WSJ Article Calls for National Standards, Complete Overhaul of Public Education

If you haven't had a chance to read Louis Gerstner's compelling piece from the Dec 1 Wall Street Journal, entitled Lessons from 40 Years of Education 'Reform,' here is the link. Mr. Gerstner is the former CEO of IBM and Chairman of the Teaching Commission from 2003-2006.

I'll leave it to the readers of this blog to decide if some of Mr. Gerstner's major suggestions echo the positions taken by this blog for the past two years.

Mr. Gerstner's article is not just another set of opinions -- it is a call for drastic change and immediate action. It will surely be controversial. I do not necessarily agree with all of his statements and/or recommendations but I agree with the 'core.'

Perhaps, the time for change has come to American Education...

Here are some excerpts -- I strongly urge you to read the entire piece:

I believe the problem lies with the structure and corporate governance of our public schools. We have over 15,000 school districts in America; each of them, in its own way, is involved in standards, curriculum, teacher selection, classroom rules and so on. This unbelievably unwieldy structure is incapable of executing a program of fundamental change. While we have islands of excellence as a result of great reform programs, we continually fail to scale up systemic change.

This is a complex problem, but countless experiments and analyses have clearly indicated we need to do four straightforward things to bring fundamental changes to K-12 education:

1) Set high academic standards for all of our kids, supported by a rigorous curriculum.

2) Greatly improve the quality of teaching in our classrooms, supported by substantially higher compensation for our best teachers.

3) Measure student and teacher performance on a systematic basis, supported by tests and assessments.

4) Increase "time on task" for all students; this means more time in school each day, and a longer school year.

Therefore, I recommend that President-elect Barack Obama convene a meeting of our nation's governors and seek agreement to the following:

- Abolish all local school districts, save 70 (50 states; 20 largest cities). Some states may choose to leave some of the rest as community service organizations, but they would have no direct involvement in the critical task of establishing standards, selecting teachers, and developing curricula.

- Establish a set of national standards for a core curriculum. I would suggest we start with four subjects: reading, math, science and social studies.

- Establish a National Skills Day on which every third, sixth, ninth and 12th-grader would be tested against the national standards. Results would be published nationwide for every school in America.

- Establish national standards for teacher certification and require regular re-evaluations of teacher skills. Increase teacher compensation to permit the best teachers (as measured by advances in student learning) to earn well in excess of $100,000 per year, and allow school leaders to remove underperforming teachers.

- Extend the school day and the school year to effectively add 20 more days of schooling for all K-12 students.

MATH WARS - Advice for Parents

A few weeks ago I received a request for an interview from Jan Wilson, education columnist for The Parent Paper, a local publication here in northern NJ:

Hello Mr. Marain --

I am the education columnist for the Parent Paper and I am writing an article about math instruction, specifically about moving beyond the rhetoric of the math wars to discover which ways of instruction work best for K-5 students. It's going to be a fairly general article, designed for the parent who hasn't thought a lot about math before but becomes concerned because her child hasn't master times tables in 3rd grade, or isn't doing long division in 4th, for example.

The following is the reply I sent Jan from which she excerpted a few of my comments:

