This study investigated whether children's inversion shortcut use (i.e., reasoning that no calculations are required for the problem 4 x 8 divided by 8, as the answer is the first number) is related to their analogical reasoning ability, short-term memory capacity, and working memory capacity. Children from Grades 6 and 8 solved multiplication and…

This study measured the amounts of different types of metacognitive statements made by students enrolled in Elementary Algebra courses at a community college in California. A total of 17 students were interviewed three times during the course of a semester. All interviews were coded for types of metacognitive statements that fell into one of three…

Now in a second edition, the award-winning "The Trouble with Maths" offers important insights into the often confusing world of numeracy. By looking at learning difficulties in maths from several perspectives, including the language of mathematics, thinking styles and the demands of individual topics, this book offers a complete overview of the…

fMRI was used to examine the differential effect of two problem-solving strategies. Participants were trained to use both a pictorial/spatial and a symbolic/algebraic strategy to solve word problems. While these two strategies activated similar cortical regions, a number of differences were noted in the level of activation. These differences…

The purpose of this research is to describe and understand the ways in which deaf middle school students understood and solved compare word problems, and to examine their overall strategy use in learning mathematics. The participants in the study were deaf middle school students, attending a residential state school for the deaf. Most of them used…

This study by Lio Moscardini of the University of Strathclyde shows how a group of 24 children in three Scottish primary schools for pupils with moderate learning difficulties responded to word problems following their teachers' introduction to the principles of Cognitively Guided Instruction (CGI). CGI is a professional development programme in…

This article explores the complementary strengths and weaknesses of grounded and abstract representations in the domain of early algebra. Abstract representations, such as algebraic symbols, are concise and easy to manipulate but are distanced from any physical referents. Grounded representations, such as verbal descriptions of situations, are…

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

In the article we compare the approaches of 3 in-service teachers and 3 student teachers when they tried to solve a verbal arithmetic problem in the classroom. Each interaction was studied using a System of Analysis that takes into account the cognitive processes involved in the solution of a mathematic problem and describes the interaction at…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

Studied patterns of self-explanation that distinguish between good and poor problem solvers. Results with 32 ninth graders identify self-explanation patterns that show that poor problem solvers are more likely to produce clarifications after inferences and good problem solvers are more likely to produce justifications after regulations. (SLD)

This paper applies APOS Theory to suggest a new explanation of how people might think about the concept of infinity. We propose cognitive explanations, and in some cases resolutions, of various dichotomies, paradoxes, and mathematical problems involving the concept of infinity. These explanations are expressed in terms of the mental mechanisms of…

A study found gifted middle schoolers (n=60) solved analogous problems better when presented in verbal form, but improved skills in both modalities once exposed to the solution of analogous problems in the visual-humorous modality. Average children (n=60) tended to solve cartoons better, but working with cartoons increased verbal problem-solving…

Two experiments were conducted to understand the processes through which 5th graders discriminate relevant from irrelevant information when solving mathematical story problems. Visual scanning was recorded and coded as directed toward relevant information, irrelevant information, the question, workspace, and elsewhere. Experiment 1 focused on the…

The focus of this article is intervention for third-grade students with serious mathematics deficits at third grade. In third grade, such deficits are clearly established, and identification of mathematics disabilities typically begins. We provide background information on two aspects of mathematical cognition that present major challenges for…