This paper illustrates the role of a "Thinking-about-Derivatives" task in identifying learners' derivative conceptions and for promoting their critical thinking about derivatives of absolute value functions. The task included three parts: "Define" the derivative of a function f(x) at x = x[subscript 0], "Solve-if-Possible" the derivative of f(x) =…

We investigated how within-stimulus heterogeneity affects the ability of rhesus monkeys to order pairs of the numerosities 1 through 9. Two rhesus monkeys were tested in a touch screen task where the variability of elements within each visual array was systematically varied by allowing elements to vary in color, size, shape, or any combination of…

This article builds on two previous ones in which we presented the processes of construction and consolidation of one student's knowledge structures about comparisons of infinite sets, according to a recently proposed theory of abstraction. In the present article, we show that under slight variations of context, knowledge structures that have…

While attending a Postgraduate Certificate in Education (PGCE) course, this author was provided with the time and encouragement to try out different activities, styles, and strategies of teaching. She used this time to develop numeracy starter lessons with Y7 students, spending two weeks with each of four sets of students. She decided from the…

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

The sequence 1, 1, 2, 3, 5, 8, 13, 21, ..., known as Fibonacci sequence, has a long history and special importance in mathematics. This sequence came about as a solution to the famous rabbits' problem posed by Fibonacci in his landmark book, "Liber abaci" (1202). If the "n"th term of Fibonacci sequence is denoted by [f][subscript n], then it may…

This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)

Citing that the concept of fractions is not a single idea, and that students may be proficient in one area of fractions while also holding contradictory beliefs, the writer reviews some common problems areas in teaching and learning about fractions, and maintains that the fraction concept does not respond to simple remediation methods. The author…

The author cites research from students' misconceptions of decimal notation that indicates that many students treat decimals as another whole number to the right of the decimal point. This "whole number thinking" leads some students to believe, in the context of comparing decimals, that "longer is larger" (for example, 0.45 is…

The main focus of this paper is on the study of students' conceptual understanding of two major concepts of Set Theory--the concepts of inclusion and belonging. To do so, we analyze two experimental classroom episodes. Our analysis rests on the theoretical idea that, from an ontogenetic viewpoint, the cognitive activity of representation of…

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a…

The introduction of educational technology to school classes promises--through the students' active engagement with mathematical concepts--the creation of teaching and learning opportunities in mathematics. However, the way technological tools are used in the teaching practice as a means of human thought and action remains an unsettled matter as…

Learning centers are a highly regarded and widely accepted practice in early childhood classrooms. Centers offer a variety of experiences during a single time segment that encourage children to explore materials, interact with peers, and accomplish new tasks. In this article, the author presents the block center, a popular mainstay among learning…

The importance of representations which are fundamental to understanding and applying mathematics, with the emphasis on the way the individuals who cannot see employ the representations is described. The teachers at Hadley school for the Blind showed the way the blind people used representations when learning mathematics with some accommodation,…

Painting the Cube is commonly used in middle and high school mathematical courses as a mathematically rich problem, wherein the exposed faces of the large cubes are painted after being assembled from small unit cubes. The problem perfectly combines algebraic as well as geometrical aspects and helps students to study and understand various linear,…