Dr. I CI 508 1 Algebra in the K-12 Classrooms Spring 2016 – Syllabus Course Instructor Algebra in the K-12 Classrooms CI 508 Mondays, 5:10 p.m. – 8:00 p.m. Lago 1680 Ji Yeong (Joann) I, Ph.D [email protected]1660B Lago Office Hours: by appointments PURPOSE OF THE COURSE This course focuses on algebraic reasoning, concepts, and procedures in elementary, middle, and high school grades. You will develop an expertise related to algebraic reasoning that supports teachers and enhances student learning. You will also examine the learning trajectories K-12 students exhibit as they develop algebraic reasoning concepts and skills. Course content includes examination of representation and analysis of mathematical situations and structures. Attention is given to algebraic habits of mind, generalization, symbols, functions, and the transition from arithmetic to algebra. RESOURCES Required reading: Articles/book chapters (See the course schedule. All readings are found on Blackboard. You MUST bring an electronic or a hard copy to class each time). Suggested reading: • Graham, K., Cuoco, A., & Zimmerman, G. (2010). Focus in high school mathematics: Reasoning and sense making in Algebra. Reston, VA: National Council of Teachers of Mathematics. • Driscoll, M. J. (1999). Fostering algebraic thinking: a guide for teachers, grades 6–10. Portsmouth, N.H: Heinemann. • Blanton, M. L. (Ed.). (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. Reston, VA: National Council of Teachers of Mathematics. Reference: • Progression drafts for the Common Core State Standards for Mathematics, http://ime.math.arizona.edu/progressions/ • Iowa Core State Standards for Mathematics, https://iowacore.gov/iowa-core/subject/mathematics COURSE EXPECTATIONS Participation All students will be expected to actively participate in online/offline small- and large-group discussions. Much of the success of this course depends on the level of interaction and participation. Your contributions to group discussions will be peer-evaluated and the evaluation result will affect your participation grade (rubric included in p. 8). Attendance Because of the nature of the material discussed and investigated in class, this class cannot be made-up. I am aware that situations may arise that are unavoidable. If you must miss class, you must notify me prior to your class. Please note that an unexcused absence or more than one excused absence may adversely affect your course grade. Likewise, punctuality is important. If there is any conflict in your schedule, please discuss (email) this with me as soon as possible. Late Submission Late assignment submission will only be accepted with or without penalty if you have contacted me prior to the due date, discussed the situation, and I have agreed to make an alternative due date. Assignments submitted without agreement will not be accepted. Weekly assignments will have a different policy. All assignments are due by midnight, 11:59PM on their due date (Friday).
This course focuses on algebraic reasoning, concepts, and procedures in elementary, middle, and high school grades. You will develop an expertise related to algebraic reasoning that supports teachers and enhances student learning. You will also examine the learning trajectories K-12 students exhibit as they develop algebraic reasoning concepts and skills. Course content includes examination of representation and analysis of mathematical situations and structures. Attention is given to algebraic habits of mind, generalization, symbols, functions, and the transition from arithmetic to algebra.
RESOURCES
Required reading: Articles/book chapters (See the course schedule. All readings are found on Blackboard. You MUST bring an electronic or a hard copy to class each time). Suggested reading:
• Graham, K., Cuoco, A., & Zimmerman, G. (2010). Focus in high school mathematics: Reasoning and sense making in Algebra. Reston, VA: National Council of Teachers of Mathematics.
• Driscoll, M. J. (1999). Fostering algebraic thinking: a guide for teachers, grades 6–10. Portsmouth, N.H: Heinemann.
• Blanton, M. L. (Ed.). (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3-5. Reston, VA: National Council of Teachers of Mathematics.
Reference:
• Progression drafts for the Common Core State Standards for Mathematics, http://ime.math.arizona.edu/progressions/
• Iowa Core State Standards for Mathematics, https://iowacore.gov/iowa-core/subject/mathematics
COURSE EXPECTATIONS
Participation All students will be expected to actively participate in online/offline small- and large-group discussions. Much of the success of this course depends on the level of interaction and participation. Your contributions to group discussions will be peer-evaluated and the evaluation result will affect your participation grade (rubric included in p. 8). Attendance Because of the nature of the material discussed and investigated in class, this class cannot be made-up. I am aware that situations may arise that are unavoidable. If you must miss class, you must notify me prior to your class. Please note that an unexcused absence or more than one excused absence may adversely affect your course grade. Likewise, punctuality is important. If there is any conflict in your schedule, please discuss (email) this with me as soon as possible. Late Submission Late assignment submission will only be accepted with or without penalty if you have contacted me prior to the due date, discussed the situation, and I have agreed to make an alternative due date. Assignments submitted without agreement will not be accepted. Weekly assignments will have a different policy. All assignments are due by midnight, 11:59PM on their due date (Friday).
