Cognitively Guided Instruction

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Cognitively Guided Instruction

• Gwenanne Salkind
• Mathematics Education Leadership
• Research Expertise Presentation
• December 11, 2004

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Addition Subtraction

• Problem Types
• Joining or separating actions
• Comparing situations
• Part-whole relations
• Combined with what is unknown
• Carpenter, T. P., Moser, J. M. (1983)
• Riley, M. S., Greeno, J. G., Heller, J. K.
  (1983)
• Carpenter, T. P. (1985)

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Classification of Word Problems
Result Unknown Change Unknown Start unknown
Join Connie had 5 marbles. Jim gave her 8 more marbles. How many does Connie have altogether? Connie has 5 marbles. How many more marbles does she need to have 13 marbles altogether? Connie had some marbles. Jim gave her 5 more marbles. Now she has 13 marbles. How many marbles did Connie have to start with?
Separate Connie had 13 marbles. She gave 5 marbles to Jim. How many marbles does she have left? Connie had 13 marbles. She gave some to Jim. Now she has 5 marbles left. How many marbles did Connie give to Jim? Connie had some marbles. She gave 5 to Jim. Now she has 8 marbles left. How many marbles did Connie have to start with?
Part-part-whole
Compare Connie has 13 marbles. Jim has 5 marbles. How many more marbles does Connie have than Jim? Jim has 5 marbles. Connie has 8 more than Jim. How many marbles does Connie have? Connie has 13 marbles. She has 5 more marbles than Jim. How many marbles does Jim have?
Connie had 5 red marbles and 8 blue marbles. How
many marbles does she have?
Connie has 13 marbles. Five are red and the rest
are blue. How many blue marbles does Connie have?
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Development of Problem-Solving Strategies

• Direct Modeling
• Counting
• Derived Facts
• Recall Facts

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CGI Framework

• Analysis of problem types and solution strategies
  provides a framework for analyzing teachers
  pedagogical content knowledge.
• Will providing research-based knowledge to
  teachers influence their instruction?

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Researchers

• Thomas P. Carpenter, University of Wisconsin
• Elizabeth Fennema, University of Wisconsin
• Penelope L. Peterson, Michigan State University
• Deborah A. Carey, University of Wisconsin
• Megan L. Franke, UCLA
• Nancy Knapp, University of Georgia

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CGI Workshops

• 40 first-grade teachers
• 4-week summer workshops
• 1986 and 1987
• Familiarize teachers with the findings of the
  research on the learning and development of
  addition and subtraction concepts in young
  children
• Provide teachers with an opportunity to think
  about and plan instruction on the basis of this
  knowledge

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Measures of Teachers Knowledge

• Knowledge of problem types
• General knowledge of strategies
• Teachers knowledge of their own students

Measures of Student Performance

• Number Facts
• Problem Solving

(Carpenter, Fennema, Peterson, Carey, 1988)
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Results

• Teachers could distinguish between major problem
  types and were capable of identifying student
  strategies
• Teachers were able to predict the success of
  their own students.
• Most teachers did not have a coherent framework
  for classifying problems.
• Many teachers did not recognize that problems
  that can be directly modeled are easier than
  problems that cannot.
• (Carpenter et al., 1988)

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Another Study

• 20 of the original 40 teachers
• Case studies of two of the teachers
• Compared a knowledgeable teacher with a less
  knowledgeable teacher
• (Peterson, Carpenter, Fennema, 1989)

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Data Collection

• Classroom observations
• Teachers Belief Questionnaire
• Teachers knowledge of their own students
• Student Measures of Achievement
• ITBS pretest/posttest
• Interviews
• (Peterson et al., 1989)

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Teachers Knowledge Beliefs

• Teachers knowledge of their students
  problem-solving abilities was the best predictor
  of students problem-solving achievement.
• Teachers beliefs were significantly positively
  correlated with students mathematics
  achievement.
• (Peterson et al., 1989)

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Difference between More Expert Teachers and Less
Expert Teachers

• More Knowledgeable
• Questioned and listened to students
• Believed that students construct their own
  knowledge
• Believed that children came to school with a lot
  of knowledge
• Believed that the role of teacher is as
  facilitator

• Less Knowledgeable
• Explained how to solve the problem
• Believed that children receive knowledge
• Skeptical of students entering knowledge
• Focused on knowledge that her children did not
  have
• Believed that role of teacher is to present
  knowledge.

