One of SL's suggestions for an activity related to Japan, origami, and paper cranes consisted of a bunch of math problems. First you memorize how to fold a paper crane, and do it enough times that you are pretty decent at it. Then you time yourself and see how long it takes to fold one crane. Gradually you do the math to determine how long it would take to fold 10 cranes, 20 cranes, 50 cranes, 100 cranes, and finally 1000 cranes.
Sly of course knows that there are 60 seconds in a minute, 60 minutes in an hour, etc. But we haven't really done much 'math' with 'time measurements.' I was curious to see how he would try to solve these math problems. Would he just borrow and carry as if he were working in base ten still, or would he think and realize that when he borrowed from the minutes column he was borrowing 60 seconds that needed to be added to the seconds column?
His initial problem was to find the elapsed time between 23:54 and 26:28. He DID think and realize that he was borrowing 60 seconds, not 10 of something. However, he didn't think about the effect of dropping a 6 in front of the 2 (in :28). I stopped him and asked about how he got 628 seconds. He thought. He realized that didn't make sense. I guided him through, saying, "You had 28 seconds, right? And you borrowed 60 seconds to add to that, right?" And then the light bulb went on and he said, "It's 88 seconds! Not 628!" Exactly. Quickly he did the right math and found that it took him 2:34 to make one paper crane.
After that, he was on a roll. He set up his next math problem to find the time it would take to fold 10 cranes: 2:34 x 10. He recognized that when you multiply by 10, you can just add a zero. But I questioned whether 23:40 was correct. I jotted down the problem like this:
2:34
x10x10
and his eyes lit up. Very quickly he calculated that 34 seconds x10 was 340 seconds, and that 340 seconds divided by 60 would be 5:40. Then he solved 2 minutes x10 and added that to his 5:40. Presto: 25:40, NOT 23:40.
How long to do 20 cranes? He solved that one easily enough: 25:40 + 25:40 = 50:80 = 51:20. He had the idea about simplifying his time units down pat. When he next calculated the time for 50 cranes, he recognized off the bat that he had to simplify 128 minutes into hours and minutes. He then doubled the time for 50 cranes to find the time for 100, and then multiplied that by 10, multiplying hours, minutes, and seconds separately. The first try around he gooned up his simplifying the time units, but once he got started, he fixed his error. It would take Sly 42 hours, 46 minutes, and 40 seconds to fold 1000 paper cranes.
Now, if you stayed with me through all that, here is the point I really wanted to make: Just like Jman had a reason to learn to cut with scissors today, Sly had a reason to learn and understand the in's and out's of doing math operations using time measurements today. He was interested. There was a real life application (because he CHOSE to do the origami project suggested vs other projects or one of his own design). Sly always does much better with understanding and doing math when it is applied math instead of math for the sake of progressing through a textbook on schedule. It is yet another reminder to me that learning is SO much easier and more effective when you use real life with a kid who is developmentally ready and interested because the real topic is meaningful to him. A follow up on this math lesson could be determining how long it would take to perform different katas (from karate) of varying lengths of time, or how long a workshop would take if you wanted to cover so many katas. Perhaps calculating how much time you should allow for a kumite (sparring) tournament if there are x number of competitors and a sparring round lasts y number of minutes. Or, being the road trippers that we are, we could calculate the arrival time based upon speed and distance traveled given a certain start time. There are all sorts of opportunities to work on math operations using time measurements that are REAL, and much more interesting than some dry textbook. But above all it's important to recognize the kid's ZPD (Zone of Proximal Development, what they are ready for and interested in having you guide them through so they can learn for themselves). The difference between trying to teach, which may be well intentioned but inappropriate at the time, and learning, sometimes despite the teaching.
No comments:
Post a Comment