The presented article is dedicated to a new way of teaching substitution in algebra. In order to effectively master the subject matter, it is necessary for students to perceive the equal sign equivalently, to learn to manipulate expressions as objects, and to perceive and use transformations based on defining their own equivalences. According to…

This study explores kindergarten students' early notions of mathematical equivalence in the United States. In particular, it uses qualitative methods to examine the understandings children hold about the equal sign prior to formal instruction and how these understandings shift throughout an 8-week classroom teaching experiment designed to develop…

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

This study addressed the problem of why students with learning disabilities in mathematics too often fail to develop multiplicative and divisional concepts/operations. We conducted a constructivist teaching experiment with 12 students (nine 5th and three 4th graders). This report focuses on three students' conceptual progress, particularly on…

Confidence intervals are beginning to play an increasing role in the reporting of research findings within the social and behavioral sciences and, consequently, are becoming more prevalent in beginning classes in statistics and research methods. Confidence intervals are an attractive means of conveying experimental results, as they contain a…

Using science experiments in life science, chemistry, and physics, helps ground students' understanding of abstract algebra concepts in real-world applications. Hands-on activities connect mathematics with science in a way that is accessible to teachers and students alike. Each activity explores a scientific phenomenon, connecting it to algebra…