Peter Gray is a research professor of psychology at Boston College. He has conducted and published research in comparative, evolutionary, developmental, and educational psychology; published articles on innovative teaching methods and alternative approaches to education; and is author of Psychology (Worth Publishers), an introductory college textbook now in its 6th edition. He did his undergraduate study at Columbia University and earned a Ph.D. in biological sciences at Rockefeller University. His current writing focuses primarily on the life-long value of play. His own play includes not only his research and writing, but also long distance bicycling, kayaking, and back-woods skiing.
His PT blog is Freedom to Learn.
Here is a link to a recent article he wrote for his blog -
Below is what I sent to Peter and his response regarding unschooling math -
Hi Peter! I will try to put some information below on how our family learns about math in our everyday life.
It would be truly difficult NOT to learn about math (or any of the traditional "subjects") by living a full, happy life. The various "subjects" are naturally part of life - they are part of our lives morning, noon, and night. Sometimes one person (or more) is very engrossed in one passion for a length of time (like my daughter Katie with dogsledding*, a certain novel or book she is writing or reading or my son Li with Magic The Gathering card game or Pokeman or creating his own bakery or something else).
* Dogsledding led to Katie writing to mushers, learning about mushing, geography of Alaska, watching the Iditarod and Yukon Quest online and following the mushers and figuring out distance and speed so we could guess who would come in first or next, having an Iditarod musher (Scott Smith) come to talk to our homeschool group, meeting some local mushers, going mushing, saving money to go mushing, having a bake sale to save money for mushing, becoming friends with mushers or musher enthusiasts on facebook and having conversations with them about the sport, etc
People can learn math and logic from so many things from reading to cooking to dividing up food or slices fairly to playing sports (figuring out the odds of winning or what angle to kick the ball, etc) to playing games (tic tac toe, sorry, connect four, tons of games...see Danielle Conger's "math" blog for some that she suggests to be related to "math"- http://danielleconger.organiclearning.org/math.html) to playing video games (yes, really!) to calculating how far it is to walk around the block or to figure out distance, rate and time when going somewhere or wanting to go somewhere and to see if you could actually do it...real life things. When you want to know something and it isn't drudgery, you just find it out. You learn. And most of all you understand concepts because they really mean something to you. For example, last night my son Li (age 8) asked me what 36 times 15 was. He knows how to do alot of calculations in his head already, but did not know how to do this one. And he doesn't know how to write out and calculate multiplication yet, so he asked me. I showed him how I do it, got the answer and asked him why he wanted to multiply those two numbers. He said it was because he wanted to buy a big pack of Magic The Gathering Booster Cards which had 36 packs of cards with 15 cards in each pack and he wanted to know how many cards he would get in all. This is just one example. Tonight we went grocery shopping and we calculated which Tropicana Orange Juice container(s) would be the cheapest - one big plastic bottle (which had twice the amount of ounces as the smaller one) or two smaller containers. We actually saved money by purchasing the two smaller containers of orange juice. (And I was glad we were not buying plastic - which made me feel like we made an environmentally friendly decision too!)
My daughter Katie is 12 1/2. Over the past year, Katie's schooled friends have told her they are learning algebra and that it is hard. A few months ago, she *asked* me to help her learn about algebra. One night, after the rest of the family was asleep, we sat on the bed and went over basic algebra together. I offerred to show her more in the morning, but she said that she had learned enough for now and that she knows if she wants to learn more in the future, she can.
When Katie was younger, she asked me to quiz her on multiplication or addition facts. We typically did this while traveling in the car or laying in bed late at night. We still do this sometimes with the other kids too, but only when it is played like a game, not to drill the kids on knowing the correct answers.
The kids and I love to play "Guess the number!" We do this whenever we are bored at the moment, waiting for an appointment, waiting in line, traveling in the car, etc. In this game, one person thinks of a number within a range of numbers and the rest of us guess. We are told higher or lower until we finally guess the right number. We take turns being the guesser or the person who thinks of the number. (When I am the guesser, I usually guess the middle number so I cut the range of possible numbers by 50%. ie..if the range is 0-100, I will guess 50. That is just the way I like to play the game for the first few guesses. I've talked to the kids about why I usually guess the middle number of the range, but they still just guess whatever number they think it is. I don't mind if they don't play it like me as it is just a game, but I do share why I do things with them sometimes. In any case, we all like that game - a favorite for sure!)
We do have a multiplication chart hanging up in the living room and we all enjoy finding out different patterns in it. (Someone once told me that an easy way to learn anything is to hang up whatever it is you wish to know (or others to know) on the wall in front of the potty! Well, our chart is not on the wall in front of the potty seat, but we do see it often by sitting or laying on the couch.) So far, Li, Katie, Jim (my dh) and I are the ones who enjoy looking at it the most.
We have these cool logic (math) books called "Math Perplexers." I love to do them and Katie and Li have enjoyed doing them with me. We also have Sudoku books and other things strewn around the house and in the bookshelves. We don't ever force the kids to do them, but they are there and sometimes come out for one reason or another. We have especially loved the Sir Cumference and other Charlesbridge math books - so clever and entertaining (http://www.charlesbridge.com/showproducts.cfm?FullCat=144)! Pattern blocks, tanagram puzzles, legos, wooden blocks, math manipulatives of various sorts (like cuisonnaire rods - which may only be used to *play* with or not....but either way it is a learning experience!)
When Li plays Magic The Gathering, he is constantly doing calculations of his life and figuring out which card would be best to attack an opponent or defend himself. There is strategy involved in it all. Many of the cards allow you to do a certain thing if you use x amounts of points or tap certain mana that you have already put down. Tokens can be used and dice is used to keep track of your life and for counters. Sometimes paper is used to keep track of each players life. I am surprised how complicated and strategic this game is.
http://joyful-abundance.blogspot.com/2009/12/december-happennings.html - Scroll to the bottom to see the Makana (age 4) and Li (age 8) playing Go Fish. Also, the two bottom pictures are things Li just made up on his own. I ask him about them and he describes them.
http://joyful-abundance.blogspot.com/2009/11/november-happennings.html - Below is from this blog post....(and there are a few other sort of math related things)
"I went shopping in Kana's store and wrote up the amount for each item I purchased. Li and I were showing each other how we added up the numbers. Me by carrying over. Li by adding up the cents first and then adding that amount to the dollar amount. The bottom was another game we were playing involving letters."
http://joyful-abundance.blogspot.com/2009/03/march-happennings.html - Below from this post - "Li explains time to Makana: I overheard Li explaining to Makana that there was 60 seconds in a minute, 60 minutes in an hour, half of an hour was thirty minutes and half of half an hour was 15 minutes, which was how much time was left before the next hour."
I would write more, but I need to attend to my kiddos as it is getting late. I hope some of what I wrote is interesting or helpful. If there is anything specific you wish to ask, please write and I'll do my best to answer. I am sure I am leaving out loads of things, but this is the best I could do while my husband watched the kids so I could try to type!
Laurie Wolfrum 207-236-4275
His response -
Laurie, this is really helpful. Thank you for taking the time for typing it out; I really appreciate it. If I have any further questions as I work on my essay on this topic, I'll not hesitate to ask.