This paper reports on a study of the instructional situation in high school Geometry that Hsu (2010) called Geometric Calculation in Algebra (GCA). In particular, we conducted a virtual breaching experiment in order to examine the extent to which high school teachers recognized breaches of two norms that we conjectured to describe geometry…

Recent research in problem solving has shifted its focus to actual classroom implementation and what is really going on during problem solving when it is used regularly in classroom. This book seeks to stay on top of that trend by approaching diverse aspects of current problem solving research, covering three broad themes. Firstly, it explores the…

In spring 2015 Mississippi began testing the college readiness of all grade 11 public high school students and found that approximately 18 percent were ready for college math, a percentage that had changed little by 2017/18. This study examined: (1) the sequences of math courses that Mississippi students took in grades 6-11; (2) the math…

The complex nature of multiplicative thinking can be challenging for students and teachers to navigate. We report on the impact on student learning of school-based professional learning that targeted teachers' pedagogical content knowledge related to Multiplicative Thinking. Analysis of Year 4 students' longitudinal data indicated greater growth…

Previous research on preservice teachers' understanding of fractions and algebra has focused on one or the other. To extend this research, we examined 85 undergraduate elementary education majors and middle school mathematics education majors' solutions and solution paths (i.e., the ways or methods in which preservice teachers solve word problems)…

The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

This article explores one segment of an extended research and development project that was conducted to better understand the ways online teacher professional development can support teachers' development of deep and connected mathematical understandings. In particular, this article discusses teachers' understandings of the concept of…

In this study, we examined the ability of grades 1-8 pre-service teachers (PSTs) to engage in thinking about patterns, relationships, and functional rules. Using the algebraic habit of mind Building Rules to Represent Functions as a framework, we examined whether and how well our PSTs (n = 18) used seven features of this habit of mind: organize…

How does one look for mathematical structure? Finding structure is a challenging yet accessible activity for all students. This article describes a lesson in which seventh graders engaged with mathematical structure. The setting was a seventh-grade prealgebra classroom in a suburban school. The classroom teacher was co-author Tatyana Finkelstein.…

This work is part of a research project that aims to enhance engineering students' learning of how to apply mathematics in modelling activities of real-world situations, through the construction (design and programming) of videogames. We want also for students to relate their mathematical knowledge with other disciplines (e.g., physics, computer…

Students who fail algebra are significantly less likely to graduate on time, and algebra failure rates are consistently high in urban districts. Identifying effective credit recovery strategies is critical for getting students back on track. Online courses are now widely used for credit recovery, yet there is no rigorous evidence about the…

Students who fail algebra are significantly less likely to graduate on time, and algebra failure rates are consistently high in urban districts. Identifying effective credit recovery strategies is critical for getting students back on track. Online courses are now widely used for credit recovery, yet there is no rigorous evidence about the…

This report examines the outcomes of the Miami-Dade County Public Schools (M-DCPS) in-class Summer Programs operated in the M-DCPS. The Summer Programs, offered to provide supplemental instruction for students in need of remediation, are comprised of Literacy for Rising 3rd Grade Students, Algebra I End-of-Course (EOC) remediation, and Course…

In this paper, we offer illustrations of a mathematics teacher's difficulties with content knowledge when trying to find connections between school mathematics and science; we do so by describing the development of this teacher's thinking and learning in her pursuit of connections between the concepts of slope of a line and density of matter. The…

Students benefit from learning multiple procedures for solving the same or related problems. However, past research on comparison instruction has focused on comparing multiple formal procedures. This study investigated whether the benefits of comparing procedures extend to comparisons that involve informal and formal procedures. We also examined…