The normal reaction from students, when being introduced to variables, is asking “why do we need letters? Letters only make things more complicated”. If students have this attitude, it might be difficult to convince them otherwise. One way to get past this problem is for students to discover variables on their own. This way students themselves will come to realize that variables actually help explain situations and problems in mathematics and that expressions are in fact really elegant and easy to work with.
How can this be done? The first lesson when introducing variables, the students are asked to write down an explanation on how to calculate the area of a rectangle so that any person walking into the room will learn how to do it from their explanation. The first thing that most students will do is write an explanation and an example. This is all very good, however, in order for someone to understand their explanation they have to, in this case, understand swedish and the explanation is supposed to be universal.
The students are now asked to improve their explanation so that anyone in the world can understand it. This is always exciting because you can see the history of math taking place in the classroom. Students will try to develop all kinds of different symbols to use for their explanation and in many cases these symbols will have many similarities with hieroglyphs. From here you can continue asking them to try to find other ways to simplify the original problem. The problem is the words “length” and “width”, is it possible to name them in a universal way?
Students will eventually replace the words with letters and -voila- we are done. All students will agree that the explanation with letters is really elegant and easy to understand. And so the students have discovered the use and elegance with variables.
Are you looking for a digital math book for junior-high with exercises that encourages research and creativity? If you are, please visit Ma.fi (Finnish) or Matematik.fi (Swedish) for more information.