Math and Programming

I will admit that I didn’t read the entire post, but I disagree with most of what I read.

Full disclosure: I am a college mathematics professor.

If geometry is taught as being about MEMORIZING proofs, then it is being taught wrong. If trigonometry is being taught as being about MEMORIZING trig identities (at least if this is the primary thing it is about), then it is being taught wrong. We had a graduation ceremony today and a programmer (someone who has had such a positive experience at a summer internship that the company is prepared to pay his way through grad school) came to me to tell me that he appreciated my ability to translate math into English .. and make things MAKE SENSE to him. The topic that he has found most important in his work (he does graphics programming — and has done some game sorts of things) was trig (and I’m sure that he did not mean the identities). Anyway, the list of topics that the author of the linked post came up with may have worked for him AFTER the fact, but is NOT appropriate as a general curriculum.

Mathematics instruction in the US could use a LOT of improvement, but to think that this guy has the answers is absurd. In fact, he has missed the most important problem with mathematics instruction (and seems to have bought into it). He talked about Calculus being about memorization: “Useful stuff, but the exact details involve a lot of memorization and a lot of tedium …”

Mathematics is NOT about memorization.

Let me repeat that.

MATHEMATICS IS NOT ABOUT MEMORIZATION. Anyone who teaches it that way is teaching it wrong. Of course memorizing the multiplication tables (up to 9×9) is important (even in the days of calculators), but addition, subtraction, multiplication, etc. are not mathematics. They are arithmetic. Arithmetic is used in support of mathematics.

Let me make another broad statement. Mathematics is not about calculation. Of course there are a lot of calculations made in a mathematics class, but they are NOT mathematics. Calculations SUPPORT mathematics, but are not mathematics. Let me give a very basic example. Knowing that three times two is six is a calculation. Knowing that a rectangle that is three units long and two units wide has an area of six square units is mathematics. Knowing how to compute integrals is a calculation. Knowing how to USE integrals is mathematics.

It’s true that calculators can do multiplication and division. It’s also true (I believe) that it is important to learn how to do these calculations by hand. WHY? Because one of the most important life skills (not just for programmers, but for EVERYONE) is estimation. Which is a better deal? The 64 ounce size at $2.79 or the 100 ounce size at $3.99? You don’t need exact answers to be able to compare these.

Anyway, I’m preparing for a trip and don’t have time to fully respond to the post, but I’d be curious what others think on this topic.

I will admit that I didn’t read the entire post, but I disagree with most of what I read.

Full disclosure: I am a college mathematics professor.

If geometry is taught as being about MEMORIZING proofs, then it is being taught wrong. If trigonometry is being taught as being about MEMORIZING trig identities (at least if this is the primary thing it is about), then it is being taught wrong. We had a graduation ceremony today and a programmer (someone who has had such a positive experience at a summer internship that the company is prepared to pay his way through grad school) came to me to tell me that he appreciated my ability to translate math into English .. and make things MAKE SENSE to him. The topic that he has found most important in his work (he does graphics programming — and has done some game sorts of things) was trig (and I’m sure that he did not mean the identities). Anyway, the list of topics that the author of the linked post came up with may have worked for him AFTER the fact, but is NOT appropriate as a general curriculum.

Mathematics instruction in the US could use a LOT of improvement, but to think that this guy has the answers is absurd. In fact, he has missed the most important problem with mathematics instruction (and seems to have bought into it). He talked about Calculus being about memorization: “Useful stuff, but the exact details involve a lot of memorization and a lot of tedium …”

Mathematics is NOT about memorization.

Let me repeat that.

MATHEMATICS IS NOT ABOUT MEMORIZATION. Anyone who teaches it that way is teaching it wrong. Of course memorizing the multiplication tables (up to 9×9) is important (even in the days of calculators), but addition, subtraction, multiplication, etc. are not mathematics. They are arithmetic. Arithmetic is used in support of mathematics.

Let me make another broad statement. Mathematics is not about calculation. Of course there are a lot of calculations made in a mathematics class, but they are NOT mathematics. Calculations SUPPORT mathematics, but are not mathematics. Let me give a very basic example. Knowing that three times two is six is a calculation. Knowing that a rectangle that is three units long and two units wide has an area of six square units is mathematics. Knowing how to compute integrals is a calculation. Knowing how to USE integrals is mathematics.

It’s true that calculators can do multiplication and division. It’s also true (I believe) that it is important to learn how to do these calculations by hand. WHY? Because one of the most important life skills (not just for programmers, but for EVERYONE) is estimation. Which is a better deal? The 64 ounce size at $2.79 or the 100 ounce size at $3.99? You don’t need exact answers to be able to compare these.

Anyway, I’m preparing for a trip and don’t have time to fully respond to the post, but I’d be curious what others think on this topic.