Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

Mathematical writing is one way for primary students to communicate their mathematical thinking. Research in the field of writing has shown that to become an effective teacher of writing, preservice teachers must have experience engaging in the kinds of writing given to their students. The study reported in this paper explored how 27 preservice…

Background: Base-ten thinking (BTT) -- children's ability to reason in tens and ones is a crucial measure of Foundation Phase learners' mathematical performance in South Africa. Aim: The study looks at the six learners using BTT to solve additive tasks through two different assessments. Setting: Six purposely selected Grade 3 learners in…

Lina, a Mexican American second grader, bilingual in Spanish and English, used a strategy for adding two two-digit numbers that the authors share as an example of the importance of listening to the mathematical ideas of children, especially when these ideas do not align with how mathematics is traditionally represented in the classroom. The…

This article investigates how students in third grade learn to reason on multiplication when they first encounter that concept in the classroom context. By analysing the data from 24 classrooms focused on teaching and learning multiplication, the article aims at contributing to the research and conceptualisations about how students learn to…

This paper considers whether or not curriculum initiatives within England are in fact leading to qualitatively improved levels of thinking among children identified as lower achievers in arithmetic. Revisiting data from two earlier studies and introducing current data, the paper draws comparisons in the strategies that 8-year-old children use to…

An experimental group (n=13) and a control group (n=15) of children with mental retardation were both shown a basic concrete counting procedure. Over six months, the experimental group was given regular opportunities to practice computing sums. Many of them invented calculational short cuts. Results suggest that children with mental retardation…

Four fifth and sixth grade students with learning disabilities were taught a strategy for comprehending word problems and devising appropriate solutions. Following instruction performance on mixed sets of addition and subtraction word problems improved. Although generalization to a different setting occurred, maintenance was mixed. (Author/DB)

A study asked 24 first grade children from 3 different classes to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Results indicated that children could be characterized into five clusters according to their flexibility in accepting alternative number sentences and that…

Discusses prerequisites that help students develop multiple strategies for solving problems as recommended in the National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards." Presents two examples of activities involving addition, subtraction, and permutations that promote multiple strategies. Suggests ways to…

Presents a three-year longitudinal study investigating the development of children's (n=82) understanding of multidigit number concepts and operations in grades one through three by using interview processes. Provides an existence proof that children can invent strategies for adding and subtracting and illustrates both what that invention affords…