Math seems to be the biggest hurdle for most homeschoolers who want to inspire and not require their kids to learn.
“How do I get my kids interested in math?”
This is one of the top questions I get asked about homeschooling.
The following is exactly what I did in our homeschool, and it has worked wonders.
Step one is to leave behind "grade level" math until high school.
Yep, you read that right.
Traditional math (whether it be “new math”, Common Core, or almost any homeschool math curriculum) is the biggest culprit in creating a hate or fear of math.
Math is fun! I won’t say it “should” be fun; it IS fun! But if you have only ever experienced traditional math taught in a conveyor-belt system, you probably have never had the joy of discovery when it comes to math.
Traditional math may be one little piece of math, but that little piece has been so blown out of proportion in the last 50 years or so, that it hardly resembles the real world of math at all.
Step two is to start seeing math in the world.
See the real math that God has put into the plants and animals he has created. Math is everywhere, and that math is real and tangible. It’s not an abstract concept, you can see it and touch it. If you’ve never looked for math this way you may not know where to start. It’s very simple and I’ll show you how to get started.
Step three is to let it flow where it wants to go.
There is no need to try to shoehorn math into a grade-level box. A love of math, or at least not a hate or fear of math, will allow the math to come naturally, and it might take surprising turns and leaps to big concepts or back into the basics. Toss math “levels” out the window and let discovery be your guide.
Okay, so let’s dig in a little deeper into what I mean by all that.
Step 1: Don't focus on "grade level" traditional math until high school, even late high school.
By “traditional math” I really mean modern math. The idea that math happens in a certain order. The idea that kids have to learn addition and subtraction, then multiplication and division, then fractions, then pre-algebra, algebra, geometry, and so on.
Math, in reality, is not a linear thing. You don’t have to learn all of Algebra 1 before you can play with Geometry concepts.
Math bubbles and flows through everything, and the problem comes--the hate or fear of math comes--when we try to box it into “grade levels” which takes all the discovery and fun out of it.
The only purpose I can see behind segmenting math into grade levels is so that large groups of students could be managed. Could you imagine a teacher trying to guide 30 students through math individually, letting each student discover math in a meandering and natural way? It would be impossible. But in our homeschools, with just a few students, we have the opportunity to let math be real, and not boxed into arbitrary levels.
The problem with that is that you probably went through the math conveyor-belt just like I did, doing math “in order”, and therefore you have no idea what math looks like without that box to put it in.
You may be thinking “But if I don’t have my kids do grade level math every day, they will eventually be so far behind that I’m afraid they will never catch up.”
To which I would reply “Did you know that all of K-12 math can be learned in 8 weeks?”
A 16 year old student, who has not done any “grade level” math, ever, can learn all he needs to get into college in a matter of a few months if that is what they choose to do. Most won’t want to do only math for two months, so they could spread it out over the last year of high school, or even the last two years, and have plenty of time.
Does that sound far-fetched?
Well it isn’t. I have heard many stories to back this up. One mom, Shawn, told this story about her son:
Oh yes, the happy ending? He was accepted as a junior at UCLA and will graduate with an Econ/business degree in June.
Breaking that down even more, he spent an average of two weeks--TWO WEEKS!--on each “year” of math, while taking a full load of college classes!
So why on earth are we dragging this out for years and years, all the while creating a hate of math?
Shawn’s story is not the only one I have heard that supports this idea, but she wrote this out herself, and I felt like that was the best representation of it.
David Albert, in the article Just Do The Math, breaks down how long is spent on the conveyor-belt to learn math. He calculates that the total hours for math, from grades 5-12, is 240 hours. That is 30 hours per year for 8 years (he discounts the early math taught in K-4 because it is so easily learned later, and drilling it “early” has no long term benefit).
I find it so astonishing that all of the “grade level” math can be learned in so little time, actually, it makes me a little angry. A little angry that I was dragged through boring, confusing and irrelevant math for 12 years. But I am also so thankful for his calculations, because knowing that has freed me from having to drag my children through the same boring and confusing math when there is no need for it.
There is another little secret that modern education won’t tell you about higher math too. That is that most students don’t need it.
Jordan Weissmann in The Atlantic states that less than 20% of adults use higher math in their work, that is Algebra or higher.
Shaunacy Ferro quotes Nicholson Baker in this Popular Science article –
“If math were an elective, ‘American science and technology would be unharmed, and a lot of poisonous math hatred would go away instantly. Kids don't hate smelting, or farming, or knitting, or highway design, or portrait painting, or neurology, or juggling rubber balls, or sonnet-writing, because they don't have to take three years of instruction in any of these arts,’ he writes. So, math is like juggling, and should be reserved for that one weird enthusiastic kid in the class. And the rest of us could be spared the effort of trying to find an equation for tears shed per problem.”’
