One would wonder how we should classify mathematics. Should we classify it to be under the category of science and technology or engineering or should it have a separate category. Indeed there is a very big relation between these fields and mathematics play a pivotal role in the advancements of these sciences. However, mathematics is fundamentally different in the way it is approached. It is approached in a way that is apposite to that of science and the goal from it is contradictory to the goal of science.
This differences between mathematics, science and technology, and engineering demand that the mathematical software calculators, that are used either to support research or the ones used to enforce the understanding of concepts, be used in a different way for each field. Indeed all fields can use the same software calculators but each one should set his experiments to suit his goals. This makes sense because the mathematics formulas are universal and are the same for everyone but the applications are different and numerous. We will go through the fundamental differences between these fields and explain how we can use software calculators differently with each field. This is to achieve the best benefit out of the calculator tools.
As we said from the start mathematics is the opposite of science in approach. In mathematics everything is given from the start. The rule is given and you proceed by trying to prove theorems. The catch is to assume a rule to prove requires a sharp brain. The fundamental idea of creating laboratory experiments using software calculators for such mathematics class is that you should set experiments to test the validity of the rules and to see if the results are sensible. The students should think just in pure numbers and equations.
In physics we observe a phenomenon and see what rules it follow. Then we see what mathematical model we can put it in. It is usually very complicated because many of the factors affecting the phenomenon may be unknown to us and usually there are many levels of uncertainties. This means that the answer usually will not be a perfect answer but will be an approximation. By experimentation and trial and error we can find out if the approximation is in acceptable tolerance from real life situation. Then and only then we can adopt the rule. The laboratory experiments that use calculators for physics training is completely different from that for mathematics training. The students should conduct an experiment on the phenomenon and record the result. They should use the rule they created and use the calculator and compare the output of the calculator with real data. They should also use the calculator to find error percentage and standard deviation. They can also use the help of an algebra calculator to plot the experimental data and derive an equation from the experimental data and see if the equation matches the equation they created.
Engineering on the other hand is application oriented. When a phenomenon is studied hard by scientists for many years and reliable rules that represent it exist and these rules show that this phenomenon is of either industrial or military value then this phenomenon is handed to engineering. It becomes a product in industry. The technology becomes public and it becomes taught in engineering schools throughout the world. Now we are ready to see how we can use software calculators to prepare laboratory experiments for engineers. One has to know that the engineers are designing a product and they want this product to have the most desirable features. What shows them that this product has a more desirable feature than another is the out put of design equations when they plug in the proper values they get a good out put. The best thing for them is to experiment with the calculators plugging in values and checking the output to see which input produces best design.