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MSED4310 MATHEMATICS IN INTERMEDIATE AND MIDDLE GRADES

Monday 12:00PM – 2:50 PM; EDUC 405; SPRING 2014

INSTRUCTOR:Joyce G. Asing-Cashman, PhD. (email: [email protected])(915) 525-8500Office Hour: Before and After Class or By Appointment

COURSE DESCRIPTION:Based on a vision articulated by the National Council of Teachers of Mathematics (NCTM) and Texas Education Agency (TEA), this course introduces pre-service teachers to pedagogy methods, strategies, and materials for teaching all students mathematics in grades 4-8.

This course will be an integrated minds-on/hands-on activities and discussions in which you will have the opportunity to:

1. Combine theory with experience in creating and implementing culturally inclusive curriculum and teaching strategies

2. Plan and participate in hands-on exploration3. Practice reflective teaching using theoretical and practical implications of these

experiences4. Demonstrate knowledge and skill in TExES Math Content Competencies and Pedagogy

and Professional Responsibility (PPR) Competencies. The TExES standards and competencies will be integrated in this course and all related assignments.

5. Understand the role that technology holds in the profession of teaching.

REQUIRED TEXTS/RESOURCES/SOFTWARE:Van de Walle, J. A. (2007). Texas Edition Elementary and middle school mathematics: Teaching developmentally. 7th Edition. Longman.

ALIGNMENT WITH TEACHING STANDARDS: State Board for Educator Certification: Grade 4-8 Educator Standards

o http://www.tea.state.tx.us/index2.aspx?id=5938&menu_id=2147483671&menu_id2=794 Comprehensive Testing Information and Preparation Manuals

o http://www.texes.ets.org/ Texas Essential Knowledge and Skills A (TEKS)

o All content areas and grade levels: http://www.tea.state.tx.us/teks/#grade English Language Proficiency Standards

o English Language Proficiency Standards for English Language Learners (ELLs) in order to provide strategies for language acquisition and academic success in all content areas for students at different levels (beginning, intermediate, advanced, and advanced high) in the domains of listening, speaking, reading and writing.o http://www.tea.state.tx.us/curriculum/biling/elps.html

MSED 4310 Syllabus Monday, Spring 2014– J. Asing-Cashman Page 1

http://www.tea.state.tx.us/index2.aspx?id=5938&menu_id=2147483671&menu_id2=794

COURSE WEBSITE:Blackboard: Make sure your Blackboard is activated and you can see this course. Any log in problems should be taken care on the first week of the class. Plan to visit Blackboard regularly. Check the course homepage regularly for announcements. Remember to log out when finished.

SUGGESTED RESOURCES WEBSITE: National Council of Teachers of Mathematics: Illuminations. Resources for Teaching

Mathematics: http://illuminations.nctm.org/ Comprehensive Testing Information and Preparation Manuals

o http://www.texes.ets.org/ Texas Essential Knowledge and Skills A (TEKS)

o All content areas and grade levels: http://www.tea.state.tx.us/teks/#grade English Language Proficiency Standards

o English Language Proficiency Standards for English Language Learners (ELLs) in order to provide strategies for language acquisition and academic success in all content areas for students at different levels (beginning, intermediate, advanced, and advanced high) in the domains of listening, speaking, reading and writing.

o http://www.tea.state.tx.us/curriculum/biling/elps.html ● McGraw Hill Mathematics

http://www.mhschool.com/math/2003/student/index.html● Internet Resources for Use in Mathematics Classroom

http://www.internet4classrooms.com/math_elem.htm● Teacher Tube

www.teachertube.com● PBS Teachers: Math

http://www.pbs.org/teachers/math/● International Society for Technology in Education, National Educational Technology

Standards for Teachers, (NETS-T) o Defined the fundamental concepts, knowledge, skills, and attitudes for applying

technology in educational settings.o http://www.iste.org/standards/nets-for-teachers.aspx

● Standard for TEXES:○ Generalist EC-6: Link○ Generalist Bilingual EC-6: Link○ Mathematics 4-8: Link○ Generalist 4-8: Link

● Appendix I: Test Framework for Field 115: Mathematics 4-8


GENERAL COURSE FORMAT:This course is a hybrid online/face-to-face course. We will meet 9 times throughout the semester (please consult course schedule) and the remainder of our sessions will be conducted online (Module 2).

For the online sessions (Module 2), discussion questions will be posted by Sunday before the scheduled discussion week. You will begin your discussion on Monday of the week of the scheduled online discussion and conclude it on the following Sunday at 11:59PM.

LEARNING AND TEACHING PHILOSOPHY:There are several things you should keep in mind as you begin this course. First, don’t think that I know it all. I enjoy teaching because in the process, I have the privilege of learning from you. I have taught different courses several times and I always come away with considerable new knowledge. Second, active participation is a must. I want and will require you to participate in the weekly discussions. My role in this class is as facilitator and not as a sole knowledge provider. As a community of learners, we will work together to achieve desired results. Learning is social and develops from experiences we have in daily living. The process of engagement in communities of practice supports learning, thinking, and knowledge. A set of shared ideas, commitments, and memories are developed in learning communities. The individual talents, interests, and needs of community members influence a community. As members gain experiences in a community, their participation increases. Ways to support an evolving and a renewing community with constructive relationships is a challenge for educators. It is their responsibility to help support professional and caring relationships that are valuable for developing social and emotional assets/skills of the participants. Social and emotional skills are linked to learning and constructive behavior.

Participants in a class include the students and facilitators/instructors. The role of the student is active and involves teaching as well as learning. The roles of the facilitator/instructor are facilitating, leading, learning, and teaching. Students and facilitators/instructors are co-investigators in the learning process. A personalized approach to constructivist/situated learning theory encourages participants to co-design learning experiences so that individual interests, talents, and needs related to the course outcomes/goals are better addressed. Democratic efforts to accomplish these goals are a priority.

Participants will frequently work in teams for reflective and learning experiences. In collaborative learning environments, participants are responsible for their own learning, as well as the learning of their colleagues. Individuals are responsible for all course assignments, however. Self- and peer-assessment are as important as assessment of progress by the facilitator/instructor. Responsible and respectful interactions are expected. The respectful sharing of diverse points of view may enhance learning of the participants.

