AN ALGEBRAIC THINKING SKILL TEST IN PROBLEM-SOLVING FOR SEVENTH GRADERS

Abstract

Diagnostic tests have been developed previously to measure algebraic thinking skills; however, the tests do not specifically address algebraic problem-solving. Thus, an Algebraic Thinking Test (ATT) Instrument was developed to measure algebraic thinking skills in problem-solving involving linear equations. ATT comprises nine open-ended questions with three algebraic thinking constructs: Generalized Arithmetic, Functions and Modeling. Generalized arithmetic involves students in efficient calculation and generalization; functional involves identifying number patterns, while modelling involves solving open-ended problems, identifying similarities, and performing calculations involving variables. This study is meant to determine the quality of ATT instruments through the validity and reliability analysis using the Rasch Measurement Model. The sample consisted of 120 seventh graders aged 12 to 13, selected from two secondary schools in the Tuaran district, Malaysia. The instrument was found to have a strong dimensionality and high construct validity. The reliability of Cronbach Alpha (KR-20) demonstrated a value of .90 (very high), and item and respondent reliability of .98 (excellent) and .86 (good), respectively, with an item separation index of 6.29 and 2.45 for the person separation index. ATT has good validity and high reliability in measuring algebraic thinking skills among seventh graders in secondary schools. Keywords: algebraic thinking skills, linear equations, problem-solving, Rasch analysis, validity and reliability