It is investigated if the mental computation strategies in the research literature are enough to satisfactorily categorize the mental computation strategy use by preservice elementary teachers in multiplication on one- and two-digit natural numbers. The preservice elementary teachers use of mental computation strategies is measured operationally…

There is broad consensus on the assumption that adults solve single-digit multiplication problems almost exclusively by fact retrieval from memory. In contrast, there has been a long-standing debate on the cognitive processes involved in solving single-digit addition problems. This debate has evolved around two theoretical accounts. Proponents of…

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study…

This study aims to explain the thinking process of students in solving combination problems considered from assimilation and accommodation frameworks. This research used a case study approach by classifying students into three categories of capabilities namely high, medium and low capabilities. From each of the ability categories, one student was…

Counting problems have applications in probability and computer science, and they provide rich contexts for problem solving. Such problems are accessible to students, but subtleties can arise that make them surprisingly difficult to solve. In this paper, students' work on the Groups of Students problem is presented, and an important issue related…

Solving simple arithmetic problems involves three stages: encoding the problem, retrieving or calculating the answer, and reporting the answer. This study compared the event-related potentials elicited by single-digit addition and multiplication problems to examine the relationship between encoding and retrieval/calculation stages. Results showed…

Mastering single-digit arithmetic during school years is commonly thought to depend upon an increasing reliance on verbally memorized facts. An alternative model, however, posits that fluency in single-digit arithmetic might also be achieved via the increasing use of efficient calculation procedures. To test between these hypotheses, we used a…

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…

In this third of a series of four articles, the author deconstructs the primary national strategy's approach to written multiplication. The approach to multiplication, as set out on pages 12 to 15 of the primary national strategy's "Guidance paper" "Calculation" (DfES, 2007), is divided into six stages: (1) mental…

We examine whether the array representation can support children's understanding and reasoning in multiplication. To begin, we define what we mean by understanding and reasoning. We adopt a "representational-reasoning" model of understanding, where understanding is seen as connections being made between mental representations of concepts, with…

Four methods of solutions and 12 calculative strategies were found from introspective reports of 15 skilled and 15 unskilled students in grades 11 and 12 doing mental multiplication. Unskilled students used strategies more suited to written than mental computation, while skilled students used strategies based on number properties. (MNS)

How children perceive doubling and halving numbers is discussed, with many examples. The use of calculators is integrated. The tendency to avoid division if other ways of solving a problem can be found was noted. (MNS)

Three experiments evaluated performance on a mental multiplication task and the adequacy of several different models of mental addition as extended to multiplication. Results are discussed in terms of a network-retrieval approach to mental arithmetic, the commonalities between addition and multiplication, and rule- versus retrieval-based…

Children use acquired knowledge as they learn basic multiplication facts. If informal thinking strategies are stressed, the border between "figuring out" and "knowing by heart" gradually disappears. Children will acquire a flexible mental structure of multiplication facts instead of a collection of rules. (MNS)

The effects of generating versus reading the answers to multiplication problems were studied with 28 2nd graders who had not yet been taught multiplication. Results are explained in terms of a procedural account of the advantage after retention interval for generation. Instructional applications are discussed. (SLD)