Bridging the Gap: Applying Algebra Cognition Research to Develop and Validate Diagnostic Classroom Algebra Testlet

Co-Principal Investigator(s): Lucariello, Joan

In the first phase of this project, the researchers are developing a series of short testlets designed to identify students' abilities to solve particular types of algebra problems and whether they possess various specific algebraic misconceptions that have been identified by previous research as being fairly common. Phase 2 studies will examine whether testlets identify the misconceptions they are designed to identify. Multiple methods will be used in a series of studies involving eighth and ninth grade algebra students, including studies comparing testlet performance with predictions of teachers and with student classroom work, and pretest-posttest studies examining the effects of targeted feedback or instruction on testlet performance. Among these will be a series of two group studies (one for each targeted algebraic misconception) in which 20 students who are identified with the misconception based on testlet performance will be randomly assigned to one of two groups (Group A or B). Students in Group A will work with an individual tutor who will provide instruction over a short period of time; students in Group B will not receive any instruction during this time. After the instructional intervention for students in Group A is complete, all students Groups A and B will retake the testlet. Students in Group B will then work individually with a tutor and all students will be tested for a third time. Changes in students' testlet performance will then be compared between the two groups.

The final phase of the project will involve an examination of whether teachers can use testlets to identify misconceptions of their eighth and ninth grade students, and to respond appropriately. Researchers will instruct teachers in how to use the testlets, after which pretest-posttest gains in testlet performance will be compared across four groups of students: 1) those who do not demonstrate a specific misconception, 2) those who have the misconception and who receive no targeted instruction, 3) those who have the misconception and receive inappropriately-targeted instruction (i.e., targeted at the wrong misconception), and 4) those who have the misconception and receive appropriately-targeted instruction. The prediction is that students in the fourth group will show greater pretest to posttest improvement in testlet performance than will students in the other three groups.