A common exercise given to students early in a molecular biology course is the creation of a restriction map of a plasmid "digested" by two restriction enzymes (RE). Meanwhile, students have learned from an early age about the properties and analyses of circles in their mathematics courses. But it is rare for students to learn using…

Nowadays, it is essential to promote an interdisciplinary approach in classrooms, integrating disciplines such as biology and mathematics. This necessitates familiarity with specific problem-solving practices employed by the expert community, such as mathematical modelling. This perspective piece explores a mathematical modelling practice to…

In XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus' "Arithmetica", Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. Of this statement, however, Fermat…

Mathematical problem-solving places heavy demands on children's developing working memory capacity. This review examines how offloading numerical information using embodied (e.g. finger counting) or external tools (e.g. manipulatives) can reduce cognitive load and improve mathematical task performance. Strategic offloading emerges in childhood;…

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.…

A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

With the ability to predict learning behaviors, artificial intelligence (AI) is increasingly involved in assessing the performance of problem solving. This study explored the potential of AI to predict whether mathematics problems could be solved based on eye movements and handwriting in a digital problem-solving environment. Sixty-one students…

Dimensional analysis is an algorithm currently in use in almost every chemistry classroom in the United States. Chemistry educators use this procedural tool in the classroom with the intention of providing students with a reliable method to solve many of the relatively simple math problems they encounter. The unintended consequence of using this…

Two problems, both from Gaspar Nicolas' "Tratado da Prática d'Arismética", published in 1519 are considered in this study. The tasks were carried out using pencil, paper and students from Portuguese schools. The aim was to explore the following students' performances: 1. The students were able to recognize the "error",…

Problem-solving skills are essential in improving the creative, critical, and logical thinking skills needed in mathematics learning and daily life. This study aims to examine the effectiveness of problem-based learning (PBL)- assisted ethnomathematics-based Geocube e-module on problem-solving skills. This quantitative research applied a…

This study reviews the literature on error patterns in mathematics among students with mathematics difficulty. We analyzed and synthesized the findings from 17 studies, focusing on the characteristics of error analysis studies, the mathematics topics examined, and the specific error patterns identified. The results revealed the following: (a) the…

In this paper, we finish describing the project and the experimentation of "Ricerca Operativa Applicazioni Reali" (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools. ROAR is composed of three teaching units addressed to grades 10, 11, and 12, respectively. To improve students'…

Algebra has been identified as a gatekeeper to careers in STEM, but little research exists on how algebra appears for practitioners in the workplace. Surveys and interviews were conducted with 77 STEM practitioners from a variety of fields, examining how they reported using algebraic functions in their work. Survey and interview reports suggest…

Mathematics plays many roles in physics and physics education. While these roles have previously been extensively discussed in the physics education research community, no systematic picture of the multifaceted considerations has yet been formed. To gain a comprehensive overview of the previous studies on the topic, we conducted a systematic…

The purpose of this article is to describe the learnings of primary school teachers in rural Guatemala as a result of an action research experience. This experience took place in the context of the "Basic Education Quality and Transitions" activity, or BEQT, funded by the United States Agency for International Development (USAID) and…