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The Use of calculators intelligently in teaching mathematics is a big challenge for teachers. When a smart partnership is created with calculators it greatly improves the dynamics of classrooms, raises student confidence, promotes understanding of mathematical concepts, and boasts problem solving abilities.This article will outline how to build a successful partnership with calculators in teaching. We will go through the merits of this partnership and then we will cover some ideas of how to create mathematics laboratory sessions.
Let us take the graphing calculator for an example. This type of calculator gives the student the chance to visualize the problem, experiment with theorems, and validate the answers. The students can learn new theorems before they are introduced by the teacher. This way the student can take an active role in his learning. Moreover, this will improve the student communication skills. Lastly, graphing calculators produce plots faster and with higher accuracy.
In essence the meaning of studying graphs has changed. Instead of studying the mathematics of how to make the plot the student studies the curve and experiments with its properties and behavior. The good student is not the one that draws the plot accurately but is the one that understands the behavior of the curve at any point.
Calculators can be thought of as special purpose computers that are dedicated to certain mathematics applications. They are very portable and inexpensive relative to personal computers. In addition, they are much easier to use than personal computers and any school laboratory can easily have enough calculators for students of a single classroom. First , I would like to point out that there are many types of calculators. For instance there are graphing calculators, algebra calculators, matrices calculators ?etc. One should choose the one suitable for the intended task. For example when one needs to experiment with plotting graphs he can use the graphing calculator and do the algebraic calculations on his own. This would keep the balance between paper and pencil skills and the use of calculators.
Now the question is how to build mathematics laboratory experiments. Before the start of any laboratory experiments the teacher should check that the laboratory has enough calculators for every student. It is crucial that each student has his own calculator. If two students use one calculator as a team one student may be faster than the other at dissolving the technology. He will pick up the idea faster and start the implementation faster. The second student will rely on his partner and will be absent minded in the laboratory session and he will not benefit. This is a serious problem that has its complications. It could lead to the student hating mathematics despite that he may be talented in mathematics.
I would like to share an experience that I had when I was a laboratory teacher in university. The laboratory contained fewer computers than students so some of the students had to share the same computer. The first few labs were demonstrations on how to use the tools. Some students had higher pace in understanding and dissolving the use of technology. This caused that their partners became so dependent on them that they did not work and did not dissolve how to use the software tools. This happened although they were mature university students. One would imagine what would happen with little infants with much more limited communications experiences.
Once the number of calculators is settled one can prepare the first laboratory experiment. The first experiment should be on how to use the calculator. All the calculators in the laboratory should be of 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 sessions. They should be given enough time to experiment with the use of these functions independently. It is very important that they thoroughly understand how to use the calculators before given any laboratory work.
Once the students are familiar with calculators they can be given the first experiment. I am going to go through a model that would hopefully inspire teachers on how to create creative laboratory experiments. Imagine one wants to teach students the equation of a straight line y= mx + b. The teacher Should ask the students to use the calculator to plot this equation using different values for the symbols. After letting the student experiment a bit on his own he should be asked that what should we do if we want the graph line to be steep? What should we do if we want to decrease the steepness of the graph 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 very easily and understand and appreciate the importance of every symbol of the straight line equation.
Once the student understands the equation of straight line as an abstract mathematical idea he can start to learn examples of real life physical problems using the straight line equation We can let him plot the relation between distance and time as a straight line relationship i.e. We should choose an example where the relation between distance and time is a straight line and give it to the students for testing.
It is crucial for the student to appreciate that the symbols of the equation this time are of physical real life quantities and not abstract quantities. This is the idea of creating mathematics laboratory experiments that will significantly improve student abilities and interest in mathematics.
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