I’m sitting on a bunch of Khan Academy questions from users that I marked as very interesting. I never posted them, and I feel a little cheap giving them all their own posts. So I figured I’d just dump the whole lot on you all. These questions reveal interesting things about the way these students are thinking. If you think that you’ve got something interesting to add, either on the diagnosis or prescription side of things, dig into the comments below.

The first is a nice probability puzzler. How did this student get 3/8?

I love this conceptual question.

Not sure exactly why I clipped the first question here, but the second question is great. “Why do they call it a limit?”

A good reminder: some vocab is tricky. Why are these two vocabulary words the one that this student confused?

This is a great point from a kid about variable use.

A little bit of context for this next one: we’re talking about protractors here.

  • Pretty sure the 3/8 is a misreading of “at least twice” to be “exactly twice”. Exactly two tails is 6/16 reducing to 3/8; it misses the five additional cases of three and four tails, which count for “at least”. (I see this a lot.)

    I suppose a perpendicular can be a specific transversal that uses right angles, which could account for that one.

    Using ‘x’ and ‘y’ for variables… well, in the Cartesian plane, for some reason they’re accepted (and then there IS more, namely ‘z’). In generic algebra, it could be anything and I’ve no idea why ‘x’ is the default.

  • Jim Doherty

    Here is a nice discussion of why we use x as our unknown


  • Andrew

    Jim — very interesting. It’s a shame (x-ame?) that this kind of history isn’t taught; the narrative is often as interesting as the methods. But anyway, here’s what I always heard about the beginnings of x. I will now use both stories when I tell my students…I got this from the book “Unknown Quantity” by John Derbyshire, who quotes from another source:

    During the printing of La geometrie…the printer reached a dilemma. While the text was being typeset, the printer began to run short of the last letters of the alphabet. He asked Descartes if it mattered whether x, y, or z was used in each of the book’s many equations. Descartes replied that it made no difference which of the three letters was used to designate an unknown quantity. The printer selected x for most of the unknowns, since the letters y and z are used in the French language more frequently than is x.

  • Kathy

    As to the question about whether perpendicular and transversal are the same, I think it’s significant that the student has gotten to the point to ask that question, in other words, that they’ve _realized_ that they might be conflating two terms that are really not the same. I know there are times in my own study of math where it’s taken me a while to get to that point, or vice versa (i.e., “oh, these terms really mean the exact same thing.”)

    (I apologize if this topic has already been covered, just discovered this site. )