![]() Drag point P to experiment with your sketch.Ģ. Open the sketch dist4.gsp supplied by the teacher. A free trial period demonstration version of Sketchpad can be downloaded from and used to manipulate the dynamic sketches downloadable from http.zaresidentsprofmddist.zip (WinZip is required to unzip the dynamic sketches).Ĭonjecture1. The next step is to use a dynamic geometry program to investigate the problem, and for further explorations. Mark a point in the equilateral pentagon corresponding to your guess.Ģ. Make a guess where you think she should build the cabin. Where should she build the cabin so that this is possible? She anticipates that visitors would visit each stream with the same frequency and decides to build the cabin so that the sum of the distances from the cabin to all five streams is as small as possible. Since trout and other fishing are quite excellent in these streams, the owner wants to build a small holiday cabin. Sum of distances A beautiful piece of mountainous land in the Drakensberg in South Africa approximates the shape of an equilateral pentagon (ie, has equal sides) and is bordered by a stream along each side. ![]() Students appear to find it more meaningful to see the exercise not as an attempt to verify, but rather to understand, why a conjecture is true. To start off with, the word “explanation” is used instead. Working with 14- to 17-year-olds, often a difficult age to engage with maths, teachers can often get through to them by using unusual conjectures to elicit surprise and create a need for further understanding. This encourages a process of discovery where pupils or students first visualise and analyse a problem, and make conjectures before attempting a proof. They can examine an entire set of similar cases in a matter of seconds, leading them naturally to generalisations. Students can transform their figures with the mouse, while preserving the geometric relationships of their constructions. This dynamic tool makes it easy to explore triangles, quadrilaterals, circles, and other geometric figures without the mechanical restraints of pencil and paper, compass, and straight edge. I have developed some activities to do this with Geometer’s Sketchpad software. Teachers may find it more meaningful to introduce proof as a means of explanation rather than as a means of verification. Which mathematics teacher has not been faced with students demanding: “Why do we have to prove this result? It’s so obvious.” Indeed, one of the biggest challenges facing maths teachers is convincing their students of the usefulness and value of proof. Try some software to help pupils approach proof via explanation, says Michael De Villiers.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |