What is Measured in Mathematics Tests? Construct Validity of Curriculum-Based Mathematics Measures

Abstract Mathematics assessment is often characterized in the literature as being composed of two broad components: Computation and Applications. Many assessment tools are available to evaluate student skill in these areas of mathematics. However, not all math tests can be used in formative evaluation to inform instruction and improve student achievement. Mathematics curriculum-based measurement (M-CBM) is one tool that has been developed for formative evaluation in mathematics. However, there is considerably less technical adequacy information on M-CBM than CBM reading. Of particular interest is the construct that M-CBM measures, computation or general mathematics achievement. This study utilized confirmatory factor analysis procedures to determine what constructs M-CBM actually measures in the context of a range of other mathematics measures. Other issues examined in this study included math assessment in general and the role of reading in math assessment. Participants were 207 fourth-grade students who were tested with math computation, math applications, and reading tests. Three theoretical models of mathematics were tested. Results indicated that a two-factor model of mathematics where Computation and Applications were distinct although related constructs, M-CBM was a measure of Computation, and reading skill was highly correlated with both math factors best fit the data. Secondary findings included the important role that reading skills play in general mathematics assessment.

[1]  L. Fuchs,et al.  Identifying a Measure for Monitoring Student Reading Progress. , 1992 .

[2]  F. Bryant,et al.  Principal-components analysis and exploratory and confirmatory factor analysis. , 1995 .

[3]  M. Shinn,et al.  Differentiating Mildly Handicapped, Low-Achieving, and Regular Education Students , 1985 .

[4]  C. Hirsch.  Curriculum and Evaluation Standards for School Mathematics , 1988 .

[5]  J. S. Long,et al.  Testing Structural Equation Models , 1993 .

[6]  S. Deno,et al.  Curriculum-Based Measurement: The Emerging Alternative , 1985, Exceptional children.

[7]  Lynn S. Fuchs,et al.  The role of skills analysis in curriculum-based measurement in math. , 1990 .

[8]  M. Shinn,et al.  Improving General Education Instruction: Relevance to School Psychologists. , 1994 .

[9]  Ina V. S. Mullis,et al.  NAEP 1992 Mathematics Report Card for the Nation and the States. , 1993 .

[10]  Stanley L. Deno,et al.  Formative evaluation of individual student programs: A new role for school psychologists. , 1986 .

[11]  H. Marsh.  Δ2 and χ2 I2 fit indices for structural equation models: A brief note of clarification , 1995 .

[12]  Lynn S. Fuchs,et al.  Effects of Instrumental Use of Curriculum-Based Measurement to Enhance Instructional Programs , 1989 .

[13]  R. Fassinger.  Use of Structural Equation Modeling in Counseling Psychology Research. , 1987 .

[14]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[15]  Rick H. Hoyle,et al.  Confirmatory Factor Analysis , 1983 .

[16]  Therese M. Kuhs,et al.  Do Textbooks and Tests Define a National Curriculum in Elementary School Mathematics? , 1983, The Elementary School Journal.

[17]  R. P. McDonald,et al.  Goodness-of-fit indexes in confirmatory factor analysis : The effect of sample size , 1988 .

[18]  D. Marston,et al.  A curriculum-based measurement approach to assessing academic performance: What it is and why do it. , 1989 .

[19]  L. Fuchs,et al.  Effects of Systematic Formative Evaluation: A Meta-Analysis , 1986, Exceptional children.

[20]  S. Messick.  Test validity and the ethics of assessment. , 1980 .

[21]  Victor Nolet,et al.  Curriculum-Based Evaluation: Teaching and Decision Making , 2000 .

[22]  Mark R. Shinn,et al.  Curriculum-Based Measurement of Oral Reading Fluency: A Confirmatory Analysis of Its Relation to Reading. , 1992 .

[23]  Linda Taylor,et al.  An introduction to learning disabilities , 1986 .

[24]  Mark R. Shinn,et al.  Advanced applications of curriculum-based measurement , 1998 .

[25]  Mark R. Shinn,et al.  Curriculum-Based Measurement: Assessing Special Children , 1989 .

[26]  Roland H. Good,et al.  Contemporary perspectives on Curriculum-Based Measurement validity. , 1998 .

[27]  Gordon Korstange,et al.  California Achievement Tests , 1988 .

[28]  K. Stanovich.  How to think straight about psychology , 1985 .