Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem…

In 1945, Bronislaw Knaster proposed a procedure to divide any number of indivisible goods between a finite number of players requiring the players to place monetary values or bids on all of the goods. Often discussed in math for liberal arts courses that concentrate on contemporary applications of mathematics for non-major students, Knaster's…

Projective techniques continue to be widely used by school psychologists despite frequent criticisms of their use. This article reviews contemporary validity issues in the use of projective techniques with children and adolescents, including incremental validity, treatment validity, and problems associated with professional judgment and…

Pupils' motivation and interest are identified as important influences on learning. Motivational orientation is a construct that links motivation and epistemology. This study attempted to explore motivational orientation as it relates to science education and two different instructional approaches. A published instrument standardized with a…

Every day nurses make practice decisions that are based on knowledge drawn from personal, cultural, and scientific sources. Nurses therefore practice from a particular perspective that involves culturally based personal, professional, and societal beliefs and values. Their practice, however, may involve clients whose beliefs and values are…

Screening and prereferral are not required by the Individuals with Disabilities Education Act; however, many educators recognize that implementation of prereferral interventions is a measure of best practices. The authors address the need to establish a family-centered approach within the prereferral process in order to promote early and…

This article describes a unique supplementary program that teaches early childhood mathematics (Pre-K to Grade 2), through a series of six problem-solving adventure stories. The mathematics concepts are taught to the children through the medium of oral storytelling sagas in an integrated approach that addresses language arts as well as early…

In this paper, we describe the skeleton of two teaching units, based on a Model for teaching mathematics, Context Orientated Teaching (COT). The first teaching unit concerns the proof of a mathematical proposition, while the second one concerns the solution of an open problem. Both are taught in the 10th grade, under the specific conditions of the…

Mathematical optimization problems are not typical in the classical curriculum of mathematics. In this paper we show how several generalizations of an easy problem on optimal transportation were solved by gifted secondary school pupils in a correspondence mathematical seminar, how they can be used in university courses of linear programming and…

Mathematical problem solving is a transfer challenge requiring children to develop schemas for recognizing novel problems as belonging to familiar problem types for which they know solutions. Schema-based transfer instruction (SBTI) explicitly teaches transfer features that change problems in superficial ways to make them appear novel even though…

Mathematical models have become an important tool for understanding the control of eye movements during reading. Main goals of the development of the SWIFT model (R. Engbert, A. Longtin, & R. Kliegl, 2002) were to investigate the possibility of spatially distributed processing and to implement a general mechanism for all types of eye movements…

College students were exposed to two pairs of mathematics assignments. Assignment Pair A included a high-effort assignment containing 18 long three-digit ? two-digit (3?2) multiplication problems with all numerals in each problem being equal to or greater than four and a moderate-effort assignment that contained nine long problems and nine…

Evaluative inquiry--systematically gathering and analyzing data for the purposes of judging program or innovation merit, worth or significance and/or supporting ongoing school-based decision making and problem solving--is an option available to educators that is not often used; this despite recent interest in action research and school-based…

Two experiments investigated the effect of achievement goals on the transfer of a problem-solving strategy in 7- and 11-year-old children. In the first experiment, motivational priming took place before the learning of the strategy, affecting the learning as well as the transfer of the strategy. In the second experiment, motivational priming took…

This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and…