Performance feedback and checklists were used to improve the degree to which middle-school teams adhered to elements of systematic problem solving as described in the Instructional Consultation literature (Bartels & Mortenson, 2002; Rosenfield, 1987). Direct observations of problem-solving meetings were conducted to determine levels of adherence…

A method for generating sums of series based on simple differential operators is presented, together with a number of worked examples with interesting properties.

This meta-analysis investigated the influence of assessment on the reported effects of problem-based learning (PBL) by applying Sugrue's (1995) model of cognitive components of problem solving. Three levels of the knowledge structure that can be targeted by assessment of problem solving are used as the main independent variables: (a) understanding…

The article raises issues about the current direction of the field of educational leadership and management. It argues that we should consider a re-orientation of the field in order to renew its concern with ideas connected with organization, which include viewing organizations as complex adaptive systems and taking an institutional perspective.…

The analysis of tautochrone problems involves the solution of integral equations. The paper shows how a reasonable assumption, based on experience with simple harmonic motion, allows one to greatly simplify such problems. Proposed solutions involve only mathematics available to students from first year calculus.

This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

This study investigated the amounts of problem-solving process information ("action," "why," "how," and "metacognitive") elicited by means of concurrent, retrospective, and cued retrospective reporting. In a within-participants design, 26 participants completed electrical circuit troubleshooting tasks under different reporting conditions. The…

Based on contemporary theories of learning, this article takes a critical view of the concept of learning objects. Learning objects decompose content into granular pieces of information that can be stored, retrieved, and reused in instruction. Current conceptualizations of learning objects support traditional, objectivist forms of instruction.…

We asked whether honeybees, "Apis mellifera," could solve a transitive inference problem. Individual free-flying bees were conditioned with four overlapping premise pairs of five visual patterns in a multiple discrimination task (A+ vs. B-, B+ vs. C-, C+ vs. D-, D+ vs. E-, where + and - indicate sucrose reward or absence of it,…

Adding gesture to spoken instructions makes those instructions more effective. The question we ask here is why. A group of 49 third and fourth grade children were given instruction in mathematical equivalence with gesture or without it. Children given instruction that included a correct problem-solving strategy in gesture were significantly more…

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

In this classroom note, the authors present a method to solve variable coefficients ordinary differential equations of the form p(x)y([squared])(x) + q(x)y([superscript 1])(x) + r(x)y(x) = 0. They propose an iterative method as an alternate method to solve the above equation. This iterative method is accessible to an undergraduate student studying…

In this paper, the properties of tangential and cyclic polygons proposed by Lopez-Real are proved rigorously using the theory of circulant matrices. In particular, the concepts of slippable tangential polygons and conformable cyclic polygons are defined. It is shown that an n-sided tangential (or cyclic) polygon P[subscript n] with n even is…

The phenomenon of nonlinear resonance (sometimes called the "jump phenomenon") is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto…