MathNotations

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.

Posted by Dave Marain at 1:32 PM 7 comments

Labels: balanced view, national math panel, personal philosophy

On March 13, 2008, the National Mathematics Advisory Panel presented its Final Report, Foundations for Success, to the President of the United States and the Secretary of Education.

As with any education report there is a both a technical and a political aspect. Each of us will view this type of document through the lens of our personal bias. As much as I'd like to believe I am fair and objective, I know that I bring my own perspective to this as one who passionately believes that one can expect both mastery of skill and conceptual understanding, the what, the how and the why. Instruction that combines skill practice with rich problem-solving and exploration. I know I am not the only one who holds these beliefs and, to me, they are self-evident.

Since the inception of this blog 15 months ago, I have not wavered from this view. You can see this in the many letters I wrote to the National Math Panel which have been published on this blog to my interview of Prof. Schmidt, to my interview with Prof. Steen, to my post in Jan 2007 describing the genesis and reason for this blog. Repeatedly I have called for more coherence and consistency in K-8 math curriculum and beyond. Repeatedly, I have asked those in a position to make a difference to listen to our dedicated professional educators who have always known the truth of what is needed for our children's math education. Perhaps some of this has not fallen on deaf ears...


You may want to view the short video of an interview with Dr. Larry Larry Faulkner,
the chair of the National Mathematics Advisory Panel. In it, he discusses the key findings of the panel, published in their recently released report.

In this post I will summarize and comment on this video interview. In later posts, I will comment on other aspects of the report.

Highlights of Dr. Faulkner's Comments
(much of this was taken verbatim from the video):

(1) We need to streamline mathematics education in the years leading up to algebra
(2) Streamlining is needed because it is well-known both inside the US and outside that we have too many topics in early grades that are covered too shallowly
(3) A principal recommendation is that we cover fewer topics and cover the most important ones more thoroughly.
(4) The panel focused on the preparation of American children for success in algebra. Algebra has a central role in mathematics curriculum, the first course leading into secondary mathematics.
(5) Success in algebra not only plays a central role because of its correlation to success in high school math courses, but also because of its correlation to college-attending and graduation rates and eligibility for the national technical workforce.
(6) Cognitive science informs us that children who believe that working harder can make one smarter, actually achieve more.
(7) To encourage their children, parents should make note of how common mathematics is in the world and how many jobs parents hold which make use of mathematical concepts.

MathNotations Reactions to Dr. Faulkner's statements:
(1) "...It is well-known outside the US and inside"! When did it become so well-known? Could it be when Prof Schmidt uttered WELL OVER A DECADE AGO his now-famous description of our math curriculum as "one inch deep and one mile wide"? You mean now his word will be heeded? Now that NCTM has recognized the need for a narrower focus as recently published in its Curriculum Focal Points? Now there will be new textbooks written that reflect this narrower focus? Is that what you mean Prof. Faulkner? Exactly who will be apologizing to the generations of students who have been exposed to such superficiality? Who will be apologizing to the dedicated educators who have been compelled to sacrifice mastery and deeper understanding for superficial coverage of a myriad of topics? Who exactly will be apologizing for not listening to Prof. Schmidt until now?

(2) We need to be informed by the research of cognitive scientists that a strong work ethic will lead to success, particularly in mathematics? That persistence and effort can lead to success in math!

This is the revelation I've been waiting two years to hear? Yes, I agree this is a wonderful message for all students to hear in all aspects of their learning. Yes, Prof. Faulkner, I believe we can also accumulate 400 million pieces of anecdotal evidence from our educators to support the truism that there is no substitute for hard work, particularly in mathematics...

Posted by Dave Marain at 3:15 PM 2 comments

Labels: national math panel

One of the primary reasons I started this poll was to provide K-12 educators an opportunity to express their opinion about a central issue in mathematics education: the teaching of algorithms, multiplication in particular, as well as the issue of the expectation of mastery.

