Wednesday, March 07, 2012

Unschooling Tools : Math Play


Unschooling math is not just about making cookies.
Same as learning chemistry is not just about making cookies.
Or even home-ec, for that matter.
(Of course, that's not to say that a child with a fire in the heart for baking and pastries would not learn all he needed to know, just by living by her passion everyday. And how delicious for the rest of the family!)

When you live and learn with children according to fascination and curiosity, you find yourself constantly on the lookout for interesting things.

So some families read Living Math books. (Things like stories and biographies about mathematicians, and tales about finding information through formulas.)
Some enter dice clubs.
Some have a passion for fractals.

Regardless, when living and learning without a script, a mama such as myself keeps resources at hand... a collection of things ranging from possibly interesting (someday) to her child to collections of engaging and beautiful boardgames.

Since this page is about my family, and the way we do things, I'll first mention a fascinating article by David Albert, Just Do the Math!. In it, Mr. Albert talks about how a child can learn math - all of it, k-12 - in eight weeks. Yup. (How's that for encouragement?)

Bubbles and inverted angles

Secondly, as I've just recently mentioned (again!) in Unschooling Tools : Games, I love the words of Mr. John Bennett as he talks about the value of thinking well over that of memorizing complex formulas.

And if you need more, go read A Mathematician's Lament, by Paul Lockhart.

Cuisenaire rods

Along this line of thinking, Mathematics become less about rigid (and dull, to some) memorization, and more about being able to think well, and even to learn some very intriguing and wonderful facts about numbers and patterns.

Wonderful things such as the magic of "1089". (Which is very cool. Go check it out.)
And the fact that any number that can be added until it's broken down to the equivalent of "9" is divisible by 9. (18, 27, 36, 1,269, etc...)
And learning how to add and subtract using a soroban abacus.
And even learning about seemingly obscure things such as binary arithmetic (that was me).

Building with skewers and clay

We can play and familiarize our children with multiplication by counting by threes when counting to 100 for hide-and-seek.
And can learn number recognition, addition, and even multiplication by jumping to numbers written in chalk around the edge of the trampoline, if that's interesting.
We can make games like our geo-dice game, and invent others.
We can show them beauty in mathematics by watching with them wonderful films like Between the Folds.
And we can know there's no reason to worry about how to teach them complicated theories and formulas that elude us (when they're curious), thanks to brilliant and giving people like Sal Khan and his Khan Academy.

Playing Big Brain Academy

Mathematics does not have to be grueling and taxing for any of us, even for us artists, naturalists, or philosophers. :)
We can just Play.


We can play with:
  • -or learn how to solve- a Rubik's cube
  • Cool Math Games (website. There is even one for the littlest kids.)
  • creating tessellations
  • building with clay (or gumdrops) and toothpicks and skewers
  • tangrams
  • pattern blocks
  • dice games
  • jigsaw puzzles
  • mazes
  • trampoline games
  • a balance scale
  • a weight scale
  • a soroban abacus
  • board games
  • fun software (Zoombinis, Math 1-2, Mazes, Carmen Sandiego Math Detective, Cluefinders, JumpStart, Math Blaster, Timez Attack
  • drawing accurately-sized dinosaur or Godzilla footprints with chalk on the driveway or street in front of our house (or other animal footprints, for size... chimpanzee? elephant? zebra? How many? How far apart are the feet?)
  • looking up sizes of buildings in our city, then driving around, making observations ("So that one is about sixty meters tall!" and "There it is! The tallest one! 422 feet... 129 meters!")
  • rulers, measuring tapes, and one inch blocks
  • Venn diagrams
  • cuisenaire rods
  • carpentry
  • measuring cups and spoons
  • counting out money in a piggy bank... enough for a slurpee :)
  • doubling recipes for favorite cookies
  • weight, using pulleys
  • building cubes and pyramids, and finding minimal surfaces (inverted angles)
  • timing things with a stopwatch
  • launching things with a catapult
  • spirals in nature; sunflowers, pinecones, the centers of daisies, and bumps in pineapples
  • learning about what The Golden Ratio is, and then looking for it (faces? buildings? seashells?)
  • making an inclinometer, then going and measuring things
  • making a parabola on grid paper, or even with nails on a board with string.
  • a trebuchet
  • polydrons
And when we need more ideas, we can visit the library, or pull something off our own shelves, something like Amazing Math Projects, Games for Math by Peggy Kaye, or Family Math.

