The study's goal was to identify the beginning of 1st grade quantitative competencies that predict mathematics achievement start point and growth through 5th grade. Measures of number, counting, and arithmetic competencies were administered in early 1st grade and used to predict mathematics achievement through 5th (n = 177), while controlling for…

Social scientists use adjacency tables to discover influence networks within and among groups. Building on work by Moler and Morrison, we use ordered pairs from the components of the first and second singular vectors of adjacency matrices as tools to distinguish these groups and to identify particularly strong or weak individuals.

While contemplating ways to extend the author's ninth-grade honors geometry students' thinking and knowledge about area and perimeter, he discovered an interesting type of problem based on Erickson's (2001) rectangle problem, which he had been using for ten years. Erickson's original problem involves creating random rectangles with lengths and…

It is important to let students see the value of mathematics in design--and how mathematics lends perspective to problem solving. In this article, the author describes a water-service challenge which enables students to design a water utility system that uses surface runoff into an open reservoir as the potable water source. This challenge…

A simple partial version of the Fundamental Theorem of Calculus can be presented on the first day of the first-year calculus course, and then relied upon repeatedly in assigned problems throughout the course. With that experience behind them, students can use the partial version to understand the full-fledged Fundamental Theorem, with further…

This paper describes how the global education community can prepare for the future of education. With the aim of promoting global education and creativity, the paper leverages case studies on Korea's education reform, including the Free Semester Program (FSP) and the SMART Initiative using ICT, which are new education initiatives focused on…

In this article, Clay and Rhee use the mathematics topic of circles and the lines that intersect them to introduce the idea of looking at the single mathematical idea of relationships--in this case, between angles and arcs--across a group of problems. They introduce the mathematics that underlies these relationships, beginning with the questions…

Introduction: This study has aimed to investigate the relationship between the development of working memory and performance on arithmetic activities. Method: We conducted a 3-year longitudinal study of a sample of 90 children, that was followed during the first, second and third year of primary school. All children were tested on measures of WM…

Solving many quantitative problems does not necessarily lead to an improved Physics understanding. However, physicists, who have learned physics largely through quantitative problems solving, often have a refined physical intuition. Assuming that the refinement of physical intuitions occurs, to a great extent, during problem solving, the question…

We adopted Brown's (1987) conceptualisation of metacognition to examine how student teachers can be taught metacognitive control while solving mathematical problems. In addition, tasks given to these student teachers were in-built with opportunities for them to be aware of the need for metacognition. We describe the use of the Practical Worksheet…

We report on a long-term study which was executed in a German secondary school with 128 eights graders (ages 14 to 15) in four different classes. Two of these classes served as control groups. The mathematics lessons of the other two classes (treatment groups) were frequently enriched by distinguished phases in which structured argumentation and…

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to…

In this sequence 1/1, 7/5, 41/29, 239/169 and so on, Thomas notes that the sequence converges to square root of 2. By observation, the sequence of numbers in the numerator of the above sequence, have a pattern of generation which is the same as that in the denominator. That is, the next term is found by multiplying the previous term by six and…

The properties of a function such as limit, continuity, derivative, growth, or concavity can be determined more easily from its graph than by doing any algebraic operation. For this reason, it is important for students of mathematics to interpret some of the properties of a function from its graph. In this study, we investigated the competence of…

The purpose of this study was to investigate the preservice secondary mathematics teachers' development of pedagogical understanding in the teaching of modular arithmetic problems. Data sources included, written assignments, interview transcripts and filed notes. Using case study and action research approaches cases of three preservice teachers…