The involvement of working memory (WM) was examined in two types of mental calculation tasks: exact and approximate. Specifically, children attending Grades 3 and 4 of primary school were involved in three experiments that examined the role of verbal and visuospatial WM in solving addition problems presented in vertical or horizontal format. For…

Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing…

In two experiments, we studied how people's strategy choices emerge through an initial and then a more considered evaluation of available strategies. The experiments employed a computer-based paradigm where participants solved multiplication problems using mental and calculator solutions. In addition to recording responses and solution times, we…

Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…

The key questions are: is it true that persons with Down's syndrome can study mathematics only at a very elementary level? Might it be possible that their difficulties are mainly restricted to some fields, such as numeracy and mental computation, but do not encompass the entire domain of mathematics? Is the use of a calculator recommended? Is…

"Number Talks" is: (1) A five- to fifteen-minute classroom conversation around purposefully crafted computation problems that are solved mentally; and (2) The best part of a teacher's day. Whether you want to implement number talks but are unsure of how to begin or have experience but want more guidance in crafting purposeful problems, this…

This paper reports on a study to examine mental computation strategies used by Year 1, Year 2, and Year 3 students to solve addition and subtraction problems. The participants in this study were twenty five 7 to 9 year-old students identified as excellent, good and satisfactory in their mathematics performance from a school in Penang, Malaysia.…

We investigated the influence of self-efficacy beliefs and working memory capacity on mathematical problem-solving performance, response time, and efficiency (i.e., the ratio of problems solved correctly to time). Students completed a letter-recoding task (Experiment 1) or an operation span task (Experiment 2), rated their self-efficacy for…

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…

Individual differences in strategy use (choice and accuracy) were analyzed. A sample of 362 Grade 6 students solved complex division problems under 2 different conditions. In the choice condition students were allowed to use either a mental or a written strategy. In the subsequent no-choice condition, they were required to use a written strategy.…

The aim of this study was to investigate the strategies used by third graders in solving the 81 elementary subtractions that are the inverses of the one-digit additions with addends from 1 to 9 recently studied by Barrouillet and Lepine. Although the pattern of relationship between individual differences in working memory, on the one hand, and…

A grounded theory approach was employed to explore the variation in strategies used by students when solving mental multiplication problems. Metacognitive prompts, externally generated stimuli that activate thoughtful cognition, were automatically generated via computer during the solving of mental multiplication problems to elicit awareness,…

Recent international studies have highlighted the success of students from Hong Kong in mathematics and problem-solving, and have begun to suggest some of the factors associated with this success. Other studies have suggested that Hong Kong students are averse to risk-taking, favouring memorisation and imitation in their solution strategies. Year…

To date, few studies have investigated the evolution of problem solving and general numeracy abilities during adulthood: skills that have obvious social importance. In this research, evolutions in adults' mental arithmetic skills were investigated using data from the IVQ 2004 French national survey, which tested 9,185 adults aged between 18 and…

The adaptive use of approximate calculation was examined using a verification task with 18 third graders with mathematics learning disabilities, 22 typically achieving third graders, and 21 typically achieving second graders. Participants were asked to make true-false decisions on simple and complex addition problems while the distance between the…