A problem-solving capstone course for mathematics and mathematics education majors can help majors synthesize material learned in the major, create a basis for lifelong learning in the discipline, develop confidence, and promote interest in graduate study. Such a course may also play a role in departmental assessment of the major. This article…

The purposes of this study are to (1) understand how elementary school students use writing to reflect their learning and problem solving in mathematics; and (2) to explore how teachers adapt their instructional approaches based upon reflection on students' writing. This qualitative exploratory study spanned six weeks and included 18…

This research study was specifically concerned with the development, testing, and revision to an instructional theory for studying the mathematical concepts of equivalence and equation solving with multiple representations and multiple tools. Following a design research approach, a collaborative teaching experiment was conducted with a ninth-grade…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…

The purpose of this study is to contribute insights into how collaborative activity can help promote students' mathematical understanding. A group of six high school students (15- to 16-year olds) worked together on a challenging probability task as part of a larger, after-school, longitudinal study on students' development of mathematical ideas…

This article reflects critically on simulations. Building on the authors' experience simulating the Palestinian-Israeli-American Camp David negotiations of 2000, they argue that simulations are useful pedagogical tools that encourage creative--but not critical--thinking and constructivist learning. However, they can also have the deleterious…

This study revisits case learning's effects on student engagement and assesses student learning as a result of the use of case studies and problem-based learning. The author replicates a previous study that used indirect assessment techniques to get at case learning's impact, and then extends the analysis using a pre- and post-test experimental…

There is no doubt that a lesson plan is a necessary product of Lesson Study. However, the collaborative work among teachers that goes into creating that lesson plan is largely under-appreciated by non-Japanese adopters of Lesson Study, possibly because the effort involved is invisible to outsiders, with our attention going to its most visible…

As education has turned towards technology to provide academic support, the incidence of e-tutoring has grown due to decreasing educational budgets and as a potential remedy for the generational digital divide. However, many service-learning e-tutoring studies have focused on tutees' academic achievement and tutors' cognitive development rather…

To help students master challenging, threshold concepts in physiology, I used the flipped learning model in a human anatomy and physiology course with very encouraging results in terms of student motivation, preparedness, engagement, and performance. The flipped learning model was enhanced by pre-training and formative assessments that provided…

Traditionally, the difficulties associated with mathematics were largely seen as coming from the cognitive demands of mathematics itself. It is now accepted that language and mathematics are connected in mathematics learning and teaching, and, the potential challenges of language in mathematics have been investigated by a number of researchers.…

In this application brief I share a case study assignment I used in my "Leadership in Complex Organizations" classes to promote creativity in problem solving. I sorted Ph.D. students into two teams and trained them to use creative writing techniques to "encode" theory into their own cases. A sense of competition emerged. Later,…

To meet the immense challenges society faces in areas such as energy, health, and environmental protection, science teachers and teacher educators need to invest in the creation of classroom cultures that turn the intellectual heavy lifting over to the students while developing students' identities as competent learners. The vision is that…

This study aims to understand students' constructs regarding mathematical problems. Fifty-one Taiwanese primary students' constructs are elicited using interviews with the repertory grid technique based on their responses to creative and non-creative problems. The results of qualitative data analysis show that students' initial constructs can be…

This study responded to a national call to improve the outcomes in mathematics in the Grade 12 matriculation examination in South Africa by reporting learners' perceptions of the introduction of computer-assisted learning in their mathematics classrooms. Three Grade 12 mathematics classes in a peri-urban school in South Africa were visited over a…