Suggestions and ideas that enable teachers to take a closer look at students' thinking are discussed. A teacher should periodically reflect on his or her own classroom practices in order to increase attention on students' mathematical thinking.

Media Clips aims to offer readers contemporary, authentic applications of quantitative reasoning based on print or electronic media. Clips may be in text or graphic format, and clip sources may be either print or electronic media.

The complexities involved in writing mathematics problems and a cooperative learning activity that gives students the challenge of writing mathematical logic problems for their peers is discussed. Making students construct mathematics problems taps into several important skills in mathematics and students are asked to consider what it means to…

A new textbook was considered which included engaging, carefully sequenced problems to help students develop skill and understanding of division. The teacher's manual encouraged Boerst to provide opportunities for the students to share multiple methods for division in order to reinforce the idea that many ways exist to solve mathematical problems.

Mathematics truly is magical, especially for students with strong number sense and algebra skills. This paper describes a variety of mathematical surprises that will capture students' interest and motivate exploration of mathematical ideas. While the tricks themselves are fascinating, push students to think about the reasons why these stunning…

In this article, the author shares some of the activities for the classroom invented by Gill Hatch. One of those activities is the activity for older students, which is for the five-year-olds through to post-graduates. Card-sorting game, geometry games, algebra games, and loop games are also some of those activities for the classroom invented by…

Two studies were conducted to investigate, firstly, children's focusing on the aspect of numerosity in utilizing enumeration in action, and, secondly, whether children's Spontaneous Focusing on Numerosity (SFON) is related to their counting development. The longitudinal data of 39 children from the age of 3.5 to 6 years showed individual…

In 3 experiments, the authors examined mathematical problem solving performance under pressure. In Experiment 1, pressure harmed performance on only unpracticed problems with heavy working memory demands. In Experiment 2, such high-demand problems were practiced until their answers were directly retrieved from memory. This eliminated choking under…

Within statistics instruction, students are often requested to sketch the curve representing a normal distribution with a given mean and standard deviation. Unfortunately, these sketches are often notoriously imprecise. Poor sketches are usually the result of missing mathematical knowledge. This paper considers relationships which exist among…

Contrasting instructional approaches were used to introduce mathematical modeling to two sets of students with weak content skills and no prior modeling experience. One group was exposed to examples of models for a particular contextual problem; the other group was asked to construct their own model for the same situation. In less than three…

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual…

The authors reviewed recent quantitative genetic research on learning disabilities that led to the conclusion that genetic diagnoses differ from traditional diagnoses in that the effects of relevant genes are largely general rather than specific. This research suggests that most genes associated with common learning disabilities--language…

Results from an earlier study conducted by the researchers [Cai, J., & Cifarelli, V.V. (2005). "Exploring mathematical exploration: How two college students formulated and solved their own mathematical problems?" "Focus on Learning Problems in Mathematics," 27(3), 43-72] illustrated and explained several characteristics of the solvers'…

In a recent edition of "Mathematics Teaching" Midge Pasternack argued the case for the use of the 0-99 square with young children rather than the ubiquitous 1-100 square. In this article, the author would like to take the opportunity to mount a defence in favour of the much maligned 1-100 square. His main criticism of the 0-99 square (apart from…

First-year undergraduate engineering students' understanding of the units of factors and terms in first-order ordinary differential equations used in modelling contexts was investigated using diagnostic quiz questions. Few students appeared to realize that the units of each term in such equations must be the same, or if they did, nevertheless…