Nov 15, 2007


The Cognitively Guided Instruction program was a four-week
workshop for 1st grade teachers, intended to provide insight on how
children develop addition and subtraction concepts. The workshop did not
prescribe specific teaching strategies, but instead gave teachers the
opportunity to explore how they might use research on children’s
mathematical development to guide their mathematics instruction.

In an experimental assignment study which 40 teachers were
randomly assigned to the treatment or control group, the workshop was found to
have significant impacts on treatment teachers’ mathematics instruction.
The workshop also had impacts for these teachers’ students. Compared
with students taught by teachers who did not receive the workshop, students
taught by teachers who did receive the workshop were significantly better at
solving complex addition and subtraction problems and were more likely to
employ appropriate problem-solving strategies when presented with word


Target population:1st grade teachers

The first half of the CGI workshop was devoted to giving
teachers access to knowledge about addition and subtraction word problems and
how children think about them. Teachers learned to classify problems and
to identify the processes that children use to solve different types of

The remainder of the workshop was devoted to discussing
principles of instruction that might be derived from research on children’s
problem-solving styles. Teachers were provided with broad principles to
guide discussion and questions to consider when planning lessons. They
were also familiarized with curricular materials available and were encouraged
to evaluate these materials on the basis of knowledge gained at the workshop.

Workshop activities included reading syntheses of research
on children’s problem-solving strategies, discussing readings, watching
videotapes of children solving problems, and interviewing children.
Teachers were given a great deal of freedom to focus on those activities
important to them and to plan for future instruction.


Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang,
C., & Loef, M. (1989). Using Knowledge of Children’s
Mathematical Thinking in Classroom Teaching: An Experimental Study. American
Educational Research Journal, 26
(4), 499-531.

Evaluated population: A total of 40 1st grade
teachers and their students served as the study sample for this
investigation. Teachers came from 24 schools in the Madison, Wisconsin
area. 22 of the schools were public; 2 were Catholic. On average,
participating teachers had been teaching for 11 years and had been teaching 1st
grade for 6 years. None of the teachers had received any prior training
on addition and subtraction problem-solving research. 12 students were
selected at random from each teacher’s class to serve in the study
sample. Students with special learning needs were not selected to be a
part of the sample.

Approach: Teachers were randomly assigned, by school,
to either the treatment group or the control group.

Teachers assigned to the treatment group took part in the
Cognitively Guided Instruction workshop. The workshop was run during
teachers’ summer vacations and was taught by the two program developers
and three of their graduate students. It involved five hours of
participation each day, four days a week, for four weeks. Treatment group
teachers were provided with a program contact person with whom they could
discuss questions that developed over the course of the school year.

Teachers assigned to the control group received four hours
of instruction on non-routine problem solving. Instruction occurred at
the beginning of and midway through the school year. Instruction did not
deal with how children think when they solve problems.

Math instruction in study classrooms was observed throughout
the school year. Students completed standardized mathematics assessments
at the beginning and end of the school year. Teachers also completed a
series of measures at these timepoints.

Results: Teachers assigned to receive the Cognitively
Guided Instruction workshop spent significantly more time teaching word
problems than did control teachers. CGI teachers also spent significantly
less time on number facts. CGI teachers were more likely to pose problems
to students and focused more on students’ problem-solving processes and
less on their answers than did control teachers. CGI teachers also
allowed their students to employ a greater variety of problem-solving
strategies than did control teachers.

Students in CGI classrooms did not perform better than
students in control classrooms on a standardized test of computational
abilities; however, they did have a higher level of recall of number facts when
interviewed. Students in CGI classrooms did not perform significantly
better than students in control classrooms on a test of simple addition and
subtraction problems (perhaps because scores were near the ceiling. An
interaction analysis found CGI in low-achieving classrooms did gain more by the
post-test), they did perform better on a test of complex addition and subtraction
problems. Additionally, CGI students more frequently employed correct
problem-solving strategies when given word problems in interviews.

Students in CGI classrooms reported greater confidence in
their ability to solve math problems than did students in control
classrooms. CGI students did not significantly differ from control
students in reports of how often they paid attention during math class.


Curriculum materials available for purchase at:


Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.,
& Loef, M. (1989). Using Knowledge of Children’s
Mathematical Thinking in Classroom Teaching: An Experimental Study. American
Educational Research Journal, 26
(4), 499-531.

KEYWORDS: Elementary, Academic Achievement, Co-ed,
School-based, Children, Manual, Mathematics

Program information last updated on 11/15/07.