(Peterson et al., 1989)
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A Case Study

• Ms. J
• First grade teacher
• Participated in the CGI studies
• Four years
• (Fennema, Franke, Carpenter, Carey, 1993)

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Data Collection

• Year 1
• Interviews
• CGI Belief Instrument
• Year 2
• Classroom observations
• CGI Belief Instrument
• Year 3 (Case Study)
• Group discussion
• Interviews
• Classroom observations
• Student Interviews
• Year 4
• Interviews
• Knowledge assessment
• (Fennema et al., 1993)

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Ms. J

• Ranked near the top of her experimental group on
  knowledge of CGI framework
• High score on CGI Belief Instrument
• Students learned mathematics at a higher level
  than most first grade children
• (Fennema et al., 1993)

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Ms. Js Instruction

• Frequently questioned her students about their
  thinking
• Listened to her students more than the other
  teachers
• Expected multiple solution strategies at a higher
  level than most of the other teachers
• Expected students to persist in their work, share
  strategies, and reflect on their own thinking
• (Fennema et al., 1993)

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Results

• Ms. J had research-based knowledge of childrens
  thinking and was able to use it to make
  instructional decisions.
• Study shows evidence that teachers can use CGI
  research to inform their instruction and increase
  learning of children.
• (Fennema et al., 1993)

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CGI After Four Years

• 20 of original 40 participants
• All 40 were contacted and asked to participate
• Phone interviews
• Interviews collected detailed descriptions of the
  participants teaching practices.
• Teachers varied widely in degree of CGI use and
  beliefs
• (Knapp Peterson, 1995)

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CGI After Four Years

• Three groups of teachers emerged
• Ten teachers used CGI as the main basis for their
  teaching.
• Four teachers had never used CGI more than
  supplementally.
• Six teachers had used CGI more extensively in
  earlier year, but now were using it only
  occasionally.
• (Knapp Peterson, 1995)

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CGI After Four Years

• Researchers did, as they had hoped, develop an
  intervention that could result in significant
  changes in elementary teachers practices and
  beliefs about mathematics.
• The positive effects of CGI intervention seem to
  have been most pervasive and long lasting in
  teachers who constructed for themselves more
  conceptual and flexible meanings for CGI rather
  than adopting means that were tied to specific
  procedures from the CGI training.
• (Knapp Peterson, 1995)

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Other Studies

• Four year longitudinal study
• 21 teachers
• Workshops Support
• Classroom observations
• Interviews
• CGI Belief Scale
• Student Interviews
• Student computation tests
• Fennema, Carpenter, Franke, Levi, Jacobs,
  Empson, 1996)

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Levels of CGI Instruction
1 Provides few, if any, opportunities for children to engage in problem solving or to share their thinking.
2 Provides limited opportunities for children to engage in problem solving or to share their thinking. Elicits or attends to childrens thinking or uses what they share in a limited way.
3 Provides opportunities for children to solve problems and share their thinking. Beginning to elicit and attend to what children share but doesnt use what is shared to make instructional decisions.
4-A Provides opportunities for children to solve a variety of problems, elicits their thinking, and provides time for sharing their thinking. Instructional decisions are usually driven by general knowledge about his or her students thinking, but not by individual childrens thinking.
4-B Provides opportunities for children to be involved in a variety of problem-solving activities. Elicits childrens thinking, attends to children sharing their thinking, and adapts instruction according to what is shared. Instruction is driven by teachers knowledge about individual children in the classroom.
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Teachers Beliefs

• The beliefs of 18 teachers in the final year were
  more cognitively guided than were their beliefs
  in the initial year.
• Beliefs were characterized by the acceptance of
  the idea that children can solve problems without
  direct instruction and that the mathematics
  curriculum should be based on childrens
  abilities.
• ( Fennema et al., 1996)

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Student Achievement

• Student achievement in problem solving was higher
  at the end of the study than at the beginning
• There was no change in computation skills.
• ( Fennema et al., 1996)

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Three Case Studies

• Three teachers chosen from the original 21
• Interviews
• Classroom observations
• Looked at teacher change
• Only one teacher showed self-sustaining,
  generative change.
• Frank, Carpenter, Fennema, Ansell, Behrend,
  1998)

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Kindergarten Childrens Problem-Solving Processes

• Carpenter, Ansell, Franke, Fennema, and Weisbeck,
  1993
• 70 kindergarten children
• Teachers participated in CGI course
• Student interviews
• Children can solve a wide range of problems,
  including multiplication and division situations,
  much earlier than generally presumed.

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Other Researchers

• Villasenor Kepner, 1993
• Used a control group
• Urban district with significant minority
  population
• CGI students scored significantly better on
  number facts and problem solving tests
• CGI students used advanced strategies
  significantly more often than non-CGI students

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Other Researchers

• Vacc Bright, 1999
• Thirty-four preservice teachers
• Two case studies (Helen and Andrea)
• University of North Carolina
• Two years of professional coursework
• Student teaching
• Observations
• CGI Belief Instrument
• Interviews

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Other Researchers

• Warfield, 2001
• Case study of one kindergarten teacher
• Sixth year as CGI teacher
• Classroom observations
• Interviews
• Looked at beliefs, knowledge, and instruction
• Teacher used CGI framework to learn about
  individual childrens mathematical thinking and
  used that knowledge to make instructional
  decisions

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Summary

• Evidence that knowledge of CGI framework changed
  teachers instructional practices and beliefs
• Evidence that CGI instruction increased student
  performance in problem-solving and computation.

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CGI in FCPS

• Have trained about 70 teachers
• Support from instructor/coach
• Share research with CGI Instructor
• Consider using CGI Instructional Levels and CGI
  Belief Instrument