Sunday, February 24, 2013

Teaching Math: What I Wish I'd Known...

Sittin' home this morning. Got a feverish kid whose only two requests are:

1. pickles
2. Brady Bunch

So in between pickle runs and echoes of "Marcia, Marcia, Marcia," I've been contemplating...

If I could give just one gift to new teachers or homeschoolers, I'd share what I wish someone had told me about teaching math.

Teaching Math: What I Wish I'd Known

1. There are many, many ways to solve problems. The "standard algorithm" that we were taught is just one way. (Imagine my surprise to learn that other countries teach other "standard" methods!")

Kids that are only taught to follow one method are at a severe disadvantage. Those who can select from a variety of strategies are able to chose the most efficient. When kids are given opportunities to test out many different strategies, they find those that work best for them. Which leads me to...

2. Trust kids. When my son started working on multi-digit subtraction, he didn't gravitate toward any familiar (to me!) strategies. When he discovered something that worked for him, I had NO. CLUE. what he was doing. He explained it to me OVER. And OVER. And OVER. I couldn't do it his way. But he could. And fast. He found his own path; had I chosen one for him, it's doubtful that my choice would have been such a perfect match.

3. Manipulatives and visual models matter. A lot! When I first saw all the pattern blocks and base ten pieces and tile and...and...and...I wondered if all this STUFF could really be anything more than glorified toys. But manipulatives and visual models have changed my life. Now I can see a multiplication problem in my head and solve it mentally thanks to base ten pieces. I can figure fraction problems after experiencing them in egg cartons, geoboards and pattern blocks. The number line--once on paper, now in my head--makes addition and subtraction fast. It would have been so much easier if I'd been taught this way in the first place.

4. Cool books make concepts come alive. Had I known about all the awesome math-related children's literature, I might have pursued math education a long time ago!

5. Teaching math is about so much more than numbers. For example, the Common Core Standards for Mathematical Practice emphasize the "doing" parts of math...things that often apply to areas of life beyond math. Who wouldn't want kids to "Make sense of problems and persevere in solving them" or "Construct viable arguments and critique the reasoning of others." Good math teaching prepares kids for a lot more than math!

What do you wish you'd known about teaching (or learning) math?

Also, a great post for further reading:

From Teaching My Baby to Read - the author talks about teaching math from a constructivist perspective. She begins, "I teach math from a Constructivist perspective, which means enabling children to develop their own meaningful strategies for solving problems, instead of just blindly teaching traditional algorithms. I believe in giving children time, space, and materials to explore mathematical concepts and create their own understanding, before you start imposing your own thinking upon them." Find the entire article here.

Credit for the graphic goes to!

And the problem solving for the many pickles can a kid eat before he starts to pickle? Or how many Brady Bunch episodes can a mom watch before she cries Marcia Uncle?


  1. Great reminders! I am a firm believer in the concrete, to pictorial, to abstract model. Manipulatives and visual models are so important!

    Eclectic Educating

    1. Amy, you are spot on and so lucky that it's a reminder and not new. This was all new to me when I started. How did you learn about it?

  2. Have you read any of Katherine Loop's stuff? She writes about Math from a Christian perspective. Her website is called She talks about the way different cultures have represented numbers and operations and even different equality signs. Reading her book, Revealing Arithmetic, helped me to allow my son to do a similar thing to what your son did. We had a difficult time with 3- and 4-digit multiplication, and I finally let him do it his way. It's backwards from my way, and he keeps the full value of the numbers instead of just using the digits as place holders. It isn't faster than my way, and it takes up more space, but it's the only way he can do it right now. It was hard for me to let go of my way. But reading her book helped me to see that there was more than one way to do it, and it didn't have to be the standard algorithm.
    I have gotten much better at Math and number sense since I started homeschooling! I'm sure age and experience have helped, too. As well as reading Katherine's stuff and great Math blogs like yours!

    1. Thanks, Penney! I'm not familiar with Katherine's stuff... I'll go look her up now. Your experience with your son sounds VERY familiar! :)

  3. I've taught on both sides of the fence. I homeschooled my daughter and now I teach in public school (first grade). Math is tough for some kids. Providing them an arsenal of ways to approach math problems, and then letting them choose which is best for them is so, so, so important. I'll be back to link up tomorrow!

    The Lightbulb Lab

    1. You are absolutely right! And so glad that you're linking up! :)

  4. Great tips! I wish I were taught mental math before the procedural paper and pencil method. Our daughter can manipulate numbers by decomposing and composing numbers in multiple ways before ever having to do them on paper.

    1. Oh, I wish I was too! Your daughter is so fortunate!

  5. A new homeschooler here and wondering what curriculum you found most helpful for students struggling with math? I have two children (middle school) who find the current way we have been doing, difficult to say the least!
    Thanks for the tips :)

    1. Hi Rach!

      Rather than naming a specific homeschool curriculum, I would encourage you to look for something that has the kids using visual models and manipulatives. As Amy said above, you want something that moves from the concrete (hands-on) to the pictoral (perhaps drawing or sketching but using a visual model that builds on what they experienced in the concrete) before moving to the abstract.

      If kids are forced to learn the abstract--particularly step-by-step algorithms--without the benefit of the concrete/visual, they likely don't have any mathematical reasoning behind what they're doing. Some kids can fake it well because they're so good at memorizing. Others can't (because they can't memorize the algorithm), but either way, it's likely to eventually catch up with both groups if they don't understand what's behind the math. Hence the reason so many kids do well on standardized testing at young ages and then plummet as they get older.

      So again, look for visual models and hands-on. Look for curricula that encourages kids to try multiple strategies to solve problems...preferably methods that they've experimented with themselves.

      Hope that's helpful. You can grab a lot of free Bridges lessons on the MLC site to get an idea of what good math curricula looks like. It's not packaged for homeschoolers, but it's awesome and you can use the free stuff to help you start to get a feel for what to look for.

      Hope that gives you a start!


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