Algebra is the gateway for students seeking careers in science, technology, engineering and mathematics (STEM). While much research has been focused on the skills required to learn basic mathematics, fewer investigations have been dedicated to those necessary for learning algebra.
Thanks to a $1.5 million grant from the Institute for Education Sciences, researchers from the University of Houston and Vanderbilt University will conduct a four-year study devoted to understanding factors connected with how students learn algebra.
Principal investigators are Paul Cirino, UH associate professor of psychology; Tammy Tolar, research associate at UH's Texas Institute for Measurement, Evaluation and Statistics (TIMES) and Lynn Fuchs, Nicholas Hobbs Professor of Special Education and Human Development at Vanderbilt University.
"We are continuing to learn much about early math development and difficulty," Cirino said. "What we know about how students learn and understand algebra, however, pales in comparison. What we want to do is fill in some of the gaps in the current research literature."
Titled "Arithmetical and Cognitive Antecedents and Concomitants of Algebraic Skill," the study will track students in grades three through nine.
Among the researchers' objectives is to evaluate whether procedural skill and conceptual knowledge are separate but related abilities in relation to learning algebra.
Procedural skills are used by students when solving routine textbook problems ("Solve: 3x + 5 = 17") and can involve implementing algorithms. Conceptual knowledge is used when students must instead rely on their understanding of the underlying mathematical principles (the associative property of multiplication) to arrive at a potential solution, as when problems are presented in a novel way ("If (3p)r = 9 then pr = __").
"There has not been enough research to indicate the differences and similarities between procedural and conceptual knowledge," Cirino said. "We're interested in distinguishing between these two types of knowledge and learning more about students who might be weak in either area. This will help us understand if there are certain characteristics among these students or if there is a certain of way of teaching that can benefit them."
Another goal of the study is to evaluate the factors that help students understand more basic arithmetic and whether such factors impact how they learn algebra. Cirino, Tolar and Fuchs will observe student data from third - sixth graders. They will follow these students and their peers as they begin learning algebra.
"Both basic arithmetic and algebra share similar procedures and concepts," Cirino said. "Weak arithmetic, conceptual or procedural skills might have implications on how well students grasp algebra. If educators are aware of these kinds of predictors, it could have implications for the way basic math is taught in schools."
Cirino and his colleagues also will explore how the cognitive skills (language, memory, visual-spatial skills) relative to basic math are applied when learning algebra.
"We know that algebra is very difficult for many students," Cirino said. "Many students don't pass their algebra classes or fully understand the material. We need to understand why that is. This study will help to do that by evaluating the skills that contribute to learning algebra and whether there are different types of knowledge that require different combinations of skills."
Cirino, Tolar and Fuchs will observe two student cohorts. One is based in Texas and another is in Tennessee. The Tennessee cohort will include students in eighth and ninth grades taking algebra. Elementary and middle school data from these same students had been compiled during a previous study. The Texas cohort will include students in middle school whose arithmetic progress will be tracked through their introduction to algebra in eighth and ninth grades.
The IES is the research arm of the U.S. Department of Education. Its mission is to provide evidence regarding effective education practices and policies. Through its sponsored research efforts, the IES aims to improve educational outcomes for all students, particularly those at risk of failure. To learn more about the IES, visit http://ies.ed.gov/.