Many research studies involving Pearson correlations are conducted in settings where one of the two variables has a restricted range in the sample. For example, this situation occurs when tests are used for selecting candidates for employment or university admission. Often after selection, there is interest in correlating the selection variable,…

Like Pascal's triangle, Faulhaber's triangle is easy to draw: all you need is a little recursion. The rows are the coefficients of polynomials representing sums of integer powers. Such polynomials are often called Faulhaber formulae, after Johann Faulhaber (1580-1635); hence we dub the triangle Faulhaber's triangle.

Processes of knowledge construction are investigated. A learner is constructing knowledge about the notion of limit in the definition of the horizontal asymptote. The analysis is based on the dynamically nested epistemic action model for abstraction in context. Different tasks are offered to the learner. In her effort to perform the different…

The story is often told of the calculation by G.I. Taylor of the yield of the first ever atomic bomb exploded in New Mexico in 1945. It has indeed become a staple of the classroom whenever dimensional analysis is taught. However, while it is true that Taylor succeeded in calculating this figure at a time when it was still classified, most versions…

The purpose of this study was to explore and compare the proficiency of Grade 11 Mathematics and Mathematical Literacy (ML) learners in solving two problems based on the temperature conversion formula. The first was a result-unknown problem that asks for the result of a formula for a given input. The second was a start-unknown problem in which the…

Schools are scrambling to prepare students for the writing assessments aligned to the Common Core State Standards. In some states, writing has not been assessed for over a decade. Yet, with the use of computerized grading of the student's writing, many teachers are wondering how to best prepare students for the writing assessments that will…

A common activity in school mathematics is to derive a function from a table of values. There are two general strategies one might adopt to determine the function f. First, one might try to determine a connection between a particular n and f(n), and then evaluate whether it holds for other values of n. An alternative strategy would be to look for…

The notion of periodicity stands for regular recurrence of phenomena in a particular order in nature or in the actions of man, machine, etc. Many examples can be given from daily life featuring periodicity. Mathematically the meaning of periodicity is that some value recurs with a constant frequency. Students learn about the periodicity of the…

It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…

A well known result due to Laplace states the equivalence between two different ways of defining the determinant of a square matrix. We give here a short proof of this result, in a form that can be presented, in our opinion, at any level of undergraduate studies.

Students' struggles in learning reasoning and proof (RP) in mathematics are well known. Despite the instantiation of RP opportunities in mathematics textbooks in the USA and the important role that textbooks play in teachers' instructional decisions, little research has been conducted on analyzing student textbook tasks and narrative sections of…

The problem of optimizing the number of circular sprinklers watering large fields is used to introduce, from a purely elementary geometrical perspective, some basic concepts in crystallography and comment on a few size effects in condensed matter physics. We examine square and hexagonal lattices to build a function describing the, so-called, dry…

This study introduced various nonlinear growth models, including the quadratic conventional polynomial model, the fractional polynomial model, the Sigmoid model, the growth model with negative exponential functions, the multidimensional scaling technique, and the unstructured growth curve model. It investigated which growth models effectively…

Schwartz and Martin ("Cogn Instr" 22:129-184, 2004) as well as Kapur ("Instr Sci", this issue, 2012) have found that students can be better prepared to learn about mathematical formulas when they try to invent them in small groups before receiving the canonical formula from a lesson. The purpose of the present research was to investigate how the…

Designers of interactive learning environments with a focus on word problem solving usually have to compromise between the amount of resolution paths that a user is allowed to follow and the quality of the feedback provided. We have built an intelligent tutoring system (ITS) that is able to both track the user's actions and provide adequate…