Integrated Teacher Education Program (ITEP)
E ED 472: Mathematics Curriculum and Methods
Instructor: Maria Czech, Ph. D.
Office Hours: Tuesdays 2-4, Saturdays (selected dates) 1-2, and by appointment
Telephone: (818) 677-3154
Michael D. Eisner College of Education Conceptual Framework
The Michael D. Eisner College of Education, as a professional school, uses a developmental approach
to promote reflection, critical thinking, and excellence in an inclusive learning community. Its
graduates are well educated, highly skilled and caring persons are lifelong learners prepared to
practice in an ever changing, multicultural world. They are committed to promoting achievement of
all students as a primary measure of successful educational practice. Graduates assume service and
leadership roles in public and private educational, health, and social programs and institutions. The
College establishes and maintains productive partnerships with community schools and agencies.
The faculty is committed to excellence in teaching, scholarship, service and collaboration with the
community and professions. The values for faculty and students that form the foundation of this
Conceptual Framework include the following:
1. We value high standards in the acquisition and application of professional knowledge and
skills in subject matter, pedagogy, and technology.
2. We value the achievement of students at all levels and promote its accomplishment in
accordance with national, state, and institutional standards.
3. We value an inclusive learning community.
4. We value creative, critical, and reflective thinking and practice.
5. We value ethical practice by caring professionals.
This course addresses the skills and understandings needed in order to effectively plan, implement,
and evaluate instructional programs in mathematics for diverse student populations. It is designed
to provide multiple subject credential candidates with models of instruction consistent with our
current understanding of learning processes, opportunities to develop related process skills, and
skills in implementing instructional models. Furthermore, the course helps teacher candidates
develop strategies for teaching children of widely differing cultural and linguistic heritages,
developmental levels and learning styles; mainstreamed special education children; and all children
to ensure them equal access to the core curriculum.
1. Develop select concepts aligned with the K-8 state-adopted academic content standards
2. Develop critical thinking in mathematics, e.g., the use of mathematical processes and
problem solving strategies.
3. Develop an appreciation for mathematics as a mode of thinking and a strategy of inquiry.
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4. Develop positive attitudes towards mathematics and the teaching of mathematics.
5. Become familiar with the scope and sequence of the state-adopted academic content
standards for mathematics, K-8 (TPE: 1A)
6. Critically examine the state-adopted K-8 mathematics content standards in light of
children’s natural development of mathematical skills, concepts, and reasoning (TPE: 1A).
7. Correlate the K-8 mathematics content standards with the elements of a comprehensive,
balanced mathematics curriculum that includes computational skills, concepts, and problem
solving (TPE: 1 & 4)
8. Identify and incorporate the elements and practices of a mathematics learning
environment in planning the mathematics curriculum (TPE: 1A, 11), e.g.,
Establishes clear expectations for student behavior
Promotes intellectual risk-taking
Promotes positive attitudes towards mathematics
Promotes caring, respect, and fairness
Promotes positive classroom interaction
Promotes student curiosity, flexibility, and persistence in problem solving
Encourages multiple approaches to problem solving
Provides discussion of different problem solutions
9. Demonstrate effective use of on-line assessment strategies, e.g., observation,
questioning, at key points in the design of a mathematics lesson (TPE: 2)
10. Become familiar with a variety of formal and informal assessment strategies, e.g., pre-
assessments, summative benchmark tests, portfolio, performance-based exercises, and
their use in monitoring student progress and achievement of the mathematics curriculum
11. Design a comprehensive assessment system for mathematics that includes multiple
measures (TPE 3):
Information from the family relevant to the mathematics abilities and achievement of
Students’ computational skills, concept formation, problem solving and reasoning skills
Attitudes towards mathematics
12. Modify assessment instruments, as appropriate, in assessing the mathematics
achievement of special populations, e.g., English language learners, students with
exceptionalities, gifted learner (TPE: 3)
13. Identify strategies and design activities to promote student self-assessment and goal
setting in relation to their progress and achievement in the mathematics curriculum (TPE:
14. Develop a record-keeping system for monitoring and communicating to families, individual
student progress and achievement in the mathematics curriculum (TPE: 3).