Participants will focus on establishing the groundwork of principles, essential skills, and habits of mind. The use of inquiry, community building, collaboration, curiosity, information literacy, dialogue, and technology skills are important tools for learning and professional development. Participants are expected to come with the dispositions to examine, use, and improve their knowledge and skills, with a commitment to seeking excellence. Expectations for performance


are high. Participants and the course facilitator will work together to support each other with the expectations.

Third, take time to think reflectively about the readings and discussions. You all have a lot of experience as learners that you can use to help you make sense of the ideas, techniques, and standards covered in this class. In fact, I will often specifically ask you to think back over your experiences. So, take time to go beyond just reading the text. Explore, discover, and look for connections that are important to you, and that will help you in your future teaching. If you find yourself getting lost and confused, take some time to reflect, and ask for help if necessary.

STUDENT LEARNING OUTCOMESUpon completion of this course, students will be able to:

1. Analyze research-based practices for improving mathematics instruction

Discussions; projects assessed through the use of a rubric; oral presentations assessed through the use of a rubric; lesson plans; thematic units; learning journal; and quizzes

2. Design effective standards-based classroom activities for Grades K-6 students and reflect on student outcomes.

Discussions; projects assessed through the use of a rubric; oral presentations assessed through the use of a rubric; lesson plans; thematic units; and learning journal.

3. Develop varied formative assessment practices and assess mastery of the same essential math concepts in different ways

Final project; statement of course goals; teaching and learning theories activities, thematic units, oral presentations, inquiry lesson presentation assessed through the use of a rubric; lesson plans; and learning journal.

4. Apply instructional strategies and appropriate practices for analyzing student work and modify lessons based on assessment information.

Online and in-class discussions, final project; teaching and learning theories activities , thematic units, oral presentations, inquiry lesson presentation assessed through the use of a rubric; lesson plans; and learning journal.

5. Apply instructional strategies to promote mathematics learning among students of a wide range of academic diversity including ESL and special needs students.

Learning/Instruction theories activities; online and in-class discussions, final project; thematic units, oral presentations, inquiry lesson presentation assessed through the use of a rubric; lesson plans; and learning journal.

6. Differentiate math instruction based on students' learning styles, interests, and readiness levels; and modify lessons based on the synthesis of the relationship between problem solving and communication.



7. Align math classroom environments with real world environments by infusing problem-solving strategies; and apply technology tools in classroom instruction and connect math activities to everyday experiences and the real world.


8. Modify lessons based on the synthesis of the relationship between problem solving and communication.


PROFESSIONAL RESPONSIBILITIES:1. Participation/Discussion/Attendance (120 points)OnlineOnline discussion contributions will be graded based on the rubric that we will review during the initial class (Refer to Rubric on page 10). In general, discussions will run from Tuesday-Monday, though posting in advance of the week is permitted. Posting after Monday will not count toward your grade.

● Online Participation - 6 Discussion sessions @ 5 points each = 30)

IMPORTANT: Your reflection to the question(s) posted is due on Tuesday at 11:59PM. Therefore, you have to complete your readings and post your reflection on the question(s) by the indicated day above (Monday @11:59PM) on the week we are doing online discussion. From Monday through Sunday (by 11:59PM), you will give feedback to three or more postings.

Face-to-faceAdvanced preparation for class meetings is particularly important for participation so that you can engage the content and ideas in the readings. Your in-class discussion, completion of assignments and participation will be worth 10 points per class. These points are not earned by simply coming to class. The expectations are:

● Come to class prepared and ready to contribute to the educational experience and the learning community

● Engage in public dialogue with course concepts and materials, not just opinion and individual experience

● Engage in reading and discussion● Collaborate with diverse students throughout the course of the semester

Attendance and In-class Participation – 9 meetings @10 points each = 90

If you will be missing or miss a class, immediately contact a classmate to find out what you missed. Excused and unexcused absences will both result in deduction of your per class points. We will begin on time. Being tardy disrupts the flow of the


class. Two tardies will equal one absence. The Department considers that missing two weeks of class is excessive. The student may be dropped for lack of attendance. If you miss two-weeks of class, contact your professor immediately.

2. Leading Facilitators (40 points)Students in a group of two or three will present chapters/activities from the chapters of the textbooks. Group assignments will be determined in Week 2. Each group will prepare a 45 minutes to 1 hour lesson plan for the chapter assigned. The lesson plan should include the following but not limited to:

● Objectives/Goals● Standards/Benchmarks addressed● Activities – at least 4 activities from the chapter. Make your activities fun and

engaging.● Materials● Closure

This lesson plan will be executed on the day of the presentation. On the day of your presentation please submit to me:

1. Your lesson plan including all handouts/materials use in your lesson presentation.

2. Each group members must print and complete the “Group Members Evaluation Form” located in the “Module 3” folder in the Blackboard. If you want your evaluation to be confidential, place it in an envelope. You must also evaluate your contribution in completing this assignment.

Please refer to the attached “Grading Rubric for Lesson’s Presentation” and “Chapter’s Presentation Guideline” to guide you with this assignment.

3. Test Review Session (10 points)Before you take your Math content exam, you are required to attend one review session at the Testing Center. Please bring a copy of the slip verifying that you have attended the review session. Please plan your schedule to attend one of the review sessions. Once I get the Review Session Schedule from the department, I will send it to all of you so that you can plan your day/time to attend the review session.

4. Review Questions (RQ) (50 points)There will be 5 review questions worth 10 points each that I will give throughout the semester. The goal of this assignment is to make sure that you acquire the knowledge or ideas presented in the chapters’ readings and you actually did your readings when other groups do their presentation on the assigned chapters. The week a RQ will be given is indicated in the column 3 of the course schedule. o 5 RQs x 10 points = 50 total points


5. Journal Entry (50 points)Using the Journal feature created on the course Blackboard, you will record a weekly journal that is representative of the goals and learning accomplished throughout the activities of this class. You must reflect on what is learned from the online discussion and from the face to face meetings, and how it could help and/or be used or implemented, in your future classroom. Please complete and organize your journal entry in weekly basis. - Your weekly entry must consist of a minimum of 150 words (except for the first journal entry).Your first journal entry must include a statement of course goal(s) - what you expect to learn from this class; how comfortable you are with mathematics (learning & teaching); and your personal goals, your professional goals and your teaching philosophy. Your first journal entry will consist more than 150 words.

