Bank Street College of Education
Fall, 2000
610 West 112th Street, N.Y. 10025
Linda Metnetsky: 875 - 4557
lmetnetsky@bankstreet.edu
TEED 530 Mathematics for Teachers in
Diverse and Inclusive Educational Settings
Classes (N-6) 2 Credits
Math Resource Room - Sixth Floor - Room 624
Welcome to Math for Teachers! A major goal of this
course is to provide teachers an opportunity to experience mathematics
as an organic, creative discipline, and to learn about approaches to the
teaching of mathematics within that context. As educators of young people
living in the Information Age, we need to be clear about what the essential
mathematics for the 21st century.
To accomplish this you will be expected to attend
all classes, complete a number of required readings, complete some readings
that you have selected yourself, and complete a variety of written and
practical assignments. The math resource room has a variety of print and
manipulative materials for your use in the room. Please do not
remove materials from room as a number of students use the information
and hands-on manipulatives.
Given the workshop nature of this course, absences
and lateness will be Wconsidered in grading. All papers, reports, and
journals are to be TYPED and submitted in a timely fashion.
COURSE OUTLINE
This course is organized into the
topics that appear below. Four threads will permeate all discussions: the
role of the teacher in an inclusive classroom, the use of language in learning,
on-going assessment, and mathematical content.
NOTE: Topics and sessions may not
always be parallel, though they will occur in the sequence described.
I. Introduction to Experiential Mathematics
-
What does it mean
to be a teacher/learner of mathematics?
-
Personal reflections
and mathematical history
-
What do you bring
to this course? What do you hope to accomplish?
-
Who are the students
we teach? Cultural backgrounds? Divergent Learners?
-
What strand is this?
Exploring the geoboard as a versatile
spatial tool in geometry.
Exploring the role of language in
learning mathematics.
II. Mathematics in 21st century!
What does it look like? The NCTM Standards 2000!
-
Discussion of the NCTM Standards 2000
- What is a Standard?
-
The mathematics reform movement and its
basis in learning theory.
-
What does it mean to "understand" math
in standards-based terms?
III. Learning Mathematics:
What cognitive frameworks are necessary for learning mathematics?
Cognitive psychology emphasizes internal mental structures and Social cognitive
theory emphasizes the outer social structures that interact
with those internal mental frameworks (Hiebert 1992). These theoretical
frames translate into two key elements for unpacking the process
of learning math. They are reflection and communication respectively
(Hiebert 1997).
Examining Cognitive Development as a means of explaining how we learn mathematics.
-
Piaget's stage theory of cognitive development
-
Piaget's theories on knowledge
-
The role of 'autonomy' in learning
-
The influences of culture on learning
mathematics.
-
The importance of knowing how you learn
mathematics and recognition of differences between your own and your students'
ways of making sense.
IV. Early Childhood Mathematics
Activities
that encourage informal mathematics; developing a sense of number and algorithms;
and geometry
-
Focus on the pre-operational learner
-
The fundamental role of counting in number
-
Development of number 0-20 through strategies,
pattern, use of composing and decomposing number.
Number games from Burns, Richardson,
and Investigations in Number, Data and Space
-
The role of assessment
-
Videos: K. Richardson's pre-number
assessment
K. Richardson's Math Talk
-
Software: Tenth
Planet
Kidpix
Investigations in Number, Data and Space
-
The use of sorting/classifying/logic
as a necessary organizational tool for understanding and developing pattern,
number, and geometry.
Software: TableTop, Jr. This
software is an excellent resource in sorting/classifying and graphing.
§ You may want
to read Principles and Standards for School Mathematics: Introduction
to Standards for Grades Pre-K-2 (http://standards.nctm.org/document/chapter4/index.htm)
Look
at the "e-examples" for the Pre-K-2 Chapter.
V . The Mathematics of Number (Lower
Elementary): Focus on Role of Place Value
-
What is place value and why is it a fundamental
understanding that every teach must know?
-
How children construct their own understanding
and create their own algorithms? The Role of Algorithms in Mathematics?
(number clusters, number strings)
-
Developing number sense through computational
strategies that incorporate the communitive and associative properties.
-
Composing and decomposing number developed
with computations from 0 to 20.
-
Creative algorithms: Strategies
for computational reasoning
-
Estimation
-
The literature connections: Good
literature whose story's focus happens to be a "big idea" in mathematics.
-
Video: Marilyn Burns' "Assessment
of Place Value."
§ You may want to read
Principles
and Standards for School Mathematics:Number& Operations. (http://standards.nctm.org/document/chapter4/
numb.htm) Look
at the "e-examples" for the Number & Operations Strand.
VI. Understanding Patterns
and Relationships: An Algebra Content Standard
-
Different Kinds of Patterns
Patterns in Number (Skip Counting,
Hundreds Board)
Pattern as a tool for problem solving
Software: Tenth Planet, Math Keys,
software from Investigations in Number, Data and Space
-
The Idea of Function
What's my rule with number!
What's my rule with ideas and geometric
pattern!
Graphing patterns in data/Linear
functions
Software: Green Glob
§ You may
want to read Principles and Standards for School Mathematics : Algebra
(http://standards.nctm.org/document/chapter4/alg.htm and http://standards.nctm.org/document/chapter5/alg.htm)
Look at the "e-examples" for the Algebra Strand.
VII. Mathematics of Rational Number
(Upper Elementary)
-
What does large number look like? Developing
landmarks in number.
-
Number Operations: Efficient strategies
for computational reasoning and invented algorithms.
-
Use of arrays and other representations
of multiplication and division.
-
What is a fraction and what does it look
like? Looking at fractions in geometry, probability and measurement.
-
Number in problem solving
-
Games, activities and problems that support
conceptual understanding and computational fluency with rational number
§ You
may want to read Principles and Standards for School Mathematics: Number
and Operations
(http://standards.nctm.org/document/chapter5/numb.htm)
Look at the "e-examples" for the Number & Operations Strand.
VIII. The Mathematics Learning
Environment
-
Components of Good Problem Solving
-
What does communication look like in a classroom?
-
Writing
-
Accountable Talk,
-
Cooperative Learning,
-
Communication through appropriate representation
-
What is evidence for learning?
IX. Meeting the needs of divergent
learners
-
The Special Needs Learner
-
How do developmental functions (attention,
memory, spatial, langauge, higher order congnition) impact on learning?
-
Exploring the role of memory
-
The role of the senses in memory and
learning
-
Implications for teaching and learning:
Modifying instruction to meet the needs of all learners.
-
Current research in how the brain functions
in learning.
X. Looking at Content Strands
-
Measurement (http://standards.nctm.org/document/chapter4/meas.htm
or http://standards.nctm.org/document/chapter5/meas.htm )
-
Data Analysis and Probability (http://standards.nctm.org/document/chapter4/data.htm
and/or http://standards.nctm.org/document/chapter5/data.htm)
-
Geometry (http://standards.nctm.org/document/chapter4/geom.htm
and/or http://standards.nctm.org/document/chapter5/geom.htm)
XI. Assessment - What is important about
assessment?
-
Reasons for assessment
-
Discussion of the role of standardized
tests
-
Exploring different types of assessment
Individual Assessment
Interviews
Performance Assessment
Portfolios
-
What's a rubic and how do I use one?
-
WEB: Exemplars.com (http://www.exemplars.com/)