The results of this study revealed students' solution strategies progressed from inefficient strategies e.g., counting on fingers to more efficient strategies with mathematical connections. These findings should enable educators to gain more insight to use Number Talks to help student develop computational fluency with numbers.

In this paper I discuss the possibilities for exploring the hundred chart kinesthetically with elementary preservice teachers using a life-size hundred chart--an innovative tool, homemade from a shower curtain--to build quantity sense. Preservice teachers explored creative approaches to teach mathematics using the life-size hundred chart and…

Physical models for exploring multiplication are fixtures in elementary classrooms. The most widely used physical models of multiplication are collections of discrete things, such as Cuisenaire rods, Unifix Cubes, or Base-10 Blocks. But discrete physical models are limited in the products they can represent. By contrast, pictorial models, such as…

The non-learning of school mathematics is now almost universally taken for granted, but this does not have to happen. This article takes a critical look at the root of this non-learning by pointing to the flagrant defects in the kind of mathematics--to be called TSM--that is predominant in almost all the school textbooks. By analyzing how the long…

This article examines how the Child Mathematics Inquiry Portfolio (CMIP), a semester-long field experience project attached to an elementary mathematics methods course, can impact preservice teachers' understanding about teaching and learning mathematics and set them on more positive mathematics teaching journeys as they prepare to enter the…

I qualitatively reviewed mathematics education literature to offer explicit classroom-based examples and recommendations on the learning opportunities that can be embedded into mathematics content courses, designed specifically for prospective elementary teachers (ePTs), to help develop their knowledge of students and their mathematical thinking,…

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

International rankings show children in the United States perform well below average in mathematics. There are also large mathematics achievement gaps between children of lower- and higher-socioeconomic status. As today's teachers face these challenges, they are also faced with the pressures of sweeping educational reforms that arrived with the…

Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

This meta-ethnography explores qualitative studies around the Cognitively Guided Instruction (CGI) framework of mathematics and illustrates how CGI epitomizes differentiation. The meta-ethnographic process is used to synthesize CGI as differentiation, specifically within the elementary mathematics classroom. Thomas P. Carpenter is credited as one…

Elementary Education pre-service teachers are noted for disliking and even fearing mathematics, so a teaching strategy that increases their enjoyment of mathematics learning must be a powerful one, indeed. When the same strategy can also support problem posing and assess mathematical knowledge and reasoning, providing an occasional alternative to…

This study investigated the effects upon elementary preservice teachers' mathematics teaching self-efficacy and interdisciplinary lesson design strategies, which resulted from an educational intervention that emphasized integrated music-mathematics instruction. The participating elementary preservice teachers (n = 152) were recruited for this…

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

Real world mathematical modeling activities can develop needed and valuable 21st century skills. The knowledge and skills to become adept at mathematical modeling need to develop over time and students in the elementary grades should have experiences with mathematical modeling. For this to occur elementary teachers need to have positive…

The purpose of this article is to present the findings of a quantitative study focused on primary mathematics teachers who participated in an intensive professional development program and then had leadership responsibility for the implementation of a new primary mathematics curriculum in their district. The study examines the effect of the…