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This research reports on the teacher language and gesture that contributed to shifts in thinking about the equal sign and equations observed in twenty kindergarteners who took part in an early algebra intervention. Our analysis revealed ways in which the teacher used language and gesture to support students in moving from describing and working with the equal sign operationally (i.e., as a signal to compute) to describing the symbol as indicating the equivalence of two amounts and successfully working with equations of various forms. We detail four kinds of language and two kinds of gesture specifically related to mathematical equivalence that we believe contributed to students' growth. [For the complete proceedings, see ED630210.]

We share results from a one-year early algebra classroom intervention. One kindergarten, one first-grade, and one second-grade classroom participated in the intervention and three classrooms of the same grade levels served as control sites. The intervention addressed the structure of even and odd numbers, mathematical equivalence and equations, properties of arithmetic, the representation of varying unknown quantities, and functional thinking. Students in the control classrooms received their regular mathematics instruction. We compare growth in algebraic thinking across the two groups as measured by an online assessment completed by 40 students per condition. Findings suggest that students who participated in the early algebra lessons experienced more overall growth in their understanding of early algebra concepts as compared to control students.

This research focuses on the retention of students' algebraic understandings one year following a Grades 3-5 early algebra intervention. Participants included 1455 Grade 6 students who had participated in a cluster randomized trial. Approximately half of these students received an early algebra intervention as part of their regular instruction in Grades 3-5, while the other half received only their regular mathematics instruction. Results show that, as was the case at the end of Grades 3, 4 and 5, treatment students outperformed control students at the end of Grade 6 on a measure of algebraic understanding. This was despite the fact that treatment students experienced a significant decline in performance and control students a significant increase in performance after the intervention. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance. [For the complete proceedings, see ED606556.]

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. Videotaped classroom observations, our primary measure of FOI, were coded by adding to and adapting the Mathematical Quality of Instruction (MQI) instrument, and student performance was measured by overall score (correctness) on an algebra assessment. Results revealed a significant positive relationship between teachers' implementation and their students' performance. [This paper was published in: Galindo, E., & Newton, J., (Eds.), "Proceedings of the Thirty-Ninth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education" (pp. 299-302). Hoosier Association of Mathematics Teacher Educators.]

Is it possible to identify instructional practices that have an impact on student learning in mathematics? The study described here is part of ongoing efforts to understand and characterize effective instruction. We drew on the work of several recently developed frameworks for understanding teaching effectiveness to develop a protocol for studying effective instruction that both coordinates and extends existing research in the context of early algebra. Using a largescale study, we characterized effective instruction in this context and documented the impact of such instruction on students' performance using both qualitative and quantitative analyses. Findings suggest that teachers' abilities to take up curriculum openings are important aspects of teaching. Furthermore, the manner with which teachers react to these moments strongly correlates with gains in student performance. [ABSTRACT FROM AUTHOR]