Three-tiered models of academic and behavioral support are being increasingly adopted across the nation, and with that adoption has come an increasing message that designing and implementing effective practices alone is not enough. Systems are needed to help staff to collectively implement best practices. These systems, as well as effective…

As knowledge for competitive advantage develops beyond the transfer of simple data and information to focus on knowledge that has meaning, values, purpose and a more integrated aspect, higher education is required to graduate students able to operate in a more worldly manner across disciplines. Government's response to this need has been to demand…

This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software "R for Statistical Computing." The author illustrates the computer simulation approach by focusing on several problems of…

Based on the dozens of interactive workshops that the author has facilitated with children, he has discovered that children are more knowledgeable about the natural and the built environment than typically accredited. Due to this discovery, he believes children should be part of the community engagement for planning projects, developments, and…

In this paper, multiple criteria optimization has been investigated. A new decision support system (DSS) has been developed for interactive solving of multiple criteria optimization problems (MOPs). The weighted-sum (WS) approach is implemented to solve the MOPs. The MOPs are solved by selecting different weight coefficient values for the criteria…

The processes of learning mathematics are immensely complex and we largely lack insights into these processes. This is especially problematic when it comes to tertiary mathematics education, which has been much less researched than primary and secondary mathematics education. It is thus far from possible to clarify all relevant issues related to…

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

Current conceptualizations of knowing and learning tend to separate the knower from others, the world they know, and themselves. In this article, we offer "relationality" as an alternative to such conceptualizations of mathematical knowing. We begin with the perspective of Maturana and Varela to articulate some of its problems and our alternative.…

In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well-known cone solution, which is locally flat, but others in which the metric coefficients are powers of the radial coordinate and the spacetime is…

In this article, the author presents the Treasure Island problem and some inquiry activities derived from the problem. Trying to find where pirates buried a treasure leads to a surprising answer, multiple solutions, and a discussion of problem solving. The Treasure Island problem is an example of an inquiry activity that can be implemented in…

We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy E[subscript T] from a given initial state (q[subscript i], p[subscript i]) by controlling its frequency [omega], [omega][subscript min] less than or equal to [omega] less than or equal to [omega][subscript max]. A brief synopsis…

The well-known Stolz-Cesaro lemma is due to the mathematicians Ernesto Cesaro (1859-1906) and Otto Stolz (1842-1905). The aim of this article is to give new forms of Stolz-Cesaro lemma involving the limit [image omitted].

A standard example used in introductory combinatoric courses is to count the number of five-card poker hands possible from a straight deck of 52 distinct cards. A more interesting problem is to count the number of distinct hands possible from a Pinochle deck in which there are multiple, but obviously limited, copies of each type of card (two…

Stimulated in large part by the advent of the Internet, research productivity in many academic disciplines has changed dramatically over the last two decades. However, the assessment system that governs professional success has not kept pace, creating a mismatch between modes of scholarly productivity and academic assessment criteria. In this…

There is a remarkable difference between formal knowledge and true understanding of the subject. While the former helps students earn top grades, the latter is crucial to the solution of real-world problems. An excellent example is the computation of capacitance, with which some students have difficulty. Also, most textbooks limit problem analysis…