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Sent at the request of Jim Fey.
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In an introductory note to the essay below, Jim Fey writes as
follows:
In September of 2008, the Center for Mathematics Education at the
University of Maryland organized a conference in Washington, DC to
examine core questions about the future of high school mathematics and
to showcase promising innovative projects. The conference theme
attracted over 300 leaders in school and college mathematics education
with shared concerns about the need for fundamental reform in the
content and teaching of mathematics in grades 9  12.
Just three weeks ago a much smaller group of senior
mathematicians, teachers, statisticians, and curriculum developers met
in Boston to revisit issues addressed by the 2008 conferencethis
time in the context of Common Core State Standards
implementation. Participants in that meeting, sponsored by the
Consortium for Mathematics and Its Applications, formulated a set of
recommendations for progressive action in the field and drafted an
essay to explain their ideas.
Since results of the most recent PISA assessment were scheduled
for release on December 3 and PISA focuses on high school mathematics,
science, and literacy, we linked our essay about needed reforms to
what would almost certainly be the principal findings of PISA.
That essay is now posted on the blog of Valerie Strauss at the
Washington Post. In what appears to be the common pattern of
reactions to blog postings, the first responses have largely ignored
our plea for a dialing down of acrimony in discussion of the issues.
We all know that your various lists reach thoughtful and influential
audiences in mathematics education, and we would be pleased if you
would help us circulate the recommendations of the Boston
meeting.
The essay drafted by the Boston group follows (and is also
attached).
The Future of High School
Math
Let's Try Something Different
Results from the most recent Program for International Student Assessment (PISA), released on December 3, showed once again that U. S. high school students are in the middle of the pack when it comes to science, mathematics, and literacy achievement. The findings quickly elicited an outburst of public hand wringing, criticism of U. S. schools and their teachers, and calls to emulate the curriculum and teaching practices of high achieving countries. Then, just as predictably, there were a variety of explanations why we cannot import the policies and practices of other quite different countries (e.g. , South Korea, Taiwan, Finland, and Singapore). Instead, schools were urged to redouble efforts along lines that have been largely ineffective for the past decade and are not common in any high performing countrya regimen of extensive standardized testing with mostly punitive consequences for schools and teachers that fail to make adequate yearly progress. Public attention to the challenge of international competition has already begun to fade and we will hear little about the meaning of the PISA results until the next 'wakeup call' arrives. What might happen if we tried something different this time around? Countries that have made real progress in their performance on international assessments share several characteristics. First and foremost is broad agreement on the goals of education and sustained commitment to change over time. In the U. S. there has been steady, if modest, improvement in student mathematics performance at the elementary and middle school levels on the National Assessment of Educational Progress (NAEP) and some improvement in results on college entrance examination tests (SAT and ACT) over the past two decadesa period when efforts have been guided by the National Council of Teachers of Mathematics (NCTM) standards for curriculum, evaluation, teaching, and assessment. Over the past three years, 46 of the 50 U. S. states have been engaged in an effort to implement Common Core State Standards (CCSS) for mathematics and literacy. With respect to mathematics, those standards, prepared under the aegis of the National Governors' Association with generous private financial support, are in many ways an extension of key ideas in the earlier NCTM standards. Despite understandable controversy about particulars of the CCSS and the processes by which they were developed and states were induced to adopt them, the Common Core standards provide a useful framework for further efforts. Partisan political pressures (from both left and right) are already leading some state governors to reconsider their participation in this national compact to improve educationbefore even the first assessments of progress are reported. But we believe that education policy makers and mathematics educators should resist the common wish for a quick fix and stay the course, modifying goals and efforts as results suggest such actions. What should students, teachers, parents, and policymakers
look for in the emerging reform of high school mathematics?
>From our perspectiveas mathematicians, teachers, statisticians,
teacher educators, and curriculum developers with extensive experience
in school mathematics innovationthere are at least four key elements
of the Common Core program that provide a basis for productive change
in U. S. high school mathematics:
o Comprehensive and Integrated Curriculum. The traditional American high school mathematics curriculum consists of two yearlong courses in algebra and a oneyear course in geometry. The CCSS for mathematics retain essential elements of those topics, but they also prescribe significant attention to important concepts and skills in statistics, probability, and discrete mathematics that are now fundamental in computer, management, and social sciences. The Common Core guidelines describe an attractive integrated curriculum optionsuggested by the common practice in other countries of addressing each mathematical content strand in each school year. That international curriculum design helps students learn and use the productive connections between algebra, geometry, probability, statistics, and discrete mathematics.
