Identifying and dealing with student errors in the mathematics classroom: Cognitive and motivational requirements

Abstract

IntroductionMathematics classrooms are typically characterized by considerable heterogeneity with respect to students’ knowledge and skills. Mathematics teachers need to be highly attentive to students’ thinking, learning difficulties, and any misconceptions that they may develop. Identification of potential errors and appropriate ways to approach them is crucial for attaining positive learning outcomes. This paper explores which knowledge and affective-motivational skills teachers most require to effectively identify and approach students’ errors.MethodsTo address this research question within the German follow-up study of the Teacher Education and Development Study in Mathematics (TEDS-M), 131 primary school mathematics teachers’ ability to identify students’ errors was assessed based on (a) a digitalized speed test showing different students’ solutions in a written notation and (b) three video vignettes that showed different scenes from mathematics classes. These scenes dealt, among other things, with children who struggled with the lesson’s mathematical content. Teachers were asked to analyze students’ thinking and to determine how best to react. In addition, teachers’ mathematics pedagogical content knowledge, mathematical content knowledge, and beliefs were assessed in separate tests and served as predictors for teachers’ abilities to identify, analyze, and deal with students’ errors.ResultsThe results indicate that all components are interrelated. However, path analysis reveals that teachers’ ability to deal with students’ errors is mainly predicted by their constructivist beliefs while their ability to quickly identify typical students’ errors is largely dependent on their mathematics content knowledge.DiscussionThe results show the central filtering function of beliefs. Teachers who believe that students must shape and create their own learning processes are more successful in perceiving and analyzing student errors in classroom situations. They may understand errors as learning opportunities and - thus - pay specific attention to these occurrences.

Future teachers’ reflections on mathematical errors made in their teaching practice

“…Identifying their mathematical errors is one of the skills teachers need to effectively address student errors, and to reframe them as valuable for future learning processes. However, in the research studies consulted seeking to identify the knowledge and competences teachers need to productively work with student errors (Hoth et al, 2022), this skill does not appear in a specific manner. It is included in the content knowledge of the correct solution and possible causes of the error.…”

Misconceptions of mathematics in higher education universities when learning with Google classroom based on learning styles and gender differences

“…One study found that various types of conceptual errors depend on students' learning styles (Winarso & Toheeri, 2021). Another study analyzed students' errors in learning mathematical problem-solving based on differences in their learning styles (Rushton, 2018;Hoth, Larrain & Kaiser, 2022). The study identified the relationship between learning styles and procedural errors made by students.…”

Teacher noticing in mathematics education: a review of recent developments

“…In terms of affective-motivational dispositions, teachers' instructional performance is likely to be shaped by their professional beliefs (Blömeke & Kaiser, 2017). While beliefs can be generally understood as "psychologically held understandings, premises, or propositions about the world that are felt to be true" (Richardson, 1996, p. 103), research on mathematics teachers' professional beliefs has focused on beliefs about the nature of mathematics as well as beliefs about teaching and learning mathematics (e.g., Hoth et al, 2022). However, previous research on teacher noticing has primarily addressed the role of beliefs about diversity (Keppens et al, 2021;Roose et al, 2019).…”

“…Notably, recent studies have explored the promotion of teacher noticing using hypothetical learning trajectories, which may provide knowledge specific to this domain (Callejo et al, 2022;Moreno et al, 2021;van den Kieboom, 2021). Teachers' beliefs can moderate the relationship between teacher noticing and knowledge, as highlighted by Hoth et al (2022). The limited evidence suggests that constructivist beliefs and student-centered orientations are associated with more elaborate teacher noticing.…”