Traditional mathematics education focuses on teaching rote procedures to solve problems, though these procedures are not usually motivated by goals. As a result, students have trouble flexibly using procedures and generalizing their knowledge to solve novel problems that differ from the problems they practice during instruction. In the following…

Enacting tasks at high levels of cognitive demand helps preservice teachers make sense of mathematical ideas and serves as a model for instruction. Small group discussions can be useful pedagogical tools for maintaining a task's cognitive demands. In this article, we contrast two small group discussions within a preservice elementary classroom to…

With deliberate system-level reform now being acted upon around the world, both successful and unsuccessful cases provide a rich source of knowledge from which we can learn to improve large-scale reform. Research surrounding the effectiveness of a theory-based system-wide numeracy reform operating in primary schools across Australia is examined to…

This paper describes a development and evaluation process used to create teacher education materials that help prepare middle and secondary mathematics teachers to teach data analysis and probability concepts with technology tools. One aspect of statistical reasoning needed for teaching is the ability to coordinate understandings of center and…

Just as ready-made clothes may not provide a perfect fit for all bodies, math lessons may not be a perfect fit for all students. Published instructional tasks, including problems in mathematics textbooks, often need to be tailored to be meaningful, relevant, or accessible to each student. Ways are possible to take high-level reasoning tasks and…

To build on prior knowledge and mathematical understanding, middle school students need to be given the opportunity to make connections among a variety of representations. Graphs, tables, algebraic formulas, and models are just a few examples of representations that can help students explore quantitative relationships. As a mathematics educator,…

The purpose of this study was to examine technical and instructional features of a kindergarten curriculum-based measurement (CBM) tool designed to track students' mathematics progress in terms of computational concepts, procedures, and counting strategies. Students in 10 kindergarten classrooms in three elementary schools completed alternate…

Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

The purpose of this study was to extend existing research relative to the predictors of early mathematics skills. Using Vygotskian theory as a framework, our primary goal was to determine whether social skills or letter awareness skills served as better mediators between receptive language and early mathematics concepts. The secondary goal was to…

The arithmetic mean is a fundamental statistical concept. Unfortunately, social science students rarely develop an intuitive understanding of the mean and rely on the formula to describe or define it. According to constructivist pedagogy, educators that have access to a variety of conceptualizations of a particular concept are better equipped to…

The activities suggested in this article are intended for use with lower secondary school students. The "Australian Curriculum: Mathematics" states that students in lower secondary school should "investigate the relationship between features of circles such as circumference, area, radius and diameter" and "use formulas to…

What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…

Professional development is a well-established component of teacher change, and action research can make that change visible. In this study, quantitative and qualitative data were collected from 237 elementary teachers and intervention specialists from 33 federally-designated Appalachian counties of Southeastern Ohio who participated in the…

We propose the development of a "population" of high-quality assessment tasks that cover the performance goals set out in the "Common Core State Standards for Mathematics." The population will be published. Tests are drawn from this population as a structured random sample guided by a "balancing algorithm."

Elementary students' math achievement in the United States is mediocre in comparison to that of students in other countries. Students in California perform below the national average on standardized tests. Reform efforts in mathematics education aim at proficiency in fact fluency, procedural knowledge, conceptual knowledge, and application of…