Although many children with reading difficulty (RD) are reported to struggle with mathematics, little research has empirically investigated whether this is the case for different types of RD. This study examined the mathematics skills of third graders with one of two types of RD: dyslexia (n = 18) or specific reading comprehension difficulty (n =…

Three experiments used dual-task suppression methodology to study the use of inner speech and visuospatial resources for mediating central executive performance by children with autism (CWA) and group-matched typically developing (TD) controls. Expt 1 revealed that CWA did not recruit inner speech to facilitate arithmetic task-switching…

Children's reasoning was examined within two educational contexts (word reading and addition) so as to understand the factors that contribute to relational reasoning in the two domains. Sixty-seven 5- to 7-year-olds were given a series of related words to read or single-digit addition items to solve (interspersed with unrelated items). The…

The nation is facing a crisis in its community colleges: more and more students are attending community colleges, but most of them are not prepared for college-level work. The problem may be most dire in mathematics. By most accounts, the majority of students entering community colleges are placed (based on placement test performance) into…

Transfer of strategies between problems sharing the same formal structure is facilitated by a semantic recoding that makes evident the structural similarities between the problems. Two experiments were carried out among 4th and 5th grade pupils, with an experimental group trained to compare strategies in order to reinterpret an arithmetic word…

Every school system has to deal with children with Learning Disabilities (LD). However, the concepts of LD, the assessment procedures, the diagnostic criteria as well as their interpretation vary widely from country to country. What they usually seem to have in common is that general cognitive abilities, as measured by standardized IQ tests, are…

In a meta-analysis of 164 studies, Alfieri, Brooks, Aldrich, and Tenenbaum (2010) found that assisted discovery learning was more effective than explicit instruction or unassisted discovery learning and that explicit instruction resulted in more favorable outcomes than unassisted discovery learning. In other words, "unassisted discovery does…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (nonradical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

Counting abilities have been described as determinative precursors for a good development of later arithmetic abilities. Mastery of the stable order, the one-one-correspondence and the cardinality principles can be seen as essential features for the development of counting abilities. Mastery of the counting principles in kindergarten was assessed…

The arithmetical performance of typically achieving 5- to 7-year-olds (N=29) was measured at four 6-month intervals. The same seven tasks were used at each time point: exact calculation, story problems, approximate arithmetic, place value, calculation principles, forced retrieval, and written problems. Although group analysis showed mostly linear…

The Lorentz velocity addition formula for one-dimensional motion presents a number of problems for beginning students of special relativity. In this paper we suggest a simple rewrite of the formula that is easier for students to memorize and manipulate, and furthermore is more intuitive in understanding the correction necessary when adding…

A number derivative is a numerical mapping that satisfies the product rule. In this paper, we determine all number derivatives on the set of integers modulo n. We also give a list of undergraduate research projects to pursue using these maps as a starting point.

Children's failure on equivalence problems (e.g., 5 + 4 = 7 + __) is believed to be the result of misunderstanding the equal sign and has been tested using symbolic problems (including "="). For Study 1 (N = 48), we designed a nonsymbolic method for presenting equivalence problems to determine whether Grade 2 children's difficulty is due…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…

A 3-week problem-solving practice phase was used to investigate concept-procedure interactions in children's addition and subtraction. A total of 72 7- and 8-year-olds completed a pretest and posttest in which their accuracy and procedures on randomly ordered problems were recorded along with their reports of using concept-based relations in…