Barlow et al. (2018) discussed three types of mistakes worthy of inspection: procedural errors, inappropriate solution processes, and misconceptions. Here, the authors focus on procedural errors, as these often led the teachers in their professional development project to limit their inspection of mistakes to correcting. Despite this narrow focus,…

The inspection of mistakes can play a powerful role in an individual's learning process (Boaler 2015). The purpose of this article is to support the reader in selecting mistakes that can be leveraged to benefit the learning of all students. Specifically, the authors focus on "which" and "why": "which" mistakes to…

Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking.…

Research has shown that any assumption that L2 learners of English do well to rely on the feedback provided by generic spell checkers (for example, the MS Word spell checker) is misplaced. Efforts to develop spell checkers specifically for L2 learners have focused on training software to offer more appropriate suggestion lists for replacing…

For English language learners (ELLs) to productively engage in classroom discussions that foster language development, content knowledge, and analytical practices, teachers must create a trusting classroom culture. How do we ensure that all ELLs have opportunities to productively use oral language in academic settings? And how do we ensure that…

For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…

This paper being an extension of Bhattacharjee (2012) is very much relevant to Year 9 to Year 10A in the "Australian Curriculum: Mathematics". It also falls within the purview of class IX to class XII curriculum of Mathematics in India (Revised NCERT curriculum) for students aged 14-17 years. In Bhattacharjee (2012), the discovery of…

Student errors are springboards for analyzing, reasoning, and justifying. The mathematics education community recognizes the value of student errors, noting that "mistakes are seen not as dead ends but rather as potential avenues for learning." To induce specific errors and help students learn, choose tasks that might produce mistakes.…

Middle school is a crucial transition period for students as they move from concrete to algebraic ways of thinking. This article describes a sequence of instruction geared toward helping prospective middle school instructors teach the topic of percentages.

Evidence from recent research suggests that in the UK the public perception of errors in national examinations is that they are simply mistakes; events that are preventable. This perception predominates over the more sophisticated technical view that errors arise from many sources and create an inevitable variability in assessment outcomes. The…

When students make mistakes, have misconceptions, or are simply wrong, how their teachers respond either builds new skills and understanding or reinforces errors. An intentional approach to responding when students don't get it includes questions to check for understanding, prompts for cognitive and metacognitive work, cues to divert attention,…

This essay attempts to distinguish and discuss the importance and limitations of different ways of being wrong. At first it is argued that strictly falsifiable knowledge is concerned with simple (instrumental) mistakes only, and thus is incapable of understanding more complex errors (and truths). In order to gain a deeper understanding of mistakes…

Surprise is of great value for learning, especially in cases where deep-seated preconceptions and assumptions are upset by vivid demonstrations. In this essay, Jonathan Adler explores the ways in which surprise positively affects us and serves as a valuable tool for motivating learning. Adler considers how students' attention is aroused and…

The focus of this paper is the use of National Assessment Program in Literacy and Numeracy (NAPLAN) items to develop students' competence in reading mathematical text, to promote thinking strategies including estimation, and to evaluate alternative solutions for errors and misconceptions. Showing students test items and discussing strategies for…

A discussion of misunderstandings occurring in the college classroom looks at the common sources of misconceptions and offers three ways to diagnose and address them: (1) asking students to think aloud as they solve problems; (2) having students teach course topics; and (3) reviewing students' notes with them. (MSE)