In this article, we report a study of two-term unit fraction expansions using a geometric approach. It provides us insight on how to find all two-term unit fraction expansions and identify the property of the expansions with smallest maximal denominators, for a given unit fraction. These findings will be useful to lecturers or teachers involved in…

This paper challenges the emphasis on counting in New Zealand's Numeracy Development Project (NDP), arguing that subitizing provides an alternative pathway to quantification. Longitudinal data is presented showing that children's subitizing skills at the age of five years were a strong predictor of their later success in mathematics at the age of…

Place value underpins much of what people do in number. In this article, the author describes some simple tasks that may be used to assess students' understanding of place value. This set of tasks, the Six Tasks of Place Value (SToPV), takes five minutes to administer and can give direct insight into a student's understanding of the number system…

An essential part of understanding number words (e.g., "eight") is understanding that all number words refer to the dimension of experience we call numerosity. Knowledge of this general principle may be separable from knowledge of individual number word meanings. That is, children may learn the meanings of at least a few individual number words…

In this article, we discuss how to use a diagrammatic approach to solve the classic sailors and the coconuts problem. It provides us an insight on how to tackle this type of problem in a novel and intuitive way. This problem-solving approach will be found useful to mathematics teachers or lecturers involved in teaching elementary number theory,…

Previous evidence has shown that 11-month-olds represent ordinal relations between purely numerical values, whereas younger infants require a confluence of numerical and non-numerical cues. In this study, we show that when multiple featural cues (i.e., color and shape) are provided, 7-month-olds detect reversals in the ordinal direction of…

This article reports the findings from a comparative analysis that examined several mathematical content strands, reasoning processes, and emphasis on technology in prior K-8 state mathematics standards and the Common Core State Standards for Mathematics (CCSSM). Various methodological tools were utilized to compare and contrast CCSSM with prior…

Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advanced mathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do…

These Proceedings are a written record of the research presented at the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2013) held in Chicago, Illinois, November 14-17, 2013. The theme of the conference is Broadening Perspectives on Mathematics Thinking and Learning.…

Student performance in mathematics has been linked to the mathematical knowledge of the teacher. Based on this finding, a 5-day professional development module was created to improve teachers' mathematical knowledge and their understanding of number sense. We found no difference prior to the professional development in mathematical content…

"Project SEED" is a supplemental mathematics program for low-achieving students in grades 3 through 8 and is intended to prepare students to be successful in high school and college math. Based on the Socratic method, instruction is delivered through a series of questions to the class. In addition to individual responses, the instructor…

Young children must develop basic concepts of numeracy--one being that numbers have magnitudes that increase linearly--before they are able to succeed in mathematics. Children from low-income families have been found to be at a greater disadvantage in the development of numeracy, but this disadvantage can be overcome through the use of a simple…

In a recent study, Gevers and colleagues (2010, "Journal of Experimental Psychology: General," Vol. 139, pp. 180-190) showed that the SNARC (spatial numerical association of response codes) effect in adults results not only from spatial coding of magnitude (e.g., mental number line hypothesis) but also from verbal coding. Because children are…

There is a concern among educators in schools with high levels of poverty that students are lacking certain academic strategies, especially in mathematics. These students struggle to explore data systematically and procedurally. The purpose of this pre-posttest design study is to intentionally teach number sense skills in order to increase…

An interview with a sixth-grade student illustrates how her number sense and understanding of variability relate to her ability and proclivity to apply a frequentist (statistical) approach to probability tasks. A general suggestion for teaching about mathematics of uncertainty through the gradual strengthening of estimation, as per the historical…