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Here are two math problems. The first is from an article linked-to in the post. The second is from Challenging Problems in Linear Algebra. Two planes, which ar
by delish 11y ago
Here are two math problems. The first is from an article linked-to in the post. The second is from Challenging Problems in Linear Algebra.
Two planes, which are 2400 miles apart, fly toward each other. Their speeds differ by 60 miles per hour. They pass each other after 5 hours. Find their speeds.
Show that a Matrix A is of rank 1 if and only if A can be written as A = xy^t for some column vectors x and y.
I'm more excited by the second problem. I'm going to use concepts I mostly understand to prove ("if and only if") a concept. In so doing, I'll understand all those concepts better.
In the first problem, it looks too much like I'm trying to tell the teacher something he/she wants to hear: the speeds. It's hard for the reader to see how he/she learns something about arithmetic.
When doing the math that mathematicians do, what you learn is often explicit: "prove that for all..." It's more motivating.
Of course I imagine the makers of Common Core have more expertise and experience in teaching students; I have no plan to reform math education.
- Espressosaurus 11y agoI'll be honest: I solve problems more like the first than the second. I have sensors for certain kinds of information. I would like to be able to process it in order to convert it into other types of information. That isn't to say the second type of problem isn't important: to be able to say "solution X is the same as solution Y, even though their forms are very different" is powerful when you're trying to analyze and evaluate solutions to a problem. It's just a less common problem to solve.
- deleted 11y ago[deleted]
- saretired 11y agoWhy are you comparing a middle school problem with a college level problem? I believe the purpose of the first problem is not to teach something about arithmetic, but to test (or reinforce or expand) the child's understanding of d = rt, a pretty important thing to understand.
- delish 11y agoI'm pointing out what makes--in my experience--a problem interesting.
- spacehome 11y ago> The second is from Challenging Problems in Linear Algebra. Show that a Matrix A is of rank 1 if and only if A can be written as A = xy^t for some column vectors x and y. This is quite the challenging problem in linear algebra, considering that it's not true! [[0]] = [0]*[0]^t