Every research study I read reinforces my belief in the children's fable, "The Emperor's New Clothes".
Why is the truth about the need for practicing math skills so evident to everyone EXCEPT those who actually develop and implement education policies in this country, the so-called 'experts'? Is it arrogance, short-sightedness or simply a reflection of a society which has lost its way? Perish the thought that there could be a profit motive in promoting new approaches to learning math...
Think of your most "talented" students/children for a moment. They may think more quickly, display more insight, have greater abstract or spatial ability. But do they ever make mechanical arithmetic errors? No? Then they are truly the exception. Because that's not what I observe. I see a generation of youngsters who are now better at problem-solving yet lack proficiency with the, should I utter the word, BASICS. Why? You all know why!
THIS IS NOT A CALL TO BASICS. DON'T ANYONE MISINTERPRET THESE WORDS. IT IS THE SAME CALL I'VE ECHOED FOR DECADES. BALANCE CONCEPTUAL DEVELOPMENT/APPLICATION WITH SKILL/PROCEDURAL PRACTICE TO BUILD THE FOUNDATION REQUIRED FOR SUCCESS IN MATHEMATICS. BALANCE...BALANCE... BALANCE.
Of course we want students to inquire. Of course we want out students to use tools to analyze the vast amounts of data they now have at their disposal. Of course we want students to understand the WHY as well as the HOW. Of course we want to reach a variety of learning styles. Of course we want to use multiple representations in class. Of course we want mathematics to be interesting and useful.
BUT THERE IS NO SUBSTITUTE FOR PRACTICE. FOR EFFORT. FOR TIME. FOR APPLYING ONESELF. FOR SELF-DISCIPLINE. IN FACT, MATHEMATICS HELPS TO DEVELOP THESE QUALITIES!
So why isn't the obvious visible to the researchers and policy makers? I'm sure they'll tell you...
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