Overview of Cognitively Guided Instruction Research

1970s: Research on Children’s Mathematical Thinking

• Thomas Carpenter and James Moser research the development of children’s strategies for addition and subtraction problems

Cognitively Guided Instruction Story Problems Carpenter, Fennema, Franke, Levi, and Empson, ©2006

Join, Result Unknown Leon has 9 pencils. He gets 5 more pencils. How many pencils does Leon have now?

Join, Change Unknown Kevin has 7 dollars. He wants to save up 11 dollars to buy a toy. How much more money does Kevin need?

Join, Start Unknown Eve found 8 pebbles on her way to school and put them in her pocket. When she got to school she counted her pebbles and found that she had 14 pebbles in her pocket. How many pebbles did she have in her pocket before she left for school?

Separate, Result Unknown TJ had 13 chocolate chip cookies. At lunch she ate 5 of them. How many cookies did TJ have left?

Separate, Change Unknown Eleven children were playing in the sandbox. Some children went home. There were 3 children left still playing in the sandbox. How many children went home?

Separate, Start Unknown Max had some money. He spent $9 on a video game. Now he has $7 left. How much money did Max have to start with?

Part-Part-Whole, Whole Unknown Fifteen girls and 5 boys were playing soccer. How many children were playing soccer?

Part-Part-Whole, Part Unknown Destyni is holding some pennies and quarters. She is holding 12 coins. If we know she has 2 quarters, how many pennies is she holding?

Compare, Different Unknown Willy has 12 crayons. Lucy has 7 crayons. How many more crayons does Willy have then Lucy?

Compare, Compare Quantity Unknown Coleman has 11 books. Kevin has 6 books more than Coleman. How many books does Kevin have?

Compare, Referent Unknown Melleri has 13 stickers. She has 5 more stickers than Kenzie. How many stickers does Kenzie have?

Children’s Solution Strategies Chart

Counting On To

Number Facts

Flexible Choice of Strategies

Direct Modeling

Counting

Join(Result Unknown)Part-Part-Whole(Whole Unknown)

Separate(Result Unknown)

Part-Part- Whole (Part

Unknown)

Join(Change

Unknown)

Compare(Difference Unknown) Join/Separate

(Start Unknown)

Joining AllSeparating

FromJoining

ToMatching

Trial and Error

Counting On From First

Counting On From Larger

Counting Down

Derivingfacts

Recalling

1984 - 1988: CGI Experimental Study

• 40 First grade teachers– 20 Attended Workshop (Treatment) – 20 did not (Control)

• Treatment and Control group were compared– Teachers’ knowledge– Teachers beliefs– Students’ achievement (problem solving and facts)– Classroom activities (amount of problem solving, type of

teacher talk, type of student talk…)

1989-1995:CGI Longitudinal Study

• Kindergarten through third grade teachers and students in four schools participated in CGI professional development for three years.

• Assessed over three years:– Teachers’ knowledge and beliefs– Students’ achievement and beliefs – Classroom practice

• Five years after the workshop ended (2001) teachers’ classroom practice, knowledge and beliefs were assessed

1996-2005: CGI/Algebra Research

• Program Development: 1996 – 2000 CGI Algebra Professional Development Program was developed by researchers in conjunction with expert CGI teachers.

• Experimental Research 2000 - 2005 – First – Sixth grade teachers– 90 Treatment Teachers; 90 Control Teachers– Treatment and Control teachers were compared

• Student Achievement• Teacher Knowledge

In CGI Professional Development:

• Teachers learn how children think about mathematics.

• Teachers are supported in developing their own approach to teaching math for understanding.

• We focus on number, operation and the algebra underlying number and operation.

Summary of CGI Research Results Characteristics of Classrooms

• Students in CGI Classrooms spend more time engaged in problem solving than students in non-CGI Classrooms.

• There is a higher ratio of student talk to teacher talk in CGI Classrooms than in non-CGI classrooms.

Summary of CGI Research Results Student Achievement

• CGI students’ achievement on problem solving tasks is higher than non-CGI students’.

• CGI students’ performance on computation and facts is not significantly different from that of non-CGI students.

• CGI students are more likely to use strategies that are based on an understanding of mathematical relationships.

Strategies that show an understanding of mathematical relationships

Summary of CGI Research Results Characteristics of Teachers

• CGI Teachers have greater knowledge of their students’ thinking than non-CGI teachers.

• CGI Teachers have greater knowledge of children’s mathematics than non-CGI teachers.

• CGI Teachers have greater knowledge of mathematics than on-CGI teachers.

• Good place to include some of your own data – either student test scores and/or number of teachers in your region who have participated in CGI

Levels of Teacher Change

• Level 1: Traditional

• Level 2: Problem Poser

• Level 3: Listener

• Level 4: Knowledge Integrator

Level 1: Traditional

• Provides few, if any, opportunities for children to engage in problem solving or to share their thinking.

When problems are presented to children, teachers explain to children how they are to solve them.

Level 2: Problem Poser

• Provides some opportunities for children to engage in problem solving and/or to share their thinking.

May show evidence of beginning to attend to children’s thinking and/or using information about children’s thinking to guide instruction.

Level 3: Listener

• Provides opportunities for children to solve problems and share their thinking.

May show evidence of beginning to probe for further information when children share their thinking. May show evidence of beginning to use information about children’s thinking to guide instructional decisions.

Level 4: Knowledge User; Integrator

• Provides opportunities for children to solve a variety of problems, elicits children’s thinking, and provides time for children to fully share their thinking.

Instructional decisions are driven by general knowledge about his or her students’ thinking, and/or by knowledge of individual children’s thinking.

CGI Research Findings: Teacher Change

• Teachers needed to both learn the CGI framework and use CGI with students.

• Teachers who began at levels 1 or 2 took at least two and usually three years to achieve levels 3 or 4.

• Teachers who grew received both professional development and support from teachers at their schools.

CGI Research FindingsFollow-up Study of Teacher Change

• All Level 1 or 2 Teachers: were at level 1 five years later.

• All Level 3 Teachers: sustained their level of implementation or improved to Level 4. (sustained change)

• All Level 4 Teachers: grew in their ability to teach math for understanding. (generative change)

Overview of Cognitively Guided Instruction Research