Problem behaviors present a significant challenge for individuals with developmental disabilities and their caregivers. Interventions based on behavioral principles are effective in treating problem behaviors; however, some caregivers have difficulty adhering to treatment recommendations. Treatment adherence may be affected by the technical nature…

Fibonacci's forgotten number is the sexagesimal number 1;22,7,42,33,4,40, which he described in 1225 as an approximation to the real root of x[superscript 3] + 2x[superscript 2] + 10x - 20. In decimal notation, this is 1.36880810785...and it is correct to nine decimal digits. Fibonacci did not reveal his method. How did he do it? There is also a…

Positive sums count. Alternating sums match. Alternating sums of binomial coefficients, Fibonacci numbers, and other combinatorial quantities are analyzed using sign-reversing involutions. In particular, we describe the quantity being considered, match positive and negative terms through an Involution, and count the Exceptions to the matching rule…

Motivated by centaurs jumping around a circular stadium, we derive Kronecker's Approximation Theorem, which in turn provides elementary solutions to difficult problems in the theory of Diophantine approximations.

Uniform sampling of binary matrices with fixed margins is known as a difficult problem. Two classes of algorithms to sample from a distribution not too different from the uniform are studied in the literature: importance sampling and Markov chain Monte Carlo (MCMC). Existing MCMC algorithms converge slowly, require a long burn-in period and yield…

With a staggering number of students dropping out of school, widespread below-grade reading proficiency, and PISA results showing a demoralizing lag internationally in math, science, and general problem solving, teachers need to exercise all the control available to them to engage students in meaningful learning. Wilhelm suggests six steps…

Background: This study examines the differential susceptibility hypothesis as it pertains to relations between infant temperament, parenting, and behavior problems in first grade. Method: Data from the NICHD Study of Early Child Care were used in a series of hierarchical regression analyses focused on interactions between three aspects of…

For researchers, committed to a research problem, finding meaningful answers is a process of careful weighting and interpreting what is actually found as an outcome of their mode of inquiry in reference to initial intentions and research goals. Particularly in doing qualitative research in/on teaching researchers have recognised the need to…

This article outlines the efforts of one man in a war-ravaged country to make a radical difference in the lives of children that have suffered the consequences of civil strife. The author was leader of a Baptist denomination in Liberia throughout a period of a civil war that devastated the country. Despite personal and political turmoil, he is an…

The overwhelming success of the commercial game market has brought increased attention to emerging work in educational game design. Much of the existing work in educational games has a strong similarity to the field of Problem-Based Learning (PBL), which has a rich history of conceptual literature as well as empirical investigations. Despite…

New people are being born, children are growing up, and young people are entering adult life; the complexity and contradictions of this process have been described very well in the literature. Leaving aside many essential aspects, people are being socialized--becoming a part of society--in a system of values that is entirely different. This paper…

The standard approach to finding antiderivatives of trigonometric expressions such as sin(ax) cos(bx) is to make use of certain trigonometric identities. The disadvantage of this technique is that it gives no insight into the problem, but relies on students using a memorized formula. This note considers a technique for finding antiderivatives of…

Two original problems in geometry are presented with solutions utilizing to differential calculus: (a) rectangle inscribed in a sector; (b) point on the ray of the angle. The possibility of applying mathematics in general and differential calculus in particular for solution of practical problems is discussed. (Contains 8 figures.)

In this article the process and outcomes of service user involvement in the analysis of data are discussed. The analysis formed part of a doctoral participatory research project, which involved researcher and service users working together. The focus of the research was on the experience and needs of service users with life limiting conditions…

Background: Although our understanding of dual diagnosis has improved, a deficit still exists in our knowledge of how schizophrenia spectrum disorders (SSD) manifest themselves in individuals with intellectual disability (ID). In addition, little is known about the relationship between behaviour problems and psychopathology in this population.…