Mandatory worksheets? I think not.

Next week for Unschooling Tools...Television!  (Movies, documentaries, netflix faves, pbs shows, etc)

This post is part of the Unschooling Tools series.
Other posts are Unschooling Tools : Games
Unschooling Tools : Television
Unschooling Tools : For Creativity
Unschooling Tools : For Reading


  1. Great post, Steph...and as you know (I'm sure) I am one hundred percent agreed.

    I detested math in school, thought I sucked at it because it was such an abstract concept to me. Nothing about it related to my everyday life. Since leaving school, ahem, 22 years ago - I've actually begun to understand math in a very practical manner. Fred actually thinks I'm gifted at math because of *how* I do it in my head (not the "normal" way, according to him). I'm not so sure about that but I do feel much more comfortable knowing that math does come to us...when we are open to it and ready to receive it in our own way...and that's not necessarily the way we are taught.

    Regarding the K-12 in eight weeks: I have read that as well and it astonishes (and angers) me that we drag out something as feared as the name of education. Arg. If only we had all been as lucky as our children.

    Recently I chatted with my husband's boss (at the Christmas party - they were all FASCINATED with unschooling) and he told me he had studied calculus all through university and really had no way to explain the concept...because he didn't understand it, despite doing well at it. Then, he met someone who put calculus into practical, everyday terms (how we determine when we need to slow our car down -and by how much- so that we don't hit the car in front of us) and he suddenly got it. All those years...all that money and time studying something he did't even understand and a five minute conversation finally made it all click for him.

    My point (as I'm sure you know) is that math needn't be taught in such a formal way, as an abstract concept...because if given the opportunity to incorporate it into our lives...we WILL be successful at math - at least the basics, which is really all most of us need.

    Rant over. Thank you for your passion, as always. It is forever inspiring. <3

  2. That story about Calculus... I'm not sure if it's funny or sad. :/ :)
    I certainly don't doubt it, however.

    Regarding the rest of your story - your words and observations are lovely, and I am so thankful that you are in my list of friends with whom I can bounce around ideas and theories.
    ♥ ♥

  3. Once again, a brilliant post Stephanie, so helpful and inspiring to us all. Thank You!

    And as an aside, your citiblocks are a gorgeous colour - ours are mostly plain wood with just a few red ones my search for a colourful top up has begun!

  4. Carol - thank you so much.
    They're inspiring to me, too... I love looking around here and seeing things with a fresh perspective, and I love talking with others about things they find interesting. :)

  5. Very, very nice post. You have put into beautiful words many things from my own heart.

  6. I really love this post, and I appreciate all the time you put into gathering all of these thoughts and resources in one place. I share your feelings and approach to math. I have also read that article by David Albert in the past, and it really made me stop worrying about what my girls are learning for math.

  7. Thank you Phyllis and Susan!

  8. This is always where my mental snags show up (heart stops - will they ever learn x,y,and z?), mostly because my own history with math is so horrid and confusing. i had a deeply reverberating relief when the other day ani completed a maze in Anno's Math Games III with no problem and when i gasped, she giggled and said, it's cause i've got a math brain, mama! the least i can do is not pass on my history, and the most i can do is make it FUN!! we have various bits of curriculum lying around, but only the blocks get used, and occasionally i look at how to explain certain concepts so i can jump in when it might be helpful!

    reminders like yours and the various links are so helpful to me...thank you!! (and i'll link if i get around to a post this week...sounds like i probably have a few things to say...)

  9. As always, another fabulous post from you my friend! Thank you for gathering us all together daily (and each Wednesday for these posts)! My list of fun items to add to our world is getting longer with each post that's added! :)

  10. Hey guys... wanted to say real quick that there is no need to feel obligated to name your posts the same thing that I do (but name them that if you want to!)... I just call it that, first because of the series of Tools posts, and secondly, that's what the list of goodlies (my family's) is about, to me. :) So don't feel like you have to call it something that doesn't jive with you... or that you must be an Unschooler to contribute.
    If you feel a burning desire to tell us about your beloved curriculum, then by all means do so... just give us the "Wow!... this is so cool!" bits. :) (tricks, interesting patterns, etc.)
    Just don't try to sell me on your logic of Pain and Worksheets... as that ain't gonna fly. :)

  11. Emma and I were just created a numbers book tonight, so I chuckled when I saw that your post today was about math!

    Thank you for all the wonderful links and ideas :)

  12. THANK YOU for this !!!!


    (Also, not directly related to math...will you ever share your Timeline with us? Unless I imagined it, I think I once saw a post wherein you revealed this fascinating timeline in your basement (?) that my brain is telling me was something like 60 feet long, but I must have made that up (?). I am trying to create something similar for us to jot our various learnings on... beginning with geologic time, and working up to the present day. Obviously it will not be to scale!)

