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,…

We share here results from a quasi-experimental study that examines growth in students' algebraic thinking practices of generalizing and representing generalizations, particularly with variable notation, as a result of an early algebra instructional sequence implemented across grades 3--5. Analyses showed that, while there were no significant…

Through a theoretical framework emphasizing the importance of fidelity of implementation (FOI), this paper explores how 3rd and 4th grade teachers implemented an early algebra intervention, and the extent to which the FOI related to student learning. The data for this report are taken from the first two years of an experimental research project.…

Within the current test-centered educational reform movement, considerable emphasis is placed on using assessment results to make instructional decisions for individual students. Test scores are used to estimate a student's current level of skill, monitor his or her progress during instruction, and identify whether the student has gained the…

Unlike old perceptions of algebra as a subject that needs to be taught in the upper grade levels of schooling, much of the recent research reports that young students are capable of reasoning algebraically. It is important to note that the recommendation to include algebraic experiences in the early grades is not made simply to introduce typical…

The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n = 279, mean age = 7.59 years) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems…

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'…