6. Final Project: Interdisciplinary Curriculum Unit and Field Experience (100 points)Since this is a teacher preparation course, one of the most important skills to practice is the art of planning. Planning lessons, activities, and student assessments that increase student mastery of the content taught while attending to the myriad other issues teachers in the classroom face is difficult. This assignment will increase that planning experience and confidence level.

This is a group assignment (up to 3 per group).

For this project, plan an interdisciplinary thematic unit for five lesson plans (five different subject areas). In your unit, four of these lesson plans must be mathematics, science, social studies and language arts. The fifth lesson plan can be from one of these curricular areas: art, music, health, or physical education. Please refer to the rubric to help you complete this project.

SUMMARY OF POINTS:

Class Attendance, Discussion, Reading 10 points/week 90 points

Online Participation/Discussion/Reading 5 points/week 30 points

Review Questions 10 points x 5 quizzes 50 points

Test Review Session 10 points 10 points

Journal Entry 50 points 50 points

Pre- & Post-survey 5 points each 10 points

Leading activity (Chapter Presentation) 40 points 40 points

Final Project 100 points 100 points

TOTAL 380 points


POLICIES:

A. Grading ScaleA = 345 – 380 points : Excellent, 4.0

D = 230 – 267 points : Passing, 1.0

B = 305 – 344 points : Good, 3.0 F = Below 229 points : Failure, 0.0

C = 268 – 304 points : Average, 2.0

B. PenaltiesAssignments are to be submitted through Blackboard on the date indicated by midnight. If assignments are submitted late, 20% of the grade value will be deducted. Assignments will not be accepted one week after the due date. Any student submitting work completed by someone else (or willingly supplying their work to someone else) will receive zero for that assignment and might receive a more severe penalty depending on the circumstances.

C. Students with DisabilitiesIf you have, or believe you have, a disability you may wish to self identify. You may do so by providing documentation to the Offices of Services for Students with Disabilities (SSD). Appropriate accommodations may then be provided for you. If you have a condition which may affect your ability to exit the premises in an emergency or which may cause an emergency during class, you are encouraged to discuss this in confidence with the instructor and/or the Specialist, Services for Students with Disabilities.

D. Incomplete GradesAn Incomplete (I) grade is seldom given, but may be given for satisfactory work that could not be completed due to cases of extreme emergencies and extraordinary circumstances (e.g. illness, family crisis) that prevent completion of course requirements over length of time that exceeds 2 weeks. These following situations are not considered extreme emergencies or extraordinary circumstances:

i. Minor illnesses and coldsii. Trips (academic or otherwiseiii. Taking more than 2 classes if your work full-timeiv. Fear of not making an A in the coursev. Opportunity to appear in a reality TV show, and the like.

If you wish to request an incomplete grade, you must submit a memo that details the circumstance(s) of the request to the course instructor prior to Finals Week. In your memo, list the submissions and grades you have earned thus far and requirements that still need to be met. Furthermore, include a timeline showing when you expect to meet the outstanding requirements. It is the students’ responsibility to know important dates, such as the University drop and withdrawal dates.


E. Professionalism● Consistent attendance, punctuality, collegiality, solidarity, supportive critique and

professionalism will be expected● Course expectations:

○ Attend events when you are scheduled to attend events (meetings with peers, instructor, whole class, etc./ Face-to-face (F2F) or on-line);

○ Come to the event and stay for the entire event (for on-line: if your computer freezes or crashes, boot it back up and come back to the event; if you are unable to do this, email the instructor and your colleagues to explain, then re-schedule)

○ Do not be distracted during scheduled event (you need to be present and focused; F2F and on-line);

○ Interact in ways with your colleagues and the instructors that promote and maintain their and your dignity and promote our collective community;

○ Be prepared to raise, share, discuss and attempt to solve any individual or collective problems you may have with your colleagues and/or your instructor in constructive ways that allows us all to maintain our dignity and continue to function effectively as a community.

○ Demonstrate an understanding that while we can, and will probably, disagree, we need to do so within a community of respect; and

○ Provide your classmates with supportive critique and feedback.

OUR CONTRACTBy remaining in this class after the UTEP designated “Course drop Deadline”, you are agreeing professionally, conscientiously and thoughtfully complete all the work and assignments in this course in a timely manner. This syllabus becomes our contract (the contract between me, your instructor, and you, the students). This contract cannot change unless mutually negotiated and agreed to.


RUBRICS1. Rubric for Online Discussions

Overview:Protocol for posting threads and contributing to an online discussion are as follows: 1. Postings should be evenly distributed during the discussion period (not concentrated

all on one day or at the beginning and/or end of the period).2. Postings should be a minimum of one short paragraph and a maximum of two

paragraphs.3. Avoid postings that are limited to 'I agree' or 'great idea', etc. If you agree (or

disagree) with a posting then say why you agree by supporting your statement with concepts from the readings or by bringing in a related example or experience.

4. Address the questions as much as possible (don't let the discussion stray).5. Try to use quotes from the articles that support your postings. Include page numbers

when you do that.6. Build on others responses to create threads.7. Bring in related prior knowledge (work experience, prior coursework, readings, etc.)8. Use proper etiquette (proper language, typing, etc.).

Posted messages should be significant – helping the discussion move forward. There are a variety of ways to do this, including (generally in some combination over the course of the week or within a posting):

● Providing concrete examples, perhaps from your own experience● Describing possible consequences or implications● Challenging something that has been posted in the discussion – perhaps by

playing “devil’s advocate”● Posing a clarifying question● Suggesting a different perspective or interpretation● Pulling in related information from other sources – books, articles, websites, other courses, etc.

Your participation score for a given week will be based on the number and quality of messages you post to that discussion. Participation will be evaluated in terms of quality as well as quantity, based on the following scale:

Criteria Excellent Good Average Poor

Timeliness and quantity of discussion responses

3-4 or more postings; well distributed throughout the week

2-3 postings distributed throughout the week.

2-3 postings; postings not distributed throughout the week

1-2 postings;

postings not distributed throughout the week

Responsiveness to discussion

Readings were understood and

Readings were understood and

Little use made of readings.

Little or no use made of


topic and demonstration of knowledge and understanding from assigned readings.

