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Math-rich baby and toddler environment
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Week 3: Good meeting times and course questions map
We met on Monday evenings during the first two weeks of the course. I want to make meetings float for the rest four weeks.
What days and times are good for you? Please note your time zone.
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Week 2 February 7th, 2011 meeting had these topics:
- The kid just plays with objects! Where is math?
- Subitizing (instant quantity recognition)
- Montessori, Waldorf, Reggio Emilia - comparing early education systems
- Recording: https://sas.elluminate.com/p.jnlp?psid=2011-02-06.1458.M.B41FC4AB0A3565F8BCAE1B600D6595.vcr&sid=2008350
I put all the questions that came up in this course, so far, in a mind map, organizing them by topics. I picked one of the topics if the question belonged to many. We will use this map for sources of discussions. Everyone who posted to ask.naturalmath got at least one answer. Keep posting questions (and answers) - I will be adding them as they come up. I will add links to where they are discussed next.
Here is the mind map: http://mind42.com/pub/mindmap?mid=be6223a0-c0f2-487b-b0a0-1c175c4499ae
You can drag it around by mouse and zoom by the scroll bar in the bottom left corner or by the mouse wheel.
Maria, I listened to the recording and have a couple of questions:
1. Subitizing - you mentioned something about the age of 5 being sort of the cut-off for subitizing (or did I totally misinterpret it?). Mark is only 4, but he only recognizes 1-4 objects. I tried many times and he just starts counting and prefers to count. Any suggestions? Or is he too used to counting at this point?
2. Mick's mention of the tic tac toe game - I tried it with Mark after listening to the recording. We used real objects to play instead of drawing a board and marking it with x and o's (easier for M). It took a couple of rounds to explain the one token per square rule. One interesting thing that occured right away was that he memorized the entire sequence of the first game (which I let him win after 3 turns) and attempted to repeat it in the second round. Took me 2 turns to realize what was going on. So when on the 3rd turn I put my token on the square that his token occupied in the previous game, he got pretty upset. But after I explained to him that there were more than one way to place tokens so he wins the game, he was just fine. The second challenge arose when I noticed that during each round, Mark was concentrating solely on getting his three tokens in a row, not on preventing me from doing the same. I tried pointing out some opportunities to him (saying "I think I'm going to win this one, you better watch out for my 3 in a row"), but it only worked half the time. It was still very interesting and he had a lot of fun for the 10 rounds or so that we played. Will try it again in a few days.
I am not sure what cut-off means. The quantities one can subitize vary from person to person, and increase until the age of 7 or so. Some researchers also believe you can train to subitize larger quantities and others don't think so. Many kids and even adults don't quite realize they can subitize and, moreover, enjoy counting just as you describe.
As for suggestions, subitizing comes in handy when you introduce multiplication. As you do more activities that involve grids, rows and columns, sets, units of measure and other multiplicative structures, subitizing will play a more active role.
Thank you for your story about tic tac toe! Cute and thoughtful examples of how a young child explores an abstract, rule-based game. If you think about it, Mark's ideas make a lot of sense! Amazing memory, too. Kids sometimes want to turn rule-based games into roleplaying games. I usually don't interfere, but ask to have a turn playing "my way" later, as well.
I would focus more on playing and having fun, rather than explaining strategies and rules. Kids can discover and notice patterns and rules, or else ask how come others win and then get some answers.
We have to be careful not to answer questions kids did not ask :-)
Sounds like you are having rich experiences there, Yelena!
Have you heard of BlockFest - http://www.blockfest.org/ They came to Raleigh last year and I took Mark to all three sessions that they offered. I thought it was a great event - kids had fun and parents learned how playing with different blocks promotes math and science learning.
Oh, I did not know they came to Raleigh! I interviewed the organizers last year for the Math 2.0 series: http://mathfuture.wikispaces.com/BlockFest
BlockFest sounds cool. What types of things did you take away from it? Any tips that we can take away from that experience?
There were quite a few surprises. For example, it was interesting to see how Mark explored different kinds of blocks (unit, cardboard, different size foam blocks, etc) while trying to build the same structure - a rocket - with each. It was interesting how he explored the symmetry, balance, angles, etc. That's when I started paying particular attention to the fact that he was estimating, measuring, counting and doing lots of planning. Then there were pattern blocks and I was surprised that not only did he choose to copy one of the most difficult patterns (multi-tier with hidden blocks), but needed practically no help from me. So two lessons that I learned were:
1. A small change in the activity can help a child learn a lot more than replacing the entire activity with a new one (for example, there were 2 different sizes of foam blocks and Mark built 2 rockets, one big one and one - small one the first day; but just 1 rocket, using both sizes of foam blocks the second day. Just using different size blocks he had to approach the tasks differently in each case as when trying to make the rockets exactly the same height regardless of the block sizes before deciding on a scaled-down version that was more stable).
2. Learn to give Mark an activity that is a bit more challenging than I think he can handle and let him work on it without much interferance (I think that's what Maria mentioned in response to my tic tac toe post). This is probably the most difficult part for me though so I have to constantly remind myself to just "let Mark be".