15. Interpret results of formal standardized measures to assess the strengths and
weaknesses of the mathematics curriculum (TPE: 3).
16. Identify strategies for providing feedback to students and parents/families and
promoting student achievement in the mathematics curriculum (TPE: 3).
17. Correlate a balanced, comprehensive mathematics curriculum with state and professional-
level standards, goals and recommendations (TPE: 4).
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18. Understand the patterns of development of students’ mathematical abilities and their
implications to the design of a balanced K-8 mathematics curriculum.
19. Discuss specific instructional models, e.g., direct instruction, cooperative problem solving,
in relation to: their distinguishing features, appropriate alignment with lesson purpose
and content in teaching the various elements of a balanced mathematics curriculum (TPE:
20. Use instructional strategies and materials, e.g., discussion, manipulatives, physical models,
graphical representations, computer technology, in a manner appropriate to the design of
learning experiences that promote student motivation, computational skill, concept
understanding, and problem solving abilities (TPE: 4).
21. Design learning experiences through which students develop academic language associated
with mathematics and that promote student comprehension of mathematical text (TPE: 4).
22. Apply pedagogical theories, principals and practices in promoting student development of
mathematical academic language and their ability to communicate orally and in writing in
mathematics (TPE: 7).
23. Design daily K-8 mathematics instruction that (TPE: 5 & 6):
Is developmentally appropriate
Make the purpose and goals of lessons explicit for students
Are relevant to students’ needs and interests
Provide for the active and equal participation of all students
Provide for sharing and evaluation of differing points of view
Extend students’ thinking through questions and challenges to existing thinking
Models the qualities of a mathematics learning environment
Is differentiated relative to the needs of special student populations
24. Identify the elements of a comprehensive instructional plan for K-8 mathematics
instruction in accordance with state-adopted mathematics content standards that (TPE: 8
Includes long-term goals and short term goals depicting appropriate scope and
Is based on entry-level assessment data on students
Incorporates explicit models of instruction based on sound theory and research and
appropriate to the purpose and content of the lesson
Differentiates instruction based varied student needs, e.g., language, cultural
Correlates learning experiences to students’ cultural backgrounds, experience,
Makes effective use of aides and volunteers in promoting the mathematics curriculum
Includes varied measures for assessing student progress during instruction
25. Design instruction that demonstrates appropriate use of instructional time to maximize
student learning, and that includes specific strategies for managing routine tasks and
lesson transitions (TPE: 10).
26. Evaluate their own mathematics content knowledge against the state-adopted
mathematics content standards and establish professional goals for increasing subject
matter knowledge (TPE: 13).
27. Engage the plan-teach-reflect-modify cycle in the continual evaluation of the existing
mathematics curriculum (TPE: 13).
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Online Feature of ITEP EED 472
A website for this course has been created that will serve as a conduit of information related to
this course and a medium through which we will conduct online discussions and course sessions. The
site will provide all students continued access to materials designed for this course:
announcements, weekly agendas, upcoming activities, e.g, the Problem of the Week, and any
handouts and overheads relevant to the content of the class session. Please be sure you regularly
visit the site to remain current on events taking place over the semester. Items will be posted on
the website according to the following schedule:
Weekly agendas Evening before the day of class (copy will be provided in class)
Problem of the Week Afternoon on day prior to its introduction in class
Handouts and overheads Afternoon on day prior to its introduction in class
Online course sessions Please see course calendar.
Reflection session topics Please see course calendar
Announcements Posted as necessary…please check the course site on a regular basis
See the student “course compass” included in the purchase of the Van de Walle textbook.
