Patterns of problem-solving among 5-to-7 year-olds' were examined on a range of literacy (reading and spelling) and arithmetic-based (addition and subtraction) problem-solving tasks using verbal self-reports to monitor strategy choice. The results showed higher levels of variability in the children's strategy choice across Years 1 and 2 on the…

Some years ago, Hatano differentiated between routine and adaptive expertise and made a strong plea for the development and implementation of learning environments that aim at the latter type of expertise and not just the former. In this contribution we reflect on one aspect of adaptivity, namely the adaptive use of solution strategies in…

Processing information in working memory requires selective access to a subset of working-memory contents by a focus of attention. Complex cognition often requires joint access to 2 items in working memory. How does the focus select 2 items? Two experiments with an arithmetic task and 1 with a spatial task investigate time demands for successive…

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…

This article investigates prospective elementary teachers' conceptions of the repeating decimal 0.999... Five students from a first-semester undergraduate course "Mathematics for Elementary School Teachers" were interviewed to ascertain their conceptions about the mathematical statement 0.999... = 1. All of the students indicated they do not…

Participants' reaction times (RTs) in numerical judgment tasks in which one must determine which of 2 numbers is greater generally follow a monotonically decreasing function of the numerical distance between the two presented numbers. Here, I present 3 experiments in which the relative influences of numerical distance and physical similarity are…

Children take years to learn symbolic arithmetic. Nevertheless, non-human animals, human adults with no formal education, and human infants represent approximate number in arrays of objects and sequences of events, and they use these capacities to perform approximate addition and subtraction. Do children harness these abilities when they begin to…

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…

Results from 2 relational-priming experiments suggest the existence of an automatic analogical coordination between semantic and arithmetic relations. Word pairs denoting object sets served as primes in a task that elicits "obligatory" activation of addition facts (5 + 3 activates 8; J. LeFevre, J. Bisanz, & L. Mrkonjic, 1988). Semantic relations…

Three studies addressed children's arithmetic. First, 50 3- to 5-year-olds judged physical demonstrations of addition, subtraction and inversion, with and without number words. Second, 20 3- to 4-year-olds made equivalence judgments of additions and subtractions. Third, 60 4- to 6-year-olds solved addition, subtraction and inversion problems that…

A study was conducted at a southern university in sophomore level production classes to assess skills such as the order of arithmetic operations, decimal and percent conversion, solving of algebraic expressions, and evaluation of formulas. The study was replicated using business statistics and quantitative analysis classes at a southeastern…