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An innocent recent post, Two SAT-Type Percent Problems Appropriate for Middle School as well..., generated some intense and passionate opinions about the current state of US education, math in particular, from one of our readers, affectionately known as Curmudgeon (I'll abbreviate his name as CM).
Unless you subscribe to my Comments feed (see link in sidebar), you might not have followed this dialog so I've decided to post a link to these comments and to copy some of the more provocative ones in this post.
Based on his comments I find CM to be highly informed, articulate and not intimidated by anyone. He eloquently challenged my difficulty rating system for the SAT-type problems I have posted and he made some excellent points. Re curriculum/instruction, his perspective is somewhat similar to mine although I lean a bit more toward a balanced view. A direct quote describing his blog summarizes his beliefs very well.
"I believe that mathematics should be taught, not collaboratively explored; algebra and geometry are better than a vague course of Integrated Math; spiraling doesn't work nearly as well as learning it properly the first time; "I don't DO math" should be an incentive rather than an excuse. "I don't DO English" should be treated the same way."
I encourage you to visit his blog, Curmudgeon.
Below is CM's long response to my remarks about the teaching of the part:part construct which, IMO, receives far less emphasis in classrooms than part:whole approaches.
Rarely taught? Probably, for three reasons. The first is that teachers are under pressure to "finish" things, to check off the standard and move on, to "get through" the material. As soon as the kids "know" the material, it's time to move on. There is rarely time for the extensive exploration that I seem to recall from my own days. Standards-based educational theory says that you need to pick and choose your topics until you get each kid to the understanding point but says nothing about total mastery. "Drill and kill" is an epithet. "Drill and Practice" is unknown. Many people have also fallen for the "spiraling" fad and never quite complete a thought before they're on to the next one. "We'll spiral around to this again in that module in next year's course" is probably the dumbest thing ever to come out of edumacation colleges. I can't tell you how many times (because I've lost count) I and the other teachers have been told that we needed to get our "bubble" kids over the line into the passing zone. "To hell with knowing math, just know enough for the test" seems to be the rallying cry. The upshot is that you can mention these things to the better students who will get it easily and gain an even better understanding. The weaker students just trundle along. The second reason is that weaker students are resistant to trying a second or third idea. They want to understand THIS one. A second approach is confusing. It takes a while before they get comfortable with multiple approaches and some never get much beyond "I'm not a good math student. I'll learn this but only to a point." It takes a determined teacher to ease them into this, but she can't have anyone breathing down her neck to do test-prep. The worst reason is that a fairly large percentage of our teachers don't really understand math to the level required. They've either bought into failed and worthless education theory or they simply are stupid. I've related the story of the fourth grade teacher in the in-service this year ... Me: "You say you want to be a guide on the side not a sage on the stage, yet you're teaching 4th graders. You still need to teach them things. They have to memorize 4*3 for example." Her: "No. We should be teaching them how to look that up on Google. Did you know that Google will give you the answer to that? It's true." She leaned back, satisfied that she had put one over on me. Is it any wonder that her kids arrive with no understanding of fractions, decimals, percents, operations? "Where's the fraction key?" "Sorry, that calculator doesn't have one, the problem you're doing doesn't need one and you wasted more time than if you just looked at it and solved it." And some elementary and middle-school teachers "just don't DO math, tee-hee-hee." They SEEM to do math - they have lots of test-prep bubbling exercises from the publisher of the math book, but they fundamentally don't understand the nuances of the material. "Let's see what the calculator says." In a different in-service this year, the presenter was showing how pre-schoolers and elementary kids learn math. She had lots of visuals and was "teaching" the teachers as if they were students. The aides were getting questions wrong and the elementary teachers weren't doing too much better. This explains a lot.
To read my response (aka, "rant'), click on Read more...
To read all the comments to this post and/or post a comment, look here.
May I call you C.M.??
I'm not going to say something inane like "I feel your pain." Most of the angst you expressed is a reflection of what I was feeling when I retired. You're describing a system that is in dire need of systemic change, not tweaking.
I will not apologize however for my advocacy of national standards in math. It is unconscionable that students across the country are not learning the same content - concepts, skills, procedures, terms, definitions,... This is truly inequitable.
However, I have also been preaching "LESS IS MORE" for the same period of time. Finally, NCTM has taken this position with their Curriculum Focal Points document. William Schmidt (of TIMSS renown) stated this obvious fact 15 years ago when he described our math curriculum as "one inch deep, one mile wide."
We cannot expect students to learn math well if we fill our textbooks each year with every topic under the sun. If, for example, our teachers could focus on the essential ideas of ratios and ALL students were required to solve a range of problems from the basic to the more challenging, then most students would eventually learn ratios and be able to handle fractions. BUT facility with ratios and fractions requires facility with division which requires mastery of multiplication, etc.
"Jack, you will learn the times tables. The facts you got wrong in class today, you will have to write five times each for homework tonight. Tomorrow, I will ask you to answer just those." I know there are some teachers out there who are doing this. Is everyone?
While base ten blocks, unifix cubes and learning software have their place, we all know that nothing replaces repetition. Some students need far less than others but all students need some.
Yes, C.M., there are serious teacher preparation issues out there. Read my comments at the bottom about Finland. Yes, C.M., I share your feelings about spiraling, although there are aspects of spiraling which make sense.
I am also concerned as you are that standards-based learning has devolved into learning only for the state assessment. While we are moving toward national standards, we have to rethink how we will evaluate student learning and the bottom line is: "WHAT IS THE REAL PURPOSE OF TESTING?" What you and I and millions of other teachers see is that testing has little to do with helping children improve. It has everything to do with POLITICS:
"MY DISTRICT IS BETTER THAN YOURS; MY STATE IS BETTER THAN YOUR STATE; LET'S HOLD THOSE D*** TEACHERS ACCOUNTABLE FOR THOSE 'HIGH' SALARIES THEY'RE GETTING PAID"; "WE HAVE TO JUSTIFY ALL THAT TAX MONEY WE PAY FOR EDUCATION."
Remember that quote:
"In other countries, education is seen as an investment; in the US, it is seen as an expense."
Perhaps this administration will "see" it differently. I truly hope so. In Finland, teachers, have to take additional years of training beyond college before they officially are certified. This additional 2-3 years culminates in a year of working in a laboratory school with real students. A true internship. And, by the way, THE GOVERNMENT PAYS EVERY PENNY FOR ALL THIS ADDITIONAL TRAINING. This is how Finland has turned around its system in the past 20 years.
INVEST IN EDUCATION, INVEST IN OUR CHILDREN, INVEST IN OUR FUTURE. Don't look for short-cuts, folks. There are none. Expedient solutions lead to students who only care about the bottom line, the grade, not about learning. This "get results without really earning it" mentality is pervasive in our society. In the worst case, this mentality produces the AIGS, the Enrons and the Madoffs of the world.
Ok, now you got me to rant too. I guess I needed that catharsis. otherwise it sounds like I'm just pontificating about challenging our best and brightest with all these problems I'm writing. But there's so much more to it, C.M...
P.S. I have a feeling that your comments and mine are not being read by most of my readers. I'm thinking I should copy them into a separate post and really incite a riot! I think I will do that unless you state an objection! THANK YOU!
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