Thursday, April 10, 2008

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

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.


Joshua Zucker said...

You write "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."

I disagree. They're far more damaging.

The reason is that an average teacher simply CANNOT find good and appropriate supplementation for exploration and challenging problem-solving, while they can easily find good supplementation for skill development or even create it themselves.

I suspect even you will tell me that if you had a book full of great problems, you could easily find ways to give extra skill practice, while if you had a book full of skill practice, it would take a lot of work to find or create great problems.

I still aim at the perhaps unattainable ideal of a curriculum full of great problems, the solution of which requires practice in just the right skills. That is, my goal is to make the skill practice invisible by talking about it only in the context of interesting problems. Even if I never reach it, that keeps me heading in a good direction.

Dave Marain said...

Yes, Joshua, even I will concede that point! Unfortunately, most educators will use essentially the materials they are given and follow the curriculum as prescribed. If one is told that non-calculator computational proficiency with, say, fractions or percents is just not that important, what do you think will happen over time to those skills?

Although one COULD easily find such supplemental practice materials, do you really believe that this happens in most cases? Particularly if one is told that state testing will emphasize a,b, and c, in favor of d,e, and f. If assessments reflected this balanced view then I would not be as concerned.

There's no question in my mind that the Joshua Zuckers of this world know how to combine the best of both. But are you the norm, Joshua?

Younger teachers today have been raised on a steady diet of problem-solving, reasoning, communication and connections, which is the best of NCTM's original 1989 document. But these teachers were not told to continue to expect proficiency with skills and algorithms (You know I'm not talking about 3-digit divisors in long division!). Yes, it is possible for students to develop and maintain essential skills in a problem-centered curriculum. But that's not what most of us have been seeing in our classrooms for the past 2 decades.

Strong students can generally overcome lack of skill practice and find a way to do the calculation when needed. Others cannot...
And, yes, Joshua, I believe that there are arithmetic skills and algebraic skills that simply cannot be learned well without a reasonable amount of practice. Not worksheet after worksheet of mindless drill, but certainly more than they are getting now. Joshua, how did you become proficient with your skills in arithmetic or algebra? You saw it once, practice 2-3 examples and it was yours forever? As for me, I needed a bit more practice and hard work than that.

A separate but equally important question is:
With technology, what are the computational and algebra skills needed in the 21st century? Surely, it has changed from the past 100 years, but just how much of that foundation that you and I received has become obsolete?

Joshua Zucker said...

"Joshua, how did you become proficient with your skills in arithmetic or algebra? You saw it once, practice 2-3 examples and it was yours forever? As for me, I needed a bit more practice and hard work than that."

I think this is a fascinating question. Yes, of course it takes practice and work. But I think we make a big mistake by saying that a certain skill is the province of a certain year and the skill should be theirs at the end.

In other words, I sure didn't know trig when I took the class. Maybe around multivariable calculus I had used it enough to be good at trig. But then, there were huge holes in my trig knowledge because there's a lot of stuff I just hadn't used. Makes me wonder if that stuff is actually important! Then, of course, I filled in those holes by tutoring or teaching, learning as I went.

I think we'd do a lot better to focus down to a smaller number of really essential skills and to see those skills USED (not just reviewed) year after year, so students HAVE to see them (not in a practice sheet but because they need them to do whatever the new goal for the year is).

I guess what this really means is I need to sit down and write a K-12 curriculum to illustrate this! Or maybe K-16? That'll take me some time though.

Dave Marain said...

I knew it - we're not on different pages after all!
Essential skills, review through application and use. Exactly why I started this blog. Let's write that curriculum, Joshua!

I was watching Mario Chalmers make the miracle shot for Kansas vs. Memphis the other night and I was thinking: Is this the first time Mario ever made that shot? In practice? Under game conditions? Of course, it was remarkable under those intense conditions but I happened to see an AAU tape of Mario when he was maybe 15 or 16 and guess what -- he made that shot repeatedly. Perfect form, all net... Ok, not an ideal metaphor for math skills or performance, just an observation about luck vs. skill...

vantilburgindo said...

Please, please, please...write that curriculum, Joshua and Dave! Parents like me (and their children) would be eternally grateful.

My kids go to an American school in Singapore that uses Everyday Math for K-5, then goes more traditional in middle school. Without getting into arguments over the benefits/drawbacks of either, it strikes many parents here that something different is needed that combines the very elements you two are discussing.

Thanks for both of your thoughtful comments.

Cheryl vT

Dave Marain said...

Thank you for that vote of confidence and I know Joshua would say the same. My family keeps telling me to write that book instead of this blog! If I could figure out how to do both, that would be great. Seriously, if i start this project, what grade level should I start with? 4th? 5th? 6th? My expertise is more from Grades 5 and up as opposed to K-4.

I am interested in knowing why Singapore Math is not used in your school from the beginning. Are you happy with Singapore Math? Are there any omissions? Certainly the problem-solving materials are outstanding, but is there something else you'd like to see?

mathmom said...

Start as young as you can! I would say 3rd or 4th is a good time to start getting serious about problem solving, though as you know I start them at 5yo! But, if you only felt comfortable doing it for middle and high school, it would still be an awesome contribution.