A vast majority of elementary students struggle with the core, pre-algebraic concept of mathematical equivalence. The Improving Children's Understanding of Equivalence (ICUE) intervention integrates four research-based strategies to improve outcomes for second grade students: (1) introducing the equal sign before arithmetic, (2) non-traditional…

This research considers the first year of a longitudinal study in which we are investigating the development of children's algebraic thinking as they take part an early algebra intervention in kindergarten through grade 2. Specifically, this study investigates kindergarteners' understanding of unknown quantities and their representation of these…

This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based…

How people see the world, even how they research it, is influenced by beliefs. Some beliefs are conscious and the result of research, or at least amenable to research. Others are largely invisible. They may feel like "common knowledge" (though myth, not knowledge), unrecognized premises that are part of the surrounding culture. As we…

This paper examines whether using "From Here to There!" ("FH2T:E"), a dynamic game-based mathematics learning technology relates to improved early algebraic understanding. We use student log files within FH2T to explore the possible benefits of student behaviors and gamification on learning gains. Using in app measures of…

The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and prealgebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other…

In this article, the authors begin with a description of an algebraic dance--the translation of composite linear growing patterns into choreographed movement--which was the last component of a research-based instructional unit that focused on fostering an understanding of linear functional rules through geometric growing patterns and…

Teachers are using technological innovations--including interactive whiteboards--in pre-K-grade 3 classrooms across the country. An IWB is a wall-mounted, touch-sensitive flat screen. When connected to a computer (or another electronic device) and a projector, it displays enlarged instructional content (such as a math word problem, pictures or…

The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…

The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which…

Common Core education standards establish a clear set of specific ideas and skills that all students should be able to comprehend at each grade level. In an effort to meet these standards, educators are turning to technology for improved learning outcomes. "Cases on Technology Integration in Mathematics Education" provides a compilation…

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…

Cognitively Guided Instruction (CGI) researchers have found that while teachers readily ask initial questions to elicit students' mathematical thinking, they struggle with how to follow up on student ideas. This study examines the classrooms of three teachers who had engaged in algebraic reasoning CGI professional development. We detail teachers'…

This paper describes the use of Kid Pix-graphics software for creative activities of young children--in the context of early algebra as determined by the mathematics core curriculum of New York state. It shows how grade-two appropriate pedagogy makes it possible to bring about a qualitative change in the learning process of those commonly…