Background: In several countries, children's math skills have been declining at an alarming rate in recent years and decades, and one of the explanations for this alarming situation is that children have difficulties in establishing the relations between arithmetical operations. Aim: In order to address this question, our goal was to determine the…

Multiplicative reasoning is a key concept in elementary school mathematics. Item statistics reported by the National Assessment of Educational Progress (NAEP) assessment provide the best current indicator for how well elementary students across the U.S. understand this, and other concepts. However, beyond expert reviews and statistical analysis,…

It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…

This design study investigated the use of multiplication and division problems to help 5-year-old children develop an early understanding of multiplication and division. One teacher and her class of 15 5-year-old children were involved in a collaborative partnership with the researchers. The design study was conducted over two 4-week periods in…

This paper shares research from a pilot study in which young children were introduced to multiplication and division problems in their first year of school. The focus was on building children's conceptual understanding of the idea of "repeated groups" as a fundamental aspect of multiplication and its relation to division. The particular…

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 the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

The introduction of negative numbers should mean that mathematics can be twice as much fun, but unfortunately they are a source of confusion for many students. Difficulties occur in moving from intuitive understandings to formal mathematical representations of operations with negative and positive integers. This paper describes a series of…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…

For over a decade, research studies of mathematics education in high-performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. To deliver on the promise of common standards, the standards…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…

Examines adults from China and Canada solving single-digit multiplication problems. Reports that Chinese adults were faster and made fewer errors than Canadian adults, and Chinese adults made more errors that reflect verbal-production processes that may occur after retrieval whereas Canadian adults made more errors that reflect retrieval…

Explores how to use Gardner's Multiple Intelligence theory to help students' master multiplication. Focuses on helping children use their different intelligence strength to attain conceptual understanding of multiplication, develop their own thinking strategies for harder facts, and build mastery through practice and problem solving. (KHR)