A rubric will be used in evaluating assignments submitted for this course. Final grade will be
determined on a percentage basis according to the following scale:
95-100% A 87-89% B+ 80-82% B- 73-76% C 67-69% 60-62% D-
90-94 A- 83-86% B 77-79% C+ 70-72% C- 63-66% D < 60% F
Shared Reflection Sessions (3, online) 30
Problem of the Week 20
Math Strands Representation 35
Detailed Math Lesson Plan 70
Review of Educational Software 15
Classroom Assessment Plan 30
California Department of Education (1999). Mathematics Framework for California Public Schools,
Grades K-12. Sacramento, CA: CDE. http://www.cde.ca.gov/cfir/math/
Van de Walle, John. A. (2000). Elementary school mathematics: Teaching developmentally.
(including student course compass) Addison-Wessley/Longman.
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All assignments completed for this course must be completed in a professional manner, i.e., typed,
edited, free of mechanical and spelling errors, submitted on-time, etc. Further, each assignment
must meet all the requirements as delineated in the description of the assignment. An assignment
will be considered late if it is not turned-in on the date it is due. Ten-percent of the total possible
points for an assignment will be deducted for each week that an assignment is late.
Assignments for this course address Teacher Performance Expectations 1-11 & 13 at a level of
application of elements to observational data: case studies, learning scenarios, learner profiles
(Level II). The mathematics lesson plan created through the lesson study (research) process
addresses TPEs 1-11 at the level of actual classroom practice (Level III)
Reflective Journal Entries (TPEs: 2, 5, 7, 11)
Record your comments, questions, and reflections related to recent readings, class
activities, or discussion. Your journal entries must be more than mere regurgitations of
classroom events and topics raised in your readings and discussion.
On certain dates, you will be asked to respond to a specific prompt related to our class
activities and discussions:
Online Reflection Sessions (TPE: varies according to topic):
Your instructor will “host” three sessions conducted through the course website, during
which you will be asked to respond to a posted prompt. Please see course calendar for
During the discussion sessions, you will be asked to:
1. respond in a reflective manner to a prompt provided, and
2. respond to at least three other contributions to the discussion board.
Problem of the Week (TPEs: 1A, 4, 11)
Solve the your choice of 2 out of 5 proposed problems of the week, each one corresponding
to a particular strand of the mathematics.
In writing up your solution to the problem, please provide a clear discussion of:
1. Your solution
2. The problem solving strategies used in arriving at your solution
3. A justification for the accuracy of your solution
4. The degree to which you enjoyed/did not enjoy solving the problem and why
Math Strand Inquiry (individual or groups of 2-3) (TPEs: 1A, 4, 6A/B)
Conduct an independent, critical review of the standards associated with the five mathematics
strands for an identified grade level (K-8).
As a member of your grade-level group, prepare a visual representation of each of the 5
strands of mathematics for your assigned grade level. The visual representation must be
appropriate for teaching at that assigned grade level.
Bring your re-presentation to class to participate in a Gallery Walk
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Mathematics Lesson Plans (TPEs: 1A, 2-11)
Design mathematics lesson for teaching K-8. Your math lesson plan must meet the appropriate
criteria listed below. Any lesson plans that do not will be returned for revision.
Concept or process/problem solving lesson developed through lesson study
1. You will be assigned to a grade-level to design a mathematics concept or process lesson
plan for that grade-level.
2. In your group, design the lesson according to the INTO-THROUGH-BEYOND format.
3. Submit the plan for review by the instructor and make any suggested modifications
4. Directives for this assignment will be provided for you.
Review of Mathematics Educational Software (TPE: 9)
Review several pieces of mathematics educational software using rubrics provided in this
course. Discuss the value of each piece of software to the mathematics curriculum you might
provide students at that grade level(s).
Classroom Assessment Plan for Mathematics (TPEs: 3 & 8)
Develop a classroom assessment and record-keeping system for mathematics
Your assessment plan must enable you as a teacher to determine the progress your students
are making in their mathematical skills and understandings against the backdrop of a
comprehensive, balanced, and standards-based mathematics curriculum at the elementary
Your record keeping system must enable you to keep clear and accurate records of the
knowledge and skills possessed by each of your students and must reflect your attention to
multiple measures of skill and knowledge.
