Place value is a phenomenon that has ominous implications for developing number sense and meaning and for using alternative algorithms and alternative representations within whole number arithmetic. For the most part, school programs examine place value at a surface level, with a primary focus on having the student identify or state a number value…

The Pythagorean Theorem, arguably one of the best-known results in mathematics, states that a triangle is a right triangle if and only if the sum of the squares of the lengths of two of its sides equals the square of the length of its third side. Closely associated with the Pythagorean Theorem is the concept of Pythagorean triples. A "Pythagorean…

This paper takes a known point from Brocard geometry, a known result from the geometry of the equilateral triangle, and bring in Euler's [empty set] function. It then demonstrates how to obtain new Brocard Geometric number theory results from them. Furthermore, this paper aims to determine a [triangle]ABC whose Crelle-Brocard Point [omega]…

A k-dimensional integer point is called visible if the line segment joining the point and the origin contains no proper integer points. This note proposes an explicit formula that represents the number of visible points on the two-dimensional [1,N]x[1,N] integer domain. Simulations and theoretical work are presented. (Contains 5 figures and 2…

Responsiveness to Intervention (RtI) is recommended both as an essential step before identifying learning disabilities (LD) and as a mechanism for preventing learning difficulties. The use of evidence-based multi-tiered interventions is of critical importance when implementing RtI. This article presents the results of a study that examined the…

The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children…

This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

The purpose was to ascertain whether there existed differential achievement effects associated with the factors and levels of context, form, item-stem and item-response format, size of common number, and school grade, as they relate to two variations of distributivity. Twelve 9-item tests were constructed and given to intact 4th-, 5th-, 6th-, and…

Several activities designed to allow students to play with and explore the special properties of the number nine are presented. A reproducible activity page is included. (MT)

Table games with special dice can help children with severe learning difficulties to improve their basic number skills (rote counting, numeral recognition, and counting out a quantity of objects from 1-200. Field testing supported the value of such games with 9- to 18-year-olds with moderate mental handicaps. (CL)

The study evaluated an errorless procedure for teaching nine educable mentally retarded students to solve missing minuend problems. Seven Ss acquired the target skill in a nearly errorless fashion in 75 to 172 minutes of individual training time. The other Ss required programatic alterations. (Author/CL)

Explores in three experiments development of three linguistic aspects of "more" in children's speech. Experiment 1 examined nature of early semantic content of "more;" Experiment 2, the child's differentiation of mass "more" from count "more"; and Experiment 3, the child's use of "more" as a…