As an extension to an activity introducing Year 5 students to the practice of statistics, the software "TinkerPlots" made it possible to collect repeated random samples from a finite population to informally explore students' capacity to begin reasoning with a distribution of sample statistics. This article provides background for the…

More than 2,200 years ago, Eratosthenes, who was a Greek astronomer, geographer, and mathematician, used a simple proportion involving the distance between two ancient cities and measures of shadows cast in those cities during a summer solstice to estimate the circumference of Earth (Nicastro 2008, 25-28). Today, middle school students can use…

Based on a study with six elementary school teachers and 115 students in grades 3, 4, and 5, this article discusses ways that teachers might support an understanding of variable as students explore pattern-finding activities. The practices emerged from interviews with teachers and a yearlong observation of teaching algebraic thinking during an…

During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

This paper explores the nature of students' quantitative reasoning and conceptions of functions supporting their ability to symbolize quadratic function rules, and the meanings students make of these rules. We analyzed middle school students' problem solving activity during a small group teaching experiment (n = 6) emphasizing quadratic growth…

The objective of this paper is to present two preservice secondary mathematics teachers' beliefs about teaching Geometric Transformations (GTs) using Geometer?s Sketchpad (GSP). The study comprised of series of five task-based interviews with each of two participants, who were senior undergraduate preservice teachers, at a medium-sized public…

This study probes students' beliefs about nature of mathematics, difficulty in learning mathematics sourcing from these and their influence on achievement in mathematics. Questionnaire survey on 458, 9th standard students randomly selected from schools of Malappuram district elicited data on nature of school mathematics and difficulty arising out…

This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

Script writing by learners has been used as a valuable pedagogical strategy and a research tool in several contexts. We adopted this strategy in the context of a mathematics course for prospective teachers. Participants were presented with opposing viewpoints with respect to a mathematical claim, and were asked to write a dialogue in which the…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…

Multiplication of numbers from 1 to 10 is very important as it provides the basis for learning multiplication of other larger numbers as well as other related mathematical operations. How do students learn multiplication? Usually students just memorize the results of multiplication. This is often performed without a complete comprehension of the…

When learning a new math concept, should learners be first taught the concept and its associated procedures and then solve problems, or solve problems first even if it leads to failure and then be taught the concept and the procedures? Two randomized-controlled studies found that both methods lead to high levels of procedural knowledge. However,…

Based on Common Core Standards (2010), mathematics interventions should emphasize conceptual understanding of numbers and operations as well as fluency. For students at risk for failure, the concrete-representational-abstract (CRA) sequence and the Strategic Instruction Model (SIM) have been shown effective in teaching computation with an emphasis…

Students learn norms of proving by observing teachers generating proofs, engaging in proving, and generalizing features of proofs deemed convincing by an authority, such as a textbook. Students at all grade levels have difficulties generating valid proof; however, little research exists on students' understandings about what makes a…

This article outlines a class activity where students prepare croissants to get an intuitive feeling for the nature of a strange attractor. In particular during the preparation of the pastry dough, students investigate the effects of stretching and folding. These physical processes force trajectories (in this case the pastry dough) to remain…