There are things that I would do over if I had the chance (like never getting the never ending pasta bowl at Olive Garden.) One of those things is the way that I approached teaching math. When my son was little he liked math, things were easy. But, some of my distaste of the subject (brought on by years of falling behind in the subject at school and with no one trying to stop the downward spiral of math hatred) rubbed off on him. Suddenly, math was too hard, ugly, not making sense, and it made both of us cry. I labored on through the years trying to shore up his shoddy foundation of math and arithmetic and promised myself that later children would do better because before I even taught them that 1+1=2, I would show them how beautiful and mysterious math could be. I would help them build a solid foundation before trying to erect a city of Mathtopia with various rooms of logic and proofs, theorems and irrational numbers.
This turning around of my fear and hatred of math did not come easy. I had to go back and fill in holes that were missing in my knowledge. I read books about math, about numbers, about Algebra and about things like math in art, in music and in nature. I had to fix my own idea of what math looked like before I could start teaching my children. Then I started going about the teaching of math, but with the strengths and weaknesses of my children put into the plan.
(Math art, weaving Pi to 13 places.)
I have visual and kinesthetic children. It’s not enough to drill them in math facts, you have to show them math, they have to touch it, hold it, see it, and sometimes eat it (chocolate math, it’s not a bribe, it’s hands-on learning!)
We started with the basics, but I used living books to tell math through stories. Books like: Life of Fred, Sir Cumference and the Dragon of Pi, The Life of Fibonacci, Reese’s Pieces Math Fun, The Greedy Triangle, The Grapes of Math, Anno books, Math Curse, The Number Devil and many more.
We added some hands-on fun to math facts like doing math problems with chalk on the driveway, using the balance scale to measure amounts and of course using the kitchen for practice with fractions and measurement (even if we were just making fraction ice cream cones.)
Sometimes we do math at the pool, calling out problems and throwing a ball to the person who needs to answer it.
We draw number lines on the driveway and walk problems like -4+(-5) and 6-(-2). (Our driveway is a big hit with the neighborhood kids, I have them all asking to be homeschooled!) I look for hands-on fun that will cement the learning into place.
Once you have a good foundation of addition and subtraction (which are opposites) and multiplication and division (again, opposites), fractions and decimals can be tackled. Fractions with unlike denominators need to be multiplied by a common denominator so they can be added or subtracted.
We used candy, math blocks or counters to show fractions as we were trying to make their bottoms the same number so they could be added or subtracted.
For younger kids make sure they get the visual concept of a fraction like ½ of a circle, then if you say ½- ¼ they won’t even have to change the denominator to be able to tell you ¼ is what is left. Picture books for fractions are a great way to introduce the topic before you start playing with hands-on examples, here are a few books: Multiplying Menace, Full House an Invitation to Fractions, The Doorbell Rang and Life of Fred (Fractions.)
You should introduce fractions and decimals together since ½ is also .5 and ¾ is the same as .75 because you are dividing the fractions. Mixed numbers can get tricky, just remember that a number like 2 ¼ goes counter-clockwise to turn into the improper fraction 9/4 and that to get an improper fraction into a mixed number you divide and read the answer clockwise from the quotient with the divisor being the bottom of the fraction in that mixed number. Add on multiplying fractions, just multiply straight across the top and then across the bottom and dividing fractions (which is just multiplication with a reciprocal.)
From the very early years you can start the process of Algebra. When you are asking a 1st grader 6+(blank)=9, you are having them think like they do in higher math. Now put a variable in there and you have 6+x=9. They probably won’t tell you that you need to subtract 6 from both sides to get an answer of 3, but you could show them how to find the answer by doing that. Once you have your basic math facts down with fractions and decimals you can start solving formulas and problems. Balance and opposites are the key to solving equations. What you do to one side you always do to the other and if you are adding, then you must subtract to get a number or variable from one side of the equation to the other. Algebra is the stepping stone to Geometry, I believe that Algebra 1 and 2 should be taken consecutively, with Geometry as a 3rd year course. There are many proofs and Algebra logic that come into Geometry and another year of study and practice is well worth it. Moreover, picture story books about Geometry read in the early years will help with the terminology later. Books like: What’s Your Angle Pythagoras?, all of the Sir Cumference series books, and Life of Fred (High school series.)
The best part about Geometry ice math? Smashing the manipulatives when you are done!
By the time your children are starting Algebra 1 in High school, they should have a city of math built on a rock solid foundation. As they continue on in higher math they can add to that without fear of toppling the whole kingdom of Mathtopia down.
Finding real world problems to attach to math skills will help children understand that math can be found all around from cooking a meal to dividing up candy among their friends, you can even find math on the playground!
Do some math yourself after checking out some of the books and websites below, you might just find yourself having fun too. Math is not something to be feared; it can be fun, it can be a mystery, but it can be taught in blocks that are easily handled so that your child can build a foundation that they can keep working on as they increase in their knowledge and mastery of the subject.
Some additional reads for adults (Yeah, I kind of really like Ian Stewart):
Fractals, Googols, and Other Mathematical Tales
by Theoni Pappas
By David Berlinski: One, two, three : absolutely elementary mathematics
Infinite ascent : a short history of mathematics
The advent of the algorithm : the idea that rules the world
By Ian Stewart: Letters to a young mathematician
In pursuit of the unknown : 17 equations that changed the world
Professor Stewart’s cabinet of mathematical curiosities
Why beauty is truth : a history of symmetry
How to cut a cake : and other mathematical conundrums
Professor Stewart’s hoard of mathematical treasures
Helpful math websites:
Vi Hart’s blog (check out her math doodles) – http://vihart.com/everything/
Khan academy (for visual math, lots of other things too) – http://www.khanacademy.org/
PBS math games for younger kids – http://pbskids.org/games/math.html
Numbernut math games and lessons – http://www.numbernut.com/