An action research case study was conducted to investigate the effects of incorporating LEGO robotics into a seventh-grade mathematics curriculum focused on the development of proportional reasoning through the lens of Social Constructivist Theory. This research, which was part of a larger study, reports the findings when LEGO EV3 robots were…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

There is increasing recognition that the underachievement of Maori, Pasifika, and other diverse students in New Zealand schools is in large part owing to systemic factors that disadvantage these students. Responding to the urgent need for significant change in our schools and classrooms, the developing mathematical inquiry communities model is a…

In this study, we investigate students' ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14-16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise…

Traditional teaching approaches are generally teacher-directed, where students are taught in a manner that is conducive to sitting and listening. It is often argued that these approaches may not provide students with valuable learning skills, and rather that non-traditional approaches to teaching and learning might better endow students with such…

This study examined whether students were reaching automaticity with single digit multiplication facts. A fourteen question interview was used to collect data. The first three questions asked the student basic information about themselves and their current math teacher. The next seven questions were math facts. The math facts chosen for the…

This chapter focuses on the interaction of two first graders as they attempt to make sense of a particular instructional context for learning negative numbers. The context is one where they move an elevator to a building's floors above and below ground in order to model integer addition and subtraction problems. In particular, the focus of the…

Problem-solving occurs when mathematical tasks create opportunities that provide challenges for increasing students' mathematical understanding and development. This research study determined the influence of the "launch-explore-summarize/extend" problem-solving framework on second-grade student performance of place value tasks. The…

In this paper, I look at multiple layers of context to explore the "figured world" of mathematics teaching in primary schools in Chile. I collected data from 15 teachers during 18 months after their participation in professional development for collaborative problem-solving mathematics. I found constraints to impact on the teachers'…

The present study used a regression discontinuity approach to test whether schema-based instruction (SBI) was effective for students identified with varying levels of mathematics difficulties (MD) who received Tier 1 instruction. The performance of these students was compared to similar students who received business as usual Tier 1 instruction.…

In this research report, the question of the role of the teacher in problem-solving contexts is addressed, particularly in relation to the development of mathematical concepts. Data extracts from a problem-solving session are used to draw out three sorts of teaching actions that aim to push forward the mathematics in the classroom. These teaching…

Elementary school students struggle in interpreting the equal sign as a symbol denoting equivalence. Although many have advocated using a pan-balance scale to help students develop this understanding, less is known about what features associated with this model support learning. To attempt to control and examine these features, the investigators…

With the goal of improving student success, the chancellor of the California State University (CSU) system issued an executive order that required all CSU campuses to eliminate remedial math courses as of Fall 2018 and place all first-year students into appropriate General Education (GE) mathematics/quantitative reasoning courses. The Mathematics…

"Ensuring Mathematical Success for All" (NCTM 2010) outlines eight teaching practices for effective teaching and learning of mathematics. One of the teaching practices, building procedural fluency from conceptual understanding, states the following: Effective teaching of mathematics builds fluency with procedures on a foundation of…

The theoretical and methodological model of Mathematical Working Space (MWS) is introduced in this paper. For over 10 years, the model has been the object of collaborative research among various researchers, generally coming from French and Spanish speaking countries. Articulating epistemological and cognitive aspects, the MWS model is aimed at…