Strategies are proposed that promote use of an Integrated Applied Mathematics (IAM) approach to enhance teaching of advanced problem-solving and analysis skills. Three scenarios of 1-dimensional transport processes are presented that support using Error Function analyses when considering short time/small penetration depths in finite geometries.…

Like other health care practices, the increasing complexity in dentistry signals the need for a reconceptualisation of dentist professional learning. Professional dental bodies, at large, still privilege formal continuing professional development (CPD) provisions focusing on off-the-job activities despite growing evidence that much invaluable…

Using data from teaching experiments and theories from quantitative reasoning, we built second-order accounts of students' mathematics with regards to how they conceived rate of change through operating on existing quantities. In this report, we explain three different ways STEM undergraduates structurally conceive rate of change as they…

Technology can play a pivotal role in mathematics education. Qualitative methods were used to report on how a Year 1-2 teacher incorporated "Conveyance technology" (iPads), to support the teaching and learning of mathematics through student reasoning and problem-solving. The study was conducted in Australia. A single case was chosen,…

Identifying students' difficulties in understanding Gauss's and Ampere's laws is important for developing educational strategies that promote an expertlike understanding of the field concept and Maxwell's equations of electromagnetic phenomena. This study aims to analyze and compare students' understanding of symmetry when applying Gauss's and…

Among different transitions that happen in a young person's life, transition to adulthood can be one of the most challenging. The new post-school environment requires increased self-determination, including self-awareness, self-advocacy, self-management, and other important skills that help one function as an independent adult. Because it takes…

When researchers code behavior that is undetectable or falls outside of the validated ordinal scale, the resultant outcomes often suffer from informative missingness. Incorrect analysis of such data can lead to biased arguments around efficacy and effectiveness in the context of experimental and intervention research. Here, we detail a new…

As a foundational evolutionary concept, the Hardy-Weinberg principle should be taught enthusiastically in introductory biology courses. In a companion Perspectives paper, I made the case that students are often given limited or incorrect information on the HW principle due to a lack of mastery or confidence on the part of their teachers. The…

Diagnostic assessment (DA) in language classrooms is reported to have a substantial role in providing immediate and quality feedback for remedial work that would improve learning (Alderson, Brunfaut & Harding; 2014; Hattie & Timperley, 2007; Huhta, 2008; Jang & Wagner, 2013). However, applying DA in class remains a challenge for many…

A historical review of mathematics textbooks suggests a canonical method to solving equations that teachers often see as "the" way to solve equations. In this paper, we examine data from a nationally-distributed sample of 524 secondary mathematics teachers who responded to scenario-based survey items that represent the instructional…

This article explores the process of finding the Fermat point for a triangle ABC in three dimensions. Three examples are presented in detail using geometrical methods. A delightfully simple general method is then presented that requires only the comparison of coordinates of the vertices A, B and C.

This paper examines a problem described as widespread and long-standing in mathematics education: supporting pupils into multiplicative reasoning, a form of reasoning that has been noted as central to large tracts of secondary mathematics and beyond. Also noted, however, is a persistent perception of multiplicative situations only in terms of…

Productive struggle leads to productive classrooms where students work on complex problems, are encouraged to take risks, can struggle and fail yet still feel good about working on hard problems (Boaler, 2016). Teachers can foster a classroom culture that values and promotes productive struggle by providing students with challenging tasks. These…

This teaching note outlines an innovative simulation game realized in response to post-pandemic experiential learning needs. The game introduces a fictional African country experiencing a series of political and financial shocks. Students are assigned membership in social groups and must implement the national policies that would improve outcomes…

This mixed-method study examines the relationship between classroom discussion and student performance in twenty 3rd and 4th grade classrooms in northern California with 50% English language learners (ELLs). Discussions were scored on features including use of multiple approaches for solving problems, students' opportunities to speak, equitable…