Describes two card games to motivate students to understand number sense concepts that can be used at the 2nd-5th grade levels. (ASK)

Describes how a teacher helped his students develop fractional number sense through a process-oriented activity. Illustrates how a teacher included a worthwhile, interesting and challenging mathematics question in his class to create a good learning environment for children. (Author/MM)

Discusses linguistic influence on children's numerical development. Describes and reviews recent papers that address the relationship between number naming systems and children's numerical concepts. (Contains 20 references.) (ASK)

Although children take over a year to learn the meanings of the first three number words, they eventually master the logic of counting and the meanings of all the words in their count list. Here, we ask whether children's knowledge applies to number words beyond those they have mastered: Does a child who can only count to 20 infer that number…

This article concludes the serialization of the Royal Statistical Society's Schools Lecture for 2004, on "Lies and statistics".

The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

A result known as the Borel-Cantelli lemma is about probabilities of sequences of events. This article presents an example in which it appears that the hypotheses of the lemma are satisfied but the conclusion is not. The explanation of why not combines elements of probability theory, number theory, and analysis.

This article discusses prime numbers, defined as integers greater than 1 that are divisible only by only themselves and the number 1. A positive integer greater than 1 that is not a prime is called composite. The number 1 itself is considered neither prime nor composite. As the name suggests, prime numbers are one of the most basic but important…

The term "random" is frequently used in discussion of the theory of evolution, even though the mathematical concept of randomness is problematic and of little relevance in the theory. Therefore, since the core concept of the theory of evolution is the non-random process of natural selection, the term random should not be used in teaching the…

After extensive laboratory testing of the famous memorist Rajan, Thompson, Cowan, and Frieman (1993) proposed that he was innately endowed with a superior memory capacity for digits and letters and thus violated the hypothesis that exceptional memory fully reflects acquired ''skilled memory.'' We successfully replicated the empirical phenomena…

This article features questions regarding logarithmic functions and hair growth. The first question is, "What is the underlying natural phenomenon that causes the natural log function to show up so frequently in scientific equations?" There are two reasons for this. The first is simply that the logarithm of a number is often used as a replacement…

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…