    Hope this humble request doesn't hijack the orderly proceedings -- I am feeling the Math Love strong and clear, here. But maybe someday, when the Wednesday category is right, may we see the timeline? :) :)
    Thank you!

  13. Ah, the timeline. I tend to sort of forget it's there. :)
    My son has like... seventeen or so? more? prehistory encyclopedias. He's collected them since he was little. Now, while he likes all of them, for different reasons, he says "Some are more accurate then others." (The same goes for documentaries. He gets so frustrated with inaccuracies in documentaries!)
    Our timeline is like that.
    Our 'Time' is subject to the information that my children and I study, and is of course influenced by our personal resources of Earth's history.
    So while I would hope that our notes are very close to the current day's estimation, it is possible, as sciencists learn more, that sometimes out info would be outdated. (Or would be, someday. Hmmph.)
    And there is looooooots of blank space. :)
    But, yes, if you wanted to know what's on there, we'd share that with you. :)

    It's funny that I hadn't even considered that mentioning the timeline would go into our notes for tools--science or history. :) Math Toys was like that, too, though... good thing I had been thinking about it for a few days, things are such a part of your life that you don't really "see them" as belonging to certain areas or subjects! :)

    Anyway, thanks for the smiles.

  14. My goodness, mama. I'm bookmarking this one so I can come back to all these amazing ideas. We recently watched The Story of One and Flatland. Great math movies that the kiddos really enjoyed.

  15. April - That's the second I've heard "Flatland" in two days. :) Guess we'd best check it out.

  16. Hi Stephanie! Thanks for stopping by my blog (Kicking Curriculum to the Curb with Living Learning Lists). I found your blog via another a few weeks ago and have been enjoying your archives and this new series of posts. I'm in the "Mama's kicking and screaming as we go" phase of unschooling so your blog has been very inspiring and helpful to me on this journey. Thanks so much.

  17. Oh! :) Well you're welcome! And I'm glad to meet you!

  18. Great post Stephanie. This math phobic mom always needs more math resources. Off to check out some of those links!

  19. This is a great post! My daughter is 7 and I am freaking out that she can't get her addition and subtraction facts down. She hates math and it's so frustrating for both of us.

    I'd love to do more unschooling, but what I can't figure out is how to log the hours for that? In MO, we have to have so many hours per subject. Heck, I can't figure out how to log the hours right now and we are doing textbooks and worksheets!

  20. It's nice to meet you! I can't classify myself as an unschooler though I am very attracted to the idea and methods for learning. Math is a sore subject with my oldest daughter - unfortunately she's admitted to hating it. Curious - how can I fill in "gaps" for my state's standardized tests? A big part of me fears "not covering enough" material for when these tests are required to administer. Thank you!

  21. Thanks for leaving your linky open so long - I'm just now getting to this one.

  22. Wonderful, inspiring post! Thank you! I find that I become more and more relaxed (not sure I even really like that word, but...) in my homeschooling as I go and find what works best for our family. One of my children in particular despises math and I have been seeking to do something different. This is so helpful.

  23. Thank you for the post. Math has always scared me, and I often wonder how in the world I will be of any help to my daughter. Thank you for all the resources listed. I have bookmarked them all!

  24. I know this was posted a while ago, but bravo! Thank you for all the information!

  25. Wow, this is the way I would have preferred to learn math. We just did problems with little explanation about why we were learning what we were learning.

    The best way to learn anything is to teach yourself in the form of a game. One of the most important segues from concrete to abstract math for me was negative numbers. There’s an easy board game you can buy online to teach kids the concept of positive & negative numbers. Kids go up & down the board in steps, learning how negative numbers work.

    Creature Quest:


Thanks so much for sharing your thoughts!