Newborn chicks were tested for their sensitivity to number vs. continuous physical extent of artificial objects they had been reared with soon after hatching. Because of the imprinting process, such objects were treated by chicks as social companions. We found that when the objects were similar, chicks faced with choices between 1 vs. 2 or 2 vs. 3…

The main purpose of this research is to determine whether the attainment of the number concept by children aged between 4-7 differs depending on age variant as well as receiving preschool education or not. Attainment of the number concept has been examined by means of One-to-One Matching Test consisting of Piaget's experiments. The test was…

Pascal's triangle is an arrangement of the binomial coefficients in a triangle. Each number inside Pascal's triangle is calculated by adding the two numbers above it. When all the odd integers in Pascal's triangle are highlighted (black) and the remaining evens are left blank (white), one of many patterns in Pascal's triangle is displayed. By…

Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

In an 8-month teaching experiment, I investigated how 4 sixth-grade students reasoned with reversible multiplicative relationships. One type of problem involved a known quantity that was a whole number multiple of an unknown quantity, and students were asked to determine the value of the unknown quantity. To solve these problems, students needed…

A dedicated, non-symbolic, system yielding imprecise representations of large quantities (approximate number system, or ANS) has been shown to support arithmetic calculations of addition and subtraction. In the present study, 5-7-year-old children without formal schooling in multiplication and division were given a task requiring a scalar…

Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…

After students have constructed a conceptual understanding of a mathematical idea, applying mathematical symbolism to represent and define the idea concisely becomes an easier task. In fact, Moore (1994) found that students "often needed to develop their concept images through examples, diagrams, graphs, and other means before they could…

Research Findings: The present study involved using a questionnaire to investigate the mathematics teaching practices of 74 U.S. and 67 Chinese early childhood teachers. Quantitative and qualitative analyses yielded several key findings. First, U.S. teachers are less intentional in mathematics teaching than their Chinese counterparts.…

How can it be explained that early literacy and numeracy share variance? We specifically tested whether the correlation between four early literacy skills (rhyming, letter knowledge, emergent writing, and orthographic knowledge) and simple sums (non-symbolic and story condition) reduced after taking into account preschool attention control,…

The purpose of this study was to determine the efficacy of specific, individualized training for students with different levels of mathematical difficulties. Fifty-four students, with either severe or mild math difficulties, were assigned to individualized training or to a control condition. Ten students with severe math difficulties…

Introduction: In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced…

Whether two-digit numbers are represented holistically (each digit pair processed as one number) or compositionally (each digit pair processed separately as a decade digit and a unit digit) remains unresolved. Two experiments were conducted to examine the distance, magnitude, and SNARC effects in a number-matching task involving two-digit numbers.…

We present a general formula for a triple product involving four real numbers. As a particular case, we get the sum of a triple product of four odd integers. Some interesting results are recovered. We derive a general formula for more than four odd numbers.

Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…