This study investigates students' and adults' performance in judging reasonableness of computational results, namely reflecting on whether these results qualify as acceptable answers to mathematical tasks. Data was gathered via task-based questionnaires from 160 participants, evenly divided between fifth-graders and adults. Their responses to a…

Background: South African learners face the double disadvantage of living in low socioeconomic conditions with access to few resources and attending schools with challenging learning conditions. Mathematics performance reflects such conditions with extreme performance gaps between wealthier and poorer learners. The need for early intervention is…

This study examined a game-based teaching activity on "Factors and Multiples" designed for the 6th grade students. The game aims to create a differentiated and enriched learning environment targeted the curriculum standard "The students determine prime numbers using their properties. The students find prime numbers using the…

Number system knowledge (NSK) is broadly defined as the understanding of number relationships and is an essential mathematics skill for young elementary school-aged students. NSK instruction that emphasizes connections between number sense and spatial reasoning could be a critical anchor for second-grade students to stay rooted in their conceptual…

Research has demonstrated that providing labels helps children notice key features of examples. Much less is known about how different labels impact children's ability to make inferences about the structure underlying mathematical notation. We tested the impact of labeling decimals such as 0.34 using formal place-value labels ("3 tenths and 4…

In this paper, we investigate the mathematical, social and affective nature of children's engagement with "TouchCounts," a multitouch application for counting and doing arithmetic. In order to study these dimensions of engagement in a way that recognizes their fundamental intertwinement, we use rhythm as a primary unit of analysis.…

This article reports on a study in which researchers asked children to "make up as story and a picture about marbles for this number sentence: 3 x 5 = 15." Students in this study came from pre - dominantly low- to average-income families living in three distinct geographical areas within the United States. A similar division task was…

Accurate monitoring and control are essential for effective self-regulated learning. These metacognitive abilities may be particularly important for developing math skills, such as when children are deciding whether a math task is difficult or whether they made a mistake on a particular item. The present experiments investigate children's ability…

This paper focuses on children's number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children's knowledge of number facts, including…

In this article, Lorraine Jacob and Joanne Mulligan discuss how arrays can be used to promote students' early learning in relation to multiplication and division. They provide examples of activities that can be used from Foundation to Year 5.

The intention of the present study is to know how students' performance on number sense based on the components of number sense and also the sub-components in it. The participants of the study are 80 six graders (12-13 year-old) from three different schools that represent the city, rural, and small town areas. The data were collected using the…

What would the curriculum look like if it were developed from the perspective of measuring? Without formal tools, the Yup'ik Eskimos of Alaska used their body as a measuring device and employed ratios extensively in their daily practices. "Math in a Cultural Context" is developing curriculum materials based on Yup'ik Elders use of…

Linear board games have shown great promise as tools to teach whole number concepts (Ramani & Siegler, 2008), but little is known about their utility for supporting negative integer concepts. This study sought to extend the use of linear board games to teach integer concepts. Forty-eight first graders (ages 6-7) counted along an integer board…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…

This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…