by Lara Francisco
It's good though. It reminds me that in the large world of mathematics our interests and levels of comprehension are unique and individual. My job is to help guide students along their personal math journey, without turning my limitations into theirs. One of the methods that I use is to look "beyond" just the numbers (to see the patterns, the art, the predictions, the commonalities, the randomness, how they work together, the connections to real life, etc...). Most of the time when I say "patterns", I mean all of these things. They are all ways of exploring math so that it makes sense, or doesn't seem so out of reach, or like something that you can actually manipulate and turn into something beautiful, or can use to predict what will happen next.
I'd like to share a few of my recent "pattern discoveries" with you.
I work with two groups of 2nd graders and we have been looking at adding large numbers (really large numbers ... I'm talking in the billions) and skip counting by ten from any number (i.e. 67, 32, 11). I don't know if there is something in the water in Ms. Dickens' classroom, but 2 of her students were on a roll - recognizing number patterns left and right! One girl recognized that it didn't matter how large a number was, but when you are adding vertically, you ALWAYS start with the ones (the right hand side) and then work your way to the left. You could see the light bulb go on and the self-satisfaction on her face. Yay! When we used a hundreds chart to practice counting by tens starting from any number, another of Ms. Dickens' students noticed that as we counted down the chart the digits in the ones place stayed the same: 27, 37, 47, 57, etc... Again, a light bulb moment! Then she looked at the large hundreds chart hanging on my wall and got up to show the rest of the group how the numbers in the tens place increased as we went down, and decreased as we went up. This is a student who is normally very shy ... and there she was with big wide eyes sharing with the group. Double yay!!
Last week I got a book in the mail that I've been waiting on for many weeks. It's calledPatterns of the Universe by Alex Bellos.
Some of these are examples of the "high-level" math that I was referring to at the beginning of the post - but I find it interesting all the same.
Petals, Flowers and Circle Packings - an article from AMS
Ramsey Theory in the Dining Room - an article from bit-player
Prime Spirals - a YouTube video from Numberphile
Vi Hart on Vimeo and YouTube (she also has example of math and music)
So that concludes my lengthy (it took me 3 days to write) post on Patterns in Math. Now on to Math Challenge #5 ... which includes ... that's right - Patterns! Did you know that numbers could be palindromes as well as words? Check it out here, explore, enjoy, and don't forget to have your child turn in their challenge byTHIS Friday, 12/11.
I'll close by sharing a completely unexpected surprise that showed up in my "inbox" yesterday. When I created this site last year I thought I would add a little math survey that I called: What's your "math-itude"?
In all honesty I had no idea how this survey format even worked, until yesterday when I received my first response which I will share below:
To be good in math you need to ... because ...
learn than 10 sums, then < 20's, 30's etc. Becaise it will be really hard if you don't learn each level
Math is hard when ...
when you do 30 minus 2
Math is easy when ...
2 + 2
How can math help you?
divide a cookie into 3
The best thing about math is ...
you learn numbers
To my anonymous survey taker - Thank you for sharing your thoughts with me and for taking my survey. You taught me something and truly made my day!