Why now? The work of the National Mathematics Advisory Panel is essentially complete and their recommendations will soon be published. MathNotation's readers for the past year know that I sent numerous emails, repeatedly urging the directors of the panel to include several practicing K-12 classroom teachers on this panel, if only in an ex officio capacity. All such requests were respectfully denied. I published both my emails and the replies of the panel in full on this blog. Classroom teachers were not able to provide direct input to the Panel because they were not represented, their voices were not heard, other than the lone voice of a single 8th grade teacher who was invited to be on the panel. If interested, go to the Labels section in the sidebar and read the (5) posts tagged with National Math Panel.

Surely, the Panel, with the cooperation of NCTM, could have developed a survey of our nation's math teachers. A survey which would have allowed tens of thousands of educators to express their knowledgeable opinions of what they believe is best for the mathematics education of their students. But this did not happen...

This was an important part of why I created this apparently insignificant little poll, consisting of just one question among the many which need to be asked and answered. Just a drop in the bucket, but I believe it is a central question for our children. It addresses perhaps the heart of the Reform vs. Traditional debate in our country.

This poll is intended for all visitors, whether they be parents, students, scientists, research mathematicians, administrators, curriculum specialists, classroom educators or anyone else who cares about the future of our children. However, I particularly urge the classroom teacher of mathematics not only to use this forum to express their feelings but also to encourage their colleagues to vote. A statistically significant sample here can be used by anyone who may need data to inform curricular decisions. Perhaps others will heed the message too.

The poll ends on February 29th. Keep it alive - spread the word! We're receiving a steady trickle of votes but we need many more. I won't yet comment on the majority opinion, however, you can see the results yourself when you submit your vote.

Posted by Dave Marain at 4:52 PM 2 comments

Labels: national math panel, poll, survey

As promised, I am posting, with the permission of the National Math Panel, the reply to my latest email to the Panel. Jennifer Graban sent me this last Friday and you can read it for yourself and decide if you believe that some of my recommendations and those of others are now being considered seriously. Below, I will also briefly discuss the conversation I had with Ms. Graban when I called her:

Dear Mr. Marain,

We apologize for the delay in responding to your e-mail of February 11 and acknowledge your ongoing concerns about the composition of the Panel. Understanding the experiences of teachers, particularly algebra teachers currently teaching in the classroom, is important to the Panel and its final report. I have shared your concern with the Panel Chair, Larry Faulkner, as well as other Panel members. We are currently considering additional opportunities that will involve teachers to obtain their vital input in the work of the Panel.

Please know that Panel is most concerned with and plans to carefully consider the perspectives of today's math teachers.

Once again, thank you for your interest in the National Math Panel.

Sincerely,

Jennifer



Jennifer Graban
National Math Panel Staff
U.S. Department of Education
400 Maryland Avenue, SW
Washington, DC 20202-1200


I decided to call Ms. Graban last Friday afternoon around 4 PM EST. She picked up the phone immediately and we spoke for about 10-15 minutes. To the best of my recollection here's how it went:
I began by saying that I felt it important to put a voice to all the emails and blogs and let her know that I am a real person and not the enemy, just someone who feels that not having at least one secondary teacher on this panel was a gross oversight. Continuing, I indicated that, although it would be better to appoint 2-3 dozen classroom math teachers immediately, the reality is that the panel has less than one year to complete its task and publish its final report. Therefore I suggested the importance of identifying a cross-section of a few current high school math teachers with broad experience in both urban and suburban/rural school settings. I also volunteered to provide whatever input I could to the Panel, but certainly this group of teachers should be allowed to serve in an advisory capacity, i.e., freely provide their ideas and be be able to review and make suggestions now and to the final draft of the report before its release. I expressed that this would significantly enhance the credibility of the report. She replied that this was already being considered and she seemed to concur with some of my statements. I also mentioned my call for a national math curriculum but she indicated that the panel has not yet endorsed this. I also asked her if she had noted that the textbook publishers, who were allowed to give extensive presentations to the Panel, had indicated they now had editions for EACH state or nearly so. I expressed how absurd I felt this was and she did not disagree! We left the conversation cordially.

