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,…

Powell, Berry, et al. (in press) conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly…

This research focuses on the retention of students' algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3-5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly…

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical…

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…

Guided by a theoretical framework emphasizing the importance of fidelity of implementation (FOI), this paper explores how teachers of grades 3, 4 and 5 implemented an early algebra intervention, and the relationship between FOI and student learning. The data shared in this paper come from a longitudinal experimental research project in which 3,208…

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded pre-algebraic reasoning instruction, improves word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or one of two variants of word-problem intervention.…

In the first chaotic days of the crisis, schools across the United States organized to assemble and distribute instructional materials and to make a rapid transformation from school-based to home-based learning. the impact of this crisis on all students is significant. As districts resume instruction in the upcoming school year, they will not only…

During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

The study of functions has traditionally received the most attention at the secondary level, both in curricula and in standards documents--for example, the Common Core State Standards for Mathematics (CCSSI 2010) and "Principles and Standards for School Mathematics" (National Council of Teachers of Mathematics [NCTM] 2000). However, the…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…

Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential…

This paper examines a pre-service teacher's content knowledge for teaching early algebra from two perspectives, i.e. using "Rowland's Knowledge Quartet" theory and "Ball's framework for Mathematical Knowledge for Testing" (MKfT). The study intends to examine the differences between the influences using each framework and to…