Using calculators intelligently in education is a big challenge for teachers. When an intelligent partnership is created with calculators it significantly improves classroom dynamics, increase student confidence, reinforce understanding of mathematical concepts, and boast problem solving abilities.
This article will give an overview of how to build a successful partnership with calculators in education. We will go through the benefits of this partnership and then we will cover some basic ideas of how to create mathematics laboratory experiments.
Let us take the graphing calculator as an example. This type of calculator gives the student the ability to visualize the problem, experiment with mathematics theorems, and validate answers. The students can learn new theorems before they are introduced in class. This way the student can take an active role in his education. In addition, this will improve the student communication skills. Finally graphing calculators produce graphs faster and with high accuracy.
The meaning of studying graphs has changed in essence. Instead of learning the mathematics of how to make the plot itself the student studies the curve and experiments with its properties. The good student is not the one that does the plot accurately but is the one that understands the behavior of the curve at different points.
Calculators are like special purpose computers that are dedicated to certain mathematics applications. They are very portable and much more affordable. Moreover, they are much easier to use than personal computers and any school laboratory can have enough calculators for students of a single classroom.
First of all I would like to say that there are many types of calculators. For example there are graphing calculators, algebra calculators, matrices calculators etc. One should choose the one suitable for the required task. For example when one needs to experiment with graphing he can use the graphing calculator and do the algebraic manipulations on his own. This keeps the balance between paper and pencil skills and the use of calculators.
Now is the important question of how to build mathematics laboratory experiments. Before the start of any laboratory work the teacher should check that the laboratory has enough calculators for each and every student. It is very important that each student has his own calculator. If two students use one tool as a team one student may be faster than the other. He will pick up the idea faster and start implementing faster. The second student will rely on the first student and will be absent minded in class and he will not benefit. This is a serious problem that has many complications. It could lead to the student hating mathematics all together despite that he may be talented in mathematics.
I would like to share an experience that I had when I was teaching a laboratory in university. The laboratory contained fewer computers than students so some students had to share the same computer. The first few labs were demonstrations on how to use the software tools. Some students had higher pace in understanding. This caused that their partners became so dependent on them that they did not work and did not understand how to use the tools. This happened although they were mature university students. One would imagine now what would happen with little infants with much more limited communication experiences.
Once the number of calculators is settled one is now ready to prepare the first laboratory experiment. The first session should be on how to use the calculator. All the calculators in the laboratory should be the same brand and model in order to have the same method of use. The student should be taught how to use all the functions that will be used during the laboratory classes. They should get enough time experimenting with the use of these functions independently. It is crucial that they thoroughly understand how to use the calculators before given any laboratory experiments.
O nce the students are familiar with calculators they can be given the first experiments. I am going to go through a model that would hopefully inspire teachers on how to create laboratory experiments.
Imagine one wants to teach students the equation of a straight line y= mx + c. The teacher Should ask the students to use the calculator and plot this equation using different values for the symbols. After letting the student experiment a bit he should be asked that what should we do if we want the line to be steep? What should we do if we want to decrease the steepness of the line? How to make the line go uphill? How to make the line go downhill? After experimenting with real numbers the students should be able to answer these questions easily and understand and appreciate the significance of every symbol of the equation of the straight line.
Once the student understands the equation of straight line as an abstract mathematical concept he can start to learn examples of real life problems using the straight line equation .Now we can let him plot the relation between distance and time as a straight line relationship i.e. choose an example where the relation between distance and time is a straight line and give it to the students for experimenting.
It is important for the student to appreciate that the symbols of the equation this time are of real life quantities and not abstract quantities. This is the basic idea of creating mathematics laboratory experiments that will significantly improve student abilities and interest in the subject.