Thursday, April 30, 2009

Who needs higher math?

In my previous post, I quoted Ron Wolk, the founder and former editor of Education Week.
Wolk states:

The main reasons students are not learning algebra and geometry is that they don’t really want to. They think higher-order math is irrelevant to their real lives. They can’t imagine that they will ever use algebra and geometry. And they are mostly right.

I am willing to bet that the majority of [students] who graduated from high school have made little, if any, use of algebra or geometry. Most, like me, probably forgot most of what they “learned” before the ink was dry on their diplomas. I squeaked through algebra, plain and solid geometry, and trigonometry, but a year later I couldn’t explain the difference between a cosine and a stop sign. And I can’t think of an instance over the past half-century when I needed algebra or geometry.

A prominent Rhode Island businessman once said to me: “I have been a successful businessman for 40 years; I founded and ran a Fortune 500 company, and all the math I ever used were addition, subtraction, division, multiplication, and figuring percentages in my head.” What are the odds that he would pass the New England Common Assessment?

But if we think we will get more kids to become scientists and engineers by force-feeding them algebra in the 8th grade and higher-order math through high school, we are deluding ourselves.

Tuesday, April 28, 2009

Five Faulty Assumptions

Education Week (required reading for all educators) has a terrific article this week:
Why We're Still 'At Risk' The Legacy of Five Faulty Assumptions  By Ronald A. Wolk (the founder and former editor of Education Week).
Our new president has looked into the abyss of our current economic, energy, environmental, and health-care policies and promises to challenge the fundamental assumptions on which they are based. He admonishes us to join him in thinking and acting boldly. We can only hope he feels the same way about education policy.  After nearly 25 years of intensive effort, we have failed to fix our ailing public schools and stem the "rising tide of mediocrity" chronicled in 1983 in A Nation at Risk. This is mainly because the report misdiagnosed the problem, and because the major assumptions on which current education policy-and most reform efforts-have been based are either wrong or unrealistic.  Most of the people running our public education systems and leading the reform movement are knowledgeable, dedicated, and experienced. But they are so committed to a strategy of standards-based accountability that different ideas are marginalized or stifled completely.  One could write a book about each of the five major assumptions on which education policy rests, but in this limited space, a few brief paragraphs will have to suffice.

Assumption One: The best way to improve student performance and close achievement gaps is to establish rigorous content standards and a core curriculum for all schools-preferably on a national basis. 

Assumption Two: Standardized-test scores are an accurate measure of student learning and should be used to determine promotion and graduation. 

Assumption Three: We need to put highly qualified teachers in every classroom to assure educational excellence. 

Assumption Four: The United States should require all students to take algebra in the 8th grade and higher-order math in high school in order to increase the number of scientists and engineers in this country and thus make us more competitive in the global economy. 

Assumption Five: The student-dropout rate can be reduced by ending social promotion, funding dropout-prevention programs, and raising the mandatory attendance age.   

National Standards

At last week's NCTM conference, the buzz was clearly about national math standards.  Secretary of Education Duncan all but said that he favors national standards.  Of course, the unanswered question is who would write such national standards and would they be voluntary or mandatory.  Time Magazine (of all places) had an article on April 15th by Walter Isaacson: How to Raise the Standard in America's Schools

Issacson states:

Fortunately, there is already a process under way that could, if properly nurtured, take charge of writing common national standards. The National Governors Association and the Council of Chief State School Officers (CCSSO) have been working with a nonprofit called Achieve Inc. In 2001, Achieve helped launch the American Diploma Project, which establishes curriculum standards that align with what a graduate will need to succeed in college, the military or a career. Gene Wilhoit, the executive director of CCSSO, hopes to kick this effort up a notch at a special meeting in Chicago on April 17 by announcing an agreement among 25 states to support an aggressive schedule to devise internationally benchmarked math and English standards for all grade levels. "I see standards as the essential foundation for all education reforms," he says.  These standards could build on the existing NAEP tests, which currently are administered every few years to a representative sample of students around the country in grades 4, 8 and 12. This type of approach was endorsed by the Commission on No Child Left Behind, a bipartisan group led by former governors Tommy Thompson and Roy Barnes that was run by the Aspen Institute, where I work.

