Both of my children expressed an interest in the natural sciences at a young age so I had a feeling that math would end up being an important subject for them both. Math is also a subject that lots of young children hate. I didn't want my kids to hate it too. For this reason, I decided to introduce as much math as I could through games rather than through textbooks and worksheets. I wanted to make it both meaningful and fun.
Early on, I fortunately stumbled onto a yahoo group called "Living Math" which provided me with a community to discuss our approach and to share ideas with other parents and teachers. As a homeschool mom, that meant a lot. Having a group of people who share your goal can help tremendously when things get tough.
More than 10 years later, the group still exists. The founder has this to say on her website:
~ Insisting a child must be taught traditional, scope-and-sequence arithmetic to learn mathematics is like saying one must learn classical notes and scales before one can learn music. You might get there, but you miss out on the inspiration of beautiful music created by the masters along the way. We need not master all the "basics" before being able to experience the appreciation that carries us through the hard work of learning. Think of applying living math principles as developing a "mathematical ear" while working toward the mastery of basic theory. ~Below the fold, I share with you some of our own Living Math experience in hopes that some of you, homeschoolers or unschoolers, public schoolers or private schoolers, students, parents, or teachers, might be intrigued and discover a possible new way to introduce your kids to more math and have them like it.
Teaching Living Math with young children is easy and most of us do it without thinking. We count the steps as we hold our 2 year olds hand; we sing counting songs; we cut cookies in half and pizzas in eighths. And we talk about these things pretty naturally with kids. If you don't, you should start. It's the beginning of holding more advanced math conversations later in their lives. If you start talking about math while they are this young, it won't seem so strange when you need to talk about how to multiply fractions, for example. And, one day you might find yourself in a conversation about why 0 is a number (still being debated) or whether or not it is positive or negative or neither.
Providing math stimulation for young kids is pretty easy - for example, an egg carton and some buttons can provide tons of entertainment while helping kids learn how to count, how to build patterns, how to discover patterns, how to differentiate size, how to organize pieces.
Where it starts to get more difficult are the ages where we start expecting kids to memorize math facts - those mid to upper elementary ages. Most of us fall for the trap that kids need to memorize in order to learn or to pass tests. Actually, IMHO what they need to do is repeatedly use math facts in meaningful ways. Then the memorization happens despite all else. Facts memorized from usage tend to stick with us. Facts memorized from flash cards are only a number in your head. It's also important that kids understand the concept behind the number. When they use the concept in real life, the concept is more concrete and easier to understand. So using games that function like flash cards and using math in games and in real life are a great combination to help kids memorize those facts they need to know.
Some of the things we would do in our house to help use math facts repeatedly:
Play games. Lots and lots of games.
- We would play War with a deck of cards but instead of the highest card winning, the person who could add the numbers first would win. When they were older we changed the rules to multiplication.
- Casino is another great card game that requires addition as well as logical deduction (an important math skill)
- Shut the Box - you can make up your own rules to include subtraction
- We played Knock-Out, an entry level math game for addition and subtraction made by an American company.
- We also introduced basic strategy games. Tic Tac Toe is the most famous but there are lots of other simple ones like Goblet
- or Labyrinth.
- We also introduced the basics of Chess and started going to a Chess Club.
Read math literature. Didn't know that it existed? There are lots for young children:
- All books by Greg Tang. Our favorite was The Grapes of Math.
- Books by Mitsumasa Anno. Our favorite was Anno's Mysterious Multiplying Jar.
- Our ultimate favorite for younger and older kids - The Math Curse by Jon Scieszka.
- And a series I forgot but absolutely love, Sir Cumference! Thanks to nuclear winter solstice for the reminder!
Cook together. Recipes all require math. This is especially true if you have to double or halve a recipe. Pancakes on Sundays were really popular in our house.
Have kids help in the grocery store, especially in the produce department. When they're really young, they can help count out 8 apples into the bag. But when they get older, make sure you need 2 pounds of apples instead.Because we played with math concepts, my kids brought math into their own play world. One son created his own money and used it in his own town where his stuffed animals all held elected office. Both children built endless creations with Legos, with blocks, with Knex, with cans from the kitchen cupboard, with moving boxes. Building teaches a lot about math concepts but, of course, kids don't consciously know that's what they were doing.