Ability of postings to move discussion forward.

incorporated into discussion as relates to topic.

Two or more responses add significantly to the discussions (e.g. identifying important relationships, offering a fresh perspective or critique of a point; offers supporting evidence).

incorporated into discussion as relates to topic.

At least one posting adds significantly to the discussion.

At least two postings supplement or add moderately to the discussion

readings.

Postings have questionable relationship to discussion question and/or readings; they are non-substantive.

Postings do little to move discussion forward

Adherence to online protocols

all on-line protocols followed

1 online protocol not adhered to

2-3 online protocols not adhered to

4 or more online protocols not adhered to

POINTS 5 4 2-3 1

*adapted from a rubric developed by Peg Ertmer/Krista Glazewski.


2. Rubric for Leading FacilitatorsI. Peer Evaluations:

Using the following rubric, you will be asked to evaluate your peer's contribution to the group assignment. This peer evaluation is worth 20 points. Your score will be calculated by averaging the scores provided by the members of your group.


II: Grading Rubric for Leading Facilitators:

Students’ Names:______________________________________________________________Title of Lesson:_______________________________________________________________


TRAIT 4 3 2 1

NONVERBALSKILLS

EYE CONTACT Holds attention of entire audience with the use of direct eye contact, seldom looking at notes.

Consistent use of direct eye contact with audience, but still returns to notes.

Displayed minimal eye contact with audience, while reading mostly from the notes.

No eye contact with audience, as entire report is read from notes.

BODY LANGUAGE Movements seem fluid and help the audience visualize.

Made movements or gestures that enhances articulation.

Very little movement or descriptive gestures.

No movement or descriptive gestures.

POISE Student displays relaxed, self-confident nature about self, with no mistakes.

Makes minor mistakes, but quickly recovers from them; displays little or no tension.

Displays mild tension; has trouble recovering from mistakes.

Tension and nervousness is obvious; has trouble recovering from mistakes.

VERBAL SKILLS

ENTHUSIASM Demonstrates a strong, positive feeling about topic during entire presentation.

Occasionally shows positive feelings about topic.

Shows some negativity toward topic presented.

Shows absolutely no interest in topic presented.

ELOCUTION Student uses a clear voice and correct, precise pronunciation of terms so that all audience members can hear presentation.

Student’s voice is clear. Student pronounces most words correctly. Most audience members can hear presentation.

Student’s voice is low. Student incorrectly pronounces terms. Audience members have difficulty hearing presentation.

Student mumbles, incorrectly pronounces terms, and speaks too quietly for a majority of students to hear.

CONTENT

SUBJECT Student Student is at Student is Student does


KNOWLEDGE demonstrates full knowledge by answering all class questions with explanations and elaboration.

ease with expected answers to all questions, without elaboration.

uncomfortable with information and is able to answer only rudimentary questions.

not have grasp of information; student cannot answer questions about subject.

ACTIVITIES Activities are very well-thought, executed very effectively, very interesting and relevant for the target grade level

Activities are well-thought, executed effectively, interesting and relevant for the target grade level

Activities are somewhat well-thought, executed somewhat effectively, somewhat interesting and relevant for target grade level

Activities are not planned effectively and are not relevant for the target grade level.

ORGANIZATION Student presents information in logical, interesting sequence which audience can follow.

Student presents information in logical sequence which audience can follow.

Audience has difficulty following presentation because student jumps around.

Audience cannot understand presentation because there is no sequence of information.

MECHANICS Presentation has no misspellings or grammatical errors.

Presentation has no more than two misspellings and/or grammatical errors.

Presentation has three misspellings and/or grammatical errors.

Student’s presentation has four or more spelling and/or grammatical errors.

AUDIENCE ADAPTATION

The student is able to effectively keep the audience engaged.

The student is able to keep the audience engaged most of time.

The student is somewhat able to keep the audience engaged.

The student is not able to keep the audience engaged.

Rubric for Learning Journal Assignment:Criteria 45 – 50 40 – 44.5 35 – 39.5 < 35


Student Learning Journal focuses upon student learning from reading, working, and / or observing. Student made the connection between this and their future learning and made the connection in terms of essential skills needed.

Journal focuses upon student learning mainly through doing or observing. Student understands skills needed and seems to understand the need for further learning but has not made connection to Essential Skills.

Journal does mention student learning, but does not elaborate or make connection to future skill acquisition.

Journal does not reflect upon learning that occurred during the week

Reflection: Topics: Expectations, Communication Skills, Challenges, Strengths, Weaknesses, people skills, and how you are planning to improve for the future.

Journal is a good reflection of the week with respect to some of the listed topics, and on how the student will use this learning in relation to their future. Or what the learning means for the future.

Student does reflect on some aspect of learning during the week and has some idea of its importance for the future, but no real plan for change.

Student does reflect on some aspect of learning during the week, but does not explain the relevance to future learning

Student does not reflect on learning during the week.

Completion / Length

Weekly journal not less than 150 words.

Journals are not only summarizing the knowledge learned in a week, but also a reflection of the acquired knowledge of the week.

Journal is between 100 – 150 words in length.


Journal is less than 150 words in length.


Journal is too short, and / or is a summarization of the knowledge learned in the week.

Mechanics All or almost all entries use correct spelling and grammar. (1-2 mistakes)

Most entries use correct spelling and grammar. (2-3 mistakes)

Few entries use correct spelling and grammar. (More than 3 mistakes)

Entries generally do not use correct spelling and grammar.

Rubric for Review Question


Component - 4 points - - 3 points - - 2 points - - 1 point-General approach - Addresses the

question;- States a relevant, justifiable answer.

- Does not address the question explicitly, although does so tangentially; - States a relevant and justifiable answer.

- Does not address the question;- States no relevant answers;- Indicates misconceptions.

Comprehension - Demonstrates an accurate and complete understanding of the question; - Backs conclusions with data and warrants;- Uses 2 or more ideas, examples and/or arguments from the reading/s that support the answer.

- Presents arguments in a logical order;- Demonstrates accurate but only adequate understanding of question because does not back conclusions with warrants and data;- Uses only one idea to support the answer;- Less thorough.

- Does not demonstrate accurate understanding of the question; - Does not provide evidence to support their answer to the question.

