In order to investigate the performance of number sense and its relationships with mathematics achievement of Taiwanese students who had just completed the 5th-grade mathematics curriculum, a computerized number sense scale has been developed. This number sense scale includes four factors which are recognizing relative number size, using multiple…

A major goal of instruction is for students to develop competence with numbers. This study attempts to determine the effect of instructional materials that develop number concepts and connect these concepts to mental computation procedures. The study used 16 classes of eighth-grade students and a pretest-posttest design with two treatment groups.…

Presented is a method of teaching adding and subtracting as an interrelated series of patterns using a number line. Examples of the use of this method as well as the materials necessary are discussed. Applications of the method to multiplication and division are given. (CW)

Tests of computational estimation ability (CEA), strategy (CES), and mental computation ability (MCA) of (n=124) fourth, (n=143) fifth, and (n=84) sixth graders found significant relationships between CEA and MCA and between CEA and CES but not between MCA and CES. (12 references) (Author/MKR)

Presents a series of reflections in which a second-grade teacher recognizes the value of encouraging children to develop various computational processes as well as a range of different solution approaches. Uses the context of mentally calculating costs of menu items. (MKR)

This sequential explanatory mixed methods study explored 34 prospective elementary teachers understanding of division of fractions at the beginning and end of their final mathematics methods course. Participants' beliefs on the teaching and learning of division with fractions were also explored. At the beginning of the course, the participants had…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

A hands-on activity is described in which students attempt to measure something that they cannot see. In small groups, students estimate the number of marbles in sealed boxes. Next, students' estimates are compared with the actual numbers. Last, values from both the students' estimates and actual numbers are used to explain measurement theory and…

This article reviews two sets of research studies from outside of mathematics education to consider how they may be relevant to the study of bilingual mathematics learners using two languages. The first set of studies is psycholinguistics experiments comparing monolinguals and bilinguals using two languages during arithmetic computation (language…

The technique of distance sampling is widely used to monitor biological populations. This paper documents an in-class activity to introduce students to the concepts and the mechanics of distance sampling in a simple situation that is relevant to their own experiences. Preparation details are described. Variations and extensions to the activity are…

The data for 104 software projects is used to develop a linear regression model that uses function points (a measure of software project size) to predict development effort. The data set is particularly interesting in that it violates several of the assumptions required of a linear model; but when the data are transformed, the data set satisfies…

In 4 experiments, the authors examined the use of the hands in simple arithmetic tasks. Experiments 1 and 2 demonstrated that pointing increases both accuracy and speed in counting arrays of items, whether those items are identical or distinctive. Experiment 3 demonstrated that individuals tend to nod their heads when not allowed to point and that…

Teachers all over the world are aware that students struggle with fractional concepts and with elementary algebra. Support for this assertion can be found in a variety of research reports. The National Assessment of Educational Progress (NAEP), a United States report, indicates that students have recurrently demonstrated a lack of proficiency in…

In this paper, we take a look at two electrostatics problems concerning hemispheres. The first problem concerns the direction of the electric field on the flat cap of a uniformly charged hemisphere. We show that the symmetry and principle of superposition coupled with Gauss's law gives a delightfully simple solution and then go on to examine how…

A general and rigorous method to deal with singularities at the origin of a polar coordinate system is presented. Its power derives from a clear distinction between the radial distance and the radial coordinate variable, which makes that all delta functions and their derivatives are automatically generated, and ensures that the Gauss theorem is…