O'Connor and Penuel (2010) argue that viewing research in education as a human science requires explicit attention to social, cultural, historical, and institutional dimensions of human activity, to the agency of participants in learning research, and to the importance of incorporating "emic" perspectives that shift the voice of the…

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

The purpose of this study was to examine the proportional reasoning skills of Turkish middle school students. It was also aimed at revealing the differences in students' performances in terms of their gender, grade level, and problem types--missing value and numerical comparison. The study was conducted with two sixth and seventh grade classes…

As part of a study on mathematical problem solving of secondary 2 (13- to 14-years old) students in Singapore, 56 Secondary two students from ten secondary schools participated in this study. The purpose of this paper is to explore difficulties faced by 56 Secondary 2 students when solving problems. These interviews were analysed using the…

Each year, well over a million students take college algebra and related courses. Very few of these students take the courses to prepare for calculus, but rather because they are required by other disciplines or to fulfill Gen Ed requirements. The present article discusses what the current mathematical needs are in most of those disciplines,…

In this study, the author aimed at measuring how much limited working memory capacity constrains early numerical development before any formal mathematics instruction. To that end, 4- and 5-year-old children were tested for their memory skills in the phonological loop (PL), visuo-spatial sketchpad (VSSP), and central executive (CE); they also…

This article is about the students' investigation about the relationship between the diameter of the view tubes (x) of constant lengths and the viewable vertical distance (y) on the wall while keeping the perpendicular distance from the eyeball to the wall constant. The students collected data and used and represented it in tabular and graphical…

I discuss my experience with teaching an advanced undergraduate Real Analysis class using both lecturing and the small-group guided discovery method. The article is structured as follows. The first section is about the organizational and administrative components of the class. In the second section I give examples of successes and difficulties…

This paper examines the extent to which mathematical knowledge, and its related pedagogy, is inextricably linked to the tools--physical, virtual, cultural--in which it is expressed. Our goal is to focus on a few exemplars of computational tools, and to describe with some illustrative examples, how mathematical meanings are shaped by their use. We…

In this article, getting access to children's perspectives is presented as a prerequisite for assessing as well as developing children's understanding. Children's perspectives are analysed through examples taken from three domains of knowledge: music, mathematics and nature. The issues of assessing and developing children's knowledge are discussed…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

This article describes several enrichment activities that connect mathematics to science in an algebra 1 curriculum. It provides a basis and suggestions for teachers to include student-produced essays about the role of mathematics in the history of civilization. (Contains 6 figures and 1 table.)

The aim of the present study is to provide further evidence that the errors that arise from improper application of the linear model are not random and not easy to overcome. Using three different types of test, we attempt to show that the errors referred to in the literature as "pseudo-analogous" are the result of an epistemological…

This article examines the "Ancient Egyptian" and "Russian Peasant" multiplication schemes and shows that they are, in essence, the same. (Contains 6 figures.)

This article presents the mathematics involved in finding and tracking celestial objects with an electronically controlled telescope. The essential idea in solving this problem is to choose several different coordinate systems that simplify the various motions of the earth and other celestial objects. These coordinate systems are then related by…