Saturday, 30 January 2016

The Quest in Question

January is the worst month. No question. It’s three weeks until exams, everyone has forgotten everything, and you have ZERO turnaround time to prepare for Semester Two, let alone generate report cards. Yet it’s also the start of the MTBoS “Blogging Initiative”... maybe that will make it better.

The Week 3 blogging challenge is “Questioning”. (My Week 1 post at this link; My Week 2 post at this other link.) Nearly didn’t post this week, for reasons I go into below. But I’m an MTBoS mentor for three other math educators, so I decided I should set a good example. In no small part because my more “hands off” approach to mentoring has a tie in with this particular subject.

So, why did I nearly opt myself out of Week 3? And what did I come up with for a question in the end?


I am not very good at asking questions of others - I’m much better at giving responses. In fact, I’m really lousy at approaching others in general, even people I know (or teach). There’s this default mode in my brain, where I tend to assume people are just fine without me, so why should I interfere and possibly make things less clear or more complicated.

It’s probably the introvert in me. Coupled with the depressive.

The paradox is that I want people to approach me with questions - mostly about my recreational writing - yet perhaps they’re assuming I’m just fine without them too. It’s the same sort of thing with teaching and mentoring, I’ll sit here waiting for the questions, so that I can respond to them. Not always to give an answer, mind you, but to give options, start research, or to turn the question back on the poser. And sometimes I interpret body language as being a question. Point being, I rarely initiate.

Given that, I don’t believe I’m someone people should look up to. In fact, I can be quite self-deprecating. It occurs to me that this could be the reason why I’m reticent to take on any sort of student teacher. Is MTBoS mentoring even a thing I should be doing? ... I don't think that's a question I can answer myself.

Let’s focus back on the classroom.

What are you thinking about?
Breaking down the MTBoS assignment options: A question to get kids thinking about something? I tend to improvise off the cuff, or ask lame questions to give them processing time. An awesome/sucky test question? I feel pretty middle of the road. A student asked a question that sparked something? This happens a lot, but it’s pretty ‘in the moment’. And while I have a great memory in that I can remember details of the story I wrote 5 years ago, I rarely retain a memory of social interactions. Plus I’m SO bad with names.

In the vein of “a question I didn’t know how to answer”, I suppose I could get into the “why is it a greater than 5 check?” in statistics. (It’s a threshold for the normal and binomial approximations, it’s referenced as the lowest indicator for the coefficient of determination, and then there’s p values. Why 5?) It’s a question that almost always comes up, yet I never really have an answer aside from “let me know if you find out”.

But if I only put that out there, this would be a really short post, and as you may have noticed, I’m bad at those.


I haven’t been teaching this past week. It’s been four days of exams, and while there was class on Monday, that was fielding final review questions. Standard form stuff. (Or factored and vertex form stuff.) I did get an interesting email from a student on Wednesday afternoon though. It cycles right back to the idea of a problematic textbook question.

For anyone in Ontario with the Nelson 3M “Functions and Applications” text, follow along on Page 188. It’s a multiple choice in the cumulative review. Question 14 gives a quadratic area formula, asking what width option gives an area of 130. The student solved the equation, ending up with two answers of 5 and 13. And BOTH were listed as options.

She dutifully subbed both answers back into the equation - and they still worked. This was when she emailed me with a snapshot, stating “I’m a bit confused” and “I might not be doing it right”. I reassured her that she was correct... but I wasn’t content to leave it there. How could the text have misfired like that?

We take many words for granted.
Not content to leave it at “textbooks are stupid, yo”, I generated the lengths for the rectangles as well. This gave me a hint, producing 5 by 26 and 13 by 10. Which suggests to me that they had rejected the 13 because this would make “width” longer than “length”. After all, properly speaking, the English definition of “length” is “the measurement of something along its greatest dimension”. Did you know that?

It’s mathematics which muddies the waters, tending to use ‘length’ and ‘width’ interchangeably, depending on which way your page is oriented in front of you - and here we had no page, only a formula. There was a rather interesting discussion of the meaning of “length” with a sixth grade class on Ask Dr. Math from 1999. This is not a new problem!

So the textbook listed “5” as the correct answer for width. Since “13”, despite being a “width” that solves the formula, is technically a length. (And “10”, also given as a possible answer, would be a valid width but doesn’t solve their formula.) Now, do I think that was the INTENT of the text? No. And it’s needlessly confusing. But wasn't that journey interesting?

All this to say, I rarely initiate questions. I respond.

Thought from a prior post.

I also respond to every comment on my blog, if you’re so inclined. Both here, and on “Any Q-Bars”, my math webcomic which is a play on words for the popular “Any Qs” mixed in with “Q bars” denoting the irrational number set. I’ll also throw in a quick plug: If you’re an educator in Ottawa, Canada, check out #OttSlowChat on Twitter!

For now, I should get back to marking exams. Wheeee. If you enjoyed reading this, I’m all about the writing. Feel free to check out some other posts:
-There’s some fun math questions in this COMA Recap Post
-The Big Question: Me blogging about my depression
-And in the vein of better questioning, “Hinge Questions” by Nik Doran.

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