This paper reports on the performance of 167 eighth graders in Singapore making generalisations for a quadratic figural pattern presented in a non-successive format. Data were collected through administering a written test in which the students had to establish the functional rule underpinning the pattern. The findings revealed that the students…

We encounter ratios on a daily basis. They also play an important role as a basic construct of thinking in many areas of school mathematics. For example, a fraction can be interpreted as the ratio of a part to the respective whole. Many children appear to have difficulties with fractions and although the concept of ratios is crucial for this…

Despite their apparent simplicity, the concepts of square numbers and square roots are problematic for high school students. I inquired into students' understanding of these concepts, focusing on obstacles that students face while attempting to solve square number problems. The study followed a modified analytic induction methodology that included…

In a developmental research approach, from a sociocultural position, we address the meanings students make of mathematics in teaching sessions and how this relates to the intentions of the teacher and approaches to teaching. Analyses of data come from small group tutorials of one tutor with first year university mathematics students (n=5). We…

The aim of this paper is to report early findings from university mathematics teaching in the tutorial setting. The study addresses characteristics of the teaching of an experienced research mathematician and through interviews, her underlying considerations. An analysis of a teaching episode illuminates her use of generic examples to reveal…

Children have a natural interest in math, and the "Teaching Math to Young Children" practice guide (ED544376) aims to help teachers capitalize on that interest to make children's preschool and school experience more engaging and beneficial. In this practice guide summary, readers will find: (1) An overview of the…

Background: Valid assessment of the understanding of Newton's mechanics is highly relevant to both physics classrooms and research. Several tests have been developed. What remains missing, however, is an efficient and fair test of conceptual understanding that is adapted to the content taught to secondary school students and that can be validly…

Instructors in higher education are very familiar with the Likert scale Students' Evaluation of Teaching (SET) used to evaluate teaching. Researchers have raised concerns about biases affecting the results of SET surveys, as well as their validity and reliability and use in high-stakes decision making. Here, we demonstrate that Q methodology,…

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

In this featured lesson, entitled "Fishy Feeding Frenzy," fourth-grade students engage in a classic science activity that requires them to experience the interdependent relationships of organisms in an ecosystem. The students explore how adaptations increase the survival of a member of a species by participating in an active "fishy…

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

This pilot study sought to examine the mathematical knowledge for teaching that pre-service teachers used when participating in an online community, and to gain insight into their epistemological stance. The participants of this study were among the pre-service teachers in a large urban university, chosen as they were completing their mathematics…

Students in this era need to grasp the concept of geometry instead of memorizing formulae. This is important for them to further their knowledge in geometry. The purpose of the research was to determine whether GeoGebra software influences year one students' performance in geometrical reflection. The research utilized an experimental research…

The exploration of proportional relationships is foundational to the mathematics studied in the middle grades and beyond. Research has shown that an early emphasis on procedures often leaves students with a shallow understanding of the important underlying mathematical concepts of proportional relationships. One approach that addresses the needs…

In this study, we follow students' modeling and covariational reasoning in the context of learning about big data. A three-week unit was designed to allow 12th grade students in a mathematics course to explore big and mid-size data using concepts such as trend and scatter to describe the relationships between variables in multivariate settings.…