The purpose of this study was to investigate the extent to which parents of first, second, and third grade students who attended a two-day workshop on mathematics strategies shifted beliefs about learning mathematics as compared to parents who did not attend the workshops. Parents impact their children's mathematics learning when the students are…

What does "to be a mathematician" mean? What is implied, and what image is created of "a mathematician"? Are "mathematicians" members of an exclusive club? Are mathematicians different to "other people"? Are mathematicians different because they are able to mathematize? These might not be the most oft asked questions, but are they questions to…

Leonardo Pisano, the son of Guilielmo Bonacci, was born in Pisa, Italy, around 1175. He is better known as Fibonacci, a shortened version of "filius Bonacci" ("son of Bonacci"). He travelled with his father and during these travels, he learned about the enormous advantages of the mathematical systems used in the countries they visited. These…

The concept of exponents has been shown to be problematic for students, especially when expanding it from the domain of positive whole numbers to that of exponents that are negative and later rational. This paper presents a theoretical analysis of the concept of exponentiation as a continuous operation and examines the deficiencies of existing…

This research shows that people can unconsciously initiate and follow arithmetic rules (e.g., addition). Participants were asked to detect whether a symbol was a digit. This symbol was preceded by 2 digits and a subliminal instruction: "add" or a control instruction. Participants were faster at identifying a symbol as a number when the…

There are two primary interpretations of the mean: as a leveler of data (Uccellini 1996, pp. 113-114) and as a balance point of a data set. Typically, both interpretations of the mean are ignored in elementary school and middle school curricula. They are replaced with a rote emphasis on calculation using the standard algorithm. When students are…

A major source of errors in rational number tasks is the inappropriate application of natural number rules. We hypothesized that this is an instance of intuitive reasoning and thus can persist in adults, even when they respond correctly. This was tested by means of a reaction time method, relying on a dual process perspective that differentiates…

We investigated whether specific input helps 3-1/2-year-olds discover that the last word in a count represents its cardinal value (i.e., the cardinal word principle). In Study 1, we contrasted four training approaches. The only approach to yield significant improvement was to label a set's cardinality and then immediately count it. This training…

Counting complete subgraphs of three vertices in complete graphs, yields combinatorial arguments for identities for sums of squares of integers, odd integers, even integers and sums of the triangular numbers.

How do children learn the meanings of number words like "one," "two," and "three"? Whereas many words that children learn in early acquisition denote individual things and their properties (e.g., cats, colors, shapes), numerals, like quantifiers, denote the properties of sets. Unlike quantifiers such as "several" and "many," numerals denote…

It is of deep interest to both linguists and psychologists alike to account for how young children acquire an understanding of number words. In their commentaries, Barner and Butterworth both point out that an important question highlighted by the work of Syrett, Musolino, and Gelman, and one that remains highly controversial, is where number…

The ability to count has traditionally been considered an important milestone in children's development of number sense. However, using counting (e.g., counting on, counting all) strategies to solve addition problems is not the best way for children to achieve their full mathematical potential and to prepare them to develop more complex and…

The goal of this study was to investigate understanding of inservice elementary school teachers in Taiwan about number sense, teaching strategies of number sense and the development of number sense of students; and the profile of integrating number sense into mathematical instruction , and teaching practice. Data was gathered through interviews of…

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…