math, Number Sense & Numeration

Understanding vs. Memorizing

When I was in elementary school my teachers regularly asked us to complete Math Mad Minutes.  These were sheets of math problems, usually just 1-digit numbers, and we had to complete as many as we could in just one minute.  Some years we did addition and subtraction, some years multiplication and division.  Sometimes we even had to do a Mad Minute that had a variety of operations on it.  When I first started learning how to become a teacher, my mentor teacher used these.  Children started with a sheet that had 20 problems, and if they could do all of those in a minute they upgraded to a sheet that had 30 problems!  The super fast kids got a sheet with 50 problems.

I hated doing these.

I remember having only one strategy:  I went through the Mad Minute, week after week, and did all the problems that had 0, 1, or 2 for an addend, subtrahend, or factor.  If I saw a number along the way that was a “double” I would do it (3+3, 6×6).  Basically, I memorized the location of the problems for which I knew an answer.   I have a clear picture of myself sitting in Mr. Goodrow’s 6th grade class and reciting to myself the answers to the top two rows of problems.  I was certainly memorizing a bunch of stuff but I wasn’t actually memorizing anything useful beyond the Mad Minute.

True confession:  In my first classroom as a teacher, I finally “memorized” the times tables for good. Nobody gave me a sticker when I could recite them all, but I did it anyway.  I was teaching math on a rotary to 90 fifth grade students every day.  I have a clear picture of myself standing at the whiteboard writing answers to multiplication problems and realizing there was a pattern to the answers.  I was 27. I was university-educated.  I feel quite confident nobody had every told me about these patterns.  It opened a door for me.

What if I had understood this sooner?  Sticking with the multiplication example (though I could also talk about how understanding addition and subtraction is equally important!) if I had understood these connections and patterns I’m sure division, fractions, decimals, algebra and statistics would have all come much easier for me.

I’m listening right now to a Ministry of Education “Town Hall” call.  People are advocating for spending the Primary grades memorizing facts. The thing is, nobody ever says, “In the Primary grades kids should just memorize words.  We’ll teach them to understand words, read sentences, and write sentences once they get to the junior grades.”  Sounds ridiculous, right?

So if you are at home at night and want to work on helping children memorize math facts, then go for it.  But in class, I have some really important foundations of understanding to build. I have concepts to connect, I have patterns to point out, and I have number sense to build. You will not find any Mad Minutes.  Do I want them to have facts memorized?  Absolutely!  Are we actively working toward that?  FOR SURE! But I’m not going to focus on this at the expense of spending time on building understanding.

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