EdGCM in a high school program

[Patrick LEE]

Originally Posted by mchandler

Always a difficult question - how much technology to allow in the classroom? The answer may depend upon whether the focus is on understanding underlying principles or on pragmatic methods for getting correct answers. Once, the calculator was banned from classrooms in the U.S. (believe me, I remember!). Now it is an essential tool (my daughter's 4th grade class REQUIRES her to have a calculator). Will laptops ever follow the same path? I hope so! Would caveman mathematicians balked at the use of pencils? "Do it in your head! It's the only way to prove you really know the material!"

Mark,

The issue is not about technology. The issus is that the purpose of those questions is let the students to apply the mathematics to sketch the graphs so that the students can get a better understanding of, say, the relationships between derivatives and maximum/minimum etc. Just typing in the function into the calculators and plot it defects the purpose of those problems. The issue is NOT just to get the graph, the issue is the USE of mathematics to sketch the graph. In this case, the use of calculators is a mis-use.
On the other hand, if you are working with a problem in physics or chemistry and you face the same mathematical problem, then there are nothing wrong to use the calculator to plot the graph. Here, the issue is the physics or chemistry problem rather than getting practice on calculus. In this case, the use of calculators is a proper use.
Hence, using the powerful calculators to plot the same function can be a proper use or a mis-use of calculators.

The use of calculators have been a big issue in almost every countries. Calculators have been banned in many countries initially and then allowed. Calculators are allowed not mainly because of technology, they are allowed because
(1) we have made the following mistake: Arithematics is not really mathematics and the students will not suffered from using calculators. The experience is that without the boring mechanical arithematics, students do less well in mathematics. Another side effect of using calculators is that a lot of students in those days thought that they do not need to study hard for mathematics because the calculators will handle the mathematics for them. Most of the wealthy countries get punished by this mistake because they are the countries who use the calculators first and more extensively. In this issue, I agree with the Bristish in that they later go abck to ban the use calculators in lower grades. May be the British can tell us the latest developments in their country.

(2) The nature of mathematics course has changed. In the old days, the so called old mathematics carries the objective of teaching advanced logical thinking. Just recall the rigorous of proving the theorems in Euclidean Geometry in high school. Then the newer mathematics courses took over the world, the students learn more topics in mathematics but less rigorous mathematical reasoning is required. So, more cookbook approach is used. Mathematics became more as a tool. This is correct and calculators should be allowed as the position of mathematics has changed in the whole education system.

(3) Finally, the use of calculators actually help students to learn mathematics. The calculators free us from the boring mechanical operations so that we can concentrate on the mathematical problem itself.

Nowadays, the students in almost all countries use calculators extenively in classroom. However, this does not mean that we should use calculators and computers blindly in classroom.

Just remember that using the calculators to solve the SAME problem in the classrooms, it is a proper use of calculators in some cases and it is a mis-use in other cases.

Nowadays, we have cars, but we still walk and run. We walk not because we do not have a car. We talk because we want to keep fit. So, we do some calculations in classrooms without using calculators because we want to keep our mind healthy (not because we do not have calculators or computers to use).

Patrick.