The overarching goals of the project were to identify instructional practices that are associated with increased student performance in early algebra. To accomplish this main goal we used a data corpus of approximately 120 videos of early algebra lessons and examined how teachers supported students' learning of early algebra. 

As a first step, we looked at "anticipated moments" and "spontaneous moments; in the former case, these are moments that are reasonable to expect based on the intended lesson (and that are also further delineated as taken up or as missed by the teacher), and in the latter case, these are moments that were not anticipated and that arise "in the moment" (i.e., spontaneous). Our finding was simple and yet powerful: increased attention to "anticipated moments" was correlated with higher student performance. In other words, the more algebraic instruction we observed, the higher were the student scores.

As a second step, we looked more closely at the spontaneous moments - those moments that arise in the moment. Each spontaneous moment was assigned one of six “response categories” (i.e., setting aside, acknowledging, responding, eliciting, facilitating, and extending). With the exception of setting aside, an indication of teachers not engaging with student reasoning, the remaining five categories occurred as a continuum with an increasing degree of responsiveness and patterns of dialogic discourse. Hence, we considered these categories as “levels”, starting with setting aside as Level 0 to “extending” as Level 5. Our findings suggest that the "quality" of these spontaneous moments is also correlated with higher performance. Students who were in classrooms in which teachers not only chose to take up the algebraic moments that arose spontaneously during classroom discourse, but also chose to respond to these moments by engaging in dialogic discourse in a manner that advances student algebraic reasoning (i.e., justification, generalization and encouraging connections), tended to have higher gains in the algebra assessment. The engagement in dialogic discourse is not a dichotomy, but a continuum of teachers’ moves that increase student engagement with these algebraic practices, and with each other’s reasoning.

Our work corroborates our earlier findings and, in fact, finds a substantial positive relation between teachers’ manner of taking up curriculum openings and actual student performance. It also brings us one step closer to understanding aspects of effective instruction regarding early algebra. Our examination of several lessons across grades shows a clear pattern that levels of implementation of these spontaneous moments have a strong correlation to gains in student performance. As teachers attended to students’ reasoning, be it correct or incorrect, and invited discussions on these issues as they organically arose, student performance on these concepts improved. These results offer promise that this is a fruitful area of research that we can continue to explore, and provide directions for improving teacher preparation to promote more rich early algebra teaching and learning.

Last Modified: 07/16/2024
Modified by: Despina A Stylianou