This article summarizes the findings of research studies focusing on number sense instruction to improve mathematics competence of school going children. Twenty-three studies were located that met the inclusion criteria. Interventions gleaned from the review were categorized based on type of instruction (i.e., constructivist, explicit or a…

In this article, one teacher describes her action research with eighth-grade prealgebra students who are working on a conceptual understanding of fractions. Examining her middle school students' standardized test scores for the previous five years, Denise S. Peppers discovered that student performance on fractions was consistently the lowest…

In this paper we describe a touchscreen application called "TouchCounts," which is designed to support the development of number sense in the early years. We first provide an a priori analysis of its affordances. Then, using Sfard's communicational approach, augmented by a focus both on the role of the body--particularly the fingers…

Mathematics educators have had a long standing interest in students' understanding of decimal numbers. Most studies of students' understanding of decimals have been conducted within Western cultural settings. Similar research in other countries is important for a number of reasons, perhaps most importantly because it can provide insights that may…

Evidence evaluation is a crucial process in many human activities, spanning from medical diagnosis to impression formation. The present experiments investigated which, if any, normative model best conforms to people's intuition about the value of the obtained evidence. Psychologists, epistemologists, and philosophers of science have proposed…

In early childhood and primary (PreK-2) grades, subitizing is a critical skill that helps children meet early mathematics standards. Discover ways teachers can infuse this critical skill into their math curriculum.

There is a need for more comprehensive assessments of young children's emerging print knowledge. Traditional letter and numeral identification assessments score children's responses as either correct or incorrect and this approach can underestimate what children know. The present study tested an assessment scale that scored three- and…

This paper deals with the modern development of matrices, linear transformations, quadratic forms and their applications to geometry and mechanics, eigenvalues, eigenvectors and characteristic equations with applications. Included are the representations of real and complex numbers, and quaternions by matrices, and isomorphism in order to show…

Place value is a key concept for numbers that is introduced in early mathematics. It is necessary to have a flexible understanding of place value for efficient arithmetic strategies and success in written algorithmic arithmetic. In our research we explore typical mistakes and misconceptions that occur with 3rd graders in German elementary school…

This paper demonstrates the explanatory power of Kieren's framework for rational number knowing (1988, 1992, 1993, 1995), renamed here the four-three-four model, by describing the different approaches of Grade 6 students to a quotient context task (sharing three or seven custard tarts between five people) using Kieren's terminology of…

One of the common tasks of inferential statistics is to compare two data sets. Long before formal statistical procedures, however, students can be encouraged to make comparisons between data sets and therefore build up intuitive statistical reasoning. Such tasks also give meaning to the data collection students may do. This study describes the…

Are numerals estranged from a sense of the actual quantities they represent? We demonstrate that, irrespective of numerical size or distance, direct comparison of the relative quantities represented by symbolic and nonsymbolic formats leads to performance markedly worse than when comparing 2 nonsymbolic quantities (Experiment 1). Experiment 2…

The internal representation of numbers generated during calculation has received little attention. Much of the mathematics learning literature focuses on symbolic retrieval of math facts; in contrast, we critically test the hypothesis that internally generated numbers are represented analogically, using an approximate number system. In an fMRI…

This study investigates the development of proportional and additive methods along primary and secondary school. In particular, it simultaneously investigates the use of additive methods in proportional word problems and the use of proportional methods in additive word problems. We have also studied the role played by integer and non-integer…

The National Mathematics Advisory Panel (NMAP, 2008) asserts that a foundational knowledge of fractions is crucial for students' success in algebra; however, empirical evidence for this claim is relatively nonexistent. In the present study, we examine the impact of middle school students' fraction and whole number magnitude knowledge on various…