Mathematics teachers have recently begun to stress the need for teaching models and modeling approaches that encompass cognitive and meta-cognitive thought processes for every level of schooling, starting from primary school through to higher education. The objective of this study is to examine modeling processes with the help of modeling…

This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem.…

A process for analyzing log files collected from open-ended learning environments is developed and tested on a virtual lab problem involving reaction stoichiometry. The process utilizes a set of visualization tools that, by grouping student actions in a hierarchical manner, helps experts make sense of the linear list of student actions recorded in…

Background: Group work is often used in Physical Education (and Health-HPE). In this paper, we propose that despite: (1) its widespread use; (2) advances surrounding HPE models that utilize group strategies; and (3) a significant amount of literature dealing with group work in other school subjects, we do not have a particularly good theoretical…

Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing…

This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…

In this reflective essay, Eric Booth utilizes his Habits of Mind for Creative Engagement to offer two suggestions for intensifying the impact of arts learning in schools. Booth's first suggestion redefines what artistic engagement really means and where it can contribute to creative learning. His second suggestion advocates for the use of…

As a percussive dancer, Malke Rosenfeld makes rhythm with her feet while she dances, and she also helps elementary students make their own percussive dance steps by integrating mathematics into her lesson plans. To do this she uses the Jump Patterns tool, a tool she developed during the first six years of her teaching artist career to help…

The standing long jump was an Olympic event until 1912. In 1904, Ray Ewry set the world record for the longest standing long jump, which was about 11.5 feet, or 138 inches. Although the standing long jump is no longer an Olympic event, the Norwegians still include it in their National Competition, and Arne Tvervaag set a new world record at about…

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger…

Parents of gifted children play a powerful role in expanding their world and helping them discover what they love. When gifted children have impassioned, open-minded, and creative family members, they are free to discover what they love and who they are as people. For gifted learners, curiosity, passion, and interest are absolute essentials.…

In this paper, we argue for a more "systematic" approach for studying the relationship between classroom practices and scientific practices--an approach that will likely better support the systemic reforms being promoted in the Next Generation Science Standards in the USA and similar efforts in other countries. One component of that…

Several studies on learning mathematics for rural area's student indicate that students have difficulty in understanding the concept of division operation. Students are more likely to be introduced by the use of the formula without involving the concept itself and learning division separate the concrete situation of learning process. This…

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged…

This article describes how a sixth-grade teacher's "missing word" task uncovered higher-level thinking and engaged her students in the Standards for Mathematical Practice. The role and selection of the task promotes higher-level thinking and connects to the Common Core State Standards for Mathematics. The task required students to apply…