This article is the second in a series of two papers which suggest some practical, spreadsheet-based ideas for helping students to make appropriate connections between particular algebraic concepts. Solving equations has traditionally been taught as a pen-and-paper process. Spreadsheets, such as that of Excel, provide a contemporary, and powerful…

Some theories from cognitive psychology and mathematics education suggest that children's understanding of mathematical concepts develops together with their knowledge of mathematical procedures. However, previous research into children's understanding of the inverse relationship between addition and subtraction suggests that there are individual…

Ah, springtime, and young people's thoughts turn to... baseball, of course. But this column is not about "how" to throw a curveball, so you'll have to look that up on your own. Here, the focus is on the "why" of the curveball. There are two different things that cause a spinning ball to curve. One is known as the "Bernoulli effect" and the other…

Writing plays an integral role in any disciplinary course setting. In the sciences, WAC and WID initiatives primarily focus on using writing to deepen student understanding of scientific concepts. Scholars, however, have paid less attention to how writing may facilitate an understanding of the link between concepts and their quantitative…

This study reports how 24 grade 4-6 students in one elementary and middle school interpreted formal and informal representations of variables. While interpretations for variables represented as letters (e.g., x and y) have been well established for students in algebra classes and beyond, little research into elementary school students'…

The goal of this research study was to gain an understanding of high school teachers' perceptions of the role of history of mathematics in the classroom as well as their underlying view of mathematics as a discipline. High school teachers from 379 Public High Schools in Massachusetts were contacted and encouraged to take an on-line Likert scale…

We report on our efforts to support teachers' development of mathematical knowledge for teaching through online professional development. In particular, we report on our investigation into the relationship between online interaction and teachers' development of mathematics content for teaching. Through the integration of content analysis and…

The classic Chickens and Pigs problem is considered to be an algebraic problem with two equations and two unknowns. In this article, the authors describe how third-grade teacher Maria is using it to develop a problem-based lesson because she is looking to her students' future needs. As Maria plans, she considers how a series of problems with the…

The purpose of the study is to determine prospective mathematics teachers' views about using computer-based instructional materials in constructing mathematical concepts and to reveal how the sample computer-based instructional materials for different mathematical concepts altered their views. This is a qualitative study involving twelve…

The algebra-based introductory statistics course is the most popular undergraduate course in statistics. While there is a general consensus for the content of the curriculum, the recent Guidelines for Assessment and Instruction in Statistics Education (GAISE) have challenged the pedagogy of this course. Additionally, some arguments have been made…

Math Snacks animations and support materials were developed for use on the web and mobile technologies to teach ratio, proportion, scale factor, and number line concepts using a multi-modal approach. Included in Math Snacks are: Animations which promote the visualization of a concept image; written lessons which provide cognitive complexity for…

Many students at an urban vocational high school have failed to pass the mathematics section of the New Jersey high school graduation assessment. Students who fail the graduation assessment are in danger of not earning their high school diploma. The purpose of this study was to learn, from the instructors' perspectives, why students were not…

The present study evaluated the stability of math learning difficulties over a 2-year period and investigated several factors that might influence this stability (categorical vs. continuous change, liberal vs. conservative cut point, broad vs. specific math assessment); the prediction of math performance over time and by performance level was also…

College students' misconceptions about probability are common and widespread. These misconceptions impede students' ability to make sound judgments in situations of uncertainty and master fundamental concepts of inferential statistics. In this paper the authors report the results of a study undertaken with the objective of correcting three common…

Current reforms in undergraduate mathematics education devoted to proof and counterexample highlight its importance in teaching and learning mathematics. While undergraduate students who have taken a number of upper-level mathematics courses are expected to have mastered the skills required to verify statements as well as to read and write proofs…