A broad and integrated vision of high school mathematics would
serve our students better than the narrow and compartmentalized
structure of traditional programs.
o Mathematical Habits of MindFor most people the phrase 'do the math' means following standard algorithms for calculation with whole numbers, fractions, decimals, and the symbolic expressions of algebra. But productive quantitative thinking also requires understanding and skill in use of what the Common Core Standards call mathematical practices. To apply mathematical concepts and methods effectively to the kind of realistic problem solving and decision making tasks that PISA assessments highlight, students need to develop the habits of: (1) analyzing complex problems and persevering to solve them; (2) constructing arguments and critiquing the reasoning of others; (3) using mathematical models to represent and reason about the structure in problem situations; and (4) communicating results of their thinking in clear and precise language.
Developing important mathematical habits of mind should become
a central goal of high school instruction, especially the process of
mathematical modeling that is required to solve significant
realworld problems.
o Balanced Attention to Technique, Understanding, and ApplicationsOne of the most common student views about mathematics is the belief that what they are asked to learn is not supposed to make sense and that it bears little relationship to the reasoning required by everyday life. Those views are expressed well in the whimsical rhyme about division of common fractions, "Yours is not to reason why, just invert and multiply," and the common student question, "When will I ever use this stuff?" Unfortunately, many teachers encourage those beliefs about mathematics learning by suggesting that understanding and application of mathematical ideas and methods can only occur after rote mastery of technical skills. Findings of cognitive and curriculum design research over the past two decades challenge such conventional beliefs and common practices. Curricula and teaching that engage students in collaborative exploration of realistic problems have been shown to be effective in developing student mathematical understanding, skills, and problem solving simultaneously. These problembased approaches in the classroom also develop the essential disposition to use mathematics as a reasoning tool outside of school. Improved performance on international assessments like PISA
are likely to result from moves toward curricula and teaching methods
that balance and integrate mathematical techniques, understanding, and
applications.
o Information TechnologiesPowerful tools that allow users to find and process information with mathematical methods are now ubiquitous in American life. But schools are only beginning to respond to the profound implications of this information technology for teaching and learning. If it is possible to simply ask your cell phone to perform any of the routine calculations taught in traditional school arithmetic, algebra, and calculus courses, what kind of mathematical learning remains essential? If those same tools can be applied to support studentcentered exploration of mathematical ideas, how will the new learning options change traditional roles of teachers and students in the mathematics classroom and raise expectations for the mathematical challenges that students can tackle? Personal computers, tablets, smartphones, and other computing devices will almost certainly transform school mathematics in fundamental ways. Intelligent response to that challenge will require creative research and development efforts and the courage to make significant changes in traditional practices. If the content and teaching of high school mathematics are transformed in the directions we recommend, schools and teachers will also need new tools for assessing student learning. One of the clearest findings of educational research is the truism that what gets tested gets taught. PISA is not a perfect or complete measure of high school student achievement. Neither are the TIMMS international assessments, the NAEP tests, the SAT and ACT college entrance exams, college placement exams, or, quite likely, the coming assessments attached to the Common Core State Standards. Some would respond to the inadequacy of current assessment tools by sharply curtailing high stakes standardized testing; others would actually increase the testing and raise the consequences for students and schools. It is almost certainly true that the best course lies somewhere between those extremes. We need new and better tools for assessing student learning, and we need to employ those assessments in constructive ways to help teachers improve instruction and to inform educational policy decisions. Finally, we need to change the tenor of public discourse about
mathematics education. If we are to reach the shared goal of preparing
young people for productive and satisfying lives, we need to work
together to develop progressive goals for school mathematics and high
quality instructional resources. Most important of all, we need
to dial down the acrimonious policy arguments and relentless criticism
of schools and teachers. Teaching is one of the most important and
demanding tasks for adults in our society, and teachers deserve our
encouragement and support as they work to provide the best possible
life preparation for their students.