Organization and Mechanics

- Presents arguments in a logical order; - Uses acceptable style and grammar (no errors).

- Is not clearly or logically organized;- Fails to use acceptable style and grammar (2-3 errors).

- Is not clearly or logically organized;- Fails to use acceptable style and grammar (more than 3 errors).

Appendix I: TEST FRAMEWORK FOR FIELD 115: MATEMATHEMATICS 4–8

Domain I: Number Concepts


Standard Assessed: I Domain II: Patterns and Algebra

Standard Assessed: II Domain III: Geometry and Measurement

Standard Assessed: III Domain IV: Probability and Statistics

Standard Assessed: IV Domain V: Mathematical Processes and Perspectives

Standards Assessed: V and VI Domain VI: Mathematical Learning, Instruction and Assessment

Standards Assessed: VII and VIII

THE STANDARDS:DOMAIN I — NUMBER CONCEPTS (approximately 16% of the test)

MATHEMATICS STANDARD I:Number Concepts: The mathematics teacher understands and uses numbers, number system and their structure, operations and algorithms, quantitative reasoning and technology

appropriate to teach the statewide curriculum (Texas Essential Knowledge and Skills[TEKS]) in order to prepare students to use mathematics.

DOMAIN II — PATTERNS AND ALGEBRA (approximately 21% of the test)MATHEMATICS STANDARD II:

Patterns and Algebra: The mathematics teacher understands and uses patterns, relations,functions, algebraic reasoning, analysis and technology appropriate to teach the statewidecurriculum (Texas Essential Knowledge and Skills [TEKS]) in order to prepare students to use mathematics.

DOMAIN III — GEOMETRY AND MEASUREMENT (approximately 21% of the test)MATHEMATICS STANDARD III:

Geometry and Measurement: The mathematics teacher understands and uses geometry,spatial reasoning, measurement concepts and principles and technology appropriate toteach the statewide curriculum (Texas Essential Knowledge and Skills [TEKS]) in order to prepare students to use mathematics.

DOMAIN IV — PROBABILITY AND STATISTICS (approximately 16% of the test)MATHEMATICS STANDARD IV:

Probability and Statistics: The mathematics teacher understands and uses probability andstatistics, their applications and technology appropriate to teach the statewide curriculum(Texas Essential Knowledge and Skills [TEKS]) in order to prepare students to usemathematics.

DOMAIN V —MATHEMATICAL PROCESSES AND PERSPECTIVES (approximately 10% of the test)

MATHEMATICS STANDARD V:


Mathematical Processes: The mathematics teacher understands and uses mathematicalprocesses to reason mathematically, to solve mathematical problems, to make mathematicalconnections within and outside of mathematics and to communicate mathematically.

MATHEMATICS STANDARD VI:Mathematical Perspectives: The mathematics teacher understands the historical development

of mathematical ideas, the interrelationship between society and mathematics, the structure of mathematics and the evolving nature of mathematics and mathematical knowledge.

DOMAIN VI — MATHEMATICAL LEARNING, INSTRUCTION AND ASSESSMENT(approximately 16% of the test)

MATHEMATICS STANDARD VII:Mathematical Learning and Instruction: The mathematics teacher understands how

children learn and develop mathematical skills, procedures and concepts, knows typical errors students make, and uses this knowledge to plan, organize andimplement instruction;to meet curriculum goals; and to teach all students to understand and use mathematics.

MATHEMATICS STANDARD VIII:Mathematical Assessment: The mathematics teacher understands assessment and uses a

variety of formal and informal assessment techniques appropriate to the learner on anongoing basis to monitor and guide instruction and to evaluate and report student progress.

C OMPETENCIES:DOMAIN I — NUMBER CONCEPTSCompetency 001


THE TEACHER UNDERSTANDS THE STRUCTURE OF NUMBER SYSTEMS, THEDEVELOPMENT OF A SENSE OF QUANTITY AND THE RELATIONSHIP BETWEENQUANTITY AND SYMBOLIC REPRESENTATIONS.

The beginning teacher:A. Analyzes the structure of numeration systems and the roles of place value and zero

in the base ten system.B. Understands the relative magnitude of whole numbers, integers, rational numbers

and real numbers.C. Demonstrates an understanding of a variety of models for representing numbers

(e.g., fraction strips, diagrams, patterns, shaded regions, number lines).D. Demonstrates an understanding of equivalency among different representations of

rational numbers.E. Selects appropriate representations of real numbers (e.g., fractions, decimals,

percents, roots, exponents, scientific notation) for particular situations.F. Understands the characteristics of the set of whole numbers, integers, rational

numbers, real numbers and complex numbers (e.g., commutativity, order, closure,identity elements, inverse elements, density).

G. Demonstrates an understanding of how some situations that have no solution in onenumber system (e.g., whole numbers, integers, rational numbers) have solutions inanother number system (e.g., real numbers, complex numbers).

Competency 002THE TEACHER UNDERSTANDS NUMBER OPERATIONS AND COMPUTATIONALALGORITHMS.

The beginning teacher:A. Works proficiently with real and complex numbers and their operations.B. Analyzes and describes relationships between number properties, operations and

algorithms for the four basic operations involving integers, rational numbers and real numbers.

C.Uses a variety of concrete and visual representations to demonstrate theconnections between operations and algorithms.

D. Justifies procedures used in algorithms for the four basic operations with integers,rational numbers and real numbers and analyzes error patterns that may occur intheir application.

E. Relates operations and algorithms involving numbers to algebraic procedures(e.g., adding fractions to adding rational expressions, division of integers todivision of polynomials).

F. Extends and generalizes the operations on rationals and integers to includeexponents, their properties and their applications to the real numbers.

Competency 003THE TEACHER UNDERSTANDS IDEAS OF NUMBER THEORY AND USES NUMBERS TOMODEL AND SOLVE PROBLEMS WITHIN AND OUTSIDE OF MATHEMATICS.


The beginning teacher:A. Demonstrates an understanding of ideas from number theory (e.g., prime

factorization, greatest common divisor) as they apply to whole numbers, integersand rational numbers and uses these ideas in problem situations.

B. Uses integers, rational numbers and real numbers to describe and quantifyphenomena such as money, length, area, volume and density.

C. Applies knowledge of place value and other number properties to developtechniques of mental mathematics and computational estimation.

