When educators started incorporating the letter A into the STEM acronym to form STEAM some science educators had reservations. Seen from a western, rationalistic way of knowing (Colucci-Gray et al. 2017, 23) the STEM community had detractors regarding the idea of integrating art into science. Hence, scientific language is often thought of as being…

In this study, the 8th grade secondary school mathematics textbook approved by the ministry in Turkey was compared with the mathematics textbooks in France and the USA in terms of the use of the multiple representation method in the probability learning domain. Document analysis, one of the qualitative research methods, was used in the study, and…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

This article aims to investigate the teaching of chance in the context of tactile models (TM) from the perspective of the Theory of Register of Semiotic Representations. In this qualitative research, we sought to identify the different types of semiotic registers and transformations (treatment and conversion), in the solutions of the tasks of the…

Conceptual model-based problem solving (COMPS) was tested for its efficacy in teaching a student diagnosed with autism spectrum disorder to solve word problems involving multiplication and division. A single-case, multiple-baseline across behaviors design was conducted. The ability to solve each of three types of multiplication problems examined…

Teachers do not directly implement new teaching materials, but rather adapt them. For changing teaching practice, research requires more insights into these adaptions. This study draws on the Theory of Instrumental Genesis to describe the ways teachers adopt the percentage bar model to create different learning opportunities. The results of the…

Developing multiplicative reasoning is an important milestone for elementary school students, which influences their learning of later mathematical concepts (Hackenberg and Tillema 2009). For children to conceptually understand multiplication, one should move beyond merely counting by ones to dealing with composites (twos, fives, etc.) and other…

Using memorized rules and algorithms without coherence and understanding is a perennial problem for teachers and students especially in the teaching and learning of fraction operations. I present data in which prospective middle school teachers explain a commonly used rule for fraction division--keep-change-flip. I argue that using both strip…

This article describes how to teach fraction and percentage word problems using a model-drawing strategy. This cognitive strategy places emphasis on explicitly teaching students how to draw a schematic diagram to represent the qualitative relations described in the problem, and how to formulate the solution based on the schematic diagram. The…

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,…

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to…

This article describes ways in which digital imagery can be used to enhance mathematics instruction. (Contains 6 figures.)

This article describes the use of the book "Inchworm and a Half" to stimulate children's investigations in measurement and number. During a two-day lesson children used physical models and visual representations to develop measurement skills and explore equivalent relationships.

We describe an easy and fun project using water rockets to demonstrate applications of single variable calculus concepts. We provide procedures and a supplies list for launching and videotaping a water rocket flight to provide the experimental data. Because of factors such as fuel expulsion and wind effects, the water rocket does not follow the…