One of the most salient arguments in favor of a semiotic approach, put forward on various occasions among others by Luis Radford, claims that semiotics is most appropriate to treat the interaction between socio-cultural and objective aspects of knowledge problems. But if we want to take such claims seriously, we have to undertake revisions of our…

The question whether to walk slowly or to run when it starts raining in order to stay as dry as possible has been considered for many years--and with different results, depending on the assumptions made and the mathematical descriptions for the situation. Because of the practical meaning for real life and the inconsistent results depending on the…

This article presents a few methods for generating Sudoku puzzles. These methods are developed based on the concepts of matrix, permutation, and modular functions, and therefore can be used to form application examples or student projects when teaching various mathematics courses. Mathematical properties of these methods are studied, connections…

This article addresses an important problem of graphing quantitative data: should one include zero on the scale showing magnitude? Based on a real time series example, the problem is discussed and some recommendations are proposed.

Student understanding of biological representations has not been well studied. Yet, we know that to be efficient problem solvers in evolutionary biology and systematics, college students must develop expertise in thinking with a particular type of representation, phylogenetic trees. The purpose of this study was to understand how undergraduates…

Eighteen adults with intellectual disability (ID) and 20 children with typical development (TD) matched for cognitive level, participated in this study. Participants solved perceptual and conceptual analogies (from the Conceptual and Perceptual Analogical Modifiability Test-CPAM) while having their eye movements monitored. As predicted, the…

The purpose of this article is to explore student-generated connections among counting problems. The literature indicates that such problems pose difficulties for students, who struggle to detect common structures and identify models of underlying problem types. A case study is presented here, in which students elaborate upon connections they make…

Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…

Researchers have argued against deficit-based explanations of students' difficulties with mathematical sense-making, pointing instead to factors such as epistemology. Students' beliefs about knowledge and learning can hinder the activation and integration of productive knowledge they have. Such explanations, however, risk falling into a…

The conceptual foundation for Direct Behavior Rating as a behavior assessment method is reviewed. A contemporary definition of Direct Behavior Rating is framed as combining strengths of systematic direct observation and behavior rating scales, which may result in a usable and defensible assessment tool for educators engaged in formative purposes.…

Intervention integrity or adherence describes qualities of carrying out an intervention plan and in research is fundamentally linked to experimental validity questions addressed by measurement of independent and dependent variables. Integrity has been well described in conceptual writing but has been a continuing thorny subject in research and…

Many mathematics students have difficulty making the transition from procedurally oriented courses such as calculus to the more conceptually oriented courses in which they subsequently enroll. What are some of the key "stumbling blocks" for students as they attempt to make this transition? How do differences in faculty expectations for students…

Recent research has reported successful training interventions that improve insight problem solving. In some ways this is surprising, because the processes involved in insight solutions are often assumed to be unconscious, whereas the training interventions focus on conscious cognitive strategies. We propose one mechanism that may help to explain…

It is widely held that, by teaching individuals how to reason through and analyse everyday problems, the teaching of critical thinking develops the deliberative capacities essential to the healthy functioning of democracy. Implicit in this view is the assumption that a certain commensurability exists between the problems presented in such…

Representation is viewed as central to mathematical problem solving. Yet, it is becoming obvious that students are having difficulty negotiating the various forms and functions of representations. This article examines the functions that representation has in students' mathematical problem solving and how that compares to its function in the…