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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 outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance. [This article was published in "Journal for Research in Mathematics Education" (EJ1298112).]

This research shares progressions in thinking about equations and the equal sign observed in ten students who took part in an early algebra classroom intervention across Kindergarten and first grade. We report on data from task-based interviews conducted prior to the intervention and at the conclusion of each school year that elicited students' interpretations of the equal sign and equations of various forms. We found at the beginning of the intervention that most students viewed the equal sign as an operational symbol and did not accept many equations forms as valid. By the end of first grade, almost all students described the symbol as indicating the equivalence of two amounts and were much more successful interpreting and working with equations in a variety of forms. The progressions we observed align with those of other researchers and provide evidence that very young students can learn to reason flexibly about equations.

A cluster randomized trial design was used to examine the effectiveness of a Grades 3 to 5 early algebra intervention with a diverse student population. Forty-six schools in three school districts participated. Students in treatment schools were taught the intervention by classroom teachers during regular mathematics instruction. Students in control schools received only regular mathematics instruction. Using a three-level longitudinal piecewise hierarchical linear model, the study explored the impact of the intervention in terms of both performance (correctness) and strategy use in students' responses to written algebra assessments. Results show that during Grade 3, treatment students, including those in at-risk settings, improved at a significantly faster rate than control students on both outcome measures and maintained their advantage throughout the intervention.

This research focuses on ways in which balance scales mediate students' relational understandings of the equal sign. Participants included 21 Kindergarten-Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks. Interview analyses revealed several categories of affordances of these tools for supporting students' productive thinking about equations.

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 outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance.

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 differences between experimental and control students on a grade 3 pre-assessment measuring students' capacity for generalizing and representing generalizations, experimental students significantly outperformed control students on post-assessments at each of grades 3-5. Moreover, experimental students were able to more flexibly interpret variable in different roles and were better able to use variable notation in meaningful ways to represent arithmetic properties, expressions and equations, and functional relationships. This study provides important evidence that young children can learn to think algebraically in powerful ways and suggests that the earlier introduction of algebraic concepts and practices is beneficial to students.

There are few studies of the impact of ubiquitous computing on high school science, and the majority of studies of ubiquitous computing report only on the early stages of implementation. The present study presents data on 3 high schools with carefully elaborated ubiquitous computing systems that have gone through at least one "obsolescence cycle" and are therefore several years past first implementation. The data from these schools shows how the elements of a 1:1, wireless environment are being deployed in these science classrooms, and the effects of the environment on science content, data analysis, labs and other uses for visualizations, and classroom interaction. While some positive effects are clearly seen in these classrooms, five years or more into the innovation, problems remain, and school cultural factors seem to play an important role in teacher uptake and integration of the technology. Implications for teacher learning are discussed. (Contains 13 figures and 3 tables.)

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K–1 students' thinking about parity arguments for sums of evens and odds, as well as underlying concepts of pair and parity of a number. Data are drawn from classroom lessons of a Grades K–1 early algebra instructional sequence, as well as task-based interviews conducted at four timepoints during the implementation of the sequence. While most students at the beginning of the study (Grade K) did not know the concepts of even or odd and could not make any viable arguments regarding parity, by the end of Grade 1 students were largely constructing representation-based arguments to justify number parity and claims about sums of evens and odds. Results of this study align with other research that shows young learners can develop viable arguments to justify mathematical generalizations. Results also provide preliminary evidence that the instructional sequence used here can foster students' practice of argumentation from the start of formal schooling. [ABSTRACT FROM AUTHOR]

One hundred and seventy-eight second grade students from two states (Georgia and Massachusetts) participated in an experiment in which they were randomly assigned to either (1) a computer program designed to increase fluency in addition and subtraction, (2) a program designed to improve cognitive strategy use for addition and subtraction, (3) a program that combined the fluency and cognitive strategy instruction programs or (4) a control condition. The intervention consisted of 40 half-hour sessions (2 sessions per week for 20 weeks). Prior to the intervention, and immediately following the intervention, the participants were tested on fluency, cognitive strategy use, and mathematics achievement. ANCOVAs indicated that children in the combined fluency and cognitive strategy use condition significantly improved their mathematics achievement in comparison to the control group. When we examined the impact of the intervention as a function of gender, boys appeared to benefit from the intervention, but girls did not. (Contains 3 tables.)

This research focuses on ways in which balance scales mediate students' relational understandings of the equal sign. Participants included 21 Kindergarten–Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks. Interview analyses revealed several categories of affordances of these tools for supporting students' productive thinking about equations. [ABSTRACT FROM AUTHOR]

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 outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance. [ABSTRACT FROM AUTHOR]

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