Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of…

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 aim of the study was to determine the effects of a dialogical argumentation instructional model (DAIM) on pre-service teachers' ability to solve conceptual maths-in-physics (MIP) problems. Using a quasi-experimental design the study included two equal groups of pre-service teachers (N = 40) to follow two instructional methods in which the…

Previous studies have identified physics students' difficulties with graph slope and area under a graph in different contexts. In this study we compared physics and nonphysics (psychology) students' understanding of graphs; i.e., we evaluated the effects of concept (graph slope vs area under graph), type of question (qualitative vs quantitative),…

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

The "mathematics problem" is a well-known source of difficulty for students attempting numerical problem solving questions in the context of science education. This paper illuminates this problem from a biology education perspective by invoking Hogan's numeracy framework. In doing so, this study has revealed that the contextualisation of…

What better way to engage young students in physical science concepts than to have them engineer flying toy rockets? The integration of engineering into science classrooms is advocated by the "Next Generation Science Standards" (NGSS) and researchers alike (Brophy et al. 2008), as engineering provides: (1) A "real-world…

Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…

We discuss common difficulties in upper-division electricity and magnetism (E&M) in the areas of Gauss's law, vector calculus, and electric potential using both quantitative and qualitative evidence. We also show that many of these topical difficulties may be tied to student difficulties with mathematics. At the junior level, some students…

This article describes how a third grade class (ages 8-9) conducted a temperature-related science experiment. The goal of the experiment was to build on the following question: What would happen if you took three different thermometers, all reading the same temperature, wrapped them in three different socks, one woollen, one silk, and one cotton,…

The classic Chickens and Pigs problem is considered to be an algebraic problem with two equations and two unknowns. In this article, the authors describe how third-grade teacher Maria is using it to develop a problem-based lesson because she is looking to her students' future needs. As Maria plans, she considers how a series of problems with the…

Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way…

Districts face increasing pressure to improve students' mastery of curriculum in the fields of science, technology, engineering and mathematics (STEM). Yet the number of students enrolling in science and math courses drops dramatically in middle and high school. At Sylvester Middle School, Chinook Middle School and Cascade Middle School of the…

Stoichiometry and related concepts are an important part of student learning in chemistry. In this interpretive-based inquiry, we investigated Thai Grade 10 and 11 students' conceptual understanding and ability to solve numerical problems for stoichiometry-related concepts. Ninety-seven participants completed a purpose-designed survey instrument…

University students' answers to a "Minds on Physics" problem revealed six distinct approaches to the solution. Discusses implications for teaching and assessment. (Author/WRM)