In this paper we study epistemological transitions across an intended engineering curriculum and recommend strategies to assist students in attaining the increasingly complex concepts and insights that are necessary for transition to advanced levels of study. We draw on Legitimation Code Theory [Maton, Karl. 2014, "Knowledge and Knowers:…

Helping students learn to think like a physicist is an important goal of many introductory physics courses. One characteristic distinguishing more experienced physicists from novice students is that they make better use of problem solving as a learning opportunity. Experts were found to spend more time than novices in monitoring their work,…

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

This column presents ideas and techniques to enhance science teaching. In this month's issue an upper elementary Science, technology, engineering, and math (STEM) challenge brings an engineer into the classroom while emphasizing cooperation, communication, and creativity. STEM activities come in various shapes and sizes. Some are quite involved…

This study is concerned with tensions between the two different perspectives on the concept of angle: angle as a static shape and angle as a dynamic turn. The goal of the study is to explore how teachers cope with these tensions. We analyze scripts of 16 in-service secondary mathematics teachers, which feature a dialogue between a teacher and…

Novel analytical solutions based on the Lambert W function for two problems in ultrafiltration and diafiltration are described. Example problems, suitable for incorporation into an introductory module in unit operations, membrane processing, or numerical methods are provided in each case.

Worldwide interest in Japanese Lesson Study as a vehicle to improve mathematics teaching practice through professional learning has left largely unanswered questions about the extent to which it can be replicated elsewhere. This paper reports on a small-scale research project, "Implementing structured problem-solving mathematics lessons…

The purpose of the present study was to portray students' misconceptions and errors while solving conceptually and procedurally oriented tasks involving length, area, and volume measurement. The data were collected from 445 sixth grade students attending public primary schools in Ankara, Türkiye via a test composed of 16 constructed-response…

Studying worked examples providing problem solutions to learners usually leads to better test performance than solving the equivalent problems without guidance, demonstrating the worked-example effect. The generation effect occurs when learners who generate answers without guidance learn better than those who read answers that provide guidance.…

The plane problem is a real-world problem, presented without any suggestion as to how it might be solved. It arose unexpectedly as the author was messing around on the internet, not thinking about maths at all. She did not encounter the problem in a maths lesson, nor as homework in the middle of a unit on a particular topic, and so she had no…

This study explored an alternative assessment procedure to examine learning trajectories of matrix multiplication. It took rule-based analytical and cognitive task analysis methods specifically to break down operation rules for a given matrix multiplication. Based on the analysis results, a hierarchical Bayesian network, an assessment model,…

Engagement in problem-solving and mathematical discussion is critical for learning mathematics. This research review describes a gap in the literature surrounding engagement of students with Learning Disabilities in standards-based mathematical classrooms. Taking a sociocultural view of engagement as participation in mathematical practices, this…

This article focuses on the importance of activity-based teaching in understanding the mole concept and the vital role of basic mathematical operations. It describes needs-based training for teachers in a professional development programme in India. Analysis of test results before and after the training indicates that teachers improved their…

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

In this article, we present a new critique of the Completion Agenda as inscribed in "Reclaiming the American dream," a policy document published in April 2012 by the American Association of Community Colleges. Our critique is grounded on the premise that community colleges should improve completion rates, but this should be motivated by…