The unanswered question:  Is NJ one of those 25 states - only the Commissioner knows and she remains silent on the issue.

Monday, April 27, 2009

NCTM Conference Blog

A number of educators created a blog about their experience during the 2009 annual meeting
It is an excellent blog that covers the opening session (Pedro Noguera, a leader in education reform, offers a dynamic, profound perspective on the challenges of racial inequality)  to the closing session (Arne Duncan, Obama’s Secretary of Education) including several webcasts.

Friday, April 24, 2009

Jo Boaler

I have posted about Jo Boaler previously and her critique of the National Math Panel Report.  Jo Boaler has just had a new book published called "What's Math Got to Do With It? Helping Children Learn to Love Their Least Favorite Subject - and 
Why It's Important for America. (Viking/Penguin).

Dr. Boaler has also researched and written numerous articles on mathematics education.  Her most recent research which she spoke about at NCTM was Creating Mathematical Futures through an Equitable Teaching Approach: The Case of Railside School.

The low and inequitable mathematics performance of students in urban American high schools has been identified as a critical issue contributing to societal inequities. In an effort to better the field’s understanding of equitable and successful teaching, we report results from a five-year longitudinal study of approximately 700 students as they progressed through three high schools.   One of the findings of the study was the important success of “Railside” school, where the mathematics department had detracked classes some years ago and taught through a reform-oriented approach. At Railside school students learned more, enjoyed mathematics more and progressed to higher mathematics levels. This paper presents large-scale evidence of these important achievements and provides detailed analyses of the ways that the\ Railside teachers brought them about, with a focus on the teaching and learning interactions within the classrooms.

The mathematical success shared by many students at Railside gave them access to mathematical careers, higher-level jobs and more secure financial futures. The fact that the teachers were able to achieve this through a multidimensional, reform-oriented approach at a time in California when unidimensional mathematics work and narrow test performance was all that was valued (Becker & Jacob, 2000) may give other teachers hope that working for equity and mathematical understanding against the constraints the system provides is both possible and worthwhile.


Monday, April 20, 2009

Scientists & Engineers

A wonderful article by Lynn Steen entitled Data, Shapes, Symbols:  Achieving Balance in School Mathematics in Quantitative Literacy: Why Numeracy Matters for Schools and Colleges discussed how mathematics has changed drastically and the importance of technology in the sciences and by engineers.  Dr. Steen's writes:

Computers also are changing profoundly how mathematics is practiced. The use of spreadsheets for storing, analyzing, and displaying data is ubiquitous in all trades and crafts. So too are computer tools of geometry that enable projection, rotation, inversions, and other fundamental operations to be carried out with a few keystrokes. Scientists and engineers report that, for students in these fields, facility with spreadsheets (as well as other mathematical software) is as important as conceptual understanding of mathematics and more valuable than fluency in manual computation (Barker 2000). With rare exceptions (primarily theoretical scientists and mathematicians) mathematics in practice means mathematics mediated by a computer.

Task Force Meeting #3

The 3rd meeting of the task force has concluded.
The AM session had three groups meet again (the same from the 2nd meeting) each examining one of three standards (Number, Geometry, and Algebra).
To date, Probability, Data, and Discrete Math nor the Process standards have been discussed.
The PM session had different groups meet by grade level to write lists of the big ideas in each grade level (sort of like the focal points).  
Another meeting has been scheduled for May 12th.  Objectives are:
(1) Focal point lists that we generated to be analyzed again
(2) CPIs to be reviewed again based on focal points lists
(3) Talk about next steps (still to be decided).  Maybe the Commissioner will address us.

I'm off to NCSM & NCTM for rest of the week.

Sunday, April 19, 2009

A Conversation with an Anti-Reformist

Below appears an exchange between myself and an anti-reformist who serves on the DOE math task force. 

On Sunday morning, I wrote to the task force members:

After reflecting on the process that has been taking place at the task force meetings, I want to suggest that to get the task force on a better track, the comparison documents prepared by the NJ Math & Science Coalition be used as the basis for the discussion of the three groups -- not because the Coalition has the "right" answers, but because it contains a summary of the two documents (Feb 09 and Dec 08) and a thoughtful review of them, and reflects a serious attempt to find common ground.  I have attached the comparison documents of the Number Strand and the Geometry Strand.  These documents contain every indicator of the Dec 08 standards (written by the math standards committee) and the Feb 09 document (written by DOE personnel).  The Coalition is meeting all day today (yes, Sunday) to prepare the Algebra Strand and I will send that out tonight.

