What once started as a simple tape machine adding machine,
has transformed time and time again from simple digital calculator, to advanced
graphing calculator, and now easily accessible computer algebra systems. This
advancement has allowed math students the world over to find the hints, tips,
and solutions they need in one convenient place. Wolfram Alpha, for example,
can, in under 10 seconds, take an equation and derive, integrate, graph,
transform, and expand an equation for you. A system like this has many
advantages for students.
For one, Wolfram Alpha does provide students with answers,
but it also provides a step by step for students to look at. By doing this students can check to see if the answers
they got were wrong and then see exactly what part of the problem they got
wrong. This provides students with a personal source they can reference and
takes the onus off the teacher to meet the needs of each individual student
independently, but at the same time.
Likewise, Wolfram Alpha has a multitude of math related
articles, definitions, and how to's any student may need. This way, even if
students get confused because they forget what an integral sign means, they can
quickly and easily look up the definition and guide on integrals that Wolfram
Alpha provides. They can then look at a couple of practice problems and
synthesize the material they read to truly understand the subject at hand.
Of course, like all pieces of technology, there are some
cons to always having Wolfram Alpha available. Students may use Wolfram Alpha
to simply look up answers and not attempt to look into how the system got the
answers or what is going on.
On the other hand, using Wolfram Alpha, or Mathematica,
Wolfram Alpha's downloadable computer algebra system, you can more easily show
students how functions look, how they operate, and compare with each other
simply by typing in the equation. Thus, the process of describing how 3 dimensional
functions look and operate become much easier than just drawing a doodle on a
paper. Students can look at, manipulate, and rotate surfaces to see what is
really going on.
Computer Algebra Systems are a fantastic way to help
students learn and visualize complex formulas in 2 and 3 dimensions, but it is
important to keep in mind that the program is designed to help teach, not
simply to show. Students learn by understanding, not by being given the answer,
and so Wolfram Alpha, or any computer Algebra System, is a great addition to
any class.
Wolfram Alpha is a great peace of technology that will assist students to gain a better conceptual understanding of algebraic concept. I am glad that you too find this useful to implement within a classroom. I agree with you in regards to the downfalls with the possibility that students could use this to simply get a right answer. However, I also agree that there are more pros than cons. Technology within a classroom will always have its downfalls in math. With the most basic calculator, students too can use it as a crutch. Nonetheless, I commend you for noticing this, and still find it a valuable peace to integrate into a classroom. I remember needing to check my answers for problems. The frustration with not knowing if your work is correct is troublesome. Students could use Wolfram Alpha to check if their first workout exercise was correct. There is nothing more frustrating than to realize that the same mistake was done for every problem, and that the bad habit and understanding now has to be retaught, re-explained and relearned. I too will use this in my classroom.
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