The Myth of Developing Math Skills Without Effort and Practice - A Rant

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...

Balancing the Equation: MathNotations Comment on edspresso

While I'm waiting for edspresso to approve the comment I posted last night, I 've decided to post it here first.

I was commenting on Barry Garelick's well-written post re the recent report from the National Math Panel: Living in a Post-National Math Panel World. This blog will eventually do a more in-depth analysis of the report but for now here is my comment...

Quoted from the edspresso post:
"There are also teachers who maintain a truly balanced approach and who, while rejecting the discovery-oriented and textbook-less programs being foisted on schools across the country, are admonished by their administrators to do as they are told."


My Comment:
Although now retired, I was one of these educators for the past several decades. I believe the Panel paid lip service to these educators. Mr. Garelick, just what benefit does this report have for this group of math teachers? There are many dedicated professionals who have always balanced the need for 'correct answers' with conceptual understanding. Educators who always knew that there must be mastery of essentials before one can move on in mathematics. Educators who continue to find creative ways to satisfy both their administration and their personal integrity...

The problem is that it is just not easy to blend skill practice, mastery and rich problem-solving experiences and explorations when one has to essentially create one's own materials. Particularly when the rewards for going 'above and beyond' are purely intrinsic in the teaching profession. Experienced math teachers know that computational proficiency is absolutely essential but, when confronted with problems that are not formulaic and require recognition of essential concepts and making connections, many of our students flounder. Yes, it is really hard to do the right thing, isn't it?

In your opinion how will textbook publishers respond to the Panel's report? IMO, skills-based texts that lack depth and neglect exploration and more challenging problem-solving would be just as damaging to this next generation as many of the reform texts have been. Perhaps such texts will not be the response to the Panel's report from textbook publishers. Perhaps...

But that's ok, the most dedicated of our profession will compensate for whatever materials they are handed. They'll continue to write their own and do what's right, just as they always have.

Dave Marain
MathNotations

What I should have added is that there was only one currently practicing teacher on the Panel. I have no evidence to indicate that the balanced approach to curriculum and instruction was represented at all on this commission. If that is the case, it would seriously detract from the credibility of this report. However, I will withhold further judgment until I've had a chance to thoroughly analyze the detailed recommendations.

Surviving the Math Wars - Both Ends Against the Middle

Identity Crisis...

I imagined the following dialogue taking place between a traditionalist (T) and a reformist (R) after both had finished reading the posts I've written on this blog for the past 6-7 months:

T: He is definitely a radical reformer. He uses phrases like investigations, explorations, discovery-learning, problem-solving, working in groups and encourages the use of the calculator for some activities. He is more concerned with conceptual understanding than with content and skills that all students must know. He actually believes that young children can think profoundly about concepts before they have completely mastered their skills. He talks 'less is more.' He has no documented research base for any of his wild ideas, and pretends that decades of classroom instruction are just as legitimate as a carefully developed research study. In what accredited journal of education research has he published?

R: Nonsense. He's one of your kind. He preaches strong foundation in basic skills, automaticity of basic facts, facility with percents, decimals and fractions and generally does not promote the use of the calculator in the lower grades. Other than some esoteric mortgage activity he wrote, most of his math challenges have little to do with the real world, focusing instead on number theory and combinatorial math, topics which are above the heads of most middle schoolers. His geometry problems are very traditional. He is often critical of calculator use. He focuses on standards and curriculum, even suggesting we need a nationalized math curriculum (and we know who will determine that!). He doesn't even applaud the efforts of his own national math teacher organization. He covers up his 'back to basics' approach by pretending he is a centrist. We all know one cannot be a centrist here. Either you're pregnant or you're not! He has no documented research base for any of his wild ideas, and pretends that decades of classroom instruction are just as legitimate as a carefully developed research study. In what accredited journal of education research has he published?

I know the regular readers of this blog know who I am and I know where their heart lies, but what can be done to move math education into a zone of reality that is sorely needed for our children. All these wonderful ideas but there is still so much confusion out there. How far have we come in the past dozen years or so to change the reality of a curriculum that is 'one inch deep and one mile wide'? Your thoughts are welcome...