develop vocabulary for
superordinate words and
concepts to indicate cognitive
categories and describe mental
operations.
Let’s compare – find the similarities and differences.
This belongs to a larger group, let’s find the class or
category that it belongs to. What is the name of this
category?
Let’s order these things. What comes next?
Let’s think this through, what thinking action(s) do we
need to use to solve this problem?
Non-elaboration of certain cognitive
categories because the verbal concepts are
not a part of the individual's verbal
inventory (on a receptive level) or they arc
not mobilized at the expressive level.
Lack of words to describe categories.
13. Accounting
for all
information
Encourage counting. Make an
inventory. How much do you have?
Are you sure we did not miss anything?
Lack of, or impaired summative behavior.
Paraphrasing
Through
Rereading
After reading (or hearing)
something, restating the main
idea in your own words.
Tell me in your own words what I just said.
Tell me in your own words what you just read.
Tell me exactly what the problem is.
Lack of or impaired need for writing or
saying something in your own words that
you have just read or seen (or heard).
Transforming a
Representation
Changing the modality of a
representation from one type
to another.
Make a diagram of what you just read.
Make a picture with stick figures to represent this
problem or story.
Use numbers and symbols to represent the
relationships and things in this word problem.
Make a table, a graph.
Lack of or impaired need for changing the
modality of presentation from one form to
another.
Inductive
Thinking
Forming relationships among
data or information so that a
general rule or formula can be
created.
What is common to all of these?
Do you see a pattern?
How could you classify these things?
Write out the rule or formula that clearly states the
relationship(s) that you discovered.
Lack of or impaired propensity for forming
abstract relationships among items or data
that seem to form a pattern, categorizing
them into general relationships, and
organizing the results to form a general
rule, principle, formula, recipe, or guide.
Analogical
Reasoning
Transferring relationships
discovered in one task to a
new task where the prior
discoveries will be helpful in
What have we just learned that may be helpful in
solving this problem?
Do we have any examples or models that will help us
Lack of or impaired need for transferring
relational information from existing
concepts to a new problem that needs to be
EDUC 566 Jan13 63
solving the new task. solve this problem? solved. Deficiency of abstracting a solution
strategy from a previous problem and
relating that information to a new problem
that one is trying to solve.
Synthesizing
Connecting things to form a
new structure. How can we modify these things and then put them
together to make something new?
Lack of or impaired propensity to connect
elements together to form a coherent or
functional whole so that a new pattern or
structure emerges that is not just a
reordering of the elements.
Output phase – expressing the solution correctly
Description of
cognitive
strength
Definition Examples of prompts and questions to ask to
develop the cognitive functions
Description of cognitive weakness and
examples
1. Expressing
yourself clearly
Put yourself in the other
person’s shoes in order to
communicate your answer
clearly.
I can understand what you mean, but please, could you
say your answer so that others can understand it as
well?
I can see you know, but nobody else sees it.
Encourage a student whose habit is to speak in one
word sentences, to speak in full sentences.
Egocentric communicational modalities.
A student who does not bother to write
down or tell his answer, because he is
satisfied he knows it.
Difficulty in explaining a familiar way to go
somewhere.
2. Projecting
virtual
relationships
Make hidden relations
explicit. Make relationships visually obvious with graphic
organizers, markers, schemata, arrows, etc.
Infer future events from present trends in a sequence of
events (making graphs, statistics, analyzing historical
processes, weather forecasting).
Difficulties in projecting virtual
relationships.
Some students may be aware and know the
relationships but are unable to make them
visible because they do not have techniques
to do this.
3. Preventing
blocking
When a solution does not
appear to be found
immediately, or is not correct,
stay calm and start looking
again in a different way.
You didn’t find it immediately? Never mind. Let’s
analyze what happened. What were you doing, looking
for, what strategy did you use? Is there another
strategy? Let’s look again at the model, the data. Where
else could we start?
Don panic when you haven’t found it! There’s no harm.
We’re going to look again.
Convey a message to the class that it’s all right to make
mistakes as long as we learn form them.
Blocking.
That student panics and doesn’t know
anything anymore.
The student stops searching.
The student has fear of failure or is angry
and doesn’t proceed.
EDUC 566 Jan13 64
4. Avoiding trial-
and-error
Stop guessing until a right
solution is found incidentally. “You’re only guessing now. Start thinking! What are
the data? Look at them. What do you think you have to
do?”
