In this article, we present the main findings of an experiment which involves teaching statistics in the 5th and 6th grade classes of Greek elementary schools. This experiment focused on the evaluation of the potentials of teaching statistical concepts and methods using directed projects.

This paper describes a sequence of lessons from two Calculus I classes for teaching the epsilon-delta definition of a limit. In these lessons, the author elicited students' misconceptions and perceptions of this definition through a reading/writing lesson and then used these student ideas to design a lesson aimed at addressing these misconceptions…

A Graeco-Latin square of order "n" is an "n[superscript x]n" array whose entries are the "n"[superscript 2] ordered pairs of numbers from 1 to "n", and in each row and each column the first elements of the ordered pairs are all different, as are the second elements. This article traces the history of the results that came out of work on a false…

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

To demonstrate concepts or rapidly create quizzes, teachers commonly encounter the need to quickly create mathematical examples. Unfortunately, by producing undesirable or overly complex solutions, extemporaneously created examples can become problematic, create tense learning environments and become more confusing than they are worth. Experience…

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

Several formulae for the inradius of various types of triangles are derived. Properties of the inradius and trigonometric functions of the angles of Pythagorean and Heronian triangles are also presented. The entire presentation is elementary and suitable for classes in geometry, precalculus mathematics and number theory.

Traditional college algebra courses focus almost exclusively on power functions such as y = x[superscript 2] and y = x[superscript 3] rather than the more general y = x[superscript p]. However, it is the more general form that is the basis of the mathematical models that arise throughout the natural sciences in a host of unexpected and highly…

Students' understanding of functions is a topic that has been researched extensively. In this qualitative study, five university students of varying mathematical backgrounds were interviewed to reveal strategies and misconceptions as they struggled with graphical and analytical tasks relating to sum functions. Weaker students are seen to rely…

An experiment is reported that investigated the development of students' understanding of the numerical value of fractions. A total of 200 students ranging in age from 10 to 16 years were tested using a questionnaire that required them to decide on the smallest/biggest fraction, to order a set of given fractions and to justify their responses.…

This paper explores the development of students' knowledge of mathematical procedures. Students' tendency to develop rote knowledge of procedures has been widely commented on. An alternative, more flexible endpoint for the development of procedural knowledge is explored here, where students choose to deviate from established solving patterns on…

This study examined the hypothesis of superior quantification abilities of persons with high functioning autism (HFA). Fourteen HFA individuals (mean age: 15 years) individually matched with 14 typically developing (TD) participants (gender, chronological age, full-scale IQ) were asked to quantify as accurately and quickly as possible…

This study examined changes in 26 fourth-grade students' early conceptions of rational number representations as a function of receiving one of two curricular interventions. The first group of 12 students received a curriculum that emphasized constructing knowledge through extended problem solving with a single perspective of the rational number…

Researchers often have one or more theories or expectations with respect to the outcome of their empirical research. When researchers talk about the expected relations between variables if a certain theory is correct, their statements are often in terms of one or more parameters expected to be larger or smaller than one or more other parameters.…

The notions of "abstract "and "concrete" are central to the conceptualization of mathematical knowing and learning. It is generally accepted that development goes from concrete toward the abstract; but dialectical theorists maintain just the opposite: development consists of an ascension from the abstract to the concrete. In this article, we…