How does one go about teaching math to a 4-year old? Last week, when asked “There were five birds in a tree and three flew away. How many are now present?”, Suhana gave the understandable answer “8”. How can this tendency to do things mechanically be countered? I have too often seen such jumping-to-conclusions in adults — “I think we should add those probabilities, or I think I should just take the product of probabilities” and I have seen similar guesswork from programmers with impressive resumes working on algorithmic problems during job interviews, and doubtless I have blundered similarly on countless occasions. Being able to see things clearly and having the patience and discipline to not “solve-problems-by-coincidence”, is I think a necessity for deeply understanding math. How does one teach carefulness?

I haven’t have a clue, but figured that now was a good time to start teaching Suhana and to see what works. I anticipate an exhilarating ride and I am unsure if that anticipation of exhilaration bodes well or bodes ill for this endeavor. I plan to document as I go along. The depth of my ignorance of teaching has started to show in my early attempts, as I will cover in the next post.

My partner-in-crime is my wife Shweta, an Assistant Professor of Math Education at Kean University. She has been watching my early forays with bemusement, and has started giving me literature from the field — empirical studies and multi-decade field work from the trenches. This, too, I shall talk about in the next post.

Realizing 3 + 5 is 8 is pretty good for that age ! I am proud of my 3.5 years daughter too who can tell 1+1 = 2.

ReplyDeleteI am happy that Suhana can add, but what I wish to ensure is that she understands when adding is appropriate.

DeleteWhen I was tutoring first-year university students, I noticed similar patterns, of unreflectively applying known "steps" in response to a new problem. For about 3/4 of the students I worked with, it made a large difference just to get them to slow down and re-express the problem, either in words or by sketching the elements on a piece of paper.

ReplyDeleteOne explanation is that this just forces people to respond less reflexively (because of the time delay); another (non-exclusive) explanation is that you are facilitating some Polya-style problem solving strategies. Usually I would expect the more contemplative and playful approach would be beyond a 4-year old, not least because of the need for sustained concentration -- but Suhana always struck me as a very naturally thoughtful person.

I am interested to see the next post!

Hi Chris,

DeleteI stole the phrase "unreflectively applying known steps" for the next post :)

I agree about sketching and re-expressing, but I am not sure I understand what you mean about Polya. I think of "Polya-style" as asking plenty of (mostly predefined) questions in order to trigger thoughts. Do you have an example handy?

Interesting!

ReplyDeleteI think this goes back to the general tendency of human brain to take shortcuts (in this case by applying a known pattern immediately). And there's a good reason behind it. Reflecting deeply before every single action would be too overwhelming and unproductive.

What is important is to learn to not apply patterns blindly, and I think that takes time and practice to learn. Asking (the student) to slow down and re-express the problem (CJH's approach) seems like a reasonable solution here.

I'm also looking forward to hearing about your future adventures here!

I agree about the general tendency and about the utility of CJH's approach. My next post suggests another strategy available to the teacher.

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ReplyDelete