the misconceptions of PEMDAS is a great example of mindless memorization without a concept of number sense and process thinking

During off-times, at a long stoplight or in grocery store line, when the kids are restless and ready to argue for the sake of argument, I invite them to play the numbers game.

"Can you tell me how to get to twelve?"

My five year old begins, "You could take two fives and add a two."

"Take sixty and divide it into five parts," my nearly-seven year old says. 

"You could do two tens and then take away a five and a three," my younger son adds. 

Eventually we run out of options and they begin naming numbers. It's a simple game that builds up computational fluency, flexible thinking and number sense. I never say, "Can you tell me the transitive properties of numbers?" However, they are understanding that they can play with numbers.

Sometimes I engage my kids with a real-world context. "I have four dozen donuts and I just have three of them. Will I have enough to feed forty people?" They ask questions like, "Does each person eat one?" or "Is anyone allergic to gluten?" I might say something asking them to organize objects into arrays or I might ask them to double or triple a recipe when we make dinner.

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I didn't learn the rules of baseball by filling out a packet on baseball facts. Nobody held out a flash card where, in isolation, I recited someone else's definition of the Infield Fly Rule. I didn't memorize the rules of balls, strikes, and how to get someone out through a catechism of recitation. 

Instead, I played baseball. I learned the basics through conversation and then I asked questions and observed and remembered the vocabulary, structures, processes and concepts of the game by playing it. In the process, I memorized a ton of facts. However, the facts were in a context, deeply rooted in my own experiences being the Strikeout King. 

 I'm not opposed to memorizing facts. Somewhere along the line, I've memorized the various spells in Harry Potter, the positions on a football field, and the lyrics to my favorite songs. I've memorized lines from conversations, verses from the Bible, and "facts" regarding Social Constructivism, Social Constructionism and Social Connectivism. I never crammed for a test. I never wrote out the facts in isolation under the watchful gaze of a teacher with a timer. 

I learned these things through immersion, critical thinking, context and play.

Note: I use the word "facts" here loosely. I don't think baseball, history, poetry, math or science have "facts," per se. They have processes, experiences, concepts, connections, theories and structures. 

15 comments:

  1. I love this approach. Andrew's (my now 2nd grader) teacher did something very similar this year and he really thrived. It was new to me b/c my own education has been very traditional. I'm curious how you'd approach spelling instruction.

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    1. That's great to hear. I love it when teachers move away from the "this is how I was taught so I'll do it this way" approach. I'm glad he's thriving. BTW, someday our families will hang out. Someday.

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    2. Phillip, I can't speak for John, but I teach ELA at the middle school level. Although we don't teach spelling there, I would recommend eliminating it completely.

      Stephen Krashen studied language acquisition for 40 years, and he suggests that the best teacher of spelling, grammar and basic language skills is books. Put books in students' hands and teach them genre exploration, along with choosing books that fit their reading levels. Then, let them read and write daily. They'll become good spellers very quickly.

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  2. Another great post, John...I'll make sure not to create a new acronym--ICCP-- when I share with my math colleagues.

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    1. I don't know. There aren't enough acronyms in education. Maybe we should create some more.

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  3. Great post. When will we learn that all things are learned in the exact way you learned baseball? Sitting and worksheeting is a dead end (even if we call the worksheet a graphic organizer). Keep up the good work.

    Mike

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    1. I agree. Drill and kill worksheets do nothing to help improve critical thinking.

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  4. I think it's clear that you don't understand how math works, John. You've said so yourself that you were not a good math student. I think your embrace of New Math is a clear example of what's wrong. Too many teachers who hate math push for anything but pure, real math in schools. What results is a class full of "do what you want" mathematics taught by someone who neither enjoys nor understands math. It's a tragedy that ideas like yours have taken hold in public education. No wonder we're getting our asses kicked by Singapore every year in math.

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    1. Hey, anonymous, first of all, have the courage to put your name on your post. Second, you not only don't understand good teaching, it's clear from your reckless Singapore reference that you don't understand global education.

      John, like you, I always struggled with math -- probably because hard-headed people, like Mr. Anonymous here, weren't willing to leave the one-room school house and the math facts behind. Thanks for yet another thought-provoking post.

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    2. I understand math, and math education. I have not found anything to criticize in this post. If you would like to support more"rigor" or more memorization, please spell out what you think works well.

      But hey, John just wrote a great new post because of your criticism, so he turned your lemons into lemonade, I guess.

      I do agree with you that teachers who don't like math are part of our problem. I just can't imagine putting John Spencer in that category.

      What is "pure, real math", in your opinion?

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    3. Mr. Anonymous,

      It's probably worth noting that your example, Singapore, uses a problem solving approach to learning mathematics, rather than a focus on starting with the things students need to know before they can problem solve. They use problem solving as a vehicle to teach mathematics, much like John is describing here.

      See http://www.thedailyriff.com/articles/singapore-math-demystified-part-2-philosophy-216.php fpr a description of the philosophy behind the Singapore Math approach.

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  5. Hey Mr. Anonymous, is "pure math" memorizing the rules for how to add fractions? finding the area of rectangle? or any other type of calculation? Or is pure math knowing why you need to add fractions? why you need the area of a rectangle?

    When they leave school, what jobs will my students have where they need to find the common denominators of two fractions and add them together? Or will a computer do that part?

    What they WILL need to know, is, "Hey, I need to know the area of this rectangle to solve this problem." That's REAL Math!

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  6. Bravo, John. Making math meaningful is critical to true understanding of the subject.

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