Post # 15 Early Thoughts and "Oh-h-h-"

An example occurred for me just the other week. I was working with a middle school student, a bright young lady, and she asked if we could work on decimals.  It quickly became apparent that she did not see decimals as fractions.  It is true that decimals can represent both rational and irrational numbers and so many teachers do not clearly make that distinction.  I am sure this child's teachers did all the correct representations using the hundred's grid and linking decimals to fraction concepts, but for this student it never really became clear.  She had never created decimals.  We do not cut pizza by decimals... or at least call those portions by decimal names. She needed some way to make the linkage in her mind. 

There it is again, that word "linkage."  For those of us trained in language it is a critical term.  This linking of new concepts to prior knowledge is so very important.  So for this young woman I knew the most effective teaching for this teachable moment, was to put things in her hands.  The entire concept took about twenty minutes.  

I first brought out the craft sticks, that beautiful bundle of one thousand and  along with hundreds, tens and ones.  We  placed them on a place value mat and spoke very quickly about the meaning of regrouping.  As we moved through the tracking activity outlined in your manual (Place Value) we whittled our quantity down to three.  I then asked her to show me two minus one half. 

Puzzled, as all students are, she asked me if she could break the stick.  "A woman's gotta do what a woman's gotta do," I said.  She did.  We renamed the new quantity two and two halves before "performing the indicated operation." 

At that point we transitioned to the base ten blocks, only this time after tracking I asked her to remove one tenth.  I had placed the clay unit cube among her units and I gave her the "handy dandy decimal fraction creator."  (Thank you Siena staff-who came up with the dental floss idea.)  She cut off her tenth, then another and another.  We renamed our quantities as we continued to cut that tiny flat into hundredths and that tiny hundredth into thousandths.  And when we cut the first tiny thousandth she said, "But it's so small!"  At that point I heard the response I most ardently await, "Oh....."