## Sunday, August 29, 2010

### There Are No Stupid Questions...Or Are There?

I gave my Survey of CompSci students my usual second-week assignment, a *gasp* WORD PROBLEM *horrors* involving conversion of numbers from one base to another -- a problem intended to not only help reinforce their grasp of what we had just covered in class, but designed to *unbelieveable!* also stretch their problem-solving skills. The math involved is not exactly rigorous -- extremely basic algebra and a reasonable grasp of arithmetic is all that is needed to use a) the formula for converting a number in any non-decimal number system to base 10, and b) the process for converting a number from base 10 to any other number base.

The only problem is that the latter calculation requires that students do old-fashioned "long division" whereby they end up with a quotient and a remainder -- NOT a fraction, NOT a decimal value, but two whole numbers. Needless to say, calculators do not do this correctly!! Does that stop students from trying to use their calculator? You tell me...

I'm used to that, and I am normally perfectly happy to give those students a whole lot of rope with which to hang themselves. But last week produced a shocker:

Ditzy Dana (up to my desk for the third time, the first being only two minutes after the problem was handed out to say "I'm so CONFUSED!!"): Is this right?

Professor SnarkyGeekChick: No, it's not. How did you get that answer?

Ditzy Dana: I did what you told me!

Professor SnarkyGeekChick: It doesn't look like it. Check your arithmetic. You should have both a quotient and a remainder here.

Ditzy Dana: But that's the answer the calculator gave me, see? *shows calculation on fancy graphing calculator*

Professor SnarkyGeekChick: Um, you can't use a calculator for this; it doesn't give you a remainder for division. Your answer shouldn't have the .5 in it, it should be a whole number *still incredulous that she has to use the term "whole number" instead of "integer" for college students*

Ditzy Dana: But that IS the remainder!!

Professor SnarkyGeekChick: Nooooo, it isn't. *looks sideways at Visiting Evil Minions to see if they are hearing the same words she is*

Ditzy Dana: You mean POINT FIVE isn't the SAME THING as a remainder of FIVE?

Visiting Evil Minion #1: *insufficiently smothered explosive snicker*

Visiting Evil Minion #2: Not unless you're dividing by 10, which you aren't!

Professor SnarkyGeekChick: *rendered speechless, thinks to herself "fifth grade, damn it, fifth grade" *

Visiting Evil Minion #1: *muttered aside* I knew I saw her not paying attention...

Ditzy Dana: *flounces away in a ditzy huff*

And my math colleagues wonder why I think the pervasive use of calculators in the teaching of mathematics is an Abomination From Hell...

1. When I was getting my masters degree many long years ago, I had an undergrad suitemate who was studying "computer technology" whatever that is. He asked me how to compute modulus with his calculator. I said, "Forget the calculator, do you know how to do long division?" He nodded. "Well, just take the number on the bottom (the remainder)." He went and tried it and came back amazed that it worked.

2. I have taught the same stuff to Computer Science and Education students for years. There is always about 30% of the class who never 'get it'. I have also battled a colleague for 25 years over the use of calculators. He thinks that it just has to be 'done right'. I think that the time for calculators is when you are proficient at doing without.

3. I agree with Paddington. Calculators are good when you know what you are doing. I have showed students how their calculators are, in fact, not smart. (It amazes me how many of them seem to think an inanimate object has a brain and can be smarter than they are. It amazes me more how often the brainless calculator is smarter than they are!)

I also think that the way schools teach their students to rely on calculators causes their sideways thinking. Ban calculators below high school level and make them actually learn the material!

Mathsquatch out.

4. (original message deleted due to a typo - I don't want to read the incessant whining about how stupid I am because I am not a better typist)

As a grad CS major, I think one problem is that computer science is no longer treated as a sub-discipline of mathematics as it really ought to be. There was a time in the not-so-distant past when CS was considered one of the more difficult majors. Now it attracts any flake who likes computer games or surfing the Web. Students are not aware that studying computer science will involve studying mathematics. In my cryptography class a few semesters ago, there was class-wide meltdown over abstract algebra and finite fields, even though those are not the most daunting cryptography topics, and anyway, if you sign up for a cryptography class you should be prepared to do lots of math. Somehow computer science has come to be treated as entirely separate from mathematics and students are surprised that any math at all is involved.

Granted, my university is pretty second-rate for the CS major but I can't tell you how many times my classmates have revealed that they don't even understand binary code, which is ridiculous for a graduate student in the major.

5. I still have flashbacks from the final I gave my principles students. I gave the formulae (big mistake) and banned calculators. To solve the problems you needed (A) to complete the homework and (B) to perform high school Algebra I. Except for 3 out of 24 students, none of them could do it. I was and am so fucking angry that college level students cannot perform basic math despite an entire term devoted to the subject.

6. Actaully, you CAN use a calculator to get the remainder of a long division problem. Assuming you know what the heck you are trying to do. It's so obvious it's ridiculous, but not to Ditzy Dana.

Dividing 82 by 7, your get 11.715 or so. subtract 11 to get 0.715, then multiply by 7. you get a number very very close to 5, but less than 5. Round up by one bizillionth to get 5.