Reimagining elementary mathematics pedagogy using a three-step process--See It, Say It, Symbolize It--author Patrick L. Sullivan provides a guide for developing a dynamic and flexible understanding of numbers and operations. By helping students develop a language that is consistent across concepts and connecting it to what is seen and symbolized,…

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240…

We conducted a multiyear project across three institutions to develop an instructional tutorial that supports student understanding of change of basis in quantum mechanics. Building from our previous work, we identified learning goals to guide activity development. The tutorial makes an analogy between spin-1/2 states and a Cartesian coordinate…

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240…

One way to emphasize students' strengths when reasoning verbally is through number talks. During a number talk, a teacher facilitates a 5- to 15-minute conversation during which students have the opportunity to engage in mental mathematics and verbally explain and justify their reasoning regarding how they make sense of numerical computations.…

Number naming, or knowledge of math numerals, has been described as a gatekeeper skill in preschool math development because it is necessary for later math tasks such as calculation. This article describes a small group intervention piloted with 10 preschoolers found to be at risk for delays in early numeracy development during universal…

Price comparison is a functional mathematics skill involving purchasing, use of money, and budgeting, with the goal of selecting the best deal based on a person's financial resources (Browder, Spooner, & Trela, 2011). The operational definition of "price comparison" is to compare the magnitudes of the price numbers and then select…

We share a subset of the 41 underlying strategies that comprise five ways of reasoning about integer addition and subtraction: formal, order-based, analogy-based, computational, and emergent. The examples of the strategies are designed to provide clear comparisons and contrasts to support both teachers and researchers in understanding specific…

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, ("Trends in Cognitive" 14(12):542-551, 2010). However, numerical symbols necessitate an understanding of both order and…

We investigated the effects of proximal grouping of numbers, problem-solving goals to make 100, and prior knowledge on students' solution strategies in an online mathematics game. Logistic regression on 857 problem-level data points from 227 middle-school students showed that students were more likely to use productive solution strategies on…

Research indicates that mathematical understanding before formal schooling influences later attainment. This study investigated the mathematical activities of preschool-aged children in Japan, a neglected topic despite the high mathematical attainment of Japanese children. Preschool activities were investigated using surveys, observations, and…

The overarching theme of this book can be simply stated: Building on a foundation of biologically based abilities, children construct number via sensorimotor and mental activity. In this chapter, we return to this theme, and we connect it to three additional themes that emerge across chapters: comparing competing models for conceptual change;…

Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…

In this article we report on a study of children's attention to numerical content in picture books. Specific research questions are 1) how the content in a designed picture book directs children's attention to numbers, and 2) what kind of numerical reasoning the book reading entails. To answer these questions, we conducted an educational design…

Mathematical learning not only produces students who succeed in mathematical and procedural calculations but also develops religious thinking. Realistic mathematics education with the context of Islamic values makes students can imagine, which is one of the right ways to develop the skills of students' creativity, collaboration, and communication.…