For a while, I have wanted to begin a MHF discussion on this gem by Lockhart. (Please see link at bottom.)
At the very least, the author is hilariously entertaining. I look forward to your responses.
http://www.maa.org/devlin/LockhartsLament.pdf
For a while, I have wanted to begin a MHF discussion on this gem by Lockhart. (Please see link at bottom.)
At the very least, the author is hilariously entertaining. I look forward to your responses.
http://www.maa.org/devlin/LockhartsLament.pdf
What in the h**l is you point?
Anyone who follows Keith Devlin's posts @Maa.org has seen this.
We all know that today's mathematics education in in the tank.
Keith himself has written on this.
Here is how bad it is. Before I retired, I quit often gave talks to groups of AP calculus teachers that are required by the state.
I would start by making sure that no calculators were active.
Then I would ask about the bounds on $\displaystyle \sqrt{13}~?$
I never had more than three who knew that it had to be between $\displaystyle 3~\&~4$ and much less WHY.
Now understand, I see no reason not to use a calculator to find $\displaystyle \sqrt{13}$. But I mean it is important to understand what answers are reasonable.
In other words, the questions we ask must enlighten the student.
The way we get the answer is irrelevant. WHAT DO THEY MEAN?
I predict that within 20 years no calculus textbook will have a chapter called Techniques of Integration.
I agree. Being a student in AP Calculus, my math teacher constantly tells our class that how my generation is inferior to that of his. I had a very nice discussion with him regarding the "modernization" of teaching mathematics, and it was quite surprising what he said. Repeatedly, he told my class about his experiences with using log and trig tables, and he is quite disgusted with the fact that such topics are not discussed today. It can be much simpler to find a value for any logarithm using such a table rather than using a calculator to estimate the same value. My mother, who minored in mathematics, also had to memorize such tables. I find it amazing how much LESS we are being taught about older ways to estimate values of numbers.
Also, I recently bought a TI-89 for my calc class. It does everything, it solves equations, finds common denominators, helps with derivatives, integrals, and even more advanced subjects such as differential equations, arc lengths, & Taylor series. The AP exam allows these types of calculators, however, such questions with calculators are more involved. Anyway, it's amazing how simple it is now to easily enter: solve the differential equation 3y''+6y'-7y=0. I guarantee you will get a solution within a few seconds. I only use these functions as a check, I do all of my work by hand first. We've entered a time where things are getting simple. Too simple.
it's hard to test understanding.
two students are asked to add 2 and 3.
both students write down the answer 5.
student A is asked how he arrived at his answer: he replies, "i took 3, added 1 twice, and got to to 5"
student B is asked the same question, and replies: "well first i doubled both numbers to get 4 and 6, then i split the difference".
which one understands what he is doing?