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I have tutored several students who don't understand how to graph complex functions. However, they do understand how to get their calculators to "spit-out" a graph.
What is so contradictory? You can't give someone who knows nothing about algebraic functions a scientific calculator and expect them to find the right answer using the tool. Calculators are merely a tool, just like a hammer, a pencil or a computer. You still need to acquire knowledge to use them properly and productively.
I needed tutoring in elementary school for long division. We weren't allowed to use calculators at that point. I had a terrible time trying to learn it. I finally did and became quite good at it. Conversely, in algebra in high school we were allowed to use scientific calculators during homework and class time. I learned the material and did very well in that class too. Calculators do not make or break one's understanding of mathematical functions.
I didn't place blame - I merely pointed-out facts.
I just attended the graduation ceremony of a VERY large public school. I had the opportunity to ask a simple combinatorial math question of the valedictorian of that school . The answer I received was a blank stare. After I explained the answer the blank stare remained.
What does your example show?
You went up to someone you presumably don't know and asked them a math question out of the blue. I'd give you a blank stare too.
...You went up to someone you presumably don't know and asked them a math question out of the blue. I'd give you a blank stare too.
Yeah, I just walked-up to a total stranger and asked a combinatorial math question . The question actually came up in a real-life situation - go figure.
...You can't give someone who knows nothing about algebraic functions a scientific calculator and expect them to find the right answer using the tool...
Sure you can - read the manual that comes with a scientific calculator . Or, better yet, do a web search for how to solve a particular problem using a scientific calculator. I have tutored several students who can solve problems with a calculator but don't have a clue about the underlying math. There are "canned" programs and procedures in the scientific calculators.
Sure you can - read the manual that comes with a scientific calculator . Or, better yet, do a web search for how to solve a particular problem using a scientific calculator. I have tutored several students who can solve problems with a calculator but don't have a clue about the underlying math. There are "canned" programs and procedures in the scientific calculators.
I remember being able to solve simple algebraic equations with the TI-81. I think it even allowed you to solve systems of equations. However, don't students usually have to demonstrate mastery of those concepts in prerequisite classes before being allowed to use calculators to solve them in more advanced classes?
I remember being able to solve simple algebraic equations with the TI-81. I think it even allowed you to solve systems of equations. However, don't students usually have to demonstrate mastery of those concepts in prerequisite classes before being allowed to use calculators to solve them in more advanced classes?
Yes they do.
You could give me a manual on how to operate a space ship. It doesn't mean I would be able to actually do it. Why? Because we are talking about tools. Tools don't work independently of their operators.
... However, don't students usually have to demonstrate mastery of those concepts in prerequisite classes before being allowed to use calculators to solve them in more advanced classes?
Nope - many high-schools simply touch on the material and tell the students to graph equations using their graphing calculators. In fact, the graphing calculators are required for the classes. They also get to use these graphing calculators on their exams.
These "exceptional" students go on to college and ...BOING!!!!!... the first time they have to graph complex functions they fall on their faces.
I state this from experience - I made sure my kid(s) could solve the problems without a calculator.
Here's an example of a simple problem where many students just use a calculator and don't understand what they're actually finding.
BTW - I have a math degree, and I have LOTS of experience helping students prepare for college and overcome their dependency on calculators.
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. The answer I received was a blank stare. After I explained the answer the blank stare remained.
. The question actually came up in a real-life situation - go figure.
