Young children are fascinated by how things "work." They are at a stage of development where they want to experiment with the many ways to use an object or take things apart and put them back together. In the process of exploring tools and machines, children use the scientific method and problem-solving skills. They observe how things work, wonder…

Cognitive load theorists have frequently used subjective measures of cognitive load to test the effectiveness of instructional procedures. This study sought to broaden the applications of subjective measures by testing their ability to detect variations in intrinsic cognitive load within tasks. In two experiments students were asked to complete…

Conceptual understanding in mathematics within the area of functions involves the ability to translate among different representations, table, graph, symbolic, or real-world situation of a function. Students' procedural knowledge for solving equations may become separated from their conceptual knowledge, and if these connections can be maintained…

The Big6 approach to information problem solving is widely used by students in the US. Use of Information is the 4th stage and marks a shift in focus from selecting and accessing information sources to using the information itself in a process that involves "critical thinking."

The effective ways of representing knowledge given the students and its use by teachers in departing the meaningful tasks are emphasized. An approach embodying five key principles like understanding big ideas, allotting tough assignments, thinking at high levels, problem solving and decision making ability are discussed.

Applications in engineering, science and technology within undergraduate programmes can be difficult for students to understand. In this paper, new results are presented which go some way to demonstrate and explain the problems faced by students in linking mathematical models to real-world applications. The study is based on student responses to…

Companies and R&D institutions increasingly collaborate not only in isolated projects but also in knowledge-based networks. In those networks, participants combine expertise and applied problems to generate both 'problem-solving knowledge' and specialized knowledge: during the process of common problem-solving each partner acquires some of the…

In this study, the teaching experiment methodology is used to observe firsthand a gifted student's mathematical learning and reasoning. A series of teaching experiments was conducted with 1 gifted and 1 average 7th-grade student to investigate how the gifted student's mathematical concepts and operation constructions differed from those of the…

This paper outlines a technique for enhancing the effectiveness of careers thinking by identifying and challenging tacit beliefs about career success. These beliefs can be understood as social scripts, i.e. cognitive structures that simplify common decision scenarios. An important contribution of careers counselling is to enable clients to…

The generation of new ideas is a complex demanding activity involving multiple processing operations. As is the case in other forms of complex cognition, biases in process execution can induce errors that limit peoples' ability to generate viable new ideas. In the present effort, the nature of these biases, and their impact on creative thought,…

This paper explores the wide range of pure mathematics that becomes accessible through the use of problems involving powers. In particular we stress the need to balance an applied and context based pedagogical and curricular approach to mathematics with the powerful pure mathematics beneath the simplicity of easily stated and understandable…

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…

In their sections on inverses most precalculus texts emphasize an algorithm for finding f [superscript -1] given f. However, inspection of precalculus and calculus texts shows that students will never again use the algorithm, which suggests the textbook emphasis may be misplaced. Inverses appear primarily when equations need to be solved, which…

Here we give an example of a problem that could be beneficially investigated by AS/A level students. It is a geometry problem that they can profitably tackle by geometric (especially geometry software) and algebraic means. Such problems naturally lead students to the need for proof--an essential part of mathematics that is often lacking in current…