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.<p><i>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.</i><p><i>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><p>I&#x27;m more excited by the second problem. I&#x27;m going to use concepts I mostly understand to <i>prove</i> (&quot;if and only if&quot;) a concept. In so doing, I&#x27;ll understand all those concepts better.<p>In the first problem, it looks too much like I&#x27;m trying to tell the teacher something he&#x2F;she wants to hear: the speeds. It&#x27;s hard for the reader to see how he&#x2F;she learns something about arithmetic.<p>When doing the math that mathematicians do, what you learn is often explicit: &quot;prove that for all...&quot; It&#x27;s more motivating.<p>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.