Proficiency in mathematics across the United States has become an area of concern as performance on state accountability tests continues to demonstrate that less than 50% of students in 4th and 8th grade are proficient in mathematics (NCES, 2013). With such large numbers of students lacking proficiency in mathematics, systematic interventions that…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

With the adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), many concepts related to area are covered in third grade: (1) Recognizing area as an attribute of a plane figure; (2) Understanding that a square with a side length of one is a unit square; (3) Measuring area by tiling figures and counting the squares it…

This case study examined competence in two third-grade classrooms where teachers centered children's mathematical thinking in instructional decision-making. Offering a synthesis of sociocultural characterizations of competence, and drawing from a variety of data sources including classroom video, student work and assessments, and teacher…

This study aimed to create a constructivist learning environment wherein third-grade students talk to problem solve, which is different from traditional approaches to math learning. The study focused on the group talk and discussions to understand the students' actions and interactions during the process of problem-solving. Fifteen students and…

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

This paper reports on 13 Grade 3 students' approaches to partitive and quotitive division word problems. Of particular interest was the extent to which students drew on their knowledge of multiplication to solve division problems. The findings suggest that developing a relationship between multiplication and division is more significant than…

Computational fluency is an important aspect of math proficiency. Despite widely held beliefs about the differential difficulty of single-digit multiplication math facts, little empirical work has examined this issue. The current study analyzed the number of repetitions needed to master multiplication math facts. Data from 15,402 3rd, 4th, and 5th…

Developing fluency in arithmetic facts is instrumental to mathematics learning. This study compares the effects of two practice conditions on children's fluency in simple multiplication facts. Third and fourth graders in the Netherlands (N = 282) practised in either a conventional "recall" condition where they produced answers to…

Mathematics is about reasoning, patterns, and making sense of things. Children's literature provides a powerful opportunity to foster unique experiences in mathematics learning. Storybooks, thinking strategies, and manipulatives offer a winning combination for mastering multiplication facts based on conceptual ideas and relationships. The most…

An adapted alternating treatments design with initial baseline and final best treatment phase was used to evaluate and compare the effects of two classwide interventions, detect--practice--repair (DPR), and self-mediated iPad instruction, on the multiplication math facts fluency in an inclusive third-grade classroom. Twelve students participated…

The purpose of the present study was to examine the effectiveness of a strategic training program for improving students' performance in solving multiplication problems. The participants were 3 third graders with math difficulties. In this teaching experiment, microgenetic analysis was used to analyze improvement in students' strategic development…

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…

This paper describes a dataset consisting of longitudinal data gathered in the BRXXX project. The aim of the project was to investigate the effectiveness of online mathematics mini-games in enhancing primary school students' multiplicative reasoning ability (multiplication and division). The dataset includes data of 719 students from 35 primary…

The purpose of this study was to determine if a typical third-grade boy and fifth-grade girl and a boy with learning disabilities could benefit from the combined use of Direct Instruction (DI) flashcard and math racetrack procedures in an after-school program. The dependent variable was accuracy and fluency of saying basic multiplication facts. A…