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Friday, May 4, 2007

Sweat the details...

`I met with a parent and tutor this pm about the progress of a student.This student is perfectly capable in math, has strong procedural knowledgeand has a long history of being successful in math.The grade began to slip in the later years of middle school in large partbecause of a lack of attention to detail. In other words, such a reliance onmental math and on "getting it" easily in earlier years had not allowed thisstudent to develop strategies to use when the answer came out wrong.Consider what is valued in algebra.Balancing equations or solving for a variable,for example.There can be many steps one has to go through before successfully finding thecorrect asnwer.One small error in arithmetic along the way, and your answer is not correct.Your procedure might be impeccable,and yet, you not only don't get the correctanswer, but you did not leave enough clues along the way to discover what wentwrong. You feel lost, confused and quite possibly, inadequate for the task at hand.In the end, you might walk away from the problem in frustration and think you arenot "good" at math, which would be a sort of "logical"(given your level of frustration and confusion at this point) yet inaccurateassessment of our algebra skills (you did the procedures correct, on you messedup on one little, itsy, bitsy arithmetic detail.Therefore:SWEAT THE DETAILS.If you make "silly" arithmetic  mistakes in doing an exercise about a newconcept you are learning, you will initially get the wrong answer, but if youleft tracks in the sand (i.e.: you wrote downyour steps in a neat and systematic manner), you can double back and rectify.SO: check each step.It's really easy even for a Ph.D. in math to multiply 6*7 and get 56 if(s)he is not being careful. These are just details, but alot of math IS details.There are some important  concepts, but there are lots of details.In order to learnthe concepts, you mustsweat the details.Algebra has some interesting ideas and techniques, but if you are not careful anddon't use the tool of arithmetic reliably, you are not going to see what algebrahas to offer.That would be a great shame!!!!`