Categories:
Economics of Education
A true homeschooling conversation between me and my son, lightly edited. He’s eleven and I’m teaching him algebra.
Father: Sorry, you got another problem wrong. Do you know why?
Son: [aggravated silence]
Father: Because you skipped steps!
Son: [further silence]
Father: Is it ever OK to skip steps?
Son: No.
Father: Wrong! It is OK to skip steps… when you are a master.
Son: And I’m not a master.
Father: You are not yet a master. Do you know how you become a master?
Son: No.
Father: By following the steps.
Son: I follow the steps, until I don’t need to follow the steps anymore?
Father: Exactly. Now start over, and follow the steps.
READER COMMENTS
Christophe Biocca
Mar 9 2021 at 9:48am
This parallels Terence Tao’s 3 stages of mathematics education (wrt. proofs specifically).
robc
Mar 9 2021 at 10:08am
Conversation with my HS calculus teacher (who knew me well as she was the math team coach also).
Her: Your answer is right, but you didn’t show your work.
Me: I showed all the work I did.
Her: [sigh]
I think we agreed that I would show a step in-between just for her sake and she would let me slide on showing all steps.
My general rule was I put down on paper the steps I needed to put on paper to solve the problem. I don’t put sub-steps on 2+2 on paper, I can do that in my head. If I can do calculus steps in my head too, why write them down? This, of course, only applies when you are right. If you are wrong, probably put of put more down on paper.
robc
Mar 9 2021 at 10:16am
It wasn’t a one off, reminded me of a later conversation with a Calculus TA.
Me: You gave me 0/20 on this problem, that I got correct (I remember it even, it was find the point where a line and a plane intersect).
Him: You didn’t show any work.
Me: I didn’t do any work, the answer was obvious (it was something like 1,0,5). If it hadn’t been obvious I would have done the calculation and shown it, but since I didn’t have to do the calculation, I didnt write anything down.
Him: How do I know you didn’t cheat?
Me: [stares]
Him: Okay, I will give you 10 pts.
I don’t know what any of this means, other than I suck it following stupid rules.
Giuseppe
Mar 9 2021 at 6:25pm
The timing of this was perfect. I just had a similar conversation with my son only he was insistent his answer was right and without showing the work I couldn’t point out the mistake. I enjoyed reading your post to him.
A Country Farmer
Mar 10 2021 at 8:42am
Being a bit pedantic, but it’s possible to reach mastery through different paths. For example, I learned programming without following many of the steps but instead through experimentation. Also, there are many different “paths of steps” one can take.
Matthias
Mar 10 2021 at 8:29pm
Experimentation involves lots of steps.
You can solve math problems with experimentation and trying things out, too. That’s how mathematicians find new things.
You can also solve (some) math problems by following established procedure, like most of what people do in school. But someone needs to find those procedures to establish first.
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