This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given…

The retention of foundational knowledge is crucial in learning and teaching mathematics. However, a significant part of university students do not achieve long-term knowledge and problem-solving skills. A possible tool to increase further retention is testing, the strategic use of retrieval to enhance memory. In this study, the effect of a special…

Covariational reasoning (or the coordination of two dynamically changing quantities) is central to secondary STEM subjects, but research has yet to fully explore its applicability to elementary and middle-grade levels within various STEM fields. To address this need, we selected a globally referenced STEM assessment--the Trends in International…

The purpose of this study is to investigate a mathematically gifted student's self-regulation behaviours while constructing and consolidating mathematical knowledge. However, the objective is to determine which self-regulation strategies influence this student's mathematical abstraction process. The case study method was used in the research. As…

This article describes part of a study in which researchers designed lesson sequences based around using a string number line to help teachers support children's development of relative thinking and understanding of linear scale. In the first year of the study, eight teachers of Years 3-5 participated in four one-day professional development…

This article explores one segment of an extended research and development project that was conducted to better understand the ways online teacher professional development can support teachers' development of deep and connected mathematical understandings. In particular, this article discusses teachers' understandings of the concept of…

This study aims to examine the enhancement of mathematical reasoning ability through reflective learning. This study used quasi-experimental method with nonequivalent pretest and posttest control group design. The subject of this study were students of Mathematics Education Program in one of private universities in Palembang, South Sumatera,…

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

Suggests that secondary school students seem to have reasonably good procedural knowledge in areas of mathematics as rational numbers, probability, measurement, and data organization and interpretation. It appears, however, that students are lacking the conceptual knowledge enabling them to successfully do the assessment items on applications,…

This document is the second of three related volumes. They present the rationale, background, and framework for a comprehensive monitoring system being developed for the National Science Foundation. The system is being designed to gather information about the effects of national, state, and local policy actions designed to change the teaching and…