Before starting school, many children reason logically about concepts that are basic to their later mathematical learning. We describe a measure of quantitative reasoning that was administered to children at school entry (mean age 5.8 years) and accounted for more variance in a mathematical attainment test than general cognitive ability 16 months…

An A-B single-case design assessed at-risk students' responsiveness to mathematics interventions. Four culturally and linguistically diverse second-grade students were given a Tier 2 standard protocol mathematics intervention that included number sense instruction, modeling procedures, guided math drill and practice of addition and subtraction…

Children's (N = 275) use of retrieval, decomposition (e.g., 7 = 4+3 and thus 6+7 = 6+4+3), and counting to solve additional problems was longitudinally assessed from first grade to fourth grade, and intelligence, working memory, and in-class attentive behavior was assessed in one or several grades. The goal was to assess the relation between…

Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic…

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the…

Counting strategies initially used by young children to perform simple addition are often replaced by more efficient counting strategies, decomposition strategies and rule-based strategies until most answers are encoded in memory and can be directly retrieved. Practice is thought to be the key to developing fluent retrieval of addition facts. This…

The "Extending Mathematical Understanding" (EMU) Program is a specialised mathematics program that aims to accelerate the learning of Grade 1 students who struggle with learning school mathematics. Forty-two students participated in an EMU Program in 2010 as part of the "Bridging the Numeracy Gap" (BTNG) project. Analysis of…

Because math fact automaticity has been identified as a key barrier for students struggling with mathematics, we examined how initial math achievement levels influenced the path to automaticity (e.g., variation in number of attempts, speed of retrieval, and skill maintenance over time) and the relation between attainment of automaticity and gains…

A multiple-baseline design across math-fact sets was used to evaluate the effects of a taped-problems intervention on students' performance with addition facts and their inverses in an intact, rural, second-grade classroom. Results suggested that the procedure was effective in improving fluency on math facts as well as their inverses. Across 3…

One hundred and seventy-eight second grade students from two states (Georgia and Massachusetts) participated in an experiment in which they were randomly assigned to either (1) a computer program designed to increase fluency in addition and subtraction, (2) a program designed to improve cognitive strategy use for addition and subtraction, (3) a…

This research study, carried out in South Africa and the United States of America, investigated issues that may hamper prospective primary school teachers from writing acceptable problem posing scenarios involving the addition of fractions. Pre-service teachers (n=44) were asked to compose real life problems involving the addition of two fractions…

High academic standards are an important first step in ensuring that all Alaska's students have the tools they need for success. These standards reflect the collaborative work of Alaskan educators and national experts from the nonprofit National Center for the Improvement of Educational Assessment. Further, they are informed by public comments.…

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…

Fourth-grade students in Title I mathematics took 40-problem tests to determine types of persistent errors made in addition and subtraction. Tests, administered to 117 students (addition) and 104 students (subtraction), were analyzed for basic fact, random, or procedural errors. Findings are reported and discussed, and recommendations for…

This cross-sectional study investigated the problem-solving strategies used by schooled and unschooled Nigerian children to solve simple addition and subtraction problems. The purpose of the study was to: (1) verify with Nigerian children, models of the knowledge and strategies underlying children's solutions to simple word problems; (2) test the…