Integer operations are typically introduced in sixth grade, but they are a consistent area of struggle among these students. This struggle also inhibits their understanding of algebraic computations involving positive and negative terms. In this article, the author provides introductory tasks and models for adding and subtracting integers that can…

This study examined the effects of the concrete-representational-abstract integrated sequence (CRA-I) on teaching place value concepts and their application. The research questions addressed the extent to which CRA-I changed student performance in (a) completing equations that required subtraction with regrouping in the tens place, (b) completing…

Students' understanding of negative integers is an important aspect of learning mathematics as it is a requirement for learning broader mathematical concepts. The purpose of this research is to explore students' initial perceptions in understanding negative integers on a number line. This descriptive exploratory qualitative research was conducted…

By the end of primary school, children are expected to acquire a range of mathematical skills that progressively develop. This study aimed to gain insight into how a large number of numerical and geometrical measures are grouped and whether the structures shift or remain invariant along child's development based on the data obtained from a sample…

Teachers can make number talks more ambitious and increase learning opportunities for students by debugging errors, promoting multi-student thinking, and orienting to make connections. This article describes the basic number talks routine and examines some common tendencies, such as "Serial Sharing." It concludes with a vignette to…

Students in developmental math classes have been documented to struggle with arithmetic. This dissertation research was a response to the calls in the literature to qualitatively understand what students are learning in a classroom. Number sequences have been well researched to document the connection of student understanding of math in elementary…

The conceptual development of natural number in preschoolers is well-researched. However, less is known about the conceptual development of zero. Recent studies suggest that children develop an understanding of zero after learning to count. It remains unclear, when a conceptual understanding of "zero" as number word for an empty set…

Studies on children's understanding of counting examine when and how children acquire the cardinal principle: the idea that the last word in a counted set reflects the cardinal value of the set. Using Wynn's (1990) Give-N Task, researchers classify children who can count to generate large sets as having acquired the cardinal principle…

Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs. 3 of 4 apples), but have considerable difficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., "1/5" vs. "3/4"). Theoretically, reducing the gap between representations of implicit versus explicit proportions…

Over three decades ago, National Council of Teachers of Mathematics (NCTM, 1991) proposed that "for students to develop the ability to formulate problems, to explore, conjecture, and reason logically, to evaluate whether something makes sense, classroom discourse must be founded on mathematical evidence" (p. 34). As math interventionists…

School reform efforts are situated within social and political contexts and, as such, are susceptible to the commonsense discourses circulating through, and shaping, society. Two discourses prevalent in US education reform are those perpetuating the ideologies of neoliberalism and neoconservatism. These ideologies are inherently…

Students' ability to operate with increasingly more complex units has been shown to be a key factor in their conceptual development. These abilities have been characterized as "stages of units coordination." This article focuses on the domain of composing and decomposing composite units. Using data from a teaching experiment with a…

The purpose of this correlational study was to investigate the relationship of number sense comprehension and mathematics attitudes on mathematics achievement and intention to pursue a mathematics-related career for final-year high school students in Kenya. The sample for the study comprised of final-year high school students from three schools,…

Rational numbers can be represented in multiple formats (e.g., fractions, decimals, and percentages), and a rational number notation can be used to express different concepts in different contexts. The present study investigated the distribution of the multiple concepts expressed by these different rational number notations in real-world contexts…

Educated adults and children engage a network of frontal and parietal brain regions for numerical thinking. Recent studies document some prominent changes as this network emerges over development, including a unilateral right to bilateral shift in number-selective parietal brain activity, a strengthening of intra- and interhemispheric parietal…