Culturally Responsive Mathematics Instruction: Cognitively Guided Mathematics Instruction

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Culturally Responsive Mathematics Instruction:

Cognitively Guided Mathematics Instruction

Course number: 730

Dr. Judith Hankes, Ph.D.

UW Oshkosh

Phone: (920) 424-7254 Email:


This course is about developing understanding of elementary level mathematics through applied problem solving. The importance applied of problem solving in the elementary mathematics curriculum cannot be over emphasized. The National Council of Teachers of Mathematics (NCTM) in its recommendations for school mathematics lists as the number one priority that “problem solving is to be the focus of school mathematics.”

Discussions throughout the course will focus on the research-based knowledge, concepts, and principles of cognitive constructivist learning theory applied to teaching mathematics and authentic assessment of student learning. Emphasis will be placed on the content and principles of Cognitively Guided Instruction, a mathematics reform approach developed at the Wisconsin Center for Education Research, Madison.
Emphasis is also place on the cultural compatibility of CGI with traditional Native American teaching practices.


This is a three-part course. A participant may register for one, two, or three credits. Part I (1 credit): participation in a week-long summer workshop (30 contact hours); Part II (1 credit): development of a CGI unit; Part III (1 credit): implementation of CGI and reporting on the implementation (mini action research) during the fall school year semester.


1. Students will develop the ability to integrate and practice skills and concepts within a problem-solving environment in the planning of teaching mathematics.

2. Students will develop the ability to practice authentic assessment of children’s mathematical thinking and plan instruction based on that thinking.

3. Students will develop the ability to practice the implementation of portfolio assessment as documentation of student learning.

4. Students will develop the ability to write mathematical word problems and match such problems to the developmental levels of children’s thinking

5. Students will develop an understanding of constuctivist-based learning theory and its impact on the teaching of mathematics.

Instruction format is distributed as follows: lecture - 30%, group work - 30%, and discussion - 40%.
Children’s Mathematical Thinking: Cognitively Guided Instruction, Carpenter et al., 1999.

Cognitively Guided Instruction Readings - 730 course manual

DAY 1: Reform in Learning theory: Where We’ve Been and Where We’re Going

Addition (Joining) and Subtraction (Separating)

DAY 2: Assessing Children’s Thinking

DAY 3: Kindergarten Interview and Base 10 Concepts

DAY 4: Fractions, Decimals, and Percent

DAY 5: Geometry and Portfolio Assessment

Assigned Readings:

There is a limited amount of reading expected for this class, but the readings that are assigned are vitally important


This is a course that requires complex processing of ideas. You will not simply be memorizing procedures or doing simple arithmetic. Attendance and class participation is vital to your learning and the learning of the entire class.

PART I Assignment:

Authentic Assessment (CGI Interview)

You, with a partner, will interview (using the Cognitively Guided Instruction Interview procedure) a primary age student and assess the child’s mathematical thinking. Interview teams will report findings and observations during class session.

PART I Assignment:

Word Problems

You, with a partner, will write 14 word problems based on the CGI Problem Type scheme. Problems will be duplicated and distributed to class participants.
PART II Assignment:

CGI Unit

Following the weeklong workshop, you will develop a math unit (5 lessons) that incorporates CGI principles. Upon completion, the unit will be emailed to me at

PART II Assignment (fall semester):

Mini Action Research

Early in the school year, you will pre-test three students (one high, one average, and one low achieving) with the CGI Interview protocol. After implementing CGI problems daily for one full month, you will post-test the same students and determine whether there is any change in each student’s problem solving ability. You will write a brief report and email this to:

Culturally Responsive Mathematics Instruction:

Cognitively Guided Instruction

Summer and Fall 2006

Mathematics Instruction (CGI)

(variable credit course - one to three credits available)
Instructor: Judith Hankes, Ph.D.

Phone (920)424-7254 e-mail:

Parts I, II, & III

Part I - Summer Workshop, 1 credit

Date: 2006 8:00 am - 3:00 pm (lunch 11 - 12:00)

Workshop Description: This week-long workshop focuses on the content of

Cognitively Guided Instruction: the structure of whole number word problems,

children’s developmental stages of mathematical understanding, and NCTM

standards-based methods of instruction, and alignment with culture-based curriculum

and pedagogy. Knowledge gained during this workshop will help teachers prepare

students for State Standardized Achievement Test.

Part II - Independent Project, 1 credit

Prerequisite: participation in Part I.

Activity: Participants will develop a month-long mathematics unit incorporating

culture-based CGI word problems.

Part III - Fall Implementation Seminar, 1 credit

Prerequisite: participation in Part I and completion of Part II.

Activity: The mathematics unit developed to satisfy Part II will be taught (at least one month of instruction). Additionally, prior to teaching the CGI unit, three students will be assessed (low, average, high achieving), following one month of CGI problem solving, these students will be reassessed to determine learning gains. A brief summary of the participant teacher’s observations about CGI problem-based teaching and the pre-post test data, will be sent via email to Judith Hankes before December 10th.

Registration Procedure

Call Karen Norton at (920) 424-3324 or e-mail:

This THREE PART COURSE emphasizes that children should:

* be engaged with instruction based on problem solving;

* base procedural knowledge on conceptual understanding;

* solve problems in ways that make sense to them - use manipulative, and invented procedures;

* explain the thinking they use to obtain their answers;

* develop the ability to monitor their own thinking.

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