The response from the anti-reformists (name withheld) was:

I appreciate that work that you and the NJ Math and Science Coalition have done.  However, I believe that best way to put NJ on the right track is to seriously consider the comments from mathematicians from around the country as well as other comments provided to the NJDOE.  I must say that I respectfully disagree with you. Just using the December draft for comparison will not put New Jersey on the right track for success; this document has failed our children.  We have a 70% math remediation rate at the community colleges. We must use the NMAP as a blueprint and look to the highest performing countries as well as highly regarded state standards.  In order to do this, we must eliminate topics to make our standards more focused, rigorous, coherent and clear.  Additionally, as recommended by the NMAP, we must consider what is necessary for our children to have mastered to lay the proper foundation for Algebra I.  Let me reiterate that it is important that our children must understand concepts first followed by mastery which then can be applied to problem solving that becomes more complex over time.

My reply to the anti-reformists was:

When it comes to standards, it's the details that are important.  And the Coalition has conducted a detailed analysis of the two documents and has tried to incorporate the meritorious recommendations of BOTH documents.  It is just one piece that will help us reach common ground. The comments of mathematicians are welcome by the task force as our recommendations from the Singapore standards.  Many of them are incorporated into the Coalition’s comparison document.  We agree that the standards have too many CPIs and we have made attempts to reduce them.  The task force will not have accomplished its task if it ignores this analysis and thus ends up with a document which will not be accepted by the mathematics education community in the state. Your failure rhetoric and restating of assumptions does not seem to give any perception that you are looking for common ground.   I challenge you to read the comparisons document. I challenge you to stop the failure rhetoric and look for real common ground solutions for the good of NJ students.

The anti-reformists responded:

I am following the directive of Commissioner Davy that our starting point must be the February draft. Enjoy the beautiful weather.

In summary, when you challenge the anti-reformist to put down their rhetoric and ask them to search for common ground, they respond with the weather.

Friday, April 17, 2009

California Here We Come

Tom O’Brien and Marianne Smith wrote an article entitled Three Strikes about the National Math Panel and much more.  The first part of the paper describes and comments upon three aspects of the back-to-basics movement: the make-up and mindset of the National Mathematics Advisory Panel (NMP),the movement’s history in California, and recent “grassroots” activities of the movement in the state of Washington. The second part reports and comments on the principal findings of the NMP report.  We, in NJ, must learn the lessons of California so that they are NOT repeated in NJ.  The authors write:

The origins of the most recent swing of the pendulum toward back-to-basics in mathematics education has been documented in books and articles about the trajectory of education policy in the state of California during the 1990s. By 1999, changes were made in the state’s mathematics framework and academic standards, in teacher professional development programs, as well as to textbook adoption guidelines. The changes were made under very controversial circumstances. The rigidity of these changes significantly affected professional development providers, who must sign a loyalty oath— an agreement to follow the back-to basics California state standards. The California back-to-basics movement has since metastasized through the years to Massachusetts, New York, Missouri, Washington, New Jersey and Utah. Despite claims made by California back-to-basics leadership that their Standards are “worldclass” and “rigorous,” 2007 data show that only 23% of California students are proficient in Algebra I by the end of high school and NAEP data showed 30 and 24 per cent of pupils proficient at grades 4 and 8 respectively. The California grade 4 NAEP results were higher than only 1 of 52 states and other jurisdictions and the grade 8 results were higher than only 4 of 52 jurisdictions.   It is clear that the data do not give much support for the Panel's embrace of California's "world class" curriculum.

 Why, then, do you read in newspapers about how terrible the mathematics programs developed in the 1990’s are and how successful California is? It has to do with an organization called Mathematically Correct, whose membership and funding is secret. Their goal is to have schools, districts, and states adopt the California standards and they recommend Saxon materials as the answer to today’s problems. They are radicals, out of the mainstream, who use fear to get their way.   Their other suggestions included replacing the Standards with California’s “world class” standards; purge the state schools of any "reform" curricula; erase the influence of the National Council of Teachers of Mathematics standards; make sure that no decision on math instruction is influenced by any educational research or anyone from a college of education; adopt alternative textbooks, such as those now published in Russia or Singapore; look to mathematicians and "good teachers" while avoiding advice of "mathematics educators" (a rung or two below the night custodian) and teachers whose instruction mirrors constructivist notions, a practice which separates them from the "good teachers.”

