(A new question of the week) I like problems that can be solved in multiple ways, which can train us in seeing the world from different perspectives. Late in November we dealt with a pair of such questions involving angles in star-like figures.
(A new question of the week) Limits can be challenging. They can be even more challenging when they require L’Hôpital’s rule or more advanced methods (Maclaurin series), and then are turned inside-out by asking not for the limit itself, but for parameters that will result in a specified limit, or what values of the limit …
(A new question of the week) We usually see limits applied to functions in a calculus class. An interesting question from late October deals with a limit in a geometrical construction based on a function. We’ll be seeing how to discover a proof, then several alternative proofs, and finally what the answer means.
(A new question of the week) A question from last month provides an opportunity to show how to develop an algebraic proof of a combinatorial identity involving factorials. We’ll be looking over Doctor Rick’s shoulder as he guides a student through the maze. I’ll also add in a previously published version of the same proof …
(A new question of the week) Usually when we have a figure labeled with some lengths and angles, we can expect to find unknown angles using trigonometry. When we are expected to do this using geometry alone, we can expect that there is something special about the figure that makes it possible. But how to …
(A new question of the week) A good way to check (and hopefully build) a student’s depth of understanding is to assign non-routine problems, in which familiar ideas are twisted around so you have to come at them from a different direction. Here we’ll look at a question about a graph that can be solved …
(A new question of the week) Here is an intriguing question we got at the end of September from an adult whose name I’ll shorten to Arun.
(A new question of the week) A question in September, about graphing a horizontally-stretched cosine function, led to a long conversation. Between a typo in the problem and some inside-out thinking, this surprisingly non-routine problem led to some good mind-stretching! I have edited this down considerably by removing distractions from the main ideas, but it …
A Mind-Stretching Exercise with a Stretched Cosine Read More »
(A new question of the week) Let’s look at a quick question from mid-September, that had a number of different answers. In some ways, this is an easy question; but we’ll take it a little further, so keep reading to the end.
(A new question of the week) I have often said that calculus class is where many students finally learn algebra, because now algebra is an essential tool, not just something to learn for an exam. This is especially true of a nontraditional student, who may not have taken math recently, or may even be learning …