Diagnostic of Students' procedural errors in Addition and subtraction of decimals Using Bayesian Networks

Decimal numbers are one of the most important and useful topics in mathematical education. However, students have trouble with decimal numbers. One way to investigate the reason of difficulty in working decimals for the students is through error analysis. Diagnosis of errors in procedural skills is difficult because of their unstable nature. This study investigates the diagnosis of procedural errors in students’ decimals addition and subtraction performance, by proposing and evaluating a probability-based approach using Bayesian networks. This approach assumes a causal network relating hypothesized decimals addition and subtraction errors to the observed test items. This study is practical and quantitative. The population of this study included all the sixth-grade students of Birjand city in academic year 2017 – 2018. A sample consisted of 407 students was selected through multi-stage sampling method. Network performance was evaluated by two types of testing situations: using binary data (scored as correct or incorrect) and diagnostic use of wrong answers by a multi-choice test. Results showed Bayesian network with binary data had poor performance in errors diagnosis but diagnostic use of students’ wrong answers improved network performance. The Kappa agreement rate for the Bayesian network with wrong answers reached above 90%. Our results suggest that reliable diagnosis of errors can be achieved by using a Bayesian network framework with students’ wrong answers.