Jim Fey
University of Maryland
Diane Briars
Intensified Algebra Project, University of Illinois
at Chicago
Andy Isaacs
University of Chicago
Henry Pollak
Teachers College, Columbia University
Eric Robinson
Ithaca College
Richard Scheaffer
University of Florida
Alan Schoenfeld
University of California, Berkeley
Cathy Seeley
Dana Center, University of Texas
Dan Teague
North Carolina School of Science and
Mathematics
Zalman Usiskin
University of Chicago
***************************************************
 Jerry P. Becker
Dept. of Curriculum & Instruction Southern Illinois University 625 Wham Drive Mail Code 4610 Carbondale, IL 629014610 Phone: (618) 4534241 [O] (618) 4578903 [H] Fax: (618) 4534244 Email: [hidden email] Future of High School Math 12 5 13.docx (235K) Download Attachment 
On Dec 10, 2013, at 5:40 PM, Jerry Becker <[hidden email]> wrote:
o Information TechnologiesPowerful tools that allow users to find and process information with mathematical methods are now ubiquitous in American life. But schools are only beginning to respond to the profound implications of this information technology for teaching and learning. If it is possible to simply ask your cell phone to perform any of the routine calculations taught in traditional school arithmetic, algebra, and calculus courses, what kind of mathematical learning remains essential? Some of what was written made sense, and then you read something like this. After a decade of studying the subject of math education and studying those that study the subject math education, it is evident to me that people who make such statements have never taught children mathematics, from kindergarten through high school. Bob Hansen 
On Tue, Dec 10, 2013 at 3:23 PM, Robert Hansen <[hidden email]> wrote:
Not something you've done professionally either as I recall. Ever been a classroom teacher for a living Bob, anywhere along K12? Just curious. Kirby 
Yes, I have taught children through all those stages. College students and post college students as well. I’ve had teaching in me all my life. In fact, I have had people come to me much later, that I have taught, and I couldn’t remember their name. That felt bad.
Bob Hansen
On Dec 11, 2013, at 1:32 PM, kirby urner <[hidden email]> wrote:

Any uncle who shows junior how to program a fractal in BASIC may claim to have taught children. What I asked was have you been professionally employed as a classroom teacher, which entails getting a paycheck from a school as compensation for teaching full time? Did you hang out in the faculty lounge, go to faculty parties, sometimes have discipline problems, have a principal to report to etc. etc. Was this a public school? In Florida? Kirby On Wed, Dec 11, 2013 at 10:43 AM, Robert Hansen <[hidden email]> wrote:

I wasn’t dodging. Your question had nothing to do with my original statement, it was leading. "it is evident to me that people who make such statements have never taught children mathematics, from kindergarten through high school.” And this was my answer to your question… "Yes, I have taught children through all those stages. College students and post college students as well. I’ve had teaching in me all my life. In fact, I have had people come to me much later, that I have taught, and I couldn’t remember their name. That felt bad.” And I wasn’t teaching family. That jabberwocky you dish out might seem to work in your head, but trust me, it doesn’t work with actual people. Bob Hansen On Dec 11, 2013, at 2:23 PM, kirby urner <[hidden email]> wrote:

In reply to this post by kirby urner4
On Dec 11, 2013, at 2:23 PM, kirby urner <[hidden email]> wrote:
Any uncle who shows junior how to program a fractal in BASIC may claim to have taught children. Oh, and you know I would never do this. I either teach or I don’t even bother. Great for mastering the art of teaching. Not so good for casual conversation.:) Bob Hansen

In reply to this post by Robert Hansen
You continue to dodge. I take your answer to be "no, I have never been a professional teacher".
Would that would be more honest? A small step in that direction? Is your resume online somewhere? I'd like to see where you come off being such a knowitall about everything. I just wanted to point out you're a pretty good spoon bender yourself sometimes. Kirby
On Wed, Dec 11, 2013 at 11:31 AM, Robert Hansen <[hidden email]> wrote:

Bob
On Dec 11, 2013, at 2:50 PM, kirby urner <[hidden email]> wrote:
Did you not understand what “leading question” meant. Yes, I was paid when I taught, so I guess I was a professional teacher. As a tutor, 1 or 2 students at a time, math and physics. As a teacher, classes of 20 students or so, programing etc.
No. Are you getting what “leading” means yet?
I’m just gifted, what can I say.
Actually, I think I used the word “lying”, you said bending. After this exchange, I am seriously sticking with “lying”.
