In 2011, the editors of this volume convened 64 researchers in mathematics education and psychometrics to promote collaboration around the measurement of constructs relevant to mathematics education. This monograph codifies much of the knowledge shared during that conference with the purpose of informing mathematics education researchers about psychometric models that can address a wide range of research questions. The underlying premise is that many mathematics educators use and work with measurement but are potentially limited in their work if they do not understand its nuances.
Leslie Nabors Oláh and André A. Rupp
Maria M. Maspons and Maria M. Llabre
This study examined the effects of training Hispanic college students in test-taking skills on the internal consistency and predictive validity of a test to predict mathematics achievement. Five hundred and thirty-five students were randomly assigned to two groups. Students in the experimental group were instructed in test-taking skills. Students in the control group received information on the college's educational programs. On the basis of the results of a computation test, the students were placed in either a basic skills or an algebra course. The test had slightly lower internal consistency and higher predictive validity for the experimental group.
Andrew Izsák, Erik Jacobson, and Laine Bradshaw
We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with measured quantities, not by executing computational algorithms, to solve problems. These components—each of which was grounded in past research—were attention to referent units, partitioning and iterating, appropriateness, and reversibility. A second part of the survey asked about teachers' professional preparation and history. We administered the survey to a national sample of in-service middle-grades mathematics teachers in the United States and received responses from 990 of those teachers. We analyzed responses to items in the first part of the survey using the log-linear diagnostic classification model to estimate each teacher's profile of strengths and weaknesses with respect to the four components of reasoning. We report on the diversity of profiles that we found and on relationships between those profiles and various aspects of teachers' professional preparation and history. Our results provide insight into teachers' knowledge resources for enacting standards-based instruction in fraction arithmetic and an example of new possibilities for mathematics education research afforded by recent advances in psychometric modeling.
Zalman Usiskin and Sharon Senk
Test instruments are an important element of almost every study in mathematics education, and the test that is used obviously affects the results of the study. Yet often a test is assumed both valid and reliable, and neither its content nor its psychometric properties are given scrutiny. The analyses Crowley and Wilson have done with the Van Hiele Geometry Test are welcome.
Lewis R. Aiken
Investigations concerned with the developing and influencing of attitude toward mathematics have dealt almost exclusively with enjoyment of the subject or anxiety in its presence. Although various psychometric procedures have been applied in constructing the measures of attitude employed in such investigations (see Aiken, 1972; Anttonen, 1969; Dutton, 1962; McCallon & Brown, 1971), the attitude dimension assessed by these instruments usually involves only one of the affective goals of mathematics instruction.
W. J. Lyda
While perusing the results obtained on a written test of thirty verbal “reasoning” problems in arithmetic, the writer noted the fact that on three of the problems the number, and hence the percentage, of secondary-school pupils who were average and/or above average in psychometric intelligence and who worked these problems correctly was distressingly low. Some idea of the situation can be gleaned from an examination of Table I which follows.
Joseph M. Petrosko
An analysis was made of the educational and psychometric quality of standardized mathematics tests aimed at high school students. Trained raters judged most of such instruments available in the United States. Tests were categorized into four areas: general mathematics (N=322), applied mathematics (N=26), algebra (N=122), and geometry (N=52). Results showed many tests to be low in common types of validity and reliability. General mathematics had, as a rule, tests with higher ratings than did the other content areas. Several implications were drawn from the study. Researchers in mathematics education should carefully analyze all aspects of tests to find those congruent with a given research need. Test developers should make renewed efforts to enhance the technical quality and curricular relevance of their products.
Andrew Izsák, Erik Jacobson, Zandra de Araujo, and Chandra Hawley Orrill
Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called the mixture Rasch model that allows for subgroups. The model was applied to middle-grades teachers' performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic. Results from psychometric modeling and evidence from video-recorded interviews and professional development sessions suggested that there were 2 subgroups of middle-grades teachers, 1 better able to reason with 3-level unit structures and 1 constrained to 2-level unit structures. Some teachers, however, were easier to classify than others.
Report Brief Report: The Role of Mathematics Teaching in Fostering Student Growth Mindset Sun Kathy Liu 1 * 05 2018 49 49 3 3 330 330 335 335 jresematheduc.49.3.0330 10.5951/jresematheduc.49.3.0330 Book Review A Review of Psychometric Methods in
3 3 163 163 176 176 jresematheduc.16.3.0163 10.5951/jresematheduc.16.3.0163 The Influence of Training Hispanics in Test Taking on the Psychometric Properties of a Test Maspons Maria M. 1 * Llabre Maria M. 2 * 05 1985 16 16 3 3 177 177 183 183