The repetitive, stereotyped and obsessive behaviours, which are core diagnostic features of autism, are thought to be underpinned by executive dysfunction. This study examined executive impairment in individuals with autism and Asperger's disorder using a verbal equivalent of an established pseudo-random number generating task. Different patterns…

There often seems to be confusion as to when young children should be ready to learn basic math concepts. The truth is, children are born ready to do mathematics. They show amazing competencies very early in life. For example, one can show an infant two objects as one moves them behind a screen. Then one more object is added. When the screen is…

This note explores ways in which the Fibonacci numbers can be used to introduce difference equations as a prelude to differential equations. The rationale is that the formal aspects of discrete mathematics can provide a concrete introduction to the mechanisms of solving difference and differential equations without the distractions of the analytic…

Mathematical historians place Heron in the first century. Right-angled triangles with integer sides and area had been determined before Heron, but he discovered such a "non" right-angled triangle, viz 13, 14, 15; 84. In view of this, triangles with integer sides and area are named "Heron triangles." The Indian mathematician Brahmagupta, born in…

The number Pi has a rich and colorful history. The origin of Pi dates back to when Greek mathematicians realized that the ratio of the circumference to the diameter is the same for all circles. One is most familiar with many of its applications to geometry, analysis, probability, and number theory. This paper demonstrates several examples of how…

In some elementary courses, it is shown that square root of 2 is irrational. It is also shown that the roots like square root of 3, cube root of 2, etc., are irrational. Much less often, it is shown that the number "e," the base of the natural logarithm, is irrational, even though a proof is available that uses only elementary calculus. In this…

Real numbers are often a missing link in mathematical education. The standard working assumption in calculus courses is that there exists a system of "numbers", extending the rational number system, adequate for measuring continuous quantities. Moreover, that such "numbers" are in one-to-one correspondence with points on a "number line". But…

This article illustrates the misconceptions that students have when using the equals sign and describes a lesson used to give students the foundation for an accurate conception of equivalency.

A mathematics curricula "Have a Heart problem" characteristically expect students to work numerically with formulas and unit conversions, assuming that they have had enough experience measuring lengths and areas physically. However, the problem shows the pitfalls of working numerically without the proper conceptual foundations.

A majority of studies on learning disabilities have focused on elementary grades. Although problems with learning disabilities are life-affecting only a few studies focus on deficits in adults. In this study adults with isolated mathematical disabilities (n = 101) and adults with combined mathematical and reading disabilities (n = 130) solved…

Useful for small groups or one-on-one instruction, this book offers successful math interventions and response to intervention (RTI) connections. Teachers will learn to target math instruction to struggling students by: (1) Diagnosing weaknesses; (2) Providing specific, differentiated instruction; (3) Using formative assessments; (4) Offering…

This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…

This document presents activities for use by middle school teachers which show how rational numbers and proportions are present in many real-world situations, including the collection and analysis of fractions, ratios, percents, and proportions, as well as rational number connections with geometry and similarity. The activities are divided into…

This brief report from the Indigenous Mathematics Project focuses on the way in which numerical reasoning is changing in the Oksapmin community of Papua New Guinea as a function of participation in new social institutions: economic exchange with currency and enrollment in school. Each of these new institutions means that arithmetic problems are…

This module is the sixth in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include calculator division, mixed number fractions,…