This study explores the communicative accommodation strategies employed by a bilingual tutor and an ELL student during the discussion of word problems involving secondary algebra and geometry concepts. Mathematics discussions are conceived as communicative events wherein ELL student comprehension is promoted through provision of simplified…

The purpose of this Executive Position Paper project was to develop resources for improving Individual Educational Program (IEP) mathematics learning goals for conceptual understanding of fractions for middle school special education students. The investigation surveyed how IEP mathematics learning goals are currently determined and proposed a new…

Technology permeates every aspect of daily life, from the sensors that control the traffic signals to the cameras that allow real-time video chats with family around the world. At times, technology may make life easier, faster, and more productive. However, does technology do the same in schools and classrooms? Will the benefits of technology…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

This study examines preservice elementary teachers' (PTs) knowledge for teaching the associative property (AP) of multiplication. Results reveal that PTs hold a common misconception between the AP and commutative property (CP). Most PTs in our sample were unable to use concrete contexts (e.g., pictorial representations and word problems) to…

This paper addresses how secondary students might reason about amounts of change in covarying quantities. Two empirically based forms of covariational reasoning are distinguished. The first form-- reasoning about quantities as varying simultaneously and independently--supports tandem comparison of amounts of change. The second form--coordination…

Many key aspects of modern theory relating to classroom discourse in mathematics education, especially the theory of didactical situations, have not progressed much further than theories put forward in the 1840s by the North American educator David Page. Aspects of Brousseau's (1997) description of what he called the Topaze effect, are remarkably…

This paper analyses the responses of 247 middle school students to items requiring the concept of average in three different contexts: a city's weather reported in maximum daily temperature, the number of children in a family, and the price of houses. The mixed but overall disappointing performance on the six items in the three contexts indicates…

The new common core standards for mathematics demand that students (and teachers!) exhibit deeper conceptual understanding. That's music to the ears of education professor John Tapper, who says teachers have overemphasized teaching procedures--and getting right answers. In his new book, "Solving for Why," he makes a powerful case for moving beyond…

The opening lines of "How the Grinch Stole Christmas!" (Geisel 1957) set the tone for an inspiring change-of-heart story about a grumpy creature that comes to value humanity and the Christmas spirit. Although the book is often considered inspirational for other reasons, the authors were particularly moved by Dr. Seuss's interesting conjecture…

This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual…

The critical power (CP) concept has received renewed attention and excitement in the academic community. The CP concept was originally conceived as a model derived from a series of exhaustive, constant-load, exercise bouts. All-out exercise testing has made quantification of the parameters for the two-component model easier to arrive at, which may…

The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…

In a recent paper, Hu, Ericsson, Yang, and Lu (2009) found that an ability to memorize very long lists of digits is not mediated by the same mechanisms as exceptional memory for rapidly presented lists, which has been the traditional focus of laboratory research. Chao Lu is the holder of the "Guinness World Record" for reciting the most decimal…

This paper describes and analyses two mathematics lessons, one with very young pupils, about subtraction, the other for lower secondary school pupils, about gradients [slopes] and graphs. The focus of the analysis is on teacher knowledge, and on the fundamental mathematical and mathematics-pedagogical prerequisites that underpin teaching these…