Statistics is used in almost every facet of our daily lives: crime reports, election results, environmental/climate change, advances in business, financial planning, and progress in multifarious research. Although understanding statistics is essential for efficient functioning in the modern world (Cerrito 1996), students often do not grasp…

This paper presents the analysis of two representative lessons drawn from a cross case study of K-12 classrooms in which students and their teachers engaged in a collaborative dialogic inquiry process (data-driven dialogue) to co-construct meaning from assessment results. The representative lessons illustrate a significant shift from…

Contemporary debates on effective pedagogies for K-12 mathematics have called for shifts in the way teachers and teacher educators conceptualise mathematics as a subject and how it should be taught. This is reflected by changes in the curriculum including the inclusion of a strand called Working Mathematically within K-12 mathematics curriculum…

One special characteristic of any exponential growth or decay function f(t) = Ab[superscript t] is its unique doubling time or half-life, each of which depends only on the base "b". The half-life is used to characterize the rate of decay of any radioactive substance or the rate at which the level of a medication in the bloodstream decays as it is…

Current mathematics education reforms devoted to reasoning and proof highlight its importance in pre-kindergarten through grade 12. In order to provide students with opportunities to experience and understand proof, mathematics teachers must have a solid understanding of proofs themselves. In light of this challenge, a growing number of…

This paper focuses on the preliminary design of a multifaceted computer-based mathematics resource for undergraduate and pre-entry engineering students. Online maths resources, while attractive in their flexibility of delivery, have seen variable interest from students and teachers alike. Through student surveys and wide consultations, guidelines…

This article explores the question, "When should you mail in your entries to a sweepstakes in order to have the best chance of winning?"

In the context of discrete Fourier transforms the idea of aliasing as due to approximation errors in the integral defining Fourier coefficients is introduced and explained. This has the positive pedagogical effect of getting to the heart of sampling and the discrete Fourier transform without having to delve into effective, but otherwise long and…

This article describes how roulette can be used to teach basic concepts of probability. Various bets are used to illustrate the computation of expected value. A betting system shows variations in patterns that often appear in random events.

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…

For many students, mathematics is anything but coherent, and textbooks often do not make connections among concepts. Mathematics teachers must teach more than what is in the text in order to help students see and understand the big picture. Doing so will also help students recognize the concept and apply it in contexts outside of mathematics. The…

This article expresses concern for the sloppy language that is often used by the media to describe numerical comparisons and suggests guidelines for how such comparisons should be described such that the meanings are unambiguous.

The purpose of this study was to determine the changes in the mathematics curriculum for grades 5-8 in the Republic of Serbia after the break-up of SFRY. In particular, the research sought to identify the changes in the mathematics curriculum in terms of curriculum content and learning objectives, textbooks, and high school entrance examination…

Students need to achieve automaticity in learning mathematics without sacrificing conceptual understanding of the algorithms that are essential in being successful in algebra and problem solving, as well as in science. This research investigated the relationship between science-contextualized problems and computational fluency by testing an…

After a test is developed, most content validation analyses shift from ascertaining domain definition to studying domain representation and relevance because the domain is assumed to be set once a test exists. We present an approach that allows for the examination of alternative domain structures based on extant test items. In our example based on…