Now don’t get me wrong, we still learn math, but math that is tangible, not arbitrary math on a schedule set by some curriculum, followed out of fear of “not keeping up”. I don’t care if my kids “keep up” with their conveyor-belt peers in math, because I know the real truth, that if they need to get to a certain “grade level” for college admission, they will be mature enough by then to dig in and fill in their own holes in a matter of a few months. Plus most of their peers probably hate math, while my kids don’t.
12 years of math stress is not needed.
In the meantime we are free to enjoy math, play with numbers and patterns, watch Vi Hart videos on YouTube and generally learn a bunch of math stuff in any order we like. We still do a lot of what looks like "traditional math" but it comes naturally, I don't let any outside source dictate what we learn or when we learn it, we simply learn it when we want to.
Besides, the “math” that is taught in the conveyor-belt system isn’t really what math is anyway, it’s only one tiny piece. Yes, a student can “catch up” on all that he missed, if he finds he needs to, but that doesn’t even take into account that all that material he is learning to “catch up” isn’t what math is all about.
Math has been reduced to memorizing formulas, practicing them over and over, and then being tested on whether you remember the formula and perform it correctly. That’s not math.
Real math is about discovery; it’s about patterns and numbers and curiosity. It is about having an idea about those patterns or numbers, and then being curious enough to see if you can figure it out, see if you can find a way to determine if your idea about those patterns or numbers is right or wrong.
In the article A Mathematician’s Lament, Paul Lockhart describes a nightmare in which music has been subjected to the same sad fate as math.
A nightmare indeed. It is so sad that this is what has become of math.
Step 2: Seek out real math in the real world.
Math is everywhere.
Go outside, wherever you live, and you can see math. Of course it is in the buildings and cars, because math was used by people to make those. But look closely at what God has made too.
Notice patterns and proportions, look for repeating shapes, see how these all work together to form our world.
Look at a flower, count the petals. Now look at a different type of flower and count those petals. Go all around and look at the flowers and count the petals on each different kind you find. Do you see any similarities? Did you find several different flowers with five petals? Or 13 or 21?
One mom I suggested this to said, “Oh, so we are going all the way back to preschool?” I guess she thought that looking for numbers in nature was baby stuff, but it’s not, it is the stuff that ideas are born from.
Look at a few pine cones. See how the little “petals” of the pine cone form a spiral? Try to count how many spirals are on the pine cone. I bet it’s 5, 8 or 13. Now count the spirals in the other direction. Probably a different number, but I’d bet money it’s also 5, 8 or 13.
What is going on here?
What you are seeing was noticed by a mathematician over 800 years ago. That mathematician’s name was Leonardo Bonacci, known today as Fibonacci. He saw that nearly everything he saw in nature had the same numbers in it: flowers, pine cones, seashells, leaves, and more. The numbers create a pattern, whereby the last two numbers in the sequence, added together, make the next number in the sequence. 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. His discovery has become known as the Fibonacci Sequence.
A fabulous picture book to start you off with seeing real math in the world is Blockhead: The Life of Fibonacci.
Another great resource we have watched over and over is the Vi Hart series on YouTube called Doodling in Math Class: Spirals, Fibonacci and Being a Plant.
The Fibonacci Sequence is only one of dozens of fascinating number patterns.
In fact, all of Vi Hart’s math videos are amazing. She shows what it looks like to play with math, to notice patterns and discover more about them. She explores, doodles, invents, sings, experiments and generally has a ball playing with math ideas.
That is what math is all about.
My 15 year old loves Vi Hart so much, she decided to make her own Vi Hart math notebook, and copied all of the doodles from several of the videos, and because of that, she knows all about logarithms, fractals, Pascal’s Triangle, Koch curves, parabolas, slopes; the list goes on and on.
Would she pass a “grade level” math test? I don’t know, and I don’t care. She loves math and that is more than I can say for most 15 year olds who pass the test, doomed to hate or fear math, for probably the rest of their lives.
So YOU start noticing math, point it out, be curious about it, play with it yourself, and the attitudes toward math in your homeschool will begin to be reshaped.
Step 3: Let math flow where it wants to go.
If you want your kids to enjoy math, you have to quit your job as the Boss of Math.
When you start looking for math in the world, or watch a few Vi Hart videos, or read books like Blockhead or Sir Cumference or Mathematicians Are People Too to your kids, don’t force a lesson out of it.
Give your kids space with math.
Give them time to heal their dislike or even their hate of math.
Expose them to lots of ideas through books and videos and nature walks.
Notice the mathy-ness in the world yourself and casually point it out.
I pointed out that most ceiling beams were 4’ apart (my dad told me this long ago), and now we can figure out how long any room with ceiling beams is. Notice this isn’t a huge deal, it’s just a casual “noticing” of the math in the space we are in.