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Writing Format All assignments should be double-spaced with 1” margins using 12-point Times New Roman and submitted to the Assignment menu on the Blackboard. All assignments handed in should be carefully proofread and should contain no spelling or grammatical errors; multiple errors will adversely impact your grade for that assignment. All documents should use the American Psychological Association (APA) formatting (6th edition). If you are not interested in purchasing (or checking one our from the library), here are two resources to supplement your work: https://owl.english.purdue.edu/owl/section/2/10/ and http://www.apastyle.org/. Join National Council of Teachers of Mathematics (NCTM) As mathematics educators, it is important to keep up with what is going on in the community. You need to join NCTM (at www.nctm.org) if you have not done so. Base student e-membership is $45/year. Cell Phone Policy Do not use your cell phone or electronic devices unless you have an emergency call or use it for class activities.
UNIVERSITY POLICY Academic Dishonesty Academic dishonesty will not be tolerated. The University’s policy can be found at http://www.dso.iastate.edu/ja/academic/misconduct.html Examples of academic misconduct are attempting to use unauthorized information in the taking of an exam; submitting as one's own work, themes, reports, drawings, laboratory notes, computer programs or other products prepared by another person; knowingly assisting another student in obtaining or using unauthorized materials; or plagiarism. Disability Resources If you have a documented disability and anticipate needing accommodation in this course, please make arrangements to meet with me soon. Please bring a completed Student Academic Accommodation Request (SAAR) form (http://www.sdr.dso.iastate.edu/student) specifying any accommodations you will need with you. Personnel in the Disability Resource Office, located on the main floor of the Student Services Building (Room 1076) will help you complete the SAAR form. Harassment and Discrimination Iowa State University strives to maintain our campus as a place of work and study for faculty, staff, and students that is free of all forms of prohibited discrimination and harassment based upon race, ethnicity, sex (including sexual assault), pregnancy, color, religion, national origin, physical or mental disability, age, marital status, sexual orientation, gender identity, genetic information, or status as a U.S. veteran. Any student who has concerns about such behavior should contact his/her instructor, Student Assistance at 515-294-1020 or email [email protected], or the Office of Equal Opportunity and Compliance at 515-294-7612.
Respect for Diversity It is my hope that all students will be well served by this course and that the diversity each of us brings to the class will be viewed as a valuable resource. If you have concerns about the respect for diversity in this class, or if you experience conflicts with major religious holidays, please bring them to my attention as soon as possible. Student Complaint Procedures If you feel that you have been treated unfairly or if you experience a problem related to this course, please bring it to my attention right away so we can work together to resolve the situation. If you remain dissatisfied, you may discuss the situation with the director of School of Education. An average grade of C- or below (less than 73%) means that a student has failed to meet the academic grade for this course and must retake the course in order to qualify to apply for initial licensure.
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COURSE ASSIGNMENT
Assignment Description Due
Reading Discussion Questions
You will have a reading assignment every week. Develop a discussion question of the reading and upload it to the Discussion Board of the Blackboard. You are encouraged to reply to someone else’s post as well. The goal of this assignment is to help future teachers improve their questioning skills that enhance student reasoning and encourage students to participate into meaningful discussions. Rubric is included in page 8.
The Friday before the next class
Concept Teaching
This is an individual assignment. You will be assigned with one algebra concept (standard). Develop a full lesson plan to teach the concept and give a teaching presentation for only an anticipatory set and an input parts. You are required to avoid direct teaching (Do not read a textbook!). Be creative and bring real-life examples. More information is included in page 5.
1 week before your presentation (2/8 – 4/18)
NCTM Journal
Manuscript
Choose an algebra related topic and write a manuscript with your team members (3 people in one writing team) to publish in one of the NCTM journals, Teaching Children Mathematics, Mathematics Teaching in the Middle School, and Mathematics Teacher. Your manuscript does not have to be accepted for publication, but must be submitted before the deadline. More information is included in page 6.