How so?
Bob Hansen

On Wed, Dec 11, 2013 at 12:06 PM, Robert Hansen <[hidden email]> wrote:
What would it matter? Am I trying to learn something from you? Not that I'd noticed.
So could be like corporate training seminar like part of your job. I've both been a full time high school teacher and done the corporate circuit. They're not the same thing exactly.
The question is whether I'm caring.
That's more for others to judge. My view is "below average" by the standards I work with.
Right, because we see how I lie a lot from reading this. What anyone would conclude.
You set yourself up as an authority in ways you haven't earned? That's how you come across to me: inexperienced and loud about it. A bit of a boor.
Anyway, back to the topic at hand, I think have a Common Core Standard is harmless if there's nothing stopping us from exceeding these standards and pointing out in what ways we do. If Euclid's Method (Algorithm) is not included when the GCD is studied, then we circle that gap and say "see, the Common Standards are *not* good enough for your kid, but our curriculum fills this gap". So good marketing, no harm done. Kirby 
Colleagues:
The ongoing discussion between Bob, Kirby et al is a bit of a hoot;) , but to segue the discussion: I'd like to see a curriculum consisting of 1/2 laid on from above, the other 1/2 at the teacher's discretion  with the only proviso being that the teacher use his/her half to broach topics not covered by the "standards" gang. Ie topics that interest the teacher  topics to which the students might contagiously be attracted. Also  no covering the following year's mandation. I'm curious how many people do sudokus but profess a dislike of math. If math were were approached as a fun subject a la gym, shop, modelbuilding etc I believe we'd be well served. What about puzzlesolving is there not to like? Gary Tupper Terrace, BC 
On Dec 11, 2013, at 5:14 PM, Gary Tupper <[hidden email]> wrote:
I'd like to see a curriculum consisting of 1/2 laid on from above, the other 1/2 at the teacher's discretion  with the only proviso being that the teacher use his/her half to broach topics not covered by the "standards" gang. Ie topics that interest the teacher  topics to which the students might contagiously be attracted. Also  no covering the following year's mandation. I think the biggest problem with your plan is that such a course would be severely lacking in providing the student the ability to earn a living. Now Lou is going to chastise me for connecting school to adulthood and work, and then go cash his paycheck, as so will you. If math were were approached as a fun subject a la gym, shop, modelbuilding etc I believe we'd be well served. What about puzzlesolving is there not to like? If math isn’t fun and you want to “make it fun like gym” wouldn’t it be more realistic and honest to just teach gym? Actually, why do you think this plan might not work? Bob Hansen 
On Wed, 11 Dec 2013 16:10:35 0700, Robert Hansen <[hidden email]> wrote:
I think the biggest problem with your plan is that such a course would be severely lacking in providing the student the ability to earn a living. Now Lou is going to chastise me for connecting school to adulthood and work, and then go cash his paycheck, as so will you. I've never chastised anyone for making a connection between the two, and if you believe I have, that's more sloppy thinking on your part. In fact, if you search the archives carefully, you should be able to find that I have said that an "education" that fails to prepare the student for work is no education at all. I have chastised you for equating the purpose of school with preparation for work, and I will do so again the next time you suggest that equivalence. And I now chastise you for misrepresenting me. Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver <http://rowdy.msudenver.edu/~talmanl> 
In reply to this post by Robert Hansen
On Wed, 11 Dec 2013 16:10:35 0700, Robert Hansen <[hidden email]> wrote:
If math isn’t fun and you want to “make it fun like gym” wouldn’t it be more realistic and honest to just teach gym? No. Some of us hated gym. We didn't think it was fun at all.  Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State University of Denver <http://rowdy.msudenver.edu/~talmanl> 
In reply to this post by Jerry Becker
Gary Tupper posted Dec 12, 2013 3:44 AM (http://mathforum.org/kb/message.jspa?messageID=9340756):
