Every student has mathematical strengths beyond knowing basic facts, solving problems quickly, or showing work clearly. In this article, the author presents Smiles as an "on-ramp" task that supports students working together by unveiling and leveraging mathematical strengths. Nielsen describes on-ramp mathematics tasks as scaffolds that…

Transform mathematics instruction with the comprehensive mathematical competencies (CMC) framework--a research-based model that integrates seven essential competencies: conceptual and procedural integration, problem solving, logical reasoning, communication, tool use, pattern recognition, and student engagement. Through practical classroom…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

The present study is a part of design research in local instructional theory in a pre-algebraic lesson using the Realistic Mathematics Education (RME) approach. The article will focus on recommendations for the type of pre-algebra class that supports elementary school students' algebraic thinking. As design research study, it followed the three…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

The problem-solving skills of logical thinking, critical thinking, visualization, and communication skills are linked with some activities for students. Sample activities with logic, strategies and patterns, breaking fixed notions, open-minded problems, spatial visualization, and communication are described. (MNS)

Games and activities which involve problem solving are presented in order to help teachers develop the numeric, geometric, and logical thought processes of elementary school students. The activities and games (many of which are pencil-and-paper) require using logic, plan-ahead strategies, spatial reasoning, strategies based on prior patterns or…

Research was conducted investigating properties of skill in learning, in the domain of elementary algebra. Thinking-aloud protocols indicate that early knowledge of the subjects studied was fragmentary, rather than involving systematically flawed procedures. Computational models, developed to simulate observed errors, focused on the role of…

This collection of activities is designed to help students develop critical thinking skills. The activities are non-graded and can be used from upper elementary to high school. Reading levels vary from no reading required to very little reading required and can be used effectively with students who are poor readers, bilingual, or at a special…

This collection of activities is designed to help students develop critical thinking skills. The activities are non-graded and can be used from upper elementary to high school. The reading levels vary from no reading required to very little reading required and can be used effectively with students who are poor readers, bilingual, or at a special…

The IADIS CELDA 2012 Conference intention was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There had been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a…