Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

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,…

Physics teachers need diagnostic competence to effectively identify students' misconceptions, but studies have yet to sufficiently investigate how this competence can be advanced through various instructional strategies. In this study, we compared a problem-solving strategy against an example-based strategy in advancing diagnostic competence in…

Peer Instruction gives practice in the abstract language of physics, addresses common misconceptions among students, and is more effective than traditional lecturing. However, it is not clear what makes Peer Instruction effective nor how we might improve the method. An emerging perspective is that what makes Peer Instruction effective is how it…

Background: Providing students with worked out problem solutions is a beneficial instructional technique in STEM disciplines, and studying examples that have been worked out incorrectly may be especially helpful for reducing misconceptions in students with low prior content knowledge. However, past results are inconclusive and the effects of…

Prior research highlights a positive effect of incorrect worked examples on mathematics learning. Yet the mechanisms underlying these benefits are unclear. To investigate potential mechanisms of the benefits of various worked example types, we examined process data from a previously published classroom-based experiment. More specifically, we…

Object-oriented programming distinguishes between instance attributes and methods and class attributes and methods, annotated by the "static" modifier. Novices encounter difficulty understanding the means and implications of "static" attributes and methods. The paper has two outcomes: (a) a detailed classification of aspects of…

Background: The COVID-19 pandemic and the shift to digital learning materials have dramatically reduced the use of paper-based textbooks in higher education. In the field of engineering, students need a comprehensive understanding of mathematical concepts, which can be achieved through the use of e-textbooks. These digital learning materials can…

This article provides insights into Grade 11 learner understanding of the roots of quadratic equations, how learners used solution strategies to find equations with given roots, how they determine the unknown values and the other root when one root is given and how they determine the unknown values when two roots of the equation are given. The…

This study examined the extent to which college algebra instructors employ pedagogical practices previously found to assist students master difficult STEM content material and address their own previous math deficits. Faculty classroom behaviors were assessed with a modified version of the Generalized Observation and Reflection Platform (GORP).…

Although testing is used mainly for assessing student learning, a new teaching strategy called concept-point recovery (CPR) makes testing a learning opportunity for engineering students to review errors and misconceptions. CPR allows students to regain points by reviewing wrong answers and explaining the solution process to the instructor to…

Effective and data-driven math instruction can maximize student learning and achievement. This Spotlight will help analyze best practices for developing math word problems; explore how showing students both the correct and incorrect solutions can improve their understanding; investigate math 'fact fluency' and strategies for strengthening it;…

The article presents one of the possible ways of overcoming the misconception that is one of the myths about mathematics, which says that teaching mathematics is based only on the transfer of mathematical knowledge in the finished form -- often in the form of certain algorithms. The newly proposed method of access to mathematics teaching is…

Understanding students' mathematical thinking in problem solving process plays an important role in facilitating the solution. Hence, teachers or pre-service teachers need to understand students' thoughts and guide them to the correct answer. The aim of this study was to examine pre-service teachers' approaches to guiding students in problem…

Despite the introduction of Common Core State Standards and the National Council of Teachers of Mathematics urging educators to explore fundamental concepts in mathematics at a deeper level, the majority of mathematics education has remained aimed at initial skill acquisition. The result has led to students learning to mimic a standard set of…