CONNECTION TO FIELD EXPERIENCES:
Classroom Observations (TPEs: 5, 9-11)
You will be given opportunities in this course to be an observer/participant in an elementary
classroom. These assignments include lesson writing and an evaluation of a classroom setting as
a mathematics learning environment.
Identify the elements of a classroom community for learning mathematics.
Conduct an observation and critical review of an existing classroom setting according to
Citing specific evidence obtained in your observation, discuss how these elements
contribute to students learning mathematics.
Written Analyses and Reflections (TPEs: 3, 13)
Write several reviews related to analyses and reflections on content presented in class.
1. Interpretation of classroom profile of standardized test scores for mathematics
and implications for curriculum planning and instruction
2. Analysis of student work in light of state-adopted mathematics standards and
implications for instruction
3. Evaluation and reflection on math content knowledge and pedagogy in reference to
state mathematics standards
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Date Topics/Guiding Questions Assignments
1/29 +Introduction and Course Overview and how to enroll online 1. READING: Van de
(week 1) +Who am I as a math learner? How will this impact me as a Walle, chapter 1 & 2
teacher? 2. Online enrollment
+Conceptions of mathematics: Chalktalk activity
+What exactly is math? What does it mean to “do math”?
2/5 +Who are my students as learners? 1. READING:
(week 2) +What are the elements of a balanced mathematics chapter 3
program? 2. Download CA
+Using children’s literature in math State Mathematics
Standards for 2/12
2/12 +How can I provide a rich learning environment for math? 1. READING
(week 3) +Roles of Constructivism and developmental approach chapter 4
+An examination of the CA Mathematics Standards 2. Online reflection
-respond by 2/18
2/19 +Teaching math through problem solving 1. READING:
(week 4) +Introduction to “problem of the week” (due 9/24) chapter 23
+Using manipulatives 2. Solve your choice
of a “problem of
2/26 +Teaching all students mathematics: diversity of learners 1. READING:
(week 5) +Various approaches: adaptations and modifications chapter 5
+Multicultural, social and gender equity 2. Begin exploring
+Intro: Math strands assignment math strands
+(Problem of the week: due)
3/5 +Making assessments integral to the curriculum 1. READING:
(week 6) +Variety of assessment capture diversity of learning chapter 22
+Examining student artifacts…what these tell us 2. Begin designing
+Developing an assessment plan an assessment plan
3/12 +Curriculum and units 1. READING:
(week 7) +Lesson planning for effective instruction chapter 24
+Getting acquainted with “lesson study” 2. Online reflection
+The place of textbooks in lesson planning session
-respond by 3/18
3/19 +The place of technology in teaching math 1. READING:
(week 8) +How to review software for elementary school math chapters 6-7
+More on lesson planning (explain final assignments) 2. Review math
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3/26 +Number concepts and number sense 1. READING:
(week 9) +”Mental math” chapters 8-9
+Developing the meaning of “operations
+Math strand presentations
+(Assessment plan due)
4/2 +Mastering basic facts 1. READING:
(week 10) +Whole-number place value development chapters 10-11
+Math strand presentations
4/9 +Strategies for whole number computation 1. READING:
(week 11) +Alternative algorithms chapters 12-13
+Number sense and estimation with whole numbers
+Math strands presentations
4/23 +Developing fraction concepts 1. READING:
(week 12) +Computation with fractions chapters 14-15
+Math strand presentations
4/30 +Decimals and percents and decimal computation 1. READING:
(week 13) +Developing concepts of ration and proportion chapters 16-17
+Math strands presentations 2. Online reflection
-respond by 5/6
5/7 +Developing measurement concepts 1. READING:
(week 14) +Geometric thinking and geometric concepts chapters 18, 19
2. Prepare lesson
5/14 +Probability and data analysis 1. Prepare lesson
(week 15) +Algebraic reasoning plan presentations
+Exploring patterns and function
+Lesson plan presentations
5/21 +Lesson plan presentations
(week 16, +Wrapping it all up
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