D. Applies knowledge of counting techniques such as permutations and combinationsto quantify situations and solve problems.

E. Applies properties of the real numbers to solve a variety of theoretical and appliedproblems.

DOMAIN II — PATTERNS AND ALGEBRACompetency 004

THE TEACHER UNDERSTANDS AND USES MATHEMATICAL REASONING TO IDENTIFY,EXTEND AND ANALYZE PATTERNS AND UNDERSTANDS THE RELATIONSHIPSAMONG VARIABLES, EXPRESSIONS, EQUATIONS, INEQUALITIES, RELATIONS ANDFUNCTIONS.

The beginning teacher:A. Uses inductive reasoning to identify, extend and create patterns using concrete

models, figures, numbers and algebraic expressions.B. Formulates implicit and explicit rules to describe and construct sequences verbally,

numerically, graphically and symbolically.C. Makes, tests, validates and uses conjectures about patterns and relationships in data

presented in tables, sequences or graphs.D. Gives appropriate justification of the manipulation of algebraic expressions.E. Illustrates the concept of a function using concrete models, tables, graphs and

symbolic and verbal representations.F. Uses transformations to illustrate properties of functions and relations and to solve

problems.

Competency 005THE TEACHER UNDERSTANDS AND USES LINEAR FUNCTIONS TO MODEL AND SOLVEPROBLEMS.

The beginning teacher:A. Demonstrates an understanding of the concept of linear function using concrete

models, tables, graphs and symbolic and verbal representations.B. Demonstrates an understanding of the connections among linear functions,

proportions and direct variation.C. Determines the linear function that best models a set of data.D. Analyzes the relationship between a linear equation and its graph.E. Uses linear functions, inequalities and systems to model problems.F. Uses a variety of representations and methods (e.g., numerical methods, tables,

graphs, algebraic techniques) to solve systems of linear equations and inequalities.G. Demonstrates an understanding of the characteristics of linear models and the


advantages and disadvantages of using a linear model in a given situation.

Competency 006THE TEACHER UNDERSTANDS AND USES NONLINEAR FUNCTIONS AND RELATIONSTO MODEL AND SOLVE PROBLEMS.

The beginning teacher:A. Uses a variety of methods to investigate the roots (real and complex), vertex and

symmetry of a quadratic function or relation.B. Demonstrates an understanding of the connections among geometric, graphic,

numeric and symbolic representations of quadratic functions.C. Analyzes data and represents and solves problems involving exponential growth

and decay.D. Demonstrates an understanding of the connections among proportions, inverse

variation and rational functions.E. Understands the effects of transformations such as f x c on the graph of a

nonlinear function f x.F. Applies properties, graphs and applications of nonlinear functions to analyze,

model and solve problems.G. Uses a variety of representations and methods (e.g., numerical methods, tables,

graphs, algebraic techniques) to solve systems of quadratic equations andinequalities.

H. Understands how to use properties, graphs and applications of nonlinear relationsincluding polynomial, rational, radical, absolute value, exponential, logarithmic,trigonometric and piecewise functions and relations to analyze, model and solveproblems.

Competency 007THE TEACHER USES AND UNDERSTANDS THE CONCEPTUAL FOUNDATIONS OFCALCULUS RELATED TO TOPICS IN MIDDLE SCHOOL MATHEMATICS.

The beginning teacher:A. Relates topics in middle school mathematics to the concept of limit in sequences

and series.B. Relates the concept of average rate of change to the slope of the secant line and

instantaneous rate of change to the slope of the tangent line.C. Relates topics in middle school mathematics to the area under a curve.D. Demonstrates an understanding of the use of calculus concepts to answer questions

about rates of change, areas, volumes and properties of functions and their graphs.

DOMAIN III — GEOMETRY AND MEASUREMENTCompetency 008

THE TEACHER UNDERSTANDS MEASUREMENT AS A PROCESS.The beginning teacher:A. Selects and uses appropriate units of measurement (e.g., temperature, money, mass,

weight, area, capacity, density, percents, speed, acceleration) to quantify, compareand communicate information.

B. Develops, justifies and uses conversions within measurement systems.


C. Applies dimensional analysis to derive units and formulas in a variety of situations(e.g., rates of change of one variable with respect to another) and to find andevaluate solutions to problems.

D. Describes the precision of measurement and the effects of error on measurement.E. Applies the Pythagorean theorem, proportional reasoning and right triangle

trigonometry to solve measurement problems.

Competency 009THE TEACHER UNDERSTANDS THE GEOMETRIC RELATIONSHIPS AND AXIOMATICSTRUCTURE OF EUCLIDEAN GEOMETRY.

The beginning teacher:A. Understands concepts and properties of points, lines, planes, angles, lengths and

distances.B. Analyzes and applies the properties of parallel and perpendicular lines.C. Uses the properties of congruent triangles to explore geometric relationships and

prove theorems.D. Describes and justifies geometric constructions made using a compass and straight

edge and other appropriate technologies.E. Applies knowledge of the axiomatic structure of Euclidean geometry to justify and

prove theorems.

Competency 010THE TEACHER ANALYZES THE PROPERTIES OF TWO- AND THREE-DIMENSIONALFIGURES

The beginning teacher:A. Uses and understands the development of formulas to find lengths, perimeters,

areas and volumes of basic geometric figures.B. Applies relationships among similar figures, scale and proportion and analyzes how

changes in scale affect area and volume measurements.C. Uses a variety of representations (e.g., numeric, verbal, graphic, symbolic) to

analyze and solve problems involving two- and three-dimensional figures such as circles, triangles, polygons, cylinders, prisms and spheres.

D. Analyzes the relationship among three-dimensional figures and related two-dimensional representations (e.g., projections, cross-sections, nets) and uses theserepresentations to solve problems.

Competency 011THE TEACHER UNDERSTANDS TRANSFORMATIONAL GEOMETRY AND RELATESALGEBRA TO GEOMETRY AND TRIGONOMETRY USING THE CARTESIAN COORDINATESYSTEM.