Define the problem, plan a solution, gather the data.
Trial-and-error responses.
Students who give answers without
thinking.
5. Using correct
wording
To express an answer
correctly, one needs precise
vocabulary.
Give the child the proper wording to formulate an
answer correctly.
Organize class discussion to talk about solutions.
Encourage journal writing.
Lack of, or impaired, verbal tools for
communicating adequately elaborated
responses.
The child knows the answer but does not
have enough or adequate vocabulary to
formulate it.
6. Being precise Have a need to communicate
an answer with enough detail
in order to avoid confusion.
Ask for more precision in formulating, in drawing, etc.
Create a need to be more precise when giving an
answer.
Lack of, or impaired, need for precision and
accuracy in communicating one's response.
Students who give vague answers.
7. Transporting
visually
Transport the data and
solution from the starting
place to the place where the
answer must be expressed or
drawn without changing the
characteristics.
Compare with the model constantly, go back and forth;
make sure you haven’t changed it.
Deficiency of visual transport.
The student who changes the4 date from the
top to the bottom of the page.
Difficulty in copying numbers, words, and
drawings from a book or the blackboard to
the page.
8. Restraining
impulsivity
Think before acting. Are you sure of your answer/ Have you checked
everything?
I want to hear you answer only when you are really
sure.
Impulsive, acting-out behavior.
The child who starts answering before
thinking or before the question has been
fully asked.
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Appendix E
Problem Solving – Due Week 2
The half-hour program includes 13 classroom excerpts from the content standards lessons which
illustrate students investigating and learning mathematics through problem solving. Teachers share
their approaches and observations.
http://www.learner.org/resources/series32.html?pop=yes&pid=1088#
17. Problem Solving
Excerpts from 10 classrooms where students are learning mathematics through problem solving.
Teachers use multilayered tasks to engage students in making conjectures, constructing meaning, and
developing strategies.
Respond in writing to one question from each group. Be prepared to discuss your written responses
with your Forum group.
Observing Student Problem Solving
How can teachers create enthusiasm and interest in all students for problem solving?
What are the criteria teachers can use to select problems for introducing new material?
Problems should offer a rewarding challenge for students, being neither so obvious that they put no
demands on them nor so difficult that they are clearly beyond their ability. How do you make a
determination about the appropriate level of difficulty in your own class?
Different students solve problems at different speeds and with different approaches in this
classroom, or in any classroom. Given this factor, what is the role of the teacher in fostering
effective problem solving? Be specific.
It is often straightforward to assess whether a student found the correct final answer. How do you
assess whether the strategies and ability to apply them were sound? If a student has found a correct
answer despite a faulty strategy, how do you respond?
Exploring Problem Solving
Examine the work you did to solve the problem, any notes you made. If you were now asked to
hand this work in to your instructor, what might it reveal to that instructor about your problem-
solving practices?
How does your personal problem-solving approach influence your teaching and assessment
practices?
As a student, do you remember using problem situations to help you make sense of new concepts
and procedures? What was the effect? Did this work help you make new connections?
How can questioning be used to help students learn from errors or wrong turns in problem solving?
What questions do you ask yourself when you are struggling while solving problems? Are these the
same questions you would ask your students? Why or why not?
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Defining Problem Solving
We've provided a range of points that help in formulating a working definition of the problem-
solving standard. If a colleague or parent were to ask you to define problem solving in the context
of your own classroom, how would you do so?
Although research has shown that problem solving can be taught, and that kids of varying skill
levels can still improve with respect to their ability at the beginning of the year, many teachers
believe deep down –– and privately –– that some kids are just good problem solvers and some
aren't. Do you believe this? Why or why not? How does this belief relate to your own problem-
solving practice?
Do you believe the practices developed in solving in high school mathematics problems can be
extended to contexts outside the mathematics classroom? Why or why not?
How does technology influence how you work with and define problems in the classroom? Has it
expanded your repertoire? Has it presented challenges?
Identify some problem-solving strategies that you wish to introduce to your class. What are
important considerations as you incorporate them in your classroom?
Applying Problem Solving
What can you do in your classroom to help students learn by exploring new concepts and skills in a
problem-solving situation rather than by direct teaching? Do you see drawbacks to this approach?
How could you address them?
What are some of the advantages of having students work in groups? When might you want
students to work individually on problem-solving experiences? Give an example.
