Abstract:

Diagnostic teaching, the ability to qualitatively analyze students’ error patterns, provides teachers the opportunity to identify students’ types of errors and to determine the misconceptions and difficulties of their students (Ashlock, 2010; O’Connell, 1999). It is important that mathematics teachers examine students’ erroneous mathematics concepts and/or procedures to provide effective instruction to their students. Analysis of error patterns in computation problems is a valuable assessment tool for teachers because it shows with what type of conceptual and/or procedural knowledge the student is having difficulty understanding. By analyzing the errors and identifying the systematic patterns of mistakes students make when solving computation problems, teachers will be able to plan appropriate and effective interventions to improve students’ performance (Luneta & Makonye, 2010; Riccomini, 2005).

The purpose of this study was to identify the most common error types in addition and subtraction calculation made by 697 Portuguese elementary students from first to fourth grade. We also investigated which variables uniquely contributed to those students’ performance in addition and subtraction computational tasks. Our goal is to offer a diagnostic analysis to guide teachers in the evaluation of their students’ error patterns in order to plan effective interventions that address the specific needs of each student.

In the present study, we examined addition and subtraction calculation tasks of 697 students from first to fourth grade, from seven elementary schools in Portugal. Students completed a written assessment test of mathematical knowledge developed by Lopes and Bueno (2014). Two researchers graded all tests three times. The first time, they identified correct/incorrect items. The second time, they used a code system to identify the types of errors made (e.g., MC= miscalculation; FR = failure to regroup). The system code used was based on Engelhardt’s (1977) and Träff and Samuelson’s (2013) work. In addition to those types of errors, we found other errors that did not fit the coding system. We noted all different types of errors found in students’ answers and added them to the original coding system. We re-examined all the problems using the new coding system.

Data frequency analyses showed that the most common type of error was miscalculation for both addition (n =164; 38.6%) and subtraction (n = 180; 21.7%) among the 697 students. Miscalculation in both addition and subtraction was also a common type of error in all grade levels. Findings from the hierarchical regression analyses indicate that students’ performance differences emerged as a function of error types which indicate students’ type of difficulties. Our qualitative data analyses suggest that instruction needs to consider students’ error patterns in order to plan effective interventions that address the specific needs of each student. These findings indicate that early intervention on students’ understanding, procedural and strategic knowledge of pre-skills may be an effective way to avoid certain type of errors in the upper grades. Learning mathematics with understanding requires teachers’ ability to identify students’ type of errors that reflect students’ lack of understanding of conceptual knowledge.

Keywords:

Mathematics, education, error patterns, error analysis, elementary grades.