Here is the only reference book you will ever need for teaching primary school mathematics and statistics. It is full of exciting and engaging snapshots of excellent classroom practice relevant to "The New Zealand Curriculum" and national mathematics standards. There are many fascinating examples of investigative learning experiences,…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…

Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the…

To prepare to teach in mathematics classrooms where children learn to justify their thinking, the teachers themselves must have experienced an environment of inquiry, communication, collaboration, and reasoning. Teacher educators strive to establish such environments for preservice teachers (PSTs) and to support their transition from rules-based…

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…

The effectiveness of a pentop computer when teaching multiplication facts to three middle school students with mild intellectual disabilities was examined. A multiple probe design was used to assess the students learning of one and two digit multiplication facts over a 2-3 week intervention period. During the intervention phase, students used a…

Subtraction problems of the type a - b = ? can be "flexibly" solved by various strategies, including the indirect addition strategy ("how much do I have to add to b to get at a?"). Little research has been done on the use of the indirect addition strategy with multi-digit numbers. The present literature review entails a summary…

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 discusses large-scale assessment of change in student achievement and takes the study by Hickendorff, Heiser, Van Putten, and Verhelst (2009) as an example. This study compared the achievement of students in the Netherlands in 1997 and 2004 on written division problems. Based on this comparison, they claim that there is a performance…

The present study concerns redundant data problems, defined as problems in which irrelevant data is provided. This type of problem provides a misleading context [Pascual-Leone, J. (1987). Organismic process for neo-Piagetian theories: A dialectical causal account of cognitive development. "International Journal of Psychology," 22, 531-570] similar…

This article describes how a crystal ball known as "The Flash Mind Reader" is played. "The Flash Mind Reader" is a mathematics game in which the player is invited to select any-two digit number and then subtract the sum of these two digits from the original number. A chart is provided in which the (adjusted) number they…

This paper describes six tricks on different mathematical concepts for mathematics classrooms. The mathematical concepts emphasized in these activities include arithmetic, modular arithmetic, limit cycles, graph theory, pairings, combinatorics, cyclic groups, induction, and sequences. (ASK)

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…

Working memory is the cognitive ability to hold a discrete amount of information in mind in an accessible state for utilization in mental tasks. This cognitive ability is impaired in many clinical populations. There have been a number of theoretical shifts in the way that working memory is conceptualized and assessed in the experimental…