Diagnostic Tests – Teaching Algebra Conceptually, University of Otago, New Zealand

What are the diagnostic tests?

Four diagnostic tests were developed from the algebra learning model by the research team to help teachers have practical ways of gathering information about how students understanding algebra. Specifically, teachers wanted more specific information about the strategies students use with letter symbols when they represent generalised numbers, unknowns, and variables. The diagnostic tests were developed to inform teachers about what strategies students can or cannot use with letter symbols rather than to generate an overall test score (For more information, go to the Interpretation Guide with Scoring Rubrics section). These four diagnostic tests have been used by teachers on our research team in high school classrooms with their students.

The first diagnostic test examines how students understand unknowns in the context of solving equations. The second diagnostic test examines the prerequisite knowledge students are required to master before they can learn many of the algebraic letter symbol strategies of algebra. For students to use these strategies successfully, we have found that basic facts knowledge is absolutely crucial. Students need to be at stage 6 or above on the New Zealand Numeracy Development Project Number Framework for basic facts. The third diagnostic test examines how students can use letter symbols to express generality. The fourth diagnostic test examines if students can use multiple representations to describe relationships and whether they can find a relationship between two variables or just use the iterative pattern within one variable.

Donna’s discusses the usefulness of the diagnostic tests

Which test should I start with first?

The Solving Equations Diagnostic Test can be administered as one-on-one diagnostic interview or as whole class written diagnostic test. Instructions for interviewing individual students or testing whole classes have been written in a step-by-step way to help teachers who are new to using the diagnostic tests. (For more information, go to the Practical Instructions section.)

We suggest teachers follow the instructions carefully so that the results can be discussed meaningfully with other teachers who are also using the algebra framework. By engaging in discussions with other teachers, we noticed that we were better able to select appropriate ways to help our students learn the challenging ideas about algebra.