Students should be given an opportunity to explore and conjecture with the help of new technology to become good problem solver. Ron Mclister, while using the Geometer's Sketchpad to explore the Pythagorean theorem, came upon a nice result about the relationship of some geometrical patterns.

Students solve a geometric problem of measuring polygons with the help of proportional reasoning. Thus the importance of conceptual reasoning is emphasized as a highly efficient technique for teaching and strengthening mathematical content.

A Mandelbrot mathematical set is an object with endless borders, and in the present exercise a graphing calculator is used to identify and examine the set points. The significance and power of technology is also displayed in the understanding and solving of problems.

The way in which a mathematical problem was used as a vehicle to introduce the joy of mathematical research to a high school student is demonstrated. The student was interested in learning about other classical problems delighting an eager high school student.

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

A mathematical problem is presented. Teachers are advised to spend time discussing the problem with their students, but they should avoid giving them too much guidance.

In a previous article in this series, it was suggested that it is part of our responsibility as teachers to attempt to induce "perturbations" in our students' mathematical thinking. Especially when teaching seniors and capable students at any level, it is important that we unsettle them, shake their perceptions and attempt, wherever…

In this article, the author talks about his experiences when he started a mathematics degree with the Open University. He shares what happened during a course on mathematical models and methods and his major influences in mathematics. He also offers his current pedagogy that is based purely on his experiences and time spent talking to other…

Often after students solve a problem they believe they have accomplished their mission and stop further exploration. The purpose of this article is to discuss ways to encourage students to "look back" so as to maximise their learning opportunities. According to Polya, by "looking back" at a completed solution, by reconsidering and re-examining the…

In the domain of electrical circuits troubleshooting, a full factorial experiment investigated the hypotheses that (a) studying worked examples would lead to better transfer performance than solving conventional problems, with less investment of time and mental effort during training and test, and (b) adding process information to worked examples…

Five studies examined how interacting with the physical environment can support the development of fraction concepts. Nine-and 10-year-old children worked on fraction problems they could not complete mentally. Experiments 1 and 2 showed that manipulating physical pieces facilitated children's ability to develop an interpretation of fractions.…

The cross-proportion method allows both the instructor and the student to easily determine where an error is made during problem solving. The C-P method supports a strong cognitive foundation upon which students can develop other diagnostic methods as they advance in chemistry and scientific careers.

The situations created by individual style of problem solving in mathematics by children are discussed. Children can solve their mathematical problem by correcting their misconceptions on their own with the use of open discussions with others.

The purpose of this article is to provide five empirically-derived guidelines for knowledge map construction tools that facilitate problem solving. First, the combinational representation principle proposes that conceptual and corresponding procedural knowledge should be represented together (rather than separately) within the knowledge map.…

In this article, urban students explore powerful ideas from multiple perspectives. It concludes that academical success and importance of maintaining good teacher-student ratio, reinforcing meaning, making learning encourages problem solving ability among the students. Exploring ideas from multiple sources like educational books, images, and…