Posted by Dave Marain at 6:01 AM 0 comments

Labels: national math curriculum, national math panel

Just to see how England is handling a national curriculum (for all subjects), here's a link to the Mathematics section. You will need to navigate this site for awhile to get the feel for it. You will also want to download the 90+ page pdf math curriculum document. I've skimmed it and it is fascinating. Of course much of it is not new or surprising or that different from NCTM's many recommendations or reports, but it's the overall structure and expectations for the four key stages of learning that make it unique. Why can't we benefit from something like this so that we don't have to reinvent the wheel? I'm certain that members of the National Math Panel are familiar with this but I'd be interested in their views. Is it possible for our society? Better yet, perhaps we need to begin to realize the vision of Robert F. Kennedy:

There are those that look at things the way they are, and ask why? I dream of things that never were, and ask why not.

Things that never were? But they are already existing elsewhere!

Better yet, download
A Coherent Curriculum: The Case for Mathematics by William Schmidt, Richard Houang, and Leland Cogan is available online in American Educator, Summer 2002, pp. 1-17.

This was a call to action five years ago and we're still arguing about it today...

Posted by Dave Marain at 6:33 AM 0 comments

Labels: national math curriculum, national math curriculum england, national math panel, national standards

1. I received a reply from Jennifer Graban of the National Math Panel. Her comments indicated recognition by the panel that there is a need for greater participation of classroom teachers, algebra teachers in particular. I decided to call Jennifer personally and we had a very pleasant conversation. Electronic communication and blogs can never replace human interaction! I'll share the email and our dialogue later...
2. I've posted a solution in the comment section to the last part of the nested radical problem -- finding an expression for N that would produce an integer value for the infinite nested radical.
3. You may want to read the comment I posted regarding Math Anxiety. It describes a method that I have found useful for conscientious students who tend to underperform on teacher-made tests. There is also a wonderful set of tips for students to prepare for standardized tests like SATs. It's entitled Ten Ways to Survive the Math Blues from Murray Bourne at squarecirclez and I will share this with the students in my school.

Posted by Dave Marain at 6:35 PM 0 comments

Labels: national math panel

I posted the following comment on edspresso on 2-12-07 in response to The Poisonous Politics of Implementation by Neal McCluskey. Same old, same old??

I have been advocating for national math standards for the past three decades. Its time has come. Despite all the negativity, skepticism and distrust the bottom line is that what we currently have in ALL disciplines is chaos with the result that our children fall further behind other industrialized nations moment my moment. Fifty states with fifty different sets of standards (yes, there is overlap but they are not congruent) with fifty different sets of assessments with fifty different levels of proficiency adds up to what -- let me get my calculator to do the math...
Ultimately, most teachers, including myself, will teach essentially what is in the textbooks and will stress the content and types of questions that are on the high-stakes tests for which they are held accountable. As an AP teacher for 35 years, I am proud to say I 'taught to the test' -- one of the better quality tests I've seen constructed. However, I never felt constricted by a straight-jacket curriculum. My methods and creativity were never affected. I felt crunched by time to cover all the topics in the BC course in 8 months but somehow we got through it and I knew in the end that my students were at least as well prepared for the next level as any other student in any other BC Calc class. I knew that because of their performance in my class which was then validated by the results of the standardized AP test. I saw a reasonable correlation between a '5' on the test and an A or B in class and so on. Could I have taught the same quality course without this 'nationalized' Calculus curriculum. Quality, yes, but I don't think the content and emphasis would have been consistent with the thousands of other calculus classes around the country. Just look at how similar or dissimilar Precalculus classes are from classroom to classroom, never mind state to state. Yes, the road to a standard curriculum is a mine field but the road we're on now leads only to an abyss. I'll take my chances...