How long do you let students struggle with a problem before helping them find a solution? What
are some questions that help without giving away a solution method?
If different individuals and groups are using different strategies on the same problem at the same
time, what tools can the teacher use to assess individual understanding?
Evaluating Problem Solving
Small changes can have big differences. What one change in your classroom could you make to
improve your students' problem-solving skills? Could you make that change the next time you walk
into your classroom, say tomorrow? Why or why not?
Imagine a video team was to arrive tomorrow to film your class as a study of problem solving in
action. What would it show? What would you be proud of? What might you want to change?
Where would you like to be as a teacher with respect to problem solving in a year? How might you
get there? How will you know you've arrived?
Eliciting Student Ideas – Due Week 4
Week 4 Annenberg Video Assignment
For Week 4 go to the Annenberg Private Universe Project in Science website by entering this URL in
your browser:
http://www.learner.org/resources/series29.html
EDUC 566 Jan13 67
Click on the icon titled VoD for Workshop 1. Astronomy: Eliciting Student Ideas.
Workhshop 1. Astronomy: Eliciting Student Ideas. Introduces constructivism by examining student
beliefs on what causes the seasons and their explanations for the phases of the moon.
What is the theme of this workshop? The theme of Workshop One is "Eliciting Student Ideas."
Pre-Workshop Activity
Prior to this workshop, workshop participants should spend 5-10 minutes interviewing a student and an adult about what
causes the changes in the seasons. Record their responses. Did you discover some good ways to uncover students' ideas?
Explain.
Whom do we see in the videotape? We see several Harvard students and faculty who are enormously
confused about what causes the seasons. We also see Heather, an articulate, intelligent high school
student who has a great many ideas about astronomy. Interviews with Heather both before and after
her classroom lessons about astronomy reveal that she has learned much but is still confused about
some key aspects of the subject.
What happens in the videotape? While some of Heather's ideas after instruction are solid, others
seem wildly "off base" from a scientist's point of view. Some of her ideas stubbornly resist change,
either in the classroom or during on-camera challenges.
What problem does this workshop address? Many of us think that the cause of the seasons has
something to do with our distance from the sun, even though this "wrong idea" was never taught to us.
Why is it we seem to learn some things that teachers don't teach us?
What teaching strategy does this workshop offer? Many techniques for eliciting student ideas have
been tested in the classroom. Interviews with students, poster presentations, prediction questions,
group discussions, and journal keeping are some of the most common approaches. This workshop will
address interviewing techniques and journal keeping.
Using the Forum, post answers to the following questions. Reply to at least one other of your classmate’s responses.
1. Is understanding the causes of the seasons or lunar phases important in the lives of students?
2. Why is an understanding of basic scientific principles important for all citizens?
3. What are some surprising ways in which a good science understanding can enhance the abilities
of non-scientists to perform their work and live their lives? (For example: Could chemical
understanding affect the work of professional cooks and homemakers; could understanding
weather and fluid dynamics help make better airline pilots and sailors; and could understanding
how plants make food affect anyone who gardens?)
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4. What are some examples of important social or political issues that require a scientific
understanding by voters and policy makers? (For example: Would knowledge of science be
important for understanding toxic waste, screening for genetic diseases, global warming, or
energy conservation issues?)
Week 6 Annenberg Video Assignment
For Week 6 go to the Annenberg Private Universe Project in Science website by entering this URL in
your browser:
http://www.learner.org/resources/series29.html
Click on the icon titled VoD for Workshop 2. Biology: Why Are Some Ideas So Difficult?
Focuses on the need for conceptual understanding and examines the scope of student ideas by exploring the central idea of photosynthesis, that the substance of plants comes mostly from the air. What is the theme of this workshop? The theme of Workshop Two is "discovering the scope of student ideas".
Whom do we see in the video? Jon, a seventh-grade student, is interviewed before and after a traditional lesson on photosynthesis. Bob Holden, Jon's teacher, watches the video of Jon's interviews, discovering that Jon's problems in biology concern his confusion about the physics and chemistry of matter and energy. Jon also has no concept of energy and the relationship of energy to chemical changes. He seems to be missing the concept that chemical changes may either require an input of energy or may release energy.
What happens in the video? Interviews with Jon suggest that teaching can be more effective when the full scope of a student's ideas are considered.
