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…

Students' competence in solving trigonometry has been in doubt but little attention has been given in the area of research. An assessment of students' answers to trigonometry problems is crucial to dealing with their conceptual challenges. This study employed a descriptive qualitative research design, with the goal of evaluating errors made by…

This research investigates errors and misconceptions among learners in algebraic education by utilizing Koch's error analysis method alongside the Structure of the Observed Learning Outcome (SOLO) taxonomy. The primary aim of the investigation is to discern the kinds of errors and cognitive stages demonstrated by Grade 9 students when engaged in…

Algebra is an important branch of mathematics which applies to many fields related to mathematics. However, many studies show algebra as posing problems even to the most gifted students. This phenomenon, therefore, necessitates more studies to be conducted in this area. As such, the study explored the types of errors that Grade 8 learners…

South African learners' performance in mathematics, both locally and internationally, has raised significant concerns, particularly in the realm of algebra. To address this issue, a mixed-methods study was conducted to explore the effectiveness of using algebra tiles to teach algebraic expressions. The study aimed to investigate algebraic…

Intellectual risk-taking, the act of engaging in learning by contributing an idea, question, or creative thought regardless of potential errors or judgments, is associated with many positive student outcomes; however, there is limited guidance on how to create an environment in which students feel empowered to be courageous in this way. In the…

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…

This qualitative study investigates the errors committed by Turkish EFL learners and the rate of spelling mistakes to grammar errors in learners' paragraphs. In order to examine these issues, 19 participants studying at a private high school in Turkey took part in this study. The qualitative data were collected through students' paragraphs written…

This study aimed to provide a deeper understanding of high school students' errors while solving genetics problems. Four students were asked to solve two genetics problems and participate in a modified think-aloud interview. Data from the interview, video clips of the problem-solving process, and test sheets were used to analyse participants'…

Problem-solving is an essential part of teaching, learning, and assessment of physics and mathematics. The continuing educational reforms have a deep impact on everyday teaching as well as working with talented students. In the Macedonian educational system, the curricula do not explicitly point out the connection between mathematics and physics,…

Purpose: It is crucial for teachers to understand what students already know and what they are thinking, before conducting their lessons, because identification of the cause is the first step of remedy. This study analyses students' conceptions that underlie the errors they make in algebraic expressions under two categories of conceptual…

Developing structure sense is an important part of learning algebra. We investigated learners' structure sense of algebraic expressions involving brackets. This led us to propose the constructs "surface structure" sense and "systemic structure" sense. Using a random sample of 58 Grade 10 learners scoring above 40% in a test, we…

In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

To date, many AI initiatives (eg, AI4K12, CS for All) developed standards and frameworks as guidance for educators to create accessible and engaging Artificial Intelligence (AI) learning experiences for K-12 students. These efforts revealed a significant need to prepare youth to gain a fundamental understanding of how intelligence is created,…