This article addresses the purposes and types of opportunities for engaging students in argumentation in the mathematics classroom. Drawing on data from a research project, we document how argumentation--a practice that is central to the work of the mathematics community--can be contextualized in secondary mathematics classrooms to serve different…

This study is part of a larger study investigating the subject matter knowledge and pedagogical content knowledge of Hong Kong prospective mathematics teachers, the relationship between the knowledge of algebraic operation and its inverse, and their teaching competency. In this paper, we address the subject matter knowledge and pedagogical content…

The Odd Shape Out task was an open-ended problem that engaged students in comparing shapes based on their properties. Four teachers submitted the work of 116 students from across the country. This article compares various student's responses to the task. The problem allowed for differentiation, as shown by the many different ways that students…

This study aimed to investigate the effectiveness of teaching Mathematics by using 7E's Learning Cycle strategy in immediate and delayed achievement and retention among Preparatory Year students at King Saud University (KSU)--Saudi Arabia, in comparison with the traditional method. The study sample consisted of (73) Preparatory Year students at…

Using Garden Based Learning (GBL) as an integrated mathematics and science unit, this article describes the mathematical journey of students as they work through the process of designing their own garden beds.

As literature has reported, it is usual that university students in statistics courses, and even statistics teachers, interpret the confidence level associated with a confidence interval as the probability that the parameter value will be between the lower and upper interval limits. To confront this misconception, class activities have been…

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…

People need the idea of transformation geometry in order to understand the nature and environment they live in. The teachers should provide learning environments towards perceptual understanding in symmetry training and development practice skills of the students. In order to make up such a learning environment, teachers should have information…