This paper explores the ways preschool teachers orchestrate instructional environments to promote mathematical play related to early number and, how they intervene during play to promote children's engagement with early number. We highlight these practices to identify resources for the growing numbers of early childhood teachers. This is important…

The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as "equal," "more," and "less," and associated number concepts would increase at-risk children's vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were…

In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication and division. They provide examples of activities that can be used from Foundation to Year 5.

The authors introduce an educational video game (application, or "app"), "CandyFactory Educational Game," designed to promote students' development of partitive understanding of fractions while demonstrating the critical need to promote that development. The app includes essential game features of immediate feedback,…

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of…

Mental abacus (MA) is a technique of performing fast, accurate arithmetic using a mental image of an abacus; experts exhibit astonishing calculation abilities. Over 3 years, 204 elementary school students (age range at outset: 5-7 years old) participated in a randomized, controlled trial to test whether MA expertise (a) can be acquired in standard…

Today, the Common Core State Standards for Mathematics (CCSSI 2010) expect students in as early as eighth grade to be knowledgeable about irrational numbers. Yet a common tendency in classrooms and on standardized tests is to avoid rational and irrational solutions to problems in favor of integer solutions, which are easier for students to…

This paper focuses on selected findings from a study that explored the use of multiplication and division with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. The focus of instructional tasks was on working with groups of ten to support the understanding of place value. Findings from relevant assessment tasks…

This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with…

Encouraging students to reason with quantitative relationships can help them develop, understand, and explore mathematical models of real-world phenomena. Through two examples--modeling the motion of a speeding car and the growth of a Jactus plant--this article describes how teachers can use six practical tips to help students develop quantitative…

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…

In this proposal, I introduce a method for modeling the dynamics of a sixth-grade student's accommodation of his fractions scheme to include a disembedding operation (Steffe & Olive, 2010). I will describe a three-part approach consisting of a constructivist teaching experiment, retrospective analysis, and stochastic modeling of the student's…

In this article, one teacher describes her action research with eighth-grade prealgebra students who are working on a conceptual understanding of fractions. Examining her middle school students' standardized test scores for the previous five years, Denise S. Peppers discovered that student performance on fractions was consistently the lowest…

Place value is a key concept for numbers that is introduced in early mathematics. It is necessary to have a flexible understanding of place value for efficient arithmetic strategies and success in written algorithmic arithmetic. In our research we explore typical mistakes and misconceptions that occur with 3rd graders in German elementary school…

It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…