Doesn't this sound just like NJ now.  Look at the language.  "world class"  "mathematicians not math educators"  "Singapore"   If we are not united, it is California here we come.


Stalkers of Math Educators

Johnny Lott, NCTM President from 2002-2004, wrote "Calling Out the Stalkers of Mathematics Education". Johnny categorized the stalkers into three categories.  In NJ, we certainly see one of these types - the type that use fear and half-truths and scare tactics.  Johnny states:

Consider people who use half-truths, fear, and innuendo to control public opinion about mathematics education. As an example, look at Web sites that continue to use a public letter written in 1999 to then Secretary of Education Richard Riley by a group of mathematicians and scientists defaming reform mathematics curricula developed with National Science Foundation grants. Even though some of those who signed the letter subsequently retracted their statements or wrote letters stating that they did not sign the letter thinking it would be used as it has been, the letter seems to surface any time there is controversy over school curricula. A small group continues to use the letter in an attempt to thwart changes to mathematics curricula. This has been done in California, Massachusetts, and most recently New York. This letter is not the only example of half-truths and innuendo being used against mathematics curricula, even though continuing research shows that such curricula do in fact work when used by knowledgeable teachers. All of us must work to stop this stalking of reform mathematics curriculum

Thursday, April 16, 2009

Comic Relief

Between all the rhetoric of the math wars in NJ, I do still teach classes at Rowan University. I have the pleasure to teach Senior Seminar which is the last class that math majors take before graduating. It is a great opportunity to discuss with students the issues that I am engaged in and seek their opinions. Students are very interested in the calculator discussion (calculator ban for the anti-reformists). One student for his final project in my class, wrote the music, lyrics, and directed the following video on the issue.

Wednesday, April 15, 2009

Mental Strategies

The Salt Lake Tribune (April 13, 2009) ran an article entitled: Students build empires to learn math Education. Teacher creates game that offers pupils real world problems and decisions by Lisa Schencker.

A Utah teacher, Scott Laidlaw, encourages students to focus on solving problems using mental strategies rather than paper and pencil using a game called Empire created by the teacher. It's a way to teach math, Laidlaw said, that keeps students interested by showing them real world applications.

Fourth-grader Carson Luke said Empire makes math interesting. He said he hopes to one day build his empire, Constitution, to the point where he can start conquering his enemies. "At my old school, we just did worksheets and tests," Luke said. "In this game, it's much more hands-on."

Tuesday, April 14, 2009

Concepts BEFORE Procedures

You Do The Math: Explaining Basic Concepts Behind Math Problems Improves Children's Learning

ScienceDaily (2009-04-12) -- Students benefit more from being taught the concepts behind math problems rather than the exact procedures to solve the problems. The findings offer teachers new insights on how best to shape math instruction to have the greatest impact on student learning.

2nd Math Task Force Meeting

The 2nd NJDOE Math Task Force meeting has concluded. The morning was spent discussing common ground on calculators and alternative algorithms. After much discussion, a few sentences were agreed upon with respect to calculators. The agreement was:
Students should be able to calculate (+, - , x, ÷ ) without calculators
Students should develop proficiency with mental mathematics
Judicious use of calculators
Students should select appropriate tools

Alternative algorithm discussion continued without a clear common ground about the use of "the" standard algorithm.

In the PM, three groups were formed which each group editing and analyzing one standard (number, geometry, and algebra only). These groups will continue their work at the next (and final) meeting on April 20th.

What happens after April 20th is anyone's guess.
One DOE senior staffer even said and I quote: "We don't have a plan."
Another DOE senior staffer said: "A writing committee might been formed to write another set of standards."