The beginning teacher:A. Describes and justifies geometric constructions made using a reflection device and

other appropriate technologies.B. Uses translations, reflections, glide-reflections and rotations to demonstrate

congruence and to explore the symmetries of figures.C. Uses dilations (expansions and contractions) to illustrate similar figures and


proportionality.D. Uses symmetry to describe tessellations and shows how they can be used to

illustrate geometric concepts, properties and relationships.E. Applies concepts and properties of slope, midpoint, parallelism and distance in the

coordinate plane to explore properties of geometric figures and solve problems.F. Applies transformations in the coordinate plane.G. Uses the unit circle in the coordinate plane to explore properties of trigonometric

functions.

DOMAIN IV — PROBABILITY AND STATISTICSCompetency 012

THE TEACHER UNDERSTANDS HOW TO USE GRAPHICAL AND NUMERICALTECHNIQUES TO EXPLORE DATA, CHARACTERIZE PATTERNS AND DESCRIBEDEPARTURES FROM PATTERNS.

The beginning teacher:A. Organizes and displays data in a variety of formats (e.g., tables, frequency

distributions, stem-and-leaf plots, box-and-whisker plots, histograms, pie charts).B. Applies concepts of center, spread, shape and skewness to describe a data

distribution.C. Supports arguments, makes predictions and draws conclusions using summary

statistics and graphs to analyze and interpret one-variable data.D. Demonstrates an understanding of measures of central tendency (e.g., mean,

median, mode) and dispersion (e.g., range, interquartile range, variance, standarddeviation).

E. Analyzes connections among concepts of center and spread, data clusters and gaps,data outliers and measures of central tendency and dispersion.

F. Calculates and interprets percentiles and quartiles.

Competency 013THE TEACHER UNDERSTANDS THE THEORY OF PROBABILITY.

The beginning teacher:A. Explores concepts of probability through data collection, experiments and

simulations.B. Uses the concepts and principles of probability to describe the outcome of simple

and compound events.C. Generates, simulates and uses probability models to represent a situation.D. Determines probabilities by constructing sample spaces to model situations.E. Solves a variety of probability problems using combinations, permutations and

geometric probability (i.e., probability as the ratio of two areas).F. Uses the binomial, geometric and normal distributions to solve problems.

Competency 014THE TEACHER UNDERSTANDS THE RELATIONSHIP AMONG PROBABILITY THEORY,SAMPLING AND STATISTICAL INFERENCE AND HOW STATISTICAL INFERENCE IS


USED IN MAKING AND EVALUATING PREDICTIONS.The beginning teacher:

A. Applies knowledge of designing, conducting, analyzing and interpreting statisticalexperiments to investigate real-world problems.

B. Demonstrates an understanding of random samples, sample statistics and therelationship between sample size and confidence intervals.

C. Applies knowledge of the use of probability to make observations and drawconclusions from single variable data and to describe the level of confidence in theconclusion.

D. Makes inferences about a population using binomial, normal and geometricdistributions.

E. Demonstrates an understanding of the use of techniques such as scatter plots,regression lines, correlation coefficients and residual analysis to explore bivariatedata and to make and evaluate predictions.

DOMAIN V — MATHEMATICAL PROCESSES AND PERSPECTIVESCompetency 015THE TEACHER UNDERSTANDS MATHEMATICAL REASONING AND PROBLEM SOLVING.

The beginning teacher:A. Demonstrates an understanding of proof, including indirect proof, in mathematics.B. Applies correct mathematical reasoning to derive valid conclusions from a set of

premises.C. Demonstrates an understanding of the use of inductive reasoning to make

conjectures and deductive methods to evaluate the validity of conjectures.D. Applies knowledge of the use of formal and informal reasoning to explore,

investigate and justify mathematical ideas.E. Recognizes that a mathematical problem can be solved in a variety of ways and

selects an appropriate strategy for a given problem.F. Evaluates the reasonableness of a solution to a given problem.G. Applies content knowledge to develop a mathematical model of a real-world

situation and analyzes and evaluates how well the model represents the situation.H. Demonstrates an understanding of estimation and evaluates its appropriate uses.

Competency 016THE TEACHER UNDERSTANDS MATHEMATICAL CONNECTIONS WITHIN ANDOUTSIDE OF MATHEMATICS AND HOW TO COMMUNICATE MATHEMATICAL IDEASAND CONCEPTS.

The beginning teacher:A. Recognizes and uses multiple representations of a mathematical concept (e.g., a

point and its coordinates, the area of circle as a quadratic function in r, probabilityas the ratio of two areas).

B. Uses mathematics to model and solve problems in other disciplines, such as art,music, science, social science and business.

C. Expresses mathematical statements using developmentally appropriate language,standard English, mathematical language and symbolic mathematics.

D. Communicates mathematical ideas using a variety of representations (e.g., numeric,


verbal, graphic, pictorial, symbolic, concrete).E. Demonstrates an understanding of the use of visual media such as graphs, tables,

diagrams and animations to communicate mathematical information.F. Uses the language of mathematics as a precise means of expressing mathematical

ideas.G. Understands the structural properties common to the mathematical disciplines.

DOMAIN VI — MATHEMATICAL LEARNING, INSTRUCTION AND ASSESSMENTCompetency 017THE TEACHER UNDERSTANDS HOW CHILDREN LEARN AND DEVELOPMATHEMATICAL SKILLS, PROCEDURES AND CONCEPTS.

The beginning teacher:A. Applies theories and principles of learning mathematics to plan appropriate

instructional activities for all students.B. Understands how students differ in their approaches to learning mathematics with

regard to diversity.C. Uses students’ prior mathematical knowledge to build conceptual links to new

knowledge and plans instruction that builds on students’ strengths and addressesstudents’ needs.

D. Understands how learning may be assisted through the use of mathematicsmanipulatives and technological tools.

E. Understands how to motivate students and actively engage them in the learningprocess by using a variety of interesting, challenging and worthwhile mathematicaltasks in individual, small-group and large-group settings.

F. Understands how to provide instruction along a continuum from concrete toabstract.

G. Recognizes the implications of current trends and research in mathematics andmathematics education.

Competency 018THE TEACHER UNDERSTANDS HOW TO PLAN, ORGANIZE AND IMPLEMENTINSTRUCTION USING KNOWLEDGE OF STUDENTS, SUBJECT MATTER ANDSTATEWIDE CURRICULUM (TEXAS ESSENTIAL KNOWLEDGE AND SKILLS [TEKS]) TOTEACH ALL STUDENTS TO USE MATHEMATICS.

