ADVANCED MATHEMATICS for YOUNG CHILDREN
CUNY THE COLLEGE OF STATEN ISLAND
DEPARTMENT OF EDUCATION
“Is like a dance in which the child leads and the adult follows, always closely in tune with the child’s actions”
Instructor: Dr. Judit Kerekes
Office: 3S/207B
Phone: (718) 982 4112
Office Hours: Wednesday 8:00 pm-9:00pm
Thursday 3:30pm- 5:30pm
By appointment
Time: Wednesday 4:40- 6:20 PM
Room: 3S/210
Course Rationale
This course will specifically focus on enabling the teacher to design and implement math lessons that will cover the needs of students with a variety of abilities, the integration of instructional technology into the curriculum, and multiple approaches to assessment of learning.
This course takes a developmental perspective on the teaching and learning of mathematics. The role of context, culture, and language are explored as they relate to the development of mathematical ideas, strategies, and emergent models in the elementary years. Students will use video of real classrooms (K-6), investigate teachers’ decision-making, and analyze children’s work. On-site fieldwork and explorations with standards-based curricula will provide participants with guided opportunities to acquire those teaching strategies that best support mathematics learning in the elementary school. In order to strengthen participants’ subject matter knowledge, this course will also engage participants in mathematical activities and investigations at their own level.
Required materials: M. Dolk, C. T. Fosnot, A. Cameron, S. Hersch, (2004) Taking Inventory The Role of Context Portsmouth, N.H.: Heinemann Press ISBN 0-325-00672-5
M. Dolk, C. T. Fosnot, A. Cameron, S. Hersch, (2004) Working with Number Line Mathematical Models Portsmouth, N.H.: Heinemann Press ISBN 0-325-00672-3
M. Dolk, C. T. Fosnot, S .Hersch, A. Cameron, (2004) Fostering Children’s Development The Landscape of Learning Portsmouth, N.H.: Heinemann Press ISBN 0-325-00672-1
Recommended: C. T. Fosnot, M. Dolk (2001) Young Mathematicians at Work
Vol. 1: Constructing Early Number Sense Addition and Subtraction Portsmouth, N.H.: Heinemann Press ISBN 0-325-00354-8
C. T. Fosnot, M. Dolk (2001) Young Mathematicians at Work Vol. 2: Constructing Multiplication and Division Portsmouth, N.H.: Heinemann Press ISBN 0-325-00353-X
Mokros, Russell, and Ekonomopoulos (1995) Beyond Arithmetic: Changing Mathematics in the Elementary Classroom Palo Alto, California: Dale Seymour ISBN 0-86651-846-0
NCTM Standards 2000; www.nctm.org
Objectives
Develop an understanding of all children’s mathematical development regardless of cognitive ability
Study learning theories and their relevance to teaching mathematics to elementary students
Learn to develop lessons to teach mathematics concepts to children of different abilities
Requirements
Attendance and participation are crucial.
Videotaped inquiry/game on the development of spatial sense of choice for grades PK-3 will be prepared and submitted. The unit consists of several investigations sequentially ordered to support the development of the topic. This includes the development of big ideas, strategies, and models related to the topic. Written lesson plan, report, and analysis of children’s ideas. Include plan and your report after teaching. What went well in the lesson? What would you change if you were to teach this lesson again?
Journal is assembled on a weekly basis. Participants are expected to read and write a reflective response to a selected article, or to a video, and/or to work on mathematics investigation. Use Dolk, Fosnot, A. Cameron, S. Hersch, Mokros, Russell, and Ekonomopoulos and NCTM materials for reference. You may include activities from these materials verbatim and you may include activities from class. The journal should include a discussion of the following: the role of teachers’ questioning and connection of the lessons to the NCTM standards.
FinalOral Presentation on your field-tested unit
Method of Evaluation
Attendance and participation 25%
Taped Lesson as above 25%
Journals 25%
Exam 25%
Conceptual Framework/ Performance-Based Learning
Course: EDE 642/7857 How Children Learn Mathematics
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Teachers and Teacher Candidates are expect to know and do |
Evidence |
Diversity (Knowledge & Skills) |
Demonstrate an understanding of the role of culture and language as it relates to meaningful problematic situations and the didactical use of such contexts in mathematical teaching.