Posted by Dave Marain at 6:38 PM 2 comments

Labels: national math panel, standards

The following is excerpted from a statement sent to the National Math Panel on 9-1-06:


Comments to National Math Panel
Cambridge MA Sessions 9-13-06, 9-14-06

From: Dave Marain, Supervisor of Mathematics

Although I would prefer to be present and read this statement personally, the risk of not getting on after making a trip of several hours and the limitation to 5 minutes makes it somewhat prohibitive.

As I’ve noted previously, the limited opportunity for concerned educators and others to express their sentiments balanced against 30-45 minute presentations for textbook publishers and ‘established’ organizations does not send an encouraging message to those who feel the outcomes from this panel are predetermined. I, for one, am more optimistic than that, but the proof will be in the black and white recommendations.

From discussing this with the secondary math teachers in my department, with many concerned parents and with students over some time now, there is broad consensus on the following points:

* Problem: For some time now, we have observed and endured students’ deficiencies in arithmetic and their impact on the ability to handle algebraic processes, comprehend the rules of algebra and retain algebraic skills and concepts. Our educators see glaring deficiencies in students’ understanding of fractions and ratios. This is not acceptable.

Recommendation: Students should master the facts of arithmetic and develop proficiency with fractions, decimals and percents WITHOUT the use of the calculator. Using the calculator to promote conceptual understanding and solve real-world problems with ‘messy’ decimals or irrationals is however strongly recommended, We believe this should COMPLEMENT the mastery of arithmetic skills – no more than that.

* Problem: Algebra for All in 8th grade? The problem is that Algebra in New Jersey is not exactly the same as Algebra in New York, Algebra in California, and Algebra here in Cambridge! Were it not so deleterious to our children’s development of mathematics, it would be almost ludicrous to consider that textbook publishers are developing state-customized textbooks for Algebra 1 and other math courses. Although the differences are minor, they are nevertheless a reflection of a serious disconnect between what ALL of our students need and the need for publishers to meet the needs of individual education departments of 50 states. Why does it appear so obvious to our educators that it is insanity to have 50 different sets of state math assessments times several grade levels, yet it seems perfectly natural to governors and state commissioners of education. Testing companies are reaping the benefits of this, but are our children? Ironically, testing companies appear to be having difficulty keeping up with the demand for quality assessments. What’s wrong with this picture?

Recommendations:
* First we have to make sure that we have ‘Arithmetic for All’ in K-7! Our consensus here is that the concepts and skills from arithmetic and prealgebra must be far more standardized than they are now. The ONLY way to insure equity for all is to standardize the curriculum and set the bar higher than it is now.
* Instead of developing massive texts containing beautiful pictures and wonderful applications to every vocation and applications that address every states’ requirements, we strongly believe that the time has come to step back and demand that essential content be given the highest priority. We feel that each of you on this panel needs to ask yourself the following question: How have our esteemed national math and science groups responded to Bill Schmidt’s concerns over a decade ago about a curriculum that is too broad and too shallow? Translating a text from Singapore is not the answer. We need to take the best knowledge we currently have about how children develop mathematical understanding and balance that with the skills needed for those ideas to take root and have meaning. How many of you on this panel have observed numerous math lessons in this country that reflect students’ ‘profound understanding of fundamental mathematics’. We can all cite a few instances for sure, particularly if you are personally working on such a project. We’re talking however about more than a small handful of classrooms. Why are Japanese students in an 8th grade classroom spending an entire class period tackling sophisticated problems that require analysis, conceptual understanding and skill? In fact, we believe that this kind of activity is precisely what enables a child to develop that profound understanding. Isn’t it all about the kinds of questions we ask and the questions we generate and encourage from our students? Isn’t it all about setting the bar higher? We believe it is. Problem-solving however should only be part of the picture. One cannot solve a problem without the proper tools. We do not believe that the majority of our children are currently provided with those tools. This must change!

Thank you for the opportunity to share our concerns. We fervently hope that the Panel will respond to these concerns and make the bold recommendations needed for our children to survive and compete in the 21st century. We await your response…

Posted by Dave Marain at 2:46 PM 0 comments

Labels: national math panel, national standards