Representations in physics possess both physical and conceptual aspects that are fundamentally intertwined and can interact to support or hinder sense making and computation. We use distributed cognition and the theory of conceptual blending with material anchors to interpret the roles of conceptual and material features of representations in…

An iterative unpacking strategy consists of sequencing empirically-based theoretical developments so that at each step of theorizing one theory serves as an overarching conceptual framework, in which another theory, either existing or emerging, is embedded in order to elaborate on the chosen element(s) of the overarching theory. The strategy is…

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…

Senior secondary mathematics students who develop conceptual understanding that moves them beyond "rules without reasons" to connections between related concepts are in a strong place to tackle the more difficult mathematics application problems. Current research is examining how the use of challenging tasks at different levels of…

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…

Entropy is a central concept in thermodynamics, but has been found to be challenging to students due to its abstract nature and the fact that it is not part of students' everyday language. Interviews with three pairs of engineering students (N = 6) were conducted and video recorded regarding their interpretation and use of the entropy concept, one…

Chemistry is a technical scientific discipline strongly underpinned by its own complex and diverse language. To be successful in the problem-solving aspects of chemistry, students must master the language of chemistry, and in particular, the definition of terms and concepts. To assist students in this challenging task, a variety of instructional…

Forty 4th and 9th grade students participated individually in tutorial interviews centered on a problem-solving activity designed for learning basic algebra mechanics through diagrammatic modeling of an engaging narrative about a buccaneering giant burying and unearthing her treasure on a desert island. Participants were randomly assigned to…

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

Research in science in early childhood is an area that has not received much attention (Fleer, M., & Robbins, J. (2003). "Hit and run research" with "hit and miss" results in early childhood science education. "Research in Science Education," 33, 405-431.) and it has been reported that early children teachers lack…

FOIL is a well-known mnemonic that is used to find the product of two binomials. We conduct a large sample (n = 252) observational study of first-year college students and show that while the FOIL procedure leads to the accurate expansion of the product of two binomials for most students who apply it, only half of these students exhibit conceptual…

In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…

In this paper we report the interview questions used in a study of middle school students' mathematical problem solving behaviors which were chosen based on Vygotsky's concept formation theory and Berger's appropriation theory. We discuss the task design/selection process along with the findings associated with the use of these tasks so to provide…

In Calculus, students are often both presented problems with and taught to use three interconnected types of representations: symbolic, graphic, and numeric. However, students often fail to notice the relationship between mathematical objects (and even the same object) that are presented using different types of representations. Using the APOS…

This study examines whether creating a mathematics-based digital story increases pre-service teachers' understanding of the problem solving process, the relationship among visual, auditory and verbal representation in critical thinking/problem solving in mathematics. Survey results indicated that pre-service teachers were unfamiliar with the uses…