Characterize mathematical development in terms of “big ideas”, the progression of strategies, and emergent models. |
Written analysis of the role of context in various mathematical investigations and its effect on children’s learning (CDROM assignment)
Selects video clips which exemplify developmental shifts in understanding and discusses them n relation to mathematical teaching and learning ( CDROM assignment)
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Content Knowledge (related to your professional standards) |
Demonstrate a deep conceptual understanding of the mathematics candidates will be teaching (PK-2nd ) as described in the NCTM Principles and Standards 2000
Show evidence of a developing ability to plan worthwhile mathematical task connected to the NCTM Principles and Standards, 2000
Show evidence of a beginning ability to create a learning environment that fosters the development of mathematical power, as described in the NCTM Principles and Standards, 2000 |
Final Exam and performance during in class mathematical investigations
Preparation of a teaching unit on a mathematical topic, to develop number and spatial sense and several sequential investigations.
Written analysis of a class, including a selection of clipped moments from digital environments where teacher is doing something to support the development of community (CDROM assignment)
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Pedagogical Knowledge |
Shows evidence of a developing ability to foster classroom mathematical discourse and reflection
Understands the importance of questioning and wait time
Understands the importance of inquiry on mathematical development |
Written analysis of teacher behaviors, including clipped moments from digital environments of mathematical discourse and reflection (CDROM assignment)
Written analysis of videotaped lessons analyzing the role of teacher’s questioning and wait time (CDROM assignment)
Preparation of teaching unit on a mathematical topic, to develop number sense and several sequential investigations to show evidence of appreciations for inquiry
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Leadership Learning |
Is aware if the political aspects of the NCTM Principles and Standards, 2000 and the need to help the public understand and appreciate the reform
Demonstrates a working knowledge of the use of new curricular materials
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Writes an accompanying letter to parents for the prepared unit, explaining the purpose of the unit (submitted with unit)
Use new curricula to plan unit |
Uses of Technology |
Proficiently uses digital environments for professional learning
Evidences a developing knowledge of available software and its uses in mathematical investigations |
Completes CDROM assignment successfully
Demonstrates flexible in-class use of Geo Logo while involved in mathematical explorations
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Disposition to: Become lifelong learner; |
Exhibits an excitement and enthusiasm for doing mathematics
Seeks out materials and reading to expand and grow as a professional
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Exhibits an excitement and enthusiasm for doing mathematics
Seeks out materials and readings to expand and grow as a professional |
Become a reflective practitioner; |
Show the ability to reflect critically on teaching decisions, both on one’s own and others |
Written reflection of videotape lesson and field experience
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Establish a professional identity; |
Sees oneself as part of caring community of discourse engaged in activity, knowledge construction, communication, and reflection
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Behaviors exhibited during in-class group work and discussion |
Build a caring community; |
Show evidence of the ability to analyze classroom interactions (student / learner and learner / learner) and the teacher actions, physical environment, and power dynamics that produce them
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Written analysis of videotaped lesson and field experience |
Build democratic schools; |
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COURSE OUTLINE
EDE 642/7857
08/31 Class1 Introduction
Overview of the course
The Playgrounds of Mathematics
History of Math
Cooperative Learning
Measurement Inventory