Draft: 3/11
Final: 4/29
Group Research Project
Choose an algebra task(s) and conduct a mini research study with your group members (3 people in one research group). You must include an algebraic task, hypotheses, description of participants, task enactment/observation, findings, and discussion. After submitting the research paper, your group will present about your research/finding. More information is included in page 7.
4/22 Friday
• The instructor reserves the right to amend the syllabus throughout the semester.
GRADING The assignments will be weighted as follows:
Participation 10
Reading discussion prompts 20
Concept teaching 25
NCTM journal manuscript 20
Group research project 25
Total 100 % Final grades will be assigned in the following manner, in accordance with the proportions of credit for each assignment shown in the table above: (𝑥 = your final score)
A if 𝑥 ∈ 94, 100 ∪ (100,∞) C+ if 𝑥 ∈ [77, 80) A– if 𝑥 ∈ [90, 94) C if 𝑥 ∈ [73, 77) B+ if 𝑥 ∈ [87, 90) C– if 𝑥 ∈ [70, 73) B if 𝑥 ∈ [83, 87) F if 𝑥 ∈ [0, 70) B– if 𝑥 ∈ [80, 83)
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CI 508 READING/ASSIGNMENT SCHEDULE
Date session Reading Presentation Main Assignment
1/11 1 None
1/18 Martin Luther King Jr. Birthday (No class)
1/25 2
Syllabus Preface of Focus in High School Mathematics: Reasoning and Sense Making–Algebra_
Lannin (2008). Developing meaning for algebraic symbols: Possibilities & pitfalls. Mathematics Teaching in the Middle School.
CT 19,20,21
3/28 10 Focus in HS Math (2010) Ch. 5 CT 22,23,24 4/4 11 Focus in HS Math (2010) Ch. 6 CT 25,26,27
4/11 12 Group Project Preparation (Group meeting)
4/18 13 Pickreign (2006). Mathematics Teaching in the Middle School. CT 28,29,30
4/25 14 No reading assignment for preparing the group project & presentation GP (6 teams) Research paper
(Due 4/22)
5/2 15 Final week GP (4 teams) NCTM Journal Submission Confirmation & Final Paper
(Due 4/29)
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Assignment: Concept Teaching Learning objectives: After completing this assignment, you will be able to
1. Design an engaging and effective lesson plan to teach an algebraic concept by developing well-structured guiding questions and connecting the concept with students’ previous experience and knowledge.
2. Engage students into an algebraic reasoning by providing an interesting and real-life connected anticipatory set. 3. Support students to conceptualize/reason an algebraic rule/term/relation by having students participate in a
creative activity and a viable argument. Procedures: Each of you will work individually to develop and present a beginning part of a lesson to teach an algebraic concept. You will plan for your lesson to take approximately 15–20 minutes
1. Planning a. Study thoroughly the assigned concept by reading CCSSM progression draft and various textbooks. b. Develop a full lesson plan by completing all required areas in the lesson plan template (will be available
on Blackboard). c. Submit your lesson plan along with all materials you are going use (e.g., PPT, handouts, pictures, etc.)
through Blackboard by the Friday before your presentation.
2. Presentation a. Start your presentation with a creative and interesting anticipatory set. Connecting to students’ life and
prior knowledge is one of the crucial keys. b. Guide students to learn a new algebraic concept through activities, discussions, or guiding questions. You
may use a discovery learning approach, but you must clearly state your learning objectives and the targeted concept during your presentation.
3. Reflection (1 page, double space)
a. After your presentation, write and submit a reflection by the Friday after your presentation. b. Your reflection should cover the followings
i. What went well/did not go well? Why do you think it did go well/didn’t go well? ii. What was different from your expectation?
iii. What and how you want to do differently if you use this task/problem/activity again for your future class?
• Meets all expectations • Provides clear links to readings
and course discussion • Includes sufficient student-
centered approaches
• Includes all required elements • Anticipatory set is designed to
connect the algebraic concept with students’ interests
• The CONCEPT is clearly explained (not just give examples/procedures)
• Does NOT include one or two required elements
• Anticipatory set is NOT included or not interesting
• The concept is NOT clearly explained
Presentation (10%)
• Meets all expectations • Exhibits confidence in
facilitating discussions • Has an appropriate pace and
waiting time
• Gives higher-order thinking questions
• Make clear explanation • Usually refrains from evaluating
student responses and telling them what to do
• Does NOT give any higher-order thinking questions
• Tends to evaluate student responses or told student what to do
Reflection (5%)
• Meets all expectations • Makes connections to CI 508
course discussion
• Includes all required responses with valuable insights
• No editing issues and proper length
• Does not include all required responses or provide sufficient reflection
• Serious editing issues
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Assignment: NCTM Journal Manuscript (You must NOT use someone else’s work without permission & citation and must obtain consent for all video/photos) Learning objectives: After completing this assignment, you will be able to
1. Develop an innovative lesson that supports students’ algebraic reasoning and sense making by collaborating with peer teachers.
