Mathematics

In this chapter, we describe a three-part fully online model for the professional development of middle school mathematics teachers. This chapter contributes to understanding how online contexts provide opportunities to collect and analyze data in ways that would be difficult to accomplish in face-to-face settings.

In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. For both grade levels, the order of the numerals, the location of the negative signs, and also the numbers’ absolute values in the problems played a role in students’ strategies used. Fifth graders’ greater strategy variability often reflected strategic use of the meanings of the minus sign. Our findings provide insights into students’ problem interpretation and solution strategies for integer addition problems and supports a blended theory of conceptual change.

This article addresses the nature of student-generated representations that support students’ early algebraic reasoning in the realm of generalized arithmetic.

Narrative as a game design feature constantly yields mixed results for learning in the literature. The purpose of this exploratory mixed-methods case study was to examine design heuristics and implications governing the role of narratives in a digital game-based learning (DGBL) environment for math problem solving.

The give-n task is widely used in developmental psychology to indicate young children’s knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and the cardinal-count concept, which she argued is a more advanced cardinality concept that underlies the counting-out process required by the give-n task with larger numbers. One aim of the present research was to evaluate Fuson’s disputed hypothesis that these two cardinality concepts are distinct and that the count-cardinal concept serves as a developmental prerequisite for constructing the cardinal-count concept. Consistent with Fuson’s hypothesis, the present study with twenty-four 3- and 4-year-olds revealed that success on a battery of tests assessing understanding of the count-cardinal concept was significantly and substantially better than that on the give-n task, which she presumed assessed the cardinal-count concept.

This study illustrates how two secondary mathematics teachers used students’ incorrect answers as they supported students’ engagement in collective argumentation.

This review synthesized insights from 27 NSF-funded projects, totaling $62 million, that studied pedagogical content knowledge (PCK) in STEM education from prekindergarten (PreK) to Grade 12, split roughly equally across mathematics and science education. The projects primarily applied correlational/observational and longitudinal methods, often targeted teaching in the middle school grades, and used a wide variety of approaches to measure teachers’ PCK. The projects advanced substantive knowledge about PCK across four major lines of research, especially regarding the measurement and development of PCK.

This review synthesizes insights from 23 NSF-funded projects, totaling $40 million, that studied mathematical and scientific argumentation in STEM education from prekindergarten (PreK) to Grade 12. The projects reported on both studies of argumentation interventions and naturalistic observations in “business-as-usual” settings. The projects advanced substantive knowledge about how to support student argumentation. In particular, the projects highlighted the importance of making an argument’s structure explicit and facilitating student-to-student discourse, especially with technological tools.

In this article, we describe the case of “Keri,” a fifth-grade teacher who had completed an Elementary Mathematics Specialist (EMS) certification program. Drawn from a larger study investigating the knowledge, beliefs, and practices of EMSs, Keri's case was unique in that she was teaching mathematics to four classes in a departmentalized structure, where students were placed into different classes according to perceived mathematics ability. Observations from the larger study revealed that Keri's instructional practices did not align with her reported beliefs and knowledge. To explore this deviation, we conducted a case study where we observed Keri's instruction across multiple classes and used interviews to explore reasons for Keri's instructional decisions in terms of her perceived professional obligations.