Measuring the Body
Compare the Metric System with the Customary System
Assessment: Reading and CD Taking Inventory
Journal #1 Write a Reflective Piece on
Measurement Inventory
09/07 Class 2 Teaching and Learning Framework,
Curriculums
Handshake Problem
The Role of Context
Build a Mathematical Community
Mathematics as a Human Activity
Progression of Strategies
Progressive Schematization
Math Congress
Assessment: Reading and CD
The Role of Context
Journal # 2 1 Write a Reflective Piece on
The Role of Context
09/14 Class 3 Young Children Constructing Number
Piaget’s Theory of Numbers
NCTM Standards
The Teacher’s Role
Strategies, Big Ideas, and Models
TERC and Everyday Mathematics
Math for Disabled Students
Use of Rekenrek
Workshop
Games for Young Children
Assessment: Reading and CD
Working with the Number Line
Journal # 3
09/21 Class 4 Progressive Mathematizing
Designing Context
Working with a Real Classroom (video)
Developing Meanings for the Operations
String, Open Number Line
Helping Children Master Addition and Subtraction Facts
Using technology in the Classroom
The integration of instructional technology into the curriculum
Assessment: Begin Work on Unit
Assessment: Reading and CD
Working with the Number Line
Journal # 4
09/28 Class 5 Library class
Assessment: Work on Unit
Journal # 5
10/05 No Classes
10/12 No Classes
10/19 Class 6 Facilitating the Development of Models
Generalizing the Model
Use the Model in other Contexts
Relationships, Doubles, Make Tens
Using Manipulatives,
Teaching for Number Sense
Developing Addition and Subtraction Strategies
Doing Math in a Mathematical Environment
The NCTM, the NY State, and the NY City Standards
Assessment: Work on Unit
Assessment: Reading Mathematical Models
Review Book 1 and two
10/26 Class 7 MID-TERM
11/02 Class 8 Virtual Classroom
Everyone’s Ideas Count
Different strategies
Learning to Mathematize
Multiplication as Repeated Addition
Exploring Cross-Cultural Multiplications
Computation with Mini-lessons,
Assessment: Work on Unit
Assessment: Reading
Fostering Children’s Mathematical Development
Journal # 6
11/09 Class 9 The Development of Early Geometry
Array, Area, Perimeter
Teaching and Learning as Development
Strategies as Schemes
Models as Tools for Teaching
Mathematics as the Living Discipline
Hypothetical Learning Trajectory
Assessment: Work on Unit
11/16 Class 10 Learning Trajectory
Landscape of Learning
Children can mathematize their Reality
Teachers Trust Give Wisdom
Pictures with Built in Constraints
The Role of the Imagination
Partitive and Quotative Division
Unitizing Groups, PT Evening
Assessment: Work on Unit
Assessment: Reading
The Landscape of Learning
11/23 Class 11 Analyzing Children’s thinking,
Their struggles, their strategies, their modeling
Principles of Learning-Teaching
Function of Context, Role of the Teacher
Characteristics of the Classroom Culture
Review Book one to three
Unit, Tape and Journals 1-6 due
11/30 Class 12 Teaching for Number Sense, Division Strings
Exploring Patterns, Mini-lessons
From the “ten times” strategy to the Long Division Algorithm
Using the Ratio Table Model for Division
The Function of Context in Dealing with Remainders
Assessment, Examining as a Meaningful Activity
Dynamic Evaluation of Journey
Various Levels of Mathematizing
Rubric that Reflected the Landscape of Learning
Oral Presentation with Video Component
12/07 Class 13 3D and 2D Representations
Building Boxes and Nets
The Cube Problem
Designing Context
Teaching/Learning Framework
Oral Presentation with Video Component
Assessment: Review Books
12/14 Class 14 Fractions as Emerging from Fair Sharing Situations
The Ratio Table and the Double Number Line
Equivalence to Decimals and Percents
Understanding Percents as Part/whole Relationships
Basic Statistics and Probabilities
Oral Presentation with Video Component
12/21 Class 15 Final Exams
Reference
Fosnot, C.T. (1989). Enquiring teachers, enquiring learners: A constructivist approach to teaching. New York Teachers College Press
Freudenthal, H. (1991) Revisiting Mathematics Education: The China Lectures. Dordrecht, the Netherlands: Kluwer.
Kamii, C. (1985). Young children reinvent arithmetic. New York: Teacher College Press.
Kamii, C. (1993) Young children continue to reinvent arithmetic: grade three. New York: Teachers College Press.
Kerekes, J., and Fosnot C. 1998. Using Pictures with Constraints to Develop Multiplication Strategies. The Constructivist 13(2): 15-20