This report describes efforts to measure teachers' knowledge of their own students' abilities in mathematics and offers preliminary findings. It provides a description of the sample, a description of the study design and its realization, and descriptive statistics for teacher judgment accuracy. The work described here was completed as part of a…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

"Math Expressions" is a curriculum for students in prekindergarten through sixth grade that aims to build students' conceptual understanding of mathematics and to develop fluency in mathematical problem solving and computation. The curriculum encourages student learning of mathematics through real-world situations, visual supports such…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

Our paper builds on the construct of the zone of proximal development (ZPD) (Vygotsky in Mind in society: the development of higher psychological processes, Harvard University Press, Cambridge, 1978) to analyze the relationship between students' answers and the help they receive as they construct them. We report on a secondary analysis of…

In this article, the authors describe how their first-grade class used the book "Inch by Inch" (Lionni 1960)--the story of an inchworm that escapes from a hungry robin by proving he is useful for measuring--as inspiration for a lesson focused on exploring length measurement through examining the meaning of an inch. The authors designed a…

This study investigated income group differences in kindergartners' and first graders' (N = 161) arithmetic by examining the link between accuracy and strategy use on simple and complex addition problems. Low-income children were substantially less accurate than high-income children, in terms of both percentage of correctly solved problems and the…

Scholars have long argued that individuals' beliefs influence their behaviors and the decisions they make throughout their lives. Focusing on beliefs as a cognitive construct, the purpose of this study was to identify several key beliefs about mathematics teaching and learning held by practicing elementary mathematics teachers. An iterative…

Scholars have long argued that individuals' beliefs influence their behaviors and the decisions they make throughout their lives. Focusing on beliefs as a cognitive construct, the purpose of this study was to identify several key beliefs about mathematics teaching and learning held by practicing elementary mathematics teachers. An iterative…

The use of enabling and extending prompts allows tasks to be both accessible and challenging within a classroom. This article provides an example of how to use enabling and extending prompts effectively when employing a challenging task in Year 2.

This study examined the impact of performance goals on arithmetic strategy use, and how same-sex peer groups contributed to the selection of strategies used by first-graders. It was hypothesized that gender differences in strategy use are a function of performance goals and the influence of same-sex peers. Using a sample of 75 first grade…

Mathematics interventions aimed at accelerating the learning of students with mathematics difficulties (MD) should be developed through a design science approach such as the Curriculum Research Framework (CRF). Precision Mathematics is a National Science Foundation-funded DRK-12 Design and Development project focused on building mathematical…

Seventy-three children between 6 and 7 years of age were presented with a problem having ambiguous subgoal ordering. Performance in this task showed reliable fingerprints: (a) a non-monotonic dependence of performance as a function of the distance between the beginning and the end-states of the problem, (b) very high levels of performance when the…

Symmetric objects are known to be perceived easier than asymmetric objects, because less information has to be processed. Therefore, symmetric objects are often used for spatial tasks. However, in perspective-taking the use of symmetric objects can also cause difficulties, as two side-views of these objects are mirror-images of each other. To…

Children in the elementary grades are expected to solve equations to demonstrate prealgebraic proficiency. Prealgebraic differences may emerge based equation type (i.e., standard vs. nonstandard), the operation shown or required for solution (i.e., addition or subtraction), and the position of the unknown. Prealgebraic differences may also be…