Because the goals of games and the object of school-based learning are fundamentally mismatched, efforts to integrate games into the curriculum have largely fallen flat despite the best intentions of teachers and the gaming industry. Arguing that educational game designers should be investigating ways to get education into games rather than…

This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher…

Fermi problems, or order of magnitude estimates, are often used in introductory physics courses. In this paper I will show that first year students studying physics at university do not arrive with the skill set to solve these problems, and they have to be actively taught how to solve them. Once they have been shown how to solve Fermi problems,…

Project-based learning is a pedagogy that involves students in applying and developing theories, skills, and techniques to solve real world problems. Three faculty members used project-based learning to involve graduate students in an interdisciplinary seminar on sustainable development in Appalachian Ohio, which was convened under the auspices of…

Times of threshold change, such as the transformation from the industrial era to the knowledge economy of today, produce pressures to redesign the institutions people live with to respond to, or better, shape this change. In America's knowledge economy, there is broad agreement that the only way to preserve the nation's economic edge will be…

The Varignon parallelogram has always provided a simple geometric investigation for students that gives rise to a surprising result. It is possible to extend the Varignon investigation by looking at special quadrilaterals or by considering different dissection points along the sides. In the second of his two-part series, the author offers some…

Proportional thinking is the mathematical basis of a wide range of topics in the middle-school mathematics curriculum. While the concept is obvious in the traditionally-named ratio and proportion sections, proportional thinking is also the key to such diverse topics as rate, gradient of a linear function, similarity, trigonometry and percentage,…

Here, we investigate what loci are produced when a square of side-length one is allowed to rotate around a square of side-length n, where n is a whole number. We find that if i = 1, 2, 3 or 4 (mod 4), the loci obtained for n [congruent to] i (mod 4) all have the same symmetry and we show how the perimeter of each class can be determined. We also…

This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional his understanding of periodic functions was unconventional David engaged…

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…

We present a general formula for a triple product involving four real numbers. As a particular case, we get the sum of a triple product of four odd integers. Some interesting results are recovered. We derive a general formula for more than four odd numbers.

We investigated age differences in reading and rereading processes associated with problem solving and explored the extent to which prior information affects rereading processes. Participants' reading times were recorded as they read short mysteries, twice, at their own pace on a computer, with the goal of providing the solution to the mystery. We…

English language learners (ELLs) struggle with solving word problems for a number of reasons beyond math procedures or calculation challenges. As a result, ELLs may not only need math support but also reading and linguistic support. The purpose of this study was to assess the effectiveness of a math comprehension strategy called Dynamic Strategic…

The aim of this dissertation is to present the procedure and proceedings of an instructional research into the teaching and learning among Luo women of Western Kenya. The purposes of the research are threefold. First, it seeks to document a system of indigenous adult education that has proved sustainable among Luo women from generation to…

These Proceedings are a written record of the research presented at the 33rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2011) held in Reno, Nevada, October 20-23, 2011. The theme of the conference is Transformative Mathematics Teaching and Learning. The Proceedings…