Wednesday, November 20, 2013

Are Standard Algorithms for All Students?

x 25
  Every so often I get asked to interview students who are enigmas in the classroom; students who are difficult for teachers to understand; students who, perhaps, do things slightly differently. When this happens I use one of the several Interactive math Interviews I have developed over the past ten years. designed to engage the student in a conversation with a purpose, the interviews provide a framework or jumping-off point from which the student's thinking can be thoroughly explored. 

As an aside, I recently came across this study at Florida State University  in which the researchers found out, after using up a 2.9 million dollar grant, that;

         "When early elementary math teachers ask students to explain their problem-solving strategies
         and then tailor instruction to address specific gaps in their understanding, students learn
         significantly more than those taught using a more traditional approach. This was the conclusion
         of a yearlong study of nearly 5,000 kindergarten and first-grade students conducted by
         researchers at Florida State University".

To me, this seems like studying whether it's raining or not but watching people week after week to see if there's relationship between  umbrella use and inclement weather. WHY WOULD TEACHERS NOT ASK STUDENTS TO EXPLAIN THEIR PROBLEM SOLVING STRATEGIES? Clearly, I'm not the only one amazed by this somewhat banal finding.

But to return to the remarkable 3rd grader. When asked to solve the problem above he said; "Hmmmm, four 25s are 100 so 40 are 1000". All in his head but was getting a bit confused so I suggested he write it down which he did. He then said "so, twelve 25s are 300 which leaves just one 25 which mans the answer is 1325". I was pretty impressed.

I probably should have given him one with "un-nice" numbers to see what he would do but I ran out of time. My hunch is that he would have worked out a similar way of doing it using his incredible understanding of number. The real question is; Should he have to learn how to do the Standard Algorithm since he will most likely be tested on it in the upcoming SBACS? 

What do you think?


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