I am speaking both as a parent and a mathematics specialist with over 35 years in mathematics education at all levels. I have also been publishing a blog for math educators for the past year and a half. It was recognized by the Washington Post as one of the Top 10 Educational Blogs for 2007. Despite all the rhetoric, there are no bad programs out there in my opinion. The reform programs like Everyday Math and TERC do a fine job of developing children's number and spatial sense and address problem-solving as well. However, the district has to be committed to the expectation that children will practice their basic facts on a daily basis. Some children will master their times tables by the end of 3rd or 4th, some later on. However, they should all be expected to learn it by the end of 4th, even if some youngsters will take longer. Parents should not hesitate to ask the teacher and/or the principal if these expectations are in place. Further, they should ask if children are given some form of practice both in class and at home on a regular basis. Some children will learn from flash cards, others need to write each fact 5-10 times, others can benefit from games or software. Excellent online games like Timez Attack from Big Brainz can be played both in school and at home. The free version is quite good, but it will not work for every child. The only constant is that the expectation of learning these basics is stated in the currlculum and that this philosophy is actually implemented. If children's learning of basic facts is assessed regularly in class, then one can reasonably assume there is follow-through. Sometimes the only way to be sure of this is to talk to parents of children who have been through the program. Just remember: Playing games and problem-solving do not replace the need for children to memorize their facts. There is no way to get around this. If the district math program does not incorporate sufficient practice, then parents will need to supplement fact practice at home, even if it's only 10-15 minutes a day. Each child learns his/her own way, but each child must do something every day, using a reward system if needed to motivate them. In addition to skills practice supplementing existing programs as needed, parents should ask what kinds of problem-solving materials are used. Is the source of these problems restricted to what is provided by the publisher or are other resources utilized? For example, are teachers provided with the problem books from Singapore Math, which generally contains more difficult challenges than are normally found in our texts. Another question parents can ask if there is a new program is, "How have or will teachers be trained?" Is there a full-time Staff Developer working with teachers? Is there a math specialist for K-5 or 5-8? Short-term staff development is not nearly as effective as ongoing training, both for experienced and new teachers. It is important for parents to be aware that NJ Ask and other state testing will be undergoing significant changes in response to the recommendations of the National Math Panel, NCTM and organizations such as Achieve. All of these groups are calling for a reduction each year in the number of topics covered so that there will be more time for children to work toward mastery of important skills AND to develop greater depth of understanding. Teachers will be able to devote more time to provide both enrichment and reinforcement. This is an exciting opportunity. The Math Wars have been fueled by extremists on both sides. In the end, our children need a more balanced math education which will incorporate the best of the traditional and reformed.

Remember, I was writing this primarily for parents. These comments represent the same positions I have taken for the past 20 years and for which I have been challenged (a euphemism for attacked) by both "sides" for the same 20 years! Hey, I may be wrong but at least I am consistent!

Edspresso Reply from Barry Garelick and MathNotations Latest Response

A few days ago I posted on MathNotations a comment I had left on Edspresso, a reply to Barry Garelick's essay, Living in a Post-National Math Panel World.

My post was entitled, Balancing the Equation.

From edspresso:

Barry Garelick is an analyst for the U.S. Environmental Protection Agency in Washington, D.C. He is a national advisor to NYC HOLD, an education advocacy organization that addresses mathematics education in schools throughout the United States.

I just replied to Mr. Garelick's reply to my original comment. Unfortunately, I received the following automatic response from edspresso:

Your comment submission failed for the following reasons: In an effort to curb malicious comment posting by abusive users, I've enabled a feature that requires a weblog commenter to wait a short amount of time before being able to post again. Please try to post your comment again in a short while. Thanks for your patience.

I assume I will be able to re-post that comment in another day or so, but I thought MathNotations' readers may want to see a preview.

Here is my original comment to Mr. Garelick's post and his recent reply:

"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."

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 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 intrisic 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 neglect exploration and more challenging problem-solving would be just as damaging to this next generation as many of the reform texts have been to the current generation. Perhaps such 'skills' 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

Posted by: Dave Marain | April 9, 2008 08:17 PM

Mr. Garelick's Reply:

Mr. Marain,

Thank you very much for your comment. I've seen your writing on MathNotations and am glad you wrote.

I am aware that there are people who hold that "problems which are not formulaic" are not well-addressed by teaching students the components of math and algebra delineated in the NMP's report. Such problems are the so-called "messy" problems that have a range of answers or are open-ended, and so forth. Problems such as the "work" problems and others in math textbooks are held in disdain and thought not to lead to problem solving skills. Proper presentation of the solution of say, work problems, however, opens the door to "rate problems" in general, and which generalize to the solution of a great many problems in engineering and science. In fact, many of the standard so-called "formulaic" problems in algebra and other math classes are widely generalizable and have their purpose as I can attest as one who majored in math and work in a field that requires knowledge of scientific and engineering principles.

Providing students the opportunity to solve non-formulaic problems does not in and of itself prepare them to solve problems. Analytic and procedural skills and knowledge of form, which generalize do in fact provide such preparation. I tend to think the term "balanced approach" is one that is not well defined. I used the term "true balanced approach" in my essay, meaning an opportunity for student-centered instruction (such as discovery) that makes use of prior knowledge, rather than the melange of "just in time" skills, procedures and concepts that some teachers, textbook writers and policy makers seem to think students will discover because they need them to solve a problem.

