Mathematics

The purpose of this study was to investigate how teachers understand one specific aspect of proportional reasoning. We were interested in understanding the extent to which practicing teachers were able to make sense of reasoning that involved the fixed number of variable-sized parts perspective. We used two items, drawn from a larger dataset, that encouraged teachers to reason about proportional situations using a variable parts perspective.

Maass, K., Cobb, P., Krainer, K., & Potari, D. (2019). Different ways to implement innovative teaching approaches at scale. Educational Studies in Mathematics, 102, 303-318.

Well-designed mathematics instruction focused on concepts and problem-solving skills associated with measurement and data analysis can build a foundational understanding for more advanced mathematics. This study investigated the efficacy of the Precision Mathematics Level 1 (PM-L1) intervention, a Tier 2 print- and technology-based mathematics intervention designed to increase first-grade students’ conceptual understanding and problem-solving skills around the areas of measurement and data analysis.

Mathematics interventions aimed at accelerating the learning of students with mathematics difficulties (MD) should be developed through a design science approach such as the Curriculum Research Framework (CRF). Precision Mathematics is a National Science Foundation-funded DRK–12 Design and Development project focused on building mathematical proficiency with the critical concepts and problem-solving skills of early measurement and data analysis among first- and second-grade students with MD.

Students who earned high marks during the proof semester of a geometry course were interviewed to understand what high-achieving students actually took away from the treatment of proof in geometry. The findings suggest that students had turned proving into a rote task, whereby they expected to mark a diagram and prove two triangles congruent.

This chapter explores a way of describing the teacher education curricular materials being developed by mathematics teacher educators through their interaction with the LessonSketch online platform (www.lessonsketch.org). We briefly describe the platform and the larger project and then using the experiences created by two fellows illustrate the kinds of materials being created by the teacher educators.

There is international and widespread recognition that early childhood education must be fully inclusive and based on the language, culture, and epistemology of local Indigenous communities (Kitson, 2010). Early childhood education (ECE) programs can only deliver on the promises ofculturally responsive schooling (Castagno & Brayboy, 2008; McCarty & Lee, 2014) when “staff members understand cultural expectations, relationships, and the subtleties of communication, including non-verbalcommunication” within the community (Kitson & Bowes, 2010, p.86).

Problem solving is central to mathematics learning (NCTM, 2014). Assessments are needed that appropriately measure students’ problem-solving performance. More importantly, assessments must be grounded in robust validity evidence that justifies their interpretations and outcomes (AERAet al., 2014). Thus, measures that are grounded in validity evidence are warranted for use by practitioners and scholars. The purpose of this presentation is to convey validity evidence for a new measure titled Problem-Solving Measure for grade four (PSM4).

Problem solving is central to mathematics learning (NCTM, 2014). Assessments are needed that appropriately measure students’ problem-solving performance. More importantly, assessments must be grounded in robust validity evidence that justifies their interpretations and outcomes (AERAet al., 2014). Thus, measures that are grounded in validity evidence are warranted for use by practitioners and scholars. The purpose of this presentation is to convey validity evidence for a new measure titled Problem-Solving Measure for grade four (PSM4).

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.