This paper reports on results of a targeted and extended (two school terms) program for building Grade 3 and Grade 4 students' facility with number facts and application for mental computation. As part of a larger project, this paper reports results from two schools. Results indicated strong gains in number fact recall and mental computation for…

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

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.…

Research literature is reviewed, identifying a need to design instruction to support multi-digit mental computation and critiquing conventional place value instruction. A distinctive instructional domain is proposed, called conceptual place value (CPV)--incrementing and decrementing numbers by units of ones, tens and hundreds. A design research…

Learning pathways capture the development of competence in a mathematical domain. They have been developed from empirical studies in the areas of mental computation and emergent numeracy concepts. These pathways afford teachers the opportunity to identify students' current levels of understanding, antecedent understandings and the steps that are…

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…

Moving from arithmetic to algebraic thinking at early grades is foundational in the study of number patterns and number relationships. This qualitative study investigates mental computational activity in a third grade classroom's and its relationship to algebraic thinking and reasoning. The data sources include classroom observations, field notes,…

The focus of this study was to investigate mental computation conceptual frameworks that Heirdsfield (2001c) formulated to explain the difference between proficient (accurate and flexible) mental computers and accurate (but not flexible) mental computers. A further aim was to explore the potential for students' developing efficient mental…

Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

"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 longitudinal study was conducted in order to determine and improve the mental addition strategies of students in their 2nd and 3rd years at elementary school. The first part of the study used the qualitative research method of case study, while the second part adopted the single group pretest-posttest quasi-experimental design. The study…

In this paper, we share the results of the piloting of national diagnostic assessments for strategic calculation with Grade 3 learners in South Africa. The diagnostic assessment pilot intervention was focused on promoting strategic use of calculation strategies and aimed to move learners on from the concrete one-to-one counting methods that…

The aim of this research was to examine the role of working memory in moderating the effects of automaticity on mental addition in 40 Chinese third-graders from the perspectives of task characteristics and individual characteristics. In Study 1, a 2 (working memory load [WML]) × 2 (automaticity), within-subjects design was utilized. There was…

The research examined the calculation methods used by pupils in Grades 3-6 when they were presented with problems that could be worked out efficiently and flexibly by applying number sense. The study was conducted with a convenience sample of 179 pupils between the ages 7 years and 10 months to 12 years and 10 months. in mainstream education in…

Many studies in the past decades have focused on low and typical mathematics achievers, yet little is known about children with high mathematics achievement, particularly at a young age. The current study aimed to fill this gap and started from the early work of Krutetskii (1976) as a theoretical lens to study the characteristics of high…