It is my hope that those teachers who use textbooks that are written topics presented logically, sequentially, with expectation of mastery, and which builds upon concepts, will not be punished for doing so. Vern Williams who I quote in the essay is one of those teachers. He gives students very tough "out of the box" problems that are not in the textbook necessarily, but he makes sure they have the requisite skills and information (which he imparts via instruction) before giving them such problems.

Posted by: Barry Garelick | April 14, 2008 11:06 AM

Here is my latest reply of 4-18-08 which was temporarily rejected:

Dear Mr. Garelick,

Your quote:
"I am aware that there are people who hold that "problems which are not formulaic" are not well-addressed by teaching students the components of math and algebra delineated in the NMP's report."

My quote:
"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..."

I never suggested that direct instruction of powerful models such as rate problems is not desirable, nor do I hold these traditional rate problems in disdain. In fact, in my classroom, I always used the same RATE X TIME = DISTANCE chart that I learned in high school, several decades ago. The emphasis on my blog is on rich open-ended investigations that one normally does not see in most textbooks. Problems that teachers have to search for in most cases. Most of my regular readers know that success with these problems require a strong base of skill and knowledge of traditional algorithms. I've stated this repeatedly.

Consider what happened when the AP Calculus Exam changed dramatically a few years ago. The tried-and-true methods still were needed and still were assessed. But the test changed dramatically from an emphasis on technique to an emphasis on application and deeper understanding of fundamental concepts. The decline in scores was predictable and occurred until textbooks and instruction were revised to address this shift in focus. The most capable students were able to 'generalize' from formulaic problems - they always will. However, the scores on the AB Exam initially reflected that many others could not. It has been my experience that students perform well on non-routine problems when they have that strong base of skill AND experience with many nonroutine problems that require more than a superficial understanding of content. When presented with such problems, students need TIME TO EXPLORE. Direct instruction initially will usually fail in this case. After giving a reasonable amount of time to grapple with the problem and discuss it, the solution is explained clearly and thoroughly, with alternate methods presented if time permits. One cannot rush this process, that's why it is called a process...

That's my definition of 'balance.' There's nothing fuzzy about it. I've never suggested that students be given challenging problems and left entirely to their own devices to invent something out of nothing. I have suggested they need to know their trig values, their trig identities, their differentiation and integration formulas well. After they have demonstrated this KNOWLEDGE, they can be challenged with problems they have never seen before. Exploration does not mean one is "a blind man, searching in the dark for a black cat." (Luv that Escalante quote!). Exploration means that one is PREPARED to explore and then given the OPPORTUNITY to EXPLORE!

Me. Williams and I share many common beliefs about teaching. But he doesn't represent even a majority of math teachers out there. This is why I repeatedly emailed the Panel asking for more frontline teacher representation on the NMP (and, of course, I was politely dismissed). There was not a single high school math teacher represented, not to mention an underrepresentation of research mathematicians.

I appreciate your thoughtful reply, but you attempted to pigeonhole my beliefs. No one yet has been able to do that and I'm afraid you did not succeed either! I welcome an opportunity to discuss this further with you, perhaps in another venue. How about a debate on my blog? We'll probably discover we have far more in common than one might think.

Oh well, nothing has changed. Does anyone out there really get my balanced perspective, other than my faithful readers of course!

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.

A Statement of Personal Philosophy re Math Wars, etc...

Although I have long espoused national math standards (as is well-documented on this blog), I have steadfastly refused to engage in the vitriolic rhetoric of the Math Wars. Despite the fact that I live 7 minutes from Ridgewood, NJ, a community that has recently found itself in the eye of the Math War storm, despite the fact that I was directly involved in developing the Mathematics Content Standards for New Jersey (working with Joe Rosenstein), despite a myriad of reasons for me to comment on this latest conflagration, I choose not to. This blog is all about MATHEMATICS CONTENT and PEDAGOGY. Mathematics is essentially pure and I will not taint it with political issues. If you want to read controversial statements about what we should teach and how to teach it, there are dozens of blogs and forums you can visit. You will not find it here. If you want meaningful discussions of real mathematics that transcend the moment in which we live, keep coming back. I hope to not disappoint you. I might not get the volume of readers by this decision, but my conscience will be clear...

Stay tuned for an in-depth treatment of recursive functions for grades 7-14. I hope you will enjoy Part I.