This piece explores conditions that stimulate classroom activities to facilitate creative habits of mind in an effort to motivate educators and students to better understand the complexities of creativity and how to promote it.

In this article, I present and build on the ideas of John Threlfall ("Educational Studies in Mathematics" 50:29-47, 2002) about strategy development in mental mathematics contexts. Focusing on the emergence of strategies rather than on issues of choice or flexibility of choice, I ground these ideas in the enactivist theory of cognition,…

Combinatorial topics have become increasingly prevalent in K-12 and undergraduate curricula, yet research on combinatorics education indicates that students face difficulties when solving counting problems. The research community has not yet addressed students' ways of thinking at a level that facilitates deeper understanding of how students…

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…

An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…

This study utilized an innovative data analysis approach to examine how engineering undergraduates engaged in mathematical modelling. Individual modelling routes were constructed via modelling activity diagrams and were used to critically examine the theoretical framework. Implications for the theoretical model are offered along with implications…

The article describes the possibilities and the main directions of development of intellectual activity in teaching mathematics in school. The aims and specific features of application of international comparative TIMSS and PISA studies, as well as their results in the field of mathematics education in relation to the pupils in Kazakhstan are…

This paper analyzes how a teacher of mathematics used problem posing in the assessment of the cognitive development of 26 students at the grade-four level. The students, ages 8 to 10 years, were from a rural elementary school in western Jamaica. Using a picture as a prompt, students were asked to generate three arithmetic problems and to offer…

The purpose of the study was to test a model of causal relationships among cognitive reserve (CR), personality variables such as Neuroticism and Openness to experience, and divergent thinking (DT), independently evaluating performance in different domains (verbal and graphic). It was hypothesized that CR, Openness, and Neuroticism would each…

The aim of this study is to analyze and document the extent to which high school teachers rely on a set of technology affordances to articulate epistemological and cognitive actions in problem solving approaches. Participants were encouraged to construct dynamic representations of tasks and always to look for different ways to identify and support…

Learning to solve a class of problems can be characterized as a search through a space of hypotheses about the rules for solving these problems. A series of four experiments studied how different learning conditions affected the search among hypotheses about the solution rule for a simple computational problem. Experiment 1 showed that a problem…

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

We propose two contrasting types of student decision-making based on social and cognitive psychology models of separate mental processes for problem solving. Informal decision-making uses intuitive reasoning and is subject to cognitive biases, whereas formal decision-making uses effortful, logical reasoning. We explored indicators of students'…

Problem solving is considered a fundamental human skill. However, large-scale assessment of problem solving in K-12 education remains a challenging task. Researchers have argued for the development of an enhanced assessment approach through joint effort from multiple disciplines. In this study, a three-stage approach based on an evidence-centered…

Feedback is generally considered a beneficial learning tool, and providing feedback is a recommended instructional practice. However, there are a variety of feedback types with little guidance on how to choose the most effective one. We examined individual differences in working memory capacity as a potential moderator of feedback type. Second-…