2. Have a better sense of current educational trends by getting through the review process of publication. Procedures: This is a group assignment. One writing team that consists of 3 people write and submit a manuscript to one of NCTM journals.
1. Choose a journal and a department section that your team will write for from the followings; a. Postscript (TCM): 1 page (see p. 9) b. Math for Real (MTMS): 1 page (see p. 10) c. Mathematical Lens (MT): 3-4 pages (see p. 10) d. The Back Page: My Favorite Lesson (MT): 1 page (see p. 11)
2. Read/gather all information (e.g., email the editor) and guidelines for authors for the chosen department (more information is attached at the end of this document).
3. Decide an algebraic topic that is suitable for the chosen department. 4. Write a manuscript draft together with evenly divided responsibilities. 5. Submit the manuscript draft through Blackboard and get feedback by 3/11, Friday. 6. Revise the draft based on feedback and submit the final manuscript to the NCTM submission website (each
journal has a different webpage. You have to make an account to submit a manuscript). 7. Submit the final manuscript and a copy of the submission confirmation letter you received from NCTM
through Blackboard by 4/29, Friday. 8. Submit the self/peer evaluation sheet (see p. 8) through Blackboard by 5/2, Monday.
• Meets all expectations • Provides clear links to readings
and course discussion • Implements sufficient algebraic
habits of mind • Creative and innovative ideas are
included • No editing issue
• Follows all instructions in the Call for Manuscript
• Writes appropriately for the designated grades
• Minor editing issues
• Does NOT satisfy the instructions in the Call for Manuscript
• Serious editing issues
Final draft (5%)
• Meets all expectations • Further revisions applied to
increase the quality of the manuscript
• Appropriate revision applied based on feedback
• Limited or inappropriate revision
Confirmation letter (2%)
• Submits a copy of confirmation letter in time.
N/A N/A
Self/Peer evaluation
(3%)
• Meets all expectations • Your peers give you all Es • Shows a great teamwork
• Complete the evaluation form with a respectful manner and sufficient details
• Your peers give you mostly E or M
• Incomplete the evaluation form or not written respectfully
• Your peers give you mostly N
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Assignment: Group Research Project Learning objectives: After completing this assignment, you will be able to,
1. Deepen an understanding of algebraic reasoning and teaching algebra by investigating how students learn algebraic reasoning.
2. Design and conduct a research study to find out a specific problem in teaching and learning algebraic reasoning by collaborating with peer teachers.
Procedures: You will design and conduct a mini research in groups (3 people). This is a task-based study.
1. Choose an algebraic reasoning task you want to use for your research. You may use the tasks we used in CI 508. 2. Discuss in your group about the task and set up several hypotheses. Some questions your group should consider
are: a. What difficulty do you expect your students may have? b. What algebraic habits of mind are required to solve it? c. What symbols or representations may work? d. What misconceptions do you expect your students may have?
3. One or more members of your group who has access to a willing participant(s) will volunteer to try out the task and report back to the group about how it went.
4. Discuss about the participants’ algebraic reasoning. Apply what you learned in CI 508 to analyze your findings. Compare the results to your hypotheses.
5. Write a report (maximum 3 pages, double space) about your research (MS Word). The report should include, a. The algebraic task b. Hypotheses c. Description of participants (grade, gender, mathematical backgrounds, etc.) and task
enactment/observation (i.e., how it goes?) d. Findings e. Discussion
i. Comparing the findings to the hypotheses ii. Connections with CI 508 reading materials
iii. Implication to your future teaching 6. Submit your research report (one report per group) and self/peer evaluation sheet (individual, see p.8)
through Blackboard by 4/22, Friday. 7. Present your group research project on 4/25 & 5/2.
