We've Come a Long Way
We started homeschool kindergarten in 2011 using the typical math education methods such as textbooks, workbooks, and flash cards. By halfway through 1st grade, my daughter was dreading math. When I had my epiphany a few years ago about how my schooling methods were actually detrimental to teaching my daughter to love learning, math was one of the subjects that was forefront in my mind. How could my only-6-year-old daughter be starting to hate math?
Over the last few years I have been implementing Leadership Education principles into our homeschool, and our math work has been transformed. Instead of dreading and hating math, my 10-year-old daughter thinks math is fun and interesting. And her 7-year-old little brother is coming right along with us, enjoying it as much as his sister.
How I Teach Math Without a Formal Curriculum
I focus on three specific approaches for teaching math: games, read-alouds, and everyday math. These three approaches form the cornerstone of our homeschool math curriculum. My children love them all, and that means that they love their math studies.
I don't push my children to engage in any of these resources. Instead, they are always free to decide whether or not they want to participate. But the thing is, our math work has become so fun and un-pressured that they almost always want to participate. I don't do math read-alouds and games with my children every day; that would take some of the fun and excitement out of it. Rather, I aim for about 3 times a week (and of course, everyday math does happen pretty much every day). My children are getting to explore math rather than getting bogged down in repetitive drills, and this exploration fosters a high level of interest in math.
Math read-alouds provide a great opportunity to introduce new mathematical concepts to my children. Often I will read these books alongside a lap-size dry erase board where I can illustrate things further, or where we can write our answers to questions posed in the books. Instead of forcing my children to answer the questions in the books, I give them the opportunity to do-so; if they don't feel like it, then I will keep it lighthearted and work through the problems myself. We read math read-alouds usually once or twice a week.
Bedtime Math - Each page includes some engaging facts and then three math problems (ranging from easy to difficult) that give my children a chance to put math concepts into practice. My children absolutely LOVE Bedtime Math, and they are always begging for one more page.
Life of Fred - Life of Fred is a series of books that tells the story of Fred Gauss, a 5-year-old math genius who teaches at a university. Life of Fred books range from elementary math all the way up through Calculus. Besides mathematical concepts, Life of Fred books also weave other topics into the story such as constellations, carnivores, and languages. At the end of every chapter, there are a few math problems to answer, but they are much more interesting than the problems in most math books. Fred and his doll Kingie are an unlikely duo that my children just adore. I wrote a post on how to use Life of Fred with kids of multiple ages here.
Sir Cumference books - These are engaging picture books that cleverly wind mathematical concepts into the stories. For instance, in Sir Cumference and the First Round Table, my children learned about diameter, radius, and circumference in a fun, easy-to-remember way. Sir Cumference and All the King's Tens introduced place value in a way that my daughter, especially, loved.
Anno's math books - Anno's books are beautifully illustrated and they show math concepts such as multiplication very clearly. My children especially love Anno's Magic Seeds, and Anno's Mysterious Multiplying Jar.
Math and Magic in Wonderland - This delightful book tells the story of two sisters and their magical adventures with math. I love that the language in this book is beautiful, that the storyline is interesting, and that the math problems are designed to elicit curiosity instead of boredom. The math problems in Math and Magic in Wonderland were too advanced for my 6-year-old son when we started reading this, but by age 7&1/2 he was ready to participate more. My daughter was 9-years-old when we started this book, and she enjoyed the math problems right away.
With Everyday Math, I look for opportunities to teach math in the context of real life. This allows my children to see that math is relevant to their lives. I don't get preachy about math in our everyday lives; rather, I just use math in meaningful ways as I go about my days, and I encourage my children to do the same.
Here are some examples of how Everyday Math can be used to teach math.
We have a thermometer outside our kitchen window that allows us to see what the temperature is outside. We use this daily to see if it is more appropriate to wear long-sleeves versus short-sleeves, sandals versus close-toed shoes, etc. Using our thermometer can also be tied into Nature Study since the children can observe that there is frost on the ground when the temperature is below freezing, that the humidity increases before it rains, etc.
We bake or cook together. I allow the kids to measure out ingredients using measuring cups and spoons, which teaches fractions as well as awareness of what different amounts look like.
When we are reading about something that mentions a size (such as the length of a snake or a distance that has been traveled), I take the time to put the measurement into context by comparing it to some known amount. The tiles in our house are 1-foot-across, so they can easily be used to see how long specific measurements are (and my daughter especially loves walking the tiles to see how large different creatures are). We relate distances to places we regularly visit [such as from the front of our property to the back, or to Grandma's house in Albuquerque (220 miles away), or to El Paso (40 miles away)].
The children help in grocery shopping by price-checking different items, counting and weighing produce, comparing prices, etc. I also send them on errands to get items from our grocery list. They thoroughly enjoy grocery shopping because they have real, meaningful work and purpose while we are at the store.