Making Room for Inspecting Mistakes

Abstract

Select errors to discuss in class, and try these three alternative lesson ideas to leverage them and move students toward deeper understanding.

The Effect of Error Analysis-Based Learning on Proportional Reasoning Ability of Seventh-Grade Students

“…Monthienvichienchai and Melis (2006) pointed out the benefits of including mathematical errors as opportunities to learn through improving the incentive and motivation of the learner, his tendencies toward failure and success, and the correct understanding of mathematical concepts, in addition to improving the ability on mathematical reasoning, such as the correct application of rules in solving mathematical problems, training on beyond reasoning including critical thinking, selfmonitoring, and imposing self-interpretation to judge the solution steps as correct or false. Lischka et al (2018) used a broad definition of mathematical errors, such as the following: Students' errors can include misconceptions, erroneous solution processes, ineffective problem-solving strategies, or incomplete mathematical arguments. They considered the following three criteria to guide our decisions when determining whether an error is inspection-worthy for an entire class: If error analysis will move the students' understanding toward the mathematical goal of the lesson, if the error is common, and if the error represents a fundamental misunderstanding.…”

“…One of the factors influences and causes the students to feel difficulty in resolving mathematical problems is the mathematical error (Pomalato et al, 2020). From the viewpoint of Lischka et al (2018), mathematical errors are for the most part worth examining and analyzing in the classroom, and that they can be a powerful opportunity in teaching and learning mathematical subjects. The proportion is one of the mathematical topics rich in regular mathematical errors that deserve to be examined and analyzed in classroom situations, as well as that many students face many difficulties in it (Pomalato et al, 2020;Ozturk et al, 2021;Makamure and Jojo, 2022); and it is one of the mathematical topics directly related to proportional reasoning, which has not received much research about using mathematical errors as an opportunity to learn it; this gives educational researchers a reason to search and investigate them.…”

The impact of mathematics learning environment supported by error-analysis activities on classroom interaction

“…The teacher, in turn, performs his/her role in meditating on the student's errors, understanding what is going on in his/her mind, analyzing the procedural and conceptual errors and attempting to solve them in order to modify them with the student. Lischka et al (2018) used a broad definition of mathematical mistakes to include erroneous understanding, faulty procedures for solution, ineffective solution strategies in solving mathematical problems and incomplete mathematical arguments. Lischka et al (2018) defined three standards for mathematical errors that deserve examination and analysis in the classroom, including the objective of the lesson, whether error-analysis stimulates student understanding and achieves goals; error prevalence and whether the error is common; and whether the learner has a fundamental misunderstanding of basic mathematical concepts.…”

“…Lischka et al (2018) used a broad definition of mathematical mistakes to include erroneous understanding, faulty procedures for solution, ineffective solution strategies in solving mathematical problems and incomplete mathematical arguments. Lischka et al (2018) defined three standards for mathematical errors that deserve examination and analysis in the classroom, including the objective of the lesson, whether error-analysis stimulates student understanding and achieves goals; error prevalence and whether the error is common; and whether the learner has a fundamental misunderstanding of basic mathematical concepts. Furthermore, Priyani and Ekawati (2018) categorized mathematical errors into three categories; conceptual errors (misconceptions), procedural errors and the inability to complete solving a problem due to a previous error.…”

فاعلية التعلم القائم على تحليل الأخطاء الرياضية في تحسين‎ ‎القدرة على التفكير ما وراء المعرفي ‏لدى طلاب الصف السابع الأساسي

“…In light of these results, the study suggested a set of recommendations for educational researchers, mathematics curriculum designers and mathematics teachers. (Brown, 1978;Flavell, 1978) ‫ﻣﻔﻬﻮم‬ Metcalfe, 2016;Lischka, Gerstenschlager, Stephens, Strayer & Barlow, 2018;Bray, 2013;Borasi, 1987;Nesher,…”