• Meets all expectations • Sufficient details are included in
each section • Thoughtful insights and analysis
are included • Innovative ideas of implication are
discussed
• Include all requirements. • Use a cognitively demanding
algebraic task that does not show a direct solution.
• Findings are sufficiently analyzed in Discussion based on the readings of CI 508
• Does NOT include all requirements
• Use a too simple task that asks only procedures without connections to concepts.
• Does NOT satisfy page limit or writing style
Presentation (5%)
• Meets all expectations • Uses a creative/engaging way to
present • Interacts actively with audience
• Present core elements of the research effectively
• All members speak evenly
• Some core elements are not presented or presented poorly (e.g., read PPT)
• Not all members speak evenly
Self/Peer evaluation
(5%)
• Meets all expectations • Your peers give you all Es • Shows a great teamwork
• Complete the evaluation form with a respectful manner and sufficient details
• Your peers give you mostly E or M
• Incomplete the evaluation form or not written respectfully
• Your peers give you mostly N
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Weekly Reading Discussion Prompts (20 % of the course grade)
Excellent (100%) Meet expectations (≈ 80%) Need to improve (≈ 60%) Upload a discussion prompt every week and mostly on time Most discussion questions are well thought and articulated to stimulate an active argument
Upload a discussion prompt almost every week and mostly on time Some discussion questions are well developed and articulated
Upload a discussion prompt sometimes or usually late Most discussion questions are too simple/superficial and poorly written
Self/Peer Evaluation: Participation Criteria
Excellent Meet expectations Need to improve Seems to complete reading before class and prepare for discussions Consistently participates actively in small group discussions and activities Actively participates in whole class discussions Poses thoughtful questions to peers and instructor Class discussions are better due to the involvement of this student
Seems to complete reading before class Generally participates in small group discussions and activities. Participates in whole class discussion on a minimal basis
Does not seem to complete reading before class Appears interested, but participates periodically Does not participate in whole class discussions
Self/Peer Evaluation: Group Project Criteria
Excellent Meet expectations Need to improve Meets all expectations Shows a positive leadership Contributes creative and useful ideas Contributes significantly to the success of the project.
Attends group meetings regularly and arrives on time. Contributes meaningfully to group discussions. Completes group assignments on time. Demonstrates a cooperative and supportive attitude.
Does not attend group meetings regularly or arrive on time. Does not participate in group discussions. Does not complete group assignments on time Continually shows a disrespectful behavior
Feedback on team dynamics:
1. How effectively did your group work? 2. Were the behaviors of any of your team members particularly valuable or detrimental to the team? Explain. 3. What did you learn about working in a group from this project that you will carry into your next group
experience?
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NCTM Journal Call for Manuscripts
Write for a department:
postscript
Do you have a mathematical activity, game, or puzzle that every elementary school teacher should know about? A rich “grab and go” type of resource that teachers can quickly incorporate into their classroom repertoire with little effort but maximum impact? It may even be one of those tried and true strategies that every teacher may have used at some point but could use a reminder that it is available in their personal reserve.
The Editorial Panel of Teaching Children Mathematics invites you to use the journal’s last page to spotlight a conceptually rich mathematics teaching idea that readers across the elementary spectrum will want to try on Monday morning. Your Postscript manuscript should include each of the following three elements:
1. A brief description of a conceptually rich mathematics teaching idea for an activity, game, or puzzle.
2. Suggestions for how teachers of different grade bands (K–1, 2–3, 4–6) can use this idea.
3. Opportunity for a strong visual component to comple-ment the text, such as a game board, manipulatives, an illustration, or a photograph.
Limit your manuscript to 200–250 words, with pictures or photographs included at the end. Additional supplemental materials that can be made available on-line, such as activity sheets, are also welcome. Submit completed manuscripts to the Postscript department by accessing tcm.msubmit.net.
Go to www.nctm.org/journalsubmissions/ for details and more information about TCM’s departments; tips for preparing manuscripts for publication; and guidelines on how to include photographs, video clips, files, and other resources. Find detailed submission guidelines for all departments at www.nctm.org/tcmdepartments.
On the back page of the journal, a one-page activity is available for teachers to use in the classroom. Each activity is a single idea applied in the real world, to answer the question “When am I ever going to use this?” Math for Real manuscripts are 250-300 words and include introductory text and 4-6 questions. Solutions should also be submitted and are not included in the word count. Submissions should be made through http://mtms.msubmit.net. If you have any questions, email to [email protected]
