Mathematics Performance Assessment in the Classroom:
Effect on Teacher Planning and Student Problem Solving
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Beatriz Kimball
Professor Nolan
Educational Foundations 7314
April 10, 2011
Fuchs, L. S., Fuchs, D., Karns, K., Hamlett, C. L., & Katzaroff, M. (1999) Mathematics
Performance Assessment in the Classroom: Effect on Teacher Planning and Student
Problem Solving American Educational Research Journal, 36(3), 609-646
The purpose of this study was to examine classroom-based Performance
Assessment (PA) driven instruction in mathematics. Researchers posed three questions:
1. How does classroom based PA driven instruction affect teachers’ knowledge
about what PA is, teachers’ knowledge about how PA might enhance
instructional decisions and teachers reports of changes in their curricular
focus?
2. What is the nature of teachers’ mathematics instructional plans when they use
classroom PA?
3. Does teachers’ use of classroom-based PA-driven instruction enhance
student’s mathematical problem solving?
Prior research indicates an approach to mathematical education that places an
emphasis on basic factual information fails to develop conceptual understanding in
students for application and transfer of knowledge. Students fail to make connections
between mathematical problems presented in and out of context (Foxman, Ruddock,
McCallum, & Schagen; 1991). They do not necessarily know how to apply the isolated
skills they acquire to novel situations (Brown, Campione, Webber, & McGilly, 1992).
Fuchs, Fuchs, Karns, Hamlett and Katzaroff conducted problem based research
with a randomized matched control group design. Participants in this study included 16
teachers from a southeastern urban school district. All teachers were female. Four taught
second grade, six taught third grade and six taught fourth. The teachers were randomly
assigned to classroom-based Performance Assessment driven instruction (PA) and no
classroom-based Performance Assessment driven instruction (no-PA) conditions.
Inferential statistics on average class size, years of experience and levels of training
indicated that the teachers were comparable on these variables.
Student participants were 272 children who were present for pretesting and
posttesting. Student demographic data was presented in table form listing Gender, Race,
Reduced/Free Lunch, SPED, Behavior, and Reading Level. 90 additional students were
absent on one or more days of pretesting or posttesting. Mathematics grade-level status
as reported by teachers was used as a study factor. Students were listed as Above, At or
Below grade level based on the Mathematics Computation and Applications Test
(MCAT) and the Comprehensive Test of Basic Skills (CTBS).
Based on the transfer literature, (Brown et al.) researchers identified problemsolving features with decreasing elements of similarity. Using these features to structure
their analysis, they refer to these measures as analogous, related and novel. Students
were pretested and posttested with an analogous problem-solving measure developed by
researchers. A related problem-solving measure involved one unseen PA from one grade
Mathematics Performance Assessment in the Classroom:
Effect on Teacher Planning and Student Problem Solving
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level below the students’ assigned grade. Novel problem-solving measures were taken
from the Iowa Test of Basic Skills (Riverside, 1995).
PA teachers attended training sessions, which covered instructional methods, as
well as the design, administration and scoring of performance assessments. Researchers
provided technical support to PA teachers and encouraged them to adapt their instruction
to enhance the problem-solving performance of all students in their classrooms.
Teachers’ knowledge about PA was examined as was their instructional planning in
response to the use of PA. One limitation of this study is that researchers did not
contribute to PA teachers’ discussions about how to strengthen instructional programs in
response to student performances on classroom PAs.
Students’ in-class problem-solving performance was analyzed on three occasions.
Assessments were administered on the Monday of Study Weeks 10, 13 and 23.
Assessments were scored according to a rubric adapted from the Kansas Quality
Performance Assessment (Kansas State Board of Education, 1991). This rubric scores
conceptual underpinnings, computational applications, problem-solving strategies and
communicative value. Each dimension was scored on a 6 point Likert-type scale where 0
= no relevant response.
To assess growth in teachers’ knowledge concerning Performance Assessments,
all teachers were asked to write a mathematical problem that might be categorized as PA.
Results presented in table form indicated that PA-driven instruction did increase teachers’
knowledge about what PA is
p <.05, effect size =1.47. Teachers were asked to complete questionnaires explaining
ways in which PA might be helpful in making instructional decisions. Results presented
in table form indicated that PA-driven instruction did improve teachers’ understanding of
how PA might enhance their mathematical instructional decisions p <.01, effect size
=1.70. To assess the nature of teachers’ mathematics instructional plans when using PAdriven instruction, teachers completed instructional plan sheets indicating how they
intended to address the curriculum. Researchers display information relating to
instructional focus by grade level and teacher.
Results of this study indicate that classroom-based PA-driven instruction can
increase teachers’ understanding of PA and how PA might be used to improve
mathematical instruction. Effect sizes comparing PA and no-Pa teachers’ knowledge
exceeded 1 standard deviation. The researchers point out that future research should
collect and compare instructional plans for the contrast group and should include
classroom observations to provide descriptions of teachers’ instruction which can be
more clearly attributed to the use of classroom-based PA-driven instruction.
Researchers examined student growth from pretreatment to posttreatment
performance. ANOVAs conducted on analogous problem-solving measures pretest to
posttest growth scores revealed significant interaction among some students. Results
presented in table form indicate that above-grade-level students grew statistically and
dramatically more than comparable no-PA students (effect sizes: 1.16 to 1.35). At gradelevel students also demonstrated impressive learning as a function of their teachers’ use
of PA (effect sizes: 0.76 to 1.15). On related problem-solving researchers found
significant interactions between treatment for above- and at-grade level students in
conceptual underpinnings, computational applications and problem-solving strategies
(effect sizes: 1.07 to 1.47). In the novel problem-solving measure on above-grade level
Mathematics Performance Assessment in the Classroom:
Effect on Teacher Planning and Student Problem Solving
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students benefited differentially from their participation in PA driven instruction
classrooms (effect sizes: 0.93). The effects on the novel measure were not statistically
significant (effect sizes: 0.30) for at-grade-level students. In communicative value PAdriven instruction benefited students across all grade-level designations.
Growth for below grade students was comparable across PA and no-PA groups in
analogous problem-solving and in most areas of related problem-solving. Below-gradelevel students did not appear to benefit from PA-driven instruction.
Researchers propose various hypotheses for future research into the lack of
significant effects of PA driven instruction on novel measures for at-grade-level students
including metacognitive awareness of the relations across problem-solving situations.
Researchers also note that results with below grade-level students are consistent with
previous work showing that students with initially low mathematics achievement
experience difficulty with mathematical problem-solving (Woodward & Baxter, 1997).
They note that their results raise questions about the education reform rhetoric asserting
that all children can learn to high standards. These findings indicate that teachers may
require intensive forms of support to develop instructional environments that promote
learning for low-achieving students.