If one rolls a coin across a chessboard and it comes to rest on the board, what is the probability that it covers some corner of one of the grid squares? The online magazine "Plus" (2004) posed this problem for students to solve. It is a useful problem for several reasons: it introduces the idea of probability in a continuous sample space, it has…

Expulsion is commonly schools' last resort to maintain discipline and keep schools safe. But increasingly, educators are turning to "restorative justice"--an alternative method from the field of criminology--with promising results. According to Randall Comfort, assistant upper-school director, Mounds Park Academy, St. Paul, Minnesota, using this…

In this article, the authors discuss how children learn to problem solve from birth to 6 years. At 0 to 2 years, children learn to be very effective problem solvers by encouraging children's explorations and supporting their efforts to resolve difficulties. When they reach 3 years old, children enjoy experimenting with a wide variety of materials,…

In this article, the author responds to a teacher's request for advice on how to handle a child in her class who keeps on shoving and bopping other children, sometimes hitting them on the head with hard objects. The author offers support and suggestions on how to help children who use negative behavior to communicate their wants and needs. She…

There are lots of ways to handle behavior problems in the classroom. Some teachers send difficult children to time out, others tell them what and what not to do, and many explain why. But these techniques have one thing in common: they all do the thinking for the child. In this article, the author discusses how to help children handle conflicts…

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…

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.

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,…

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…

A inquiry-based approach called the "modelling discussion" is introduced for structuring beginning modelling activity, teaching new mathematics from examining its applications in contextual situations, and as a general classroom management technique when students are engaged in mathematical modelling. An example which illustrates the style and…