# Preservice elementary teachers' mathematical content knowledge of prerequisite algebra concepts

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## Date

2007

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## Publisher

Montana State University - Bozeman, College of Letters & Science

## Abstract

Research illustrating that student achievement is affected by teachers' knowledge advocates for K-8 teachers to be knowledgeable regarding prerequisite algebra concepts: (1) numbers (numerical operations), (2) ratios/proportions, (3) the order of operations, (4) equality, (5) patterning, (6) algebraic symbolism (including letter usage), (7) algebraic equations, (8) functions, and (9) graphing. The theoretical framework for the knowledge for teaching mathematics built for this study suggests that the mathematical content knowledge needed for teaching consists of specialized content knowledge in addition to common content knowledge. Specialized mathematical content knowledge extends beyond solving mathematical problems to encompass how and why mathematical procedures work and an awareness of structuring and representing mathematical content for learners. The effects of an undergraduate mathematics content course for elementary education students on preservice teachers' common and specialized content knowledge of prerequisite algebra concepts was investigated, using a pre-experimental one-group pretest-posttest design.

A quantitative, 51-item, multiple-choice instrument, developed specifically to measure both types of content knowledge with respect to prerequisite algebra concepts, was constructed from the Learning Mathematics for Teaching Project's Content Knowledge for Teaching Mathematics Measures question bank. This instrument was administered to all students enrolled in Mathematics for Elementary Teachers I (n = 48), at Montana State University, during the fall semester of 2006. Matched pairs t-tests, comparing pretest and posttest scores within the single sample, show significant gains (p = .000) in both common and specialized content knowledge and in all tested aspects of prerequisite algebra knowledge (numbers and equations/functions). Results also suggest a significant correlation (r = .716, p = .000) between preservice teachers' common and specialized content knowledge. Lastly, a oneparameter linear model was constructed to predict the number of participants to incorrectly answer each item, based on item difficulty. Items missed by notably more or less students than predicted were identified and analyzed. The one item students performed better than expected on addresses common content knowledge regarding a linear graph. The set of troublesome items address both common and specialized content knowledge of reading, writing, and representing functions in a variety of contexts and using ratios to write and solve proportions.

A quantitative, 51-item, multiple-choice instrument, developed specifically to measure both types of content knowledge with respect to prerequisite algebra concepts, was constructed from the Learning Mathematics for Teaching Project's Content Knowledge for Teaching Mathematics Measures question bank. This instrument was administered to all students enrolled in Mathematics for Elementary Teachers I (n = 48), at Montana State University, during the fall semester of 2006. Matched pairs t-tests, comparing pretest and posttest scores within the single sample, show significant gains (p = .000) in both common and specialized content knowledge and in all tested aspects of prerequisite algebra knowledge (numbers and equations/functions). Results also suggest a significant correlation (r = .716, p = .000) between preservice teachers' common and specialized content knowledge. Lastly, a oneparameter linear model was constructed to predict the number of participants to incorrectly answer each item, based on item difficulty. Items missed by notably more or less students than predicted were identified and analyzed. The one item students performed better than expected on addresses common content knowledge regarding a linear graph. The set of troublesome items address both common and specialized content knowledge of reading, writing, and representing functions in a variety of contexts and using ratios to write and solve proportions.