We also used a math curriculum known as Miquon. It was introduced to the education world in the 1960's and though it never took off in public schools, it is still used in some. It is a curriculum that lent itself to our style of learning and teaching. To help kids conceptualize math concepts, they recommended the use of Cuisinaire Rods, which also meant my kids could build while learning math. I could jump around the book and not introduce topics in a specific order. That meant if a child was asking about fractions, we could concentrate on fractions. If they were interested in shapes, we could concentrate on geometry. Miquon made it easy to for us to be flexible and take advantage of child centered learning.
I also relied on Peggy Kaye's Games for Math and Strewing, a term coined by Sandra Dodd, a self-defined Radical Unschooler. It is the art of allowing your child to discover something you have casually left out. Just leave a ruler out on the table and see what your kid starts to do with it. Don't call attention to it. Just let them discover it and see what they do. Be warned, it might take a couple of days or so before they even realize it is there.
Ironically, despite my efforts to help my boys love math, both have had moments in the upper primary grades where they hated math, despite all my attempts to help them love it. What they actually hated was the process of learning math alogrithms - such as how to multiply and how to divide. They are both global learners, not sequential ones, and processes that are sequential have been very difficult for them to learn (that's a diary for another day!). During this time, we decreased our curriculum based math and increased the math games because they liked them and found more literature books that included math:
- Muggins and Opps - games by the makers of Knock-Out, above. I ordered a wooden board with Muggins on one side (a game that uses addition, subtraction, multiplication, and division) and Opps on the other (a game that adds the element of integers to the four operations of Muggins).
- Any game with strategy - chess was a big one but also Japanese Go, Carcassone, Elvenland (board game that plays off the Seven Bridges of Konigsberg conundrum), Settlers of Catan, Tayu and Blokus
Our favorite books were:
We used building toys like:
For the computer we discovered:
We also watched science and math videos like:I still needed the occasional book to turn to for ideas. We had outgrown Peggy Kaye so I found Family Math from the Lawrence Hall of Science instead. And, for those times when we felt like a little bookwork was called for but we weren't ready to face a full curriculum, we turned to Singapore Word Problems and the Key To series of workbooks.
And I found a book for myself - Math Matters. It is a book for teachers that:
helps K-6 teachers clarify their own understanding of the mathematical concepts they are required to teach. It is a resource for math teaching no matter what instructional program is being used. Math Matters not only will help teachers become more comfortable with the important underlying ideas in the elementary math curriculum, it will also prompt teachers to ask better questions of students, explain ideas more accurately, and stress important relationships and concepts.It provided me with the clues to help my kids learn algorithms. I learned that there isn't one way to multiply multiple digits and proceeded to introduce Lattice Work Multiplication to my boys. It made a huge difference because it removed the heavy sequencing necessary for learning the traditional algorithm. They still use lattice today and enjoy seeing the looks on people's faces as they complete multiplications problems quickly and easily but in a very different method:
Where are we today?
When I published the first diary about living math we were here:
Both boys are attending school in Buenos Aires, Argentina for the year due to their father's military assignment. They were more than prepared to tackle math in the classroom and have held their own, even in a foreign language.Today, we are in Washington DC. Both boys passed their math classes in Argentina though my oldest will be taking more Algebra II here in the States. Math in Argentina is covered differently and he learned a little more Algebra, Trig, and Geometry but not enough of any to progress through an entire year. He will take his classes at the local community college under their dual enrollment plan for high school students. My youngest learned that he is great at math puzzles but still hates long division. He is looking forward to using math in his science projects this year - more real life for him than the classroom instruction of last year.
As for practical matters, my kids have their own savings accounts and my teen has his own checking account. They spend their own money when on vacation so that they understand the value of a dollar (or an Argentine peso). They have helped measure furniture and floors and walls for placement of our things when we move (as a military family, we do this a lot). They figure out gas mileage on long trips. They figure out the tip at restaurants without the use of a calculator. We listen to audiobooks as a family and often choose titles like Freakanomics. We read the newspaper and magazines and analyze graphs and data presented in articles.
Some of you may be wondering where we found the time to do all these things. First and foremost, we turned off the television at a young age. You would be amazed how much time that adds to the average day. It doesn't hurt to be a stay-at-home mom and to homeschool but a lot of these things were actually done during normal family time - cooking normal meals, sitting at the dinner table, and on weekends and during family vacations. Anyone can start to include these activities into their daily life, not just homeschool families. I bet a lot of you already do. I would love to hear about your Living Math experiences in the comments below!
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Sun Jul 08, 2012 at 5:54 AM PT: Please check out Tomster's comment below - he has three great additions to the list: