Mathematics is mental play, the essence of creative problem solving. This is the truth we need to impart to our children, more important than fractions or decimals or even the times tables. Math is a game, playing with ideas.I discovered the Let's Play Math website a few years ago. I felt like my oldest son was learning his math skills just fine, but he was also learning to hate math with a passion. He dreaded every minute of math and was convinced he was terrible at math, despite my protestations. Ever since, I have been open to ideas to reveal to all my children the beauty and joy of mathematics, even though I've never felt certain I understood it myself. I recently joined the review team for new Let's Play Math books and was excited to read and review the updated version of Let's Play Math.
The book is divided into five main sections. The first one, "How to Understand Math," is one of the most valuable. It describes how mathematicians, people who revel in math, think about math. They play. It's not just about skills and arithmetic; it's about how people learn and the problems that have fascinated them for centuries.
Real mathematics is intriguing and full of wonder—an exploration of patterns and mysterious connections. It rewards us with the joy of the “Aha!” feeling. These characteristics make it easy to stick with real math, even when a particular concept or problem presents a difficult challenge. Workbook math, on the other hand, is several pages of long division by hand followed by a rousing chorus of the fraction song: “Ours is not to reason why, just invert and multiply.”"Playful Problem-Solving" explores math through stories, manipulatives, and solving interesting and challenging problems that are about more than just arithmetic. It's full of stories you can tell your children and games you can play together, describing interactions that are centered not around a school day but around family life. (All the problems mentioned have solutions listed at the end of the book.) "Math with Living Books" encourages parents to present math history with children, to trace the excitement of mathematical discoveries and advances over the centuries. Also, math concepts can be presented more interestingly than most textbooks in picture books, chapter books, and puzzles.
In "Let's Get Practical," the author describes what math might look like in a homeschool setting, starting with some of the ideas she herself has implemented. Buddy math, for example, involves taking turns solving practice problems and talking through the process. (I was particularly struck by this idea which I've used for years in reading but never considered for math.) Working through problems together is not about getting the right answer at all.
Our discussion is the important thing. The answers are an almost insignificant byproduct. Sometimes we don’t even bother to work out the final calculation because what intrigues us is the web of ideas: how can we think our way through this problem?She answers frequently asked questions and provides some descriptions of educational offerings, textbooks, and online resources for different ages. These are not homeschool curricula reviews, but rather highlights of materials she has found to be comprehensive, adaptable, or particularly useful for different subjects.
The "Resources and References" section begins with a booklist for parents and teachers and just gets better after that. There are probably hundreds of print and online resources mentioned including worksheets and lessons found online.
|A Table-ful of Math|
Reading this book, however, has made me consider challenging myself even more.
I'm considering adding a puzzle time or math read aloud to our "cultural studies loop."
I'm considering how to incorporate more time with me into math lessons with First Son and First Daughter. The author points out how families, especially homeschooling families, make family read-aloud time a priority; we read to our children and we ask them to read to us. When it's time for math, though, we send them off to another room with a book and then just point out all their mistakes. This accusation struck home. How can I maintain the personal connection with my children as they explore math without spending an additional two or three hours each day in one-on-one lessons?
I'm considering how we might take time every now and then, at natural breaks in our current math curriculum (with which I am still quite happy), to explore some of the intriguing ideas or websites mentioned in Let's Play Math.
I'm considering ways to foster a relationship between my children and math that encourages problem-solving for it's own sake rather than merely to get the answer to a question. I think most math worksheets and lessons inherently reward behavior that just gets it done. Get the answer right and you can move on.
We recognize that children are short-term thinkers, wanting to finish their school work with as little effort as possible so they can get back to the truly important things in life, such as Minecraft. We resist their efforts to turn math into answer-getting and insist on their taking time to explain and justify their conclusions.I've already decreased the time we spend on math facts and drilling for the younger ones and will continue to consider how to ensure we're memorizing the facts well enough to facilitate higher level math without drilling so much we damage the growing love of math. Let's Play Math acknowledges the necessity of learning math facts and practicing skills, but insists we must consider the larger goal when we decide on our methods.
Mathematical literacy is a worthy challenge. But most of us want more than literacy for our children. We want them to be educated. An educated person is interested in more than merely what is useful. He or she loves to learn, studies for the sake of gaining knowledge, and grows in wisdom.Math facts and skill practice are important but not sufficient. Mathematicians don't just add, subtract, multiply, and divide: they solve puzzles.
Instead, we need to introduce our students to the thrill of tackling tough, challenging puzzles. We need to give children a taste of the joy that comes from figuring things out, the “Aha!” factor. We need to adopt the mathematician’s view of math as mental play. Learning to think a problem through can be hard work—and that is exactly what makes it fun.Changing how we address math can be frightening, especially for parents that learned math in the very kind of environment or with the kind of attitude we're attempting to avoid. My oldest is in sixth grade and I feel like I'm just beginning to find our way in approaching math, even though we've been learning math all along. I believe I can establish a few small changes, a little at a time, and we'll see results in the end.
Don’t worry about taking a less formal approach to math in the elementary school years. If you are always doing something—reading library books, telling each other stories, enjoying math crafts, drawing geometric pictures, playing with calendar numbers, and so on—then your children will pick up an amazing amount of knowledge. As Julie Brennan explains: “Early exposure to real mathematics in natural settings, without requiring mastery of arithmetic on a set timetable—this has been a key to the ease with which my kids attain mastery when the time is right for them.”Here on the Range, I'm determined to establish an environment where math is not just numbers and answers. I firmly believe my children can learn all the math they want, when they're ready, as long as they don't convince themselves they can't learn it, they don't like it, or that it's too hard. To reach this goal, math must be a regular part of our lives in a way that encourages conversation and exploration.
Our kids can only see the short term. If we adults hope to help them learn math, our primary challenge is to guard against viewing the mastery of facts and procedures as an end in itself. We must never fall into thinking that the point of studying something is just to get the right answers. We understand this in other school subjects. Nobody imagines that the point of reading is to answer comprehension questions. We know that there is more to learning history than winning a game of Trivial Pursuit. But when it comes to math, too many parents (and far too many politicians) act as though the goal of our children’s education is to produce high scores on a standardized test.Let's Play Math could be the very introduction a young family needs as they contemplate the first few years of homeschooling. First Son's early years may have been completely different if I had read this book when he was five. It could be a fantastic book for a family with a child that's struggling (in homeschool or otherwise) with math. A few years ago, when First Son first showed signs of a potentially life-long hatred of all things numerical, reading this book may have helped me adapt the curriculum we were then using to meet his needs and enrich him. (We ended up switching and I'm happy with that, but I could have avoided quite a bit of angst.) This book would be perfect for a parent who has always struggled with inadequacies in math or for someone like me, who always did just fine in math but never understood the claims of math's beauty or fascination. I find myself excited to explore some of the resources the author has gathered together for my own growth and new challenges.
In the few years we have our children at home, we cannot possibly teach them everything they will need to know as adults. At best, we can give them the tools for learning and the ability to reason, so they can continue their own education. And one of the most important tools for learning is a solid understanding of real mathematics—math taught the mathematician’s way, as mental play.
THE GIVEAWAY - Win Your Own Copy of Let's Play Math
Denise Gaskins has graciously offered her book as a giveaway hosted right here at Our Home on the Range! She is providing an autographed paperback copy of Let's Play Math for the grand-prize winner AND an electronic version (winner's choice of Kindle, PDF, etc.) for the runner-up.
I'm trying something new here on the Range. Use Rafflecopter below to enter the giveaway.
- One comment and you're entered. Tell me your favorite math resource or, if you don't have one, that you need this book to discover one.
- Contest opens on Thursday, February 25th, at 7:00 am and ends at midnight on Monday, February 29th. (Central time - it's Kansas folks!)
- I'll email the winners on Monday or Tuesday and will choose new ones if I don't hear back within 48 hours - so be sure to watch your email!
a Rafflecopter giveaway
I received a free copy of a PDF version of this book in advance of its publication as part of Denise Gaskins's review program. This post is my honest opinion. The link above is an Amazon affiliate link. I receive a small commission if you click the link, add something (anything) to your cart at Amazon, and make a purchase in whatever time frame Amazon currently employs.