LAWRENCE — Everyone has taken a math test at some point and saw they score they received, based on the number of questions they got right. The problem with that age-old method of testing is, while it reveals which answers were correct and which weren’t, it doesn’t give a full understanding of how well students grasp mathematical concepts and how well they fully understand the material. A University of Kansas professor has co-authored and contributed to a new book that examines how psychometrics — a field aimed at better testing and measurement — and mathematics educators can work together to create better math teachers.
Jonathan Templin, associate professor of educational psychology and associate research professor at the Achievement and Assessment Institute at KU, has co-edited “Psychometric Methods in Mathematics Education: Opportunities, Challenges, and Interdisciplinary Collaborations" with Andrew Izsák of the University of Georgia and Janine T. Remillard of the University of Pennsylvania. The peer-reviewed monograph was published by the National Council of Teachers of Mathematics and was born from a National Science Foundation-supported conference that was among the first to bring together scholars who study how to best teach math and those who study testing and assessment.
Templin, a specialist in psychometrics and statistics, said the conference revealed overlap between the two fields, examined how they could work together and discussed strategies for future research combining the disciplines. The ultimate goal of such research is to both prepare better math teachers and design better tests that more fully reveal what each student understands about math concepts.
“We see what the student got right and want to see what they know based on that,” Templin said of psychometrics. “It’s basically the advanced statistics, not just the number of items correct, but determining the quality of items and making sure a score is valid.”
Throughout the book’s 10 chapters, scholars from across the country outline opportunities and challenges for research in combining mathematics and psychometrics research. In the book’s first chapter, Izsák and Templin detail work they’ve done with teachers on how to know mathematics material, how to know the material in a way that they can relay to students through teaching and how to design better, more valid tests. Other chapters examine how to develop instruments to measure teaching knowledge in math, developing assessments for educational research, applications of various academic theories in mathematics education research, integrating psychometric methodology into educational research and other topics.
The book can be especially helpful to scholars looking to begin research in mathematics education, psychometrics or a combination thereof, as well as people who are educating future math teachers. The overarching goal is to facilitate research that finds better ways to integrate the two fields, thereby creating teachers who have a better understanding of what their students do and do not know, as well as helping test designers create tests that better reveal students’ mathematical understanding.
“People sometimes think getting your test score is like getting your height or weight. It’s not like that at all, though,” Templin said. “We know how height and weight are defined, but how you choose to define items on a test is important. We try to get a better understanding of that and help students learn more.”
“Psychometric Methods” details what test designers need to do to determine what students understand about mathematics, how they can share that data with teachers and what teachers can then do, in turn, to relay that information to the students. For example, if a student misses or struggles with a word problem, a well-designed test could determine if the student simply miscalculated or perhaps struggled with the problem due to reading trouble, not being proficient in English or other factors. Psychometrics could be applied in any educational subject, but as it relates to math, the book’s authors relate how taking data produced by tests can control for numerous factors and provide more robust data, which in turn can improve both teaching and learning.
“The newer way we’re doing psychometrics now is to do just that,” Templin said of analyzing testing results. “We’re asking, ‘What do you want to do with the test?’ Then trying to provide a better number with more validity.”