Monday, April 13, 2009

Anti-Reformists & Common Ground: Not Likely

The purpose of the NJDOE task force is to reach common ground on the ongoing math discussion in NJ.  I am beginning to believe, however, that reaching common ground is not really the goal of the anti-reformists in NJ.  To date, I have resisted direct confrontation with these anti-reformists.  However, they have now decided to call my University (several times) and now have made open public records act (OPRA) to find out information about my grants.  Although I have nothing to hide and am very proud of my grants, why would the anti-reformists make such requests?  (To learn more about my grants, see newspaper articles in the Courier and the Chronicle.)   One can only imagine that the anti-reformists want to use such information to disqualify me from the NJDOE task force (even though DOE and the Commissioner is well aware of my successful grant activity.)  Seems that they really don't want to reach consensus, they want to remove anyone who disagrees with them.  There is further evidence of this as below appears an email that I received from one of the anti-reformists.  This email was received when the Concerned Mathematics Educators of NJ was initial formed.  The rhetoric is both disturbing and distressing and show the lengths that the anti-reformists will resort to.  Common ground is certainly not their goal.

I have reviewed the information on your web site and would like to comment.  Given the name of your organization, it is not surprising that the vast majority of those endorsing the positions on your web site are not individuals who are practicing mathematicians, engineers or scientists.  This is a serious flaw.
As educators, your role should be one of teaching, and not driving, the curriculum.  The curriculum goals should be driven by the expected outcomes, which in this case are success in the fields dependent upon proficiency in mathematics.   I find it abhorrent that mathematics educators are hoping to continue to dictate the content of math standards that will drive curricula throughout the state of NJ.  It is becoming increasingly evident that there is a clear divide between those who teach mathematics (or teach mathematics teachers), and those who actually use mathematics in their daily life as scientists, engineers, or in other professions. 

The failures in this educator-driven approach to curriculum are reflected in the continued decline of the United States dominant position in science, engineering and mathematics. Since the NCTM recommendations of ~20 years ago were developed into various curricula, the level of mathematics competency within the US has been abysmal.  Now, with the State of NJ poised to draft new core curriculum content standards for math that eschew many of the components of the NCTM recommendations, your group hopes to continue to hold NJ's students back by holding fast to the status quo.

Your listing of endorsers includes some individuals who have financially benefited from the standards development process.  These individuals have engaged in activities such as:  received grants, acted as consultants for school districts and/or the State of NJ to draft or select standards and/or curricula, or provided training to teachers and administrators regarding the selected standards or curricula.  In other industries, a situation where those who help to make policy then also receive financial benefit as a result of those policies could be considered a conflict of interest.  This is truly distressing. 

I urge the members of your organization to actually LISTEN to the parents, the taxpayers, the mathematicians, the scientists, the engineers, the IT professionals, the economists and others in NJ who are becoming increasingly concerned with the standards that your organization wishes to perpetuate.  I urge the members of your organization to review the studies showing a disconnect between what math educators believe to be important and what is actually important.  It's time for your organization and its membership to realize that the standards that you wish so dearly to hold onto are resulting in NJ's students being poorly-equipped for college or life.  

Please, please, please--for the sake of our children, STOP the pursuit of sub-standard mathematics standards and curricula and partner with parents, mathematicians, scientists and engineers to provide a solid mathematics education for NJ's students.

What is TRULY distressing is the rhetoric and tactics used by the anti-reformists. Common ground - very unlikely.

Constructivism vs Rote Learning in Science

A conversation with Dr. Eric Mazur (the Balkanski Professor of Physics and Applied Physics at Harvard University and an internationally recognized scientist and researcher) entitled Using the ‘Beauties of Physics’ to Conquer Science Illiteracy by Claudia Dreifus appeared in the NY Times in July 2007.

Dr. Mazur discusses rote memorization versus constructivism in his University classroom.

Dr. Mazur states:

It’s important to mentally engage students in what you’re teaching, he explains. We’re way too focused on facts and rote memorization and not on learning the process of doing science. From what I’ve seen, students in science classrooms throughout the country depend on the rote memorization of facts. I want to change this. The students who score high do so because they’ve learned how to regurgitate information on tests. On the whole, they haven’t understood the basic concepts behind the facts, which means they can’t apply them in the laboratory. Or in life.
Today, by having the students work out the physics problems with each other, the learning gets done. I’ve moved from being “the sage on the stage” to “the guide on the side.”

