Research suggests that troubleshooting activities that require students to reflect on teacher-crafted erroneous examples; i.e., erroneous solutions to problems that correspond to widespread naïve ideas, are beneficial to learning. One possible explanation to these beneficial effects is that troubleshooting activities encourage students to test the…

Graded Troubleshooting (GTS) is a powerful routine that teachers can use easily to engender students' metacognitive thinking and boost their understanding of mathematics concepts and procedures. This article describes a new GTS activity designed to prompt students to efficiently exploit worked examples when asked to diagnose erroneous examples…

The present study investigates the effect of the separator lines on the learning of 8th grade students in simplifying algebraic expressions with parenthesis. An experimental study was designed to achieve this goal involving 60 girl students in 8th Grade (13 and 14 years old) randomly selected and assigned to two experimental and control groups.…

Written corrective feedback (WCF) in enhancing writing proficiency has been the subject of numerous studies, but few studies have examined students' perceptions about the value of feedback on their written errors. Language teachers use global tools and techniques to give students feedback on their written work. How feedback is delivered and…

This paper reports on the findings of a baseline study that fed on to a broader investigation exploring ICT integration in the teaching of functions. The baseline study was premised on the observation that the notion of function, despite being a fundamental and central idea in the mathematics school curriculum, presents pedagogical challenges to…

Because of the improvement-oriented nature of peer-feedback activities, students have to deal with errors (e.g., spelling and argumentation errors) when providing and processing peer-feedback on writing assignments. Despite the central role of errors in feedback activities, it is uncertain how students deal with errors and whether the dealing with…

Research on practice-based teacher education [PBTE], such as rehearsals or teaching simulations, assumes that preservice teachers [PSTs] prefer such practical approaches in comparison to more theoretical work. Few studies test this assumption or incorporate PSTs voices and perspectives on PBTE approaches. This study draws on survey data and…

This study examines the pedagogical content knowledge (PCK) of Lithuanian mathematics teachers at different stages of their professional careers. The research sample comprised 134 participants ranging from novice teachers with no teaching experience to experienced educators, with the longest career spanning 45 years. The participants were divided…

Enhancing the problem-solving skills of learners belonging to socio-economically disadvantaged groups is a great concern in general and particularly in the Indian context. Problem-solving skills are the most important skills of the 21st century for all learners to acquire necessary competencies. The main purpose of this work is to investigate the…

This study illustrates how two secondary mathematics teachers used students' incorrect answers as they supported students' engagement in collective argumentation. Three ways of supporting argumentation when students contributed incorrect answers are exemplified, and the structures of these arguments are investigated. Then, by focusing on the…

Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers' learning of these rules when being taught them explicitly. Our data come from academically motivated…

Effective written feedback is crucial to student learning and developing writing skills. Responding to student writing is a multifaceted and complex process that requires a more nuanced understanding of second language writing research. This study explored teachers' beliefs and practices about written feedback, which may be influenced by a range…

Engaging with learner errors in mathematics classrooms is an important aspect of teacher pedagogy which can support learner identification with mathematics. This study examined the opportunities that teachers provided for the construction of learner identities based on how the teachers spoke about and interacted with learner errors in two…

Background: Students make many errors in visual programming. In order to learn from these, it is important that students regulate their emotions and view errors as learning opportunities. Aims: This study aimed to explore to what extent momentary emotions, specifically enjoyment, anxiety and boredom, as well as the error learning orientation of…

Error analysis is an instructional strategy that can assist teachers to identify learners' areas of weakness in mathematics and that can point to remediation of those errors. This article explores the errors learners exhibit when solving quadratic equations by completing the square using Newman's Error Analysis Model. A research study explored the…