> Colleagues: <snip> > I'd like to see a curriculum consisting of 1/2 laid > on from above, the > other 1/2 at the teacher's discretion  with the only > proviso being that > the teacher use his/her half to broach topics not > covered by the > "standards" gang. Ie topics that interest the teacher >  topics to which > the students might contagiously be attracted. Also  > no covering the > following year's mandation. > Why not think in terms of curricula developed with 'sufficient and necessary' inputs from ALL STAKEHOLDERS (including teachers, students, parents and others interested in education)? I.e., students and parents should ALSO be *enabled* to have their say in the process. Of course, the ideas of teachers and educational experts should be fundamental in any such undertaking. I agree that, using the 'conventional approach(es)', it might be very difficult  perhaps even impossible  to accomplish the above. So that is probably a good reason to think in terms of 'unconventional' approaches. Actually, what I'm suggesting is not really all that 'unconventional'  call it a 'simple and systematic' approach. OK, that is, I guess, 'unconventional'. Some practical (and really quite simple) tools to enable ALL of the above are described in the attachments to my post heading the thread "Democracy: how to achieve it?"  see http://mathforum.org/kb/thread.jspa?threadID=2419536. [Some (a very small amount of) learning along with a fair bit of 'unlearning' are involved in applying these tools. It is, after all, 'education' we are thinking of, and, hopefully, 'educators' who will do the needful]. GSC 
In reply to this post by Louis Talman
I agree that reading through the sequence was "hoot" but, as
usual, I agree with Bob. I would have jumped st in earlier except
that I was spending Thanksgiving and most of the day after in the
intensive care ward at Huntington Hospital with an acute UTI
absolutely convinced that I was dead, I clearly remember dying but I
appear to have been mistaken. Although I consider deductive logic
as the greatest gift of the ancient Greeks to modern thought processes
("democracy" for a substantial minority doesn't really cut it)
and consider myself pretty good, in my altered state, arguing with
several people that their argument that them speaking to me and me
responding coherently precluded my being dead wasn't coming
through. Needless to say, that was one argument I was absolutely
delighted to have lost when I really did wake up with an instantaneous
start late Thursday.
Wayne At 07:51 PM 12/11/2013, Louis Talman wrote: On Wed, 11 Dec 2013 16:10:35 0700, Robert Hansen <[hidden email]> wrote: 
In reply to this post by Jerry Becker
Robert Hansen (RH) posted Dec 12, 2013 4:40 AM (http://mathforum.org/kb/message.jspa?messageID=9340850):
> <snip> > > I think the biggest problem with your plan is that > such a course would be severely lacking in providing > the student the ability to earn a living. Now Lou is > going to chastise me for connecting school to > adulthood and work, and then go cash his paycheck, as > so will you. > RH is mistaken in all his assertions above. i) An *effective* course would NOT be "severely lacking", as RH suggests, "in providing the student the ability to earn a living": any sound course would always be tied to providing students the ability to earn a living"; and ii) I don't believe Lou Talman has ever chastised RH or anyone else for connecting school to adulthood and work  and it is unlikely that he'll do that now. This appears to be more of the 'false flag argument' that RH puts up every now and then. Ah yes, I note that Lou Talman makes the very same point in his post dt. Dec 12, 2013 9:20 AM (http://mathforum.org/kb/message.jspa?messageID=9341255). GSC ("Still Shoveling! Not PUSHING!! Not GOADING!!!") 
In reply to this post by Louis Talman
On Dec 11, 2013, at 10:50 PM, Louis Talman <[hidden email]> wrote:
An education that failed to prepare the student for work is no education at all. <— I like this by the way. But the purpose of school is not to prepare one for work? Do you mean the sole purpose? Bob Hansen

In reply to this post by GS Chandy
On Dec 12, 2013, at 5:56 AM, GS Chandy <[hidden email]> wrote:
i) An *effective* course would NOT be "severely lacking", as RH suggests, "in providing the student the ability to earn a living": any sound course would always be tied to providing students the ability to earn a living"; and I suggested that an effective course would not be effective? Gary never said “effective”. He said halfandhalf, sudoku and puzzles. I was suggesting (obviously) that such a course, based on sudoku and puzzles, would not be effective in providing the student the ability to earn a living.
http://mathforum.org/kb/message.jspa?messageID=7425490 Lou’s cheering of “liberal arts" is not new. My cheering of “vocation" is not new. With the state that college is in though, we are probably both wrong. Bob Hansen

In reply to this post by Louis Talman
On Dec 11, 2013, at 10:51 PM, Louis Talman <[hidden email]> wrote:
That dodge ball hurt didn’t it?:) Bob Hansen 
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