The beginning teacher:A. Demonstrates an understanding of a variety of instructional methods, tools and

tasks that promote students’ ability to do mathematics described in the TEKS.B. Understands planning strategies for developing mathematical instruction as a

discipline of interconnected concepts and procedures.C. Develops clear learning goals to plan, deliver, assess and reevaluate instruction

based on the TEKS.D. Understands procedures for developing instruction that establishes transitions

between concrete, symbolic and abstract representations of mathematicalknowledge.

E. Applies knowledge of a variety of instructional delivery methods, such asindividual, structured small-group and large-group formats.


F. Understands how to create a learning environment that provides all students,including English-language learners, with opportunities to develop and improvemathematical skills and procedures.

G. Demonstrates an understanding of a variety of questioning strategies toencourage mathematical discourse and to help students analyze and evaluate theirmathematical thinking.

H. Understands how technological tools and manipulatives can be used appropriatelyto assist students in developing, comprehending and applying mathematicalconcepts.

I. Understands how to relate mathematics to students’ lives and a variety of careersand professions.

Competency 019THE TEACHER UNDERSTANDS ASSESSMENT AND USES A VARIETY OF FORMAL ANDINFORMAL ASSESSMENT TECHNIQUES TO MONITOR AND GUIDE MATHEMATICSINSTRUCTION AND TO EVALUATE STUDENT PROGRESS.

The beginning teacher:A. Demonstrates an understanding of the purpose, characteristics and uses of various

assessments in mathematics, including formative and summative assessments.B. Understands how to select and develop assessments that are consistent with what is

taught and how it is taught.C. Demonstrates an understanding of how to develop a variety of assessments and

scoring procedures consisting of worthwhile tasks that assess mathematicalunderstanding, common misconceptions and error patterns.

D. Understands how to evaluate a variety of assessment methods and materials forreliability, validity, absence of bias, clarity of language and appropriateness ofmathematical level.

E. Understands the relationship between assessment and instruction and knows howto evaluate assessment results to design, monitor and modify instruction to improvemathematical learning for all students, including English-language learners.

Sample Questions:







TENTATIVE SCHEDULENote: All topics, assignments and due dates are subject to change at the instructor’s discretion.

DATE TOPICS READINGS & ASSIGNMENTS DUE

Module 1 Introduction

Week 1:1/20

Martin Luther King Day - No class

Week 2: 1/27

- Introduction: Expectations & Format- Course Tools: Blackboard; Weebly- Web 2.0 tools for Teaching & Learning- Set up blog site on Weebly.com

- Please print-out the syllabus and schedule. Bring it with you to our first class meeting – 1/27

- Theories: About Learning- Theories: Instruction- Bloom’s Taxonomy- Assign group to facilitate chapter presentation- Discuss EC-6 Competency: Domain II

- Print, read and bring with you to class these two documents: “Funderstanding: About Learning” and “Funderstanding: Instruction”. - These files are located in “Module 01” folder --> “Theories” folder on the Blackboard.- Journal Entry #1

Module 2 The “Why”, “What”, “How” of Teaching Mathematics: Online Discussion/Blackboard--- We will not meet in class ---

Module 3 The Concepts & Procedures of Mathematics: Leading Facilitators will facilitate the class with presentation and activities from the reading/s

Week 3: 2/03

Discussion #1:- NCTM and TEKS standards

- Van de Walle, Chapter 1- Standards: Link; - TEKS: Link- Participate in the Online Discussion #1- Journal Entry #2

Week 4: 2/10

- Number Concepts & Number Sense- Meanings for Operations- Basic Facts

- Van de Walle, Chapters 8 & 9 & 10- Assigned group/s facilitating presentations and activities - RQ #1 - Journal Entry #3



Week5: 2/17

Discussion #2:- What it means to know and do Mathematics

- Van de Walle, Chapter 2 - Adam article- Participate in the Online Discussion #2- Journal Entry #4

Week 6: 2/24

- Whole Number Place-Value Development- Strategies for Whole Number Computation- Using Computational Estimation with Whole Numbers

- Van de Walle, Chapters 11, 12 & 13- Assigned group/s facilitating presentations and activities- RQ #2- Journal Entry #5

Week 7: 3/03

Discussion #3:- Problem Solving- Planning in the Problem-Based Classroom

- Van de Walle, Chapters 3 & 4- Participate in the Online Discussion #3- Journal Entry #6

3/10 - 3/14 - Spring Break -

Week 8:

3/17

- Algebraic Thinking- Fraction Concepts- Computation with Fractions

- Van de Walle, Chapters 14, 15, & 16- Assigned group/s facilitating presentations and activities- RQ #3- Journal Entry #7

Week 9: 3/24

Discussion #4:- Assessment

- Van de Walle, Chapter 5- Participate in the Online Discussion #4- Journal Entry #8

Week 10: 3/31

- Developing Concepts of Decimals & Percents- Proportional Reasoning- Developing Measurement Concepts

- Van de Walle, Chapter 17, 18, & 19- Assigned group/s facilitating presentations and activities- RQ #4- Journal Entry #9

Week 11: 4/07

Discussion #5:- Mathematics for All Children

- Van de Walle, Chapter 6- National Educational Technology Standards (NETS) for Teachers: Link- Participate in the Online Discussion #5- Journal Entry #10

Week 12: 4/14

- Geometric Thinking & Concepts- Concepts of Data Analysis- Exploring Concepts of Probability

- Van de Walle, Chapters 20, 21, & 22- Assigned group/s facilitating presentations and activities- RQ #5- Journal Entry #11



Week 13: 4/21

- Discussion #6:- Technology Integration

Van de Walle, Chapter 7- National Educational Technology Standards (NETS) for Teachers: Link- Participate in the Online Discussion #6- Journal Entry #12

Module 4 Mathematics Educators’ Showcase

Week 14: 4/28

- Work on your Final Project Will Not Meet Face-to-Face

Week 15: 5/05

- Curriculum Unit Presentation - Due: Final Project (Hardcopy- submit in class)

Week 16:5/12

- Curriculum Unit Presentation (cont.)- Finalize and post last entry on your Learning Journal

- Due: Final Project (Hardcopy- submit in class)- Journal Entry #13 (Include reflections on the final project and final thoughts)



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