Online and on-demand tests are increasingly used in assessment. Although the main focus has been cheating and test security (e.g., Selwyn, 2008) the cross-setting equivalence of scores as a function of contrasting test conditions is also an issue that warrants attention. In this study, the impact of environmental and cognitive distractions, as…

Research about emerging best practices in the learning sciences points to the potential of deploying digital games as one possible solution to the twin challenges of weak student engagement and the need for more robust achievement in literacy, science, technology, and math. This chapter reviews key cross-cutting themes in this special volume,…

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…

The use of metaphors in design can help students reflect over a problem situation under an innovative point of view. During their design studies, students are supposed to acquire design skills, gain knowledge and enhance their level of expertise. This research explores the aid provided by metaphors in design problem solving, and its relationship…

This paper reports a teaching experiment in which two students engaged in tasks that challenged them to describe a final state for a variety of infinite iterative processes. The results from the study indicate that the students used multiple reasoning strategies for addressing these tasks. Refinements in the students' reasoning occurred as…

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…