What problem does this workshop address? Photosynthesis is among the most widely taught of all concepts in biology. Why, then, do many people have difficulty grasping the central idea of photosynthesis-that most of the substance of plants comes from the air?
What teaching strategy does this workshop offer? Among many possibilities to help students reflect on their own thinking, we offer such techniques as concept mapping and journal keeping.
Using the Forum, post answers to the following questions. Reply to at least one other of your classmate’s responses.
EDUC 566 Jan13 69
1. Devise a simple explanation, demonstration, or activity for understanding how plants convert carbon dioxide from the air and water from the ground into food through photosynthesis.
2. Invent a way that allows even the skeptical students to convince themselves that the air does, indeed, have mass/weight. Whenever possible, allow students to test the idea.
3. Often the ideas established prior to and outside the teaching of a subject block learning. How can this problem be addressed in the classroom? For instance, the student in the video has trouble
understanding photosynthesis because of his belief that air has no weight. An understanding that air
is made of invisible particles with weight is usually a topic for chemistry or a physics lesson, and a
lack of this understanding prevents the student from learning an idea in biology.
Week 8 Annenberg Video Assignment
For Week 8 go to the Annenberg Private Universe Project in Science website by entering this URL in
your browser:
http://www.learner.org/resources/series29.html
Click on the icon titled VoD for Workshop 5. Vision: Can We Believe Our Own Eyes?
Explores the origins of student ideas to find out whether experience equals learning. Shows how
experience can work for or against learning because students can disbelieve concepts that they have
“learned.”
What is the theme of this workshop? The theme of Workshop Five is "the origins of student ideas."
Whom do we see in the video? Richard and Karen, eighth graders, and Conor, a fifth grader, are three
students who constructed many of their ideas from personal experience, television nature specials, and
classroom activities. Conor blends the various resources and constructs rich and imaginative
explanations of light and vision; Richard vacillates between scientific and non-scientific ideas, even
after instruction; and Karen never waivers from her personal construction about vision.
What happens in the video? Students of various ages discuss their ideas of how we "see." Their
ideas, many of which seem to come from sources outside of school, often differ from those accepted
by scientists. Where do students' ideas come from and can (or should) they be changed?
What problem does this workshop address? Although mirrors are among the most common of
scientific devices, they remain enigmatic. The average adult in the United States may use a mirror
30,000 times in a lifetime. Why is it that, even with all of this experience, so many adults still cannot
answer simple questions about the properties of mirrors?
"Can We Believe Our Own Eyes?" addresses students' "conceptual change," a process by which
students replace old ideas when new ones become more acceptable. This workshop explores how
students construct ideas from the many sources available to them. Television, radio, books, parents,
teachers, and peers all play a role in promoting the ways in which students see and understand natural
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phenomena. In contrast, seeing often contradicts their understanding and, as a result, seeing is not
always believing. What can we learn about children's concepts of light and vision that can shed some
light on this problem?
What teaching strategy does this workshop offer? The role of students' experience can be very
powerful in shaping their ideas and beliefs. Does this experience always lead to a better understanding?
Teachers learn to confront students' understanding by offering alternative experiences that contradict
old ideas.
Using the Forum, post answers to the following questions. Reply to at least one other of your classmate’s responses.
1. Do you think it is possible for a teacher to control the way a student interprets ideas? Please
explain your response.
2. When teachers see their students espousing non-scientific ideas picked up from television,
books, and other sources, often the immediate reaction is to suggest ways to eradicate the
sources of "misconceptions" and replace the alternative ideas with the science ideas. The more
experience we have with something, the more difficult it can be to understand. Experience can
reinforce or create misconceptions. Experience does not equal understanding. Should or can
we as educators "misconception-proof" the student's world? Explain. 3. Light allows us to see and yet light itself seems invisible. What activities might we
devise to help students in grades K-3 develop concrete images of the abstract concept of
light?
Following Children’s Ideas in Mathematics - Due Week 10
An unprecedented long-term study conducted by Rutgers University followed the development of
mathematical thinking in a randomly selected group of students for 12 years - from 1st grade through
high school - with surprising results. In an overview of the study, we look at some of the conditions
that made their math achievement possible.
Private Universe Project in Mathematics. Following Children’s Ideas in Mathematics.
http://www.learner.org/resources/series120.html
Using the Forum, describe what you learned about the long-term development of students’
mathematical thinking. Respond to the post of at least one other student.
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