Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan…

Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations--problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered…

Learning to compute integrals via the various techniques of integration (e.g., integration by parts, partial fractions, etc.) is difficult for many students. Here, we look at how students in a college level Calculus II course develop the ability to categorize integrals and the difficulties they encounter using a card sort-resort activity. Analysis…

This article describes a comprehensive and novel approach to assessment in early numeracy. Topics include the significance of early numeracy, developing a nomenclature for early numeracy, and describing the context for the development of this approach to assessment. The largely unrealised importance of numerals and numeral sequences in early…

As a result of the use of random assignment to treatment, randomized experiments typically have high internal validity. However, units are very rarely randomly selected from a well-defined population of interest into an experiment; this results in low external validity. Under nonrandom sampling, this means that the estimate of the sample average…

There are increasing calls to prepare K-12 students to use computational tools and principles when exploring scientific or mathematical phenomena. The purpose of this paper is to explore whether and how constructionist computer-supported collaborative environments can explicitly engage students in this practice. The Categorizer is a…

Background: This article reports on an analysis of errors that were displayed by students who studied mathematics in Chemical Engineering in derivatives of mostly trigonometric functions. The poor performance of these students triggered this study. The researcher (lecturer) works in a mathematics support programme to enhance students'…

Receiver operating characteristic curve (ROC) analysis was used to investigate the ability of early numeracy curriculum-based measures (EN-CBM) administered in preschool to predict performance below the 25th and 40th percentiles on a quantity discrimination measure in kindergarten. Areas under the curve derived from a sample of 279 students ranged…

We calculate the number of subgroups in a direct product of finite cyclic groups by applying the fundamental theorem of finite abelian groups and a well-known structure theorem due to Goursat. We also suggest ways in which the results can be generalized to a direct product of arbitrary finite groups.

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to…

Background: The increasing numbers of teaching assistants (TAs) and their widening role in English primary classrooms is part of wider international developments. Several large quantitative studies have been influential in shaping debate, but little qualitative research exists on TAs and the content of their activity in the key area of…

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer…

Presents various simple activities to use with two-color counters as a vehicle for teaching concepts such as observation, classification, counting, recording, graphing, developing relational language, number sense, and beginning ideas of probability. (AIM)

This paper presents an overview of the Comprehensive School Mathematics Program (CSMP) elementary school mathematics curriculum. The philosophy behind the program, content goals, and teaching strategies are briefly discussed. Then ways in which the program develops facility in mathematics are described in discussions of the language of arrows, in…