The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

Many children fail to master fraction arithmetic even after years of instruction, a failure that hinders their learning of more advanced mathematics as well as their occupational success. To test hypotheses about why children have so many difficulties in this area, we created a computational model of fraction arithmetic learning and presented it…

Mental computation and mathematical reasoning are two intertwined top-level mental activities. In deciding which strategy to use when doing mental computing, mathematical reasoning is essential. From this reciprocal influence, the current study aims at examining the relationship between mental computation and mathematical reasoning. The study was…

The plane problem is a real-world problem, presented without any suggestion as to how it might be solved. It arose unexpectedly as the author was messing around on the internet, not thinking about maths at all. She did not encounter the problem in a maths lesson, nor as homework in the middle of a unit on a particular topic, and so she had no…

This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…

Online planning of good teaching sequences has the potential to provide a truly personalized teaching experience with a huge impact on the motivation and learning of students. In this work we compare two main approaches to achieve such a goal, POMDPs that can find an optimal long-term path, and Multi-armed bandits that optimize policies locally…

Taped problems is an intervention strategy for addressing mathematics fluency that has been evaluated in multiple single-case design studies. Although its efficacy has been supported in individual studies, no comprehensive quantitative synthesis has been conducted on taped problems. The purpose of this study was to synthesize the literature that…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

This article presents research into human mental spatial reasoning with orientation knowledge. In particular, we look at reasoning problems about cardinal directions that possess multiple valid solutions (i.e., are spatially underdetermined), at human preferences for some of these solutions, and at representational and procedural factors that lead…

This mixed methods study examined how engagement in robotics and game design influenced students' self-efficacy, STEM attitudes, and computational thinking (CT) skills. Predominantly African-American students engaged in engineering and computer science tasks during informal learning environments. Results revealed students' self-efficacy scores on…

This study revealed how students' understanding of negative numbers and identified their difficulties related with the concept of integer and its counting operation as part of identifying epistemological obstacles about negative numbers. Even though teachers have explained counting operation procedure of integer, but there was concept…

Getting students adopt the habits of mind specific to many disciplines can be seen as an anchor that will support them to solve the problems in their daily lives. Starting from this premise, a new subject, featuring the habits of mind and how to use and improve them in educational environments seems to worth thinking on. This article describes an…

Patterns are a ubiquitous phenomenon. They exist in nature's plant species emerging as a complete order from truncated matter. Patterns are also present in the fine arts where the aesthetic properties of form exist and conjugate through paintings and sculptures. Mathematical patterns, the focus of this position paper, dominate financial scenarios,…

Intelligent tutoring systems and computer aided learning environments aimed at developing problem solving produce large amounts of transactional data which make it a challenge for both researchers and educators to understand how students work within the environment. Researchers have modeled student-tutor interactions using complex networks in…