I’m an elementary math coach in Wisconsin, so like you, I am always toying with ways to make math more engaging, fun, and meaningful for students. Some of what you eluded to in your post about allowing natural curiosity to guide a lesson or math task reminds of this Ted Talk, which you may have already seen: http://www.ted.com/talks/dan_meyer_math_curriculum_makeover?language=en

I think the more students are able to see how math relates to ideas, concepts, products, and procedures that they are genuinely interested in or intrigued by, the more they will want to continue to pursue math throughout their educational journey. Do all of those rich mathematical tasks need to be exceedingly difficult? That is hard to answer. I guess that those types of activities require a more in-depth thought process and trail of operations… but in the end the result is more satisfying and meaningful. I think it is satisfying and meaningful even for students who may have been a little lost during the journey. As long as their is an organized closure to the lesson, filled with great reasoning and discussion around strategies and efficient ways to arrive at the final answer, then maybe it doesn’t matter who was initially right or wrong, lost or leading the pack…

I also agree with the responses above! So much can be gained from revisiting “easy” math and taking a second look at what else you could “wonder” about it. Good stuff.

Anyway, very fun post to read! Thanks again ðŸ™‚

Feel free to check out my blog at http://www.rfsdmath.blogspot.com

On twitter @MrsBingenheimer

(1) it is enjoyable

(2) it allows you/the student to groove the patterns and check to see that you really understood the idea. For example, when Kevin was playing with the first puzzle again, he was probably exploring how far ahead he could see the answer or how the different moves linked together. Not consciously/explicitly, perhaps.

(3) it allows you the opportunity to uncover hidden depths/connections. The 1+1 = 2 story is probably the most famous.

(4) it is easier to learn without a conscious strain.

Also, the definition of “hard/not hard” is very fuzzy. Some examples:

– Playing NIM vs finding a perfect strategy

– Folding hexominoes into cubes vs classifying all hexominoes (a recent activity for us)

– reading a proof for the main ideas and not reproducing every step or filling important gaps (which I recently did with this paper)

To borrow your reading comparison, these are like reading for pleasure rather than practicing literary criticism. In fact, there can be (at least) three levels:

– pure reading (equivalent to open math play)

– speculation (“maybe this book is actually about …” and “I wonder if this pattern continues like …”)

– focused analysis

http://followinglearning.blogspot.fr/search/label/hard%20learning

so I feel I’ve earned the right to write heresy now. ]]>

So easiness can lead to hardness…

]]>-Kristin ]]>