You do math stuff, tangible, real-life math stuff, not Trigonometry or Calculus (unless of course you absolutely love that type of math and can share your enthusiasm in a way that helps your kids love it too). Let your kids see you calculate how much paint you will need for a redecorating project, or working on your budget, or making patterns with blocks, or figuring out how much the gas will cost for your upcoming road trip. You do the projects in the Sir Cumference books, you copy down some of Vi Hart’s math doodles, you make a hexaflexagon. Sure, your kids can join you if they like, but don’t make them feel like they are supposed to.
Be casual, act as if playing with math and noticing patterns is a normal activity for everyone.
You are showing your kids how to interact with math by simply showing them, not telling them.
Eventually they will start noticing and playing with math too. They will point out when they see a Fibonacci pattern, they will recognize Pascal’s Triangle, they will begin doodling and playing with math on their own.
This is the way you let math flow.
When your daughter asks for a notebook and pens to copy down Vi Hart’s doodles, simply get her what she needs.
When your son starts calculating something out loud while you are on a car drive, just let him do it his own way.
When your daughter wants to use a calculator for some simple math, let her.
When your son wants to buy a new Lego set, and he decides to sell cookies to earn the money, leave him be and see if he decides to figure out how many cookies he will have to sell to make enough. If it doesn’t occur to him, you might say “I know of a way you can figure that out”, but if he’s not interested, drop it. Either way, don’t make it a math lesson. The math lesson will come on it’s own if we let it.
Play games that involve math, and by the way, don’t tell them they are learning math, just play the game. They will learn lots of math without even realizing it. Battleship, Chess, Uno, Monopoly, Blokus, there are tons of games that teach logic, math ideas and concepts without being “math games”.
All of these things will lead them toward a love of math, or at the very least not a hate or fear of math.
When kids learn math concepts and ideas this way, without even knowing it, later, when they do decide to “catch up” so they can go to college, all that math knowledge will give them an aptitude for numbers and concepts and logic which will help them recognize and connect the ideas and memorize the formulas easier.
My daughter hasn’t had a formal math lesson given by me since she was 9. Is she math illiterate at 15? Absolutely not! At 11 she was taking Danika McKellar Algebra books to her room for before bed reading. She has claimed the entire set of four books as her own and they now live in her room. She has read so many books about math and numbers, watched and copied Vi Hart videos, and she notices math concepts and ideas everywhere! Math is natural for her.
In fact, as I was writing this, she sat down by the computer and started reading it. She then read the Just Do the Math article, and when she started reading the Mathematician’s Lament she begged to read it aloud to us! She read several pages to us, and then went on to read the whole thing, commenting the whole time. She’s been talking about math stuff ever since. This is because playing with math and chatting about it is a normal, no-stress, natural occurrence in our home.
Will she go to college? I don’t know. My guess is probably not, not because of a lack of education, but because she is learning all she actually needs without college already. If she later chooses a college-degree-necessary career, then we will cross that bridge when we come to it, but for now, she is educating herself in math and so many other areas.
But it looks nothing like school.
And I can see my 11 year old son following the same pattern. Just today he was singing a Vi Hart song about Parabolas!
You really can let the math conveyor-belt go.
You don’t have to keep trying to ‘make math fun’ for your kids.
Just playing games, having great math resources, reading aloud and noticing real math is enough when your kids are young, really! The rest will come about naturally when math is no longer a dreaded thing.
Even if your child never becomes a math-lover, at least this way he won't be a math-hater.
Yes, some kids will never be excited about or even interested in math, try to remember that it's okay if she never becomes a "math person", not everyone needs to be.
"But my son is required by my state to take standardized tests, so I can't Let Math Flow."
If this is something that concerns you, if you have to comply to state testing to legally homeschool, do some real research into what happens if your child doesn't test well. You might be surprised that they don't do much with the test scores, sometimes they don't even look at them. So ask around, find some other homeschoolers in your state who's child didn't do well on the test, and ask them what happened.
You also might be surprised that kids who learn lots of natural, free flowing math, actually do reasonably well on standardized tests, because their "logic muscle" is working, and they can figure out many things even if they haven't spent lots of time drilling on that kind of math problem. They may not score in the top 10%, but they don't completely fail either.
So to sum up:
Leave “grade level” math behind.
Seek out real math in the real world.
And let math flow where it wants to go.
The math conveyor-belt is so ingrained in us all, even if we let all the other subjects happen in a more natural manner, we just can’t seem to let go of the math curriculum.
Well, I hereby give you permission to toss the curriculum (or at least leave it in the closet to be used as a resource when a child asks for it).
I'd love to hear your favorite "Mathy" resources, so comment below!