Sunday, April 12, 2009

National Math Panel Part2

The National Math Panel report continues to get huge "play" by the anti-reformists.  However the report is far from accurate.  Another critique of the report can be found by Jere Confrey (pictured), Alan P. Maloney, and Kenny H. Nguyen entitled Breaching the Conditions for Success for a National Advisory Panel. Confrey, Malonet and Nguyen identify six conditions for success for the work of high-level national panels and identify breaches in these conditions in the recent Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008). They question the trustworthiness, validity, and intellectual integrity of its findings and advice to the nation because of (a) an inappropriate composition of Panel expertise and biased selection of literature (Condition 1); (b) failure to appropriately and consistently apply methodological standards (Condition 2); and (c) inconsistencies between the task group and subcommittee reports and the final report (Condition 6). In asking what difference these breaches make, the authors recount recent events suggesting that these breaches have already contributed to degrading the national discussion of curriculum standards for K–12 mathematics education.

First, they review the composition of the panel members as follows:
The responsibility for the composition of the NMAP was unusual, considering the charge. The chair of the Panel was a chemist and distinguished emeritus university president. The other Panel members included six psychologists, four mathematics educators (one of these added during the final year), four mathematicians, one special educator, one middle school mathematics teacher, one policy researcher, and one reading researcher (U.S. Department of Education, 2008). This means that, of 19 members, only 5 (the mathematics educators and the mathematics teacher) regularly had sustained interactions with mathematics instruction at the K–12 level; fewer than half the Panel members had documented academic preparation in mathematics.

And what about the research cited by the report:
Despite the NMAP report’s focus on the learning of mathematics, of the total of 466 journal articles referenced in the task group’s report, mathematics education articles constituted only slightly more than 10%, whereas psychological accounts (i.e., those published in journals on psychology, child development, and educational psychology) constituted approximately 70% of the references. Of the 10 journals with 10 citations or more each, 9 (90%) were psychology-oriented.3 Only one leading research journal in mathematics education had more than 10 citations.

And the recommendations & conclusions:
Perhaps even more fundamental, however, are the ways in which the breaches of the conditions for success may have distorted the particular recommendations in the report. It will take much more time and a variety of critical reviews to discern the extent of the damage in this regard. Because the U.S. Department of Education was responsible for the composition and the oversight of the NMAP, it should be held responsible for breaching the conditions for success of the Panel and, in effect, undermining the potential benefits to the country of this endeavor. The result was a loss of opportunity for improving mathematics education in our nation.

Saturday, April 11, 2009

Fordham Institute Nonsense

Many anti-reformists often refer to a report entitled The State of State Standards 2006 by Fordham Institute as evidence of the failure of NJ Mathematics Standards. of course these same anti-reformists always ignore the tremendous performance of NJ students on the NAEP (but that will be a future post). The Fordham report has been reviewed by The Education Policy Research Unit at the Arizona State University. The full review can be found here. An excerpt is below.

The reviewed report assigns grades to the content standards of 49 states and the District of Columbia, on an A-F scale, and uses those grades as a basis for criticizing schools for lack of progress in improving standards. This review found no evidence supporting the validity of the grades and also found no evidence of a relationship to student academic performance, contrary to the report’s conclusions. The report’s claims in support of its grading practice were selectively data-mined and were seriously lacking in methodological rigor. Policymakers and educators would be ill-advised to base any decisions about policy or practice on the grades assigned by this report.

In summary, these three analyses were selectively mined from data gathered by Fordham – data which themselves are flawed and for which there is no evidence of validity. No rationale for Fordham’s unorthodox ad hoc analyses is provided, and those analyses are sorely lacking in methodological rigor. Indeed, the post-hoc massaging of the data reaches the point of absurdity, as the authors search for some approach to the data that might lend support to Fordham’s conclusion that content standards of the kind it rates highly do result, in fact, in improved student performance

Wednesday, April 8, 2009

Response to the National Math Panel

As the NJDOE math task force gets ready to meet for a second time next Tuesday, some members believe that NJ must follow the National Math Panel (NMP) report and recommendation. However, the NMP report was not exactly a balanced report by any means. Jo Boaler wrote a wonderful review of the report. Dr. Boaler is the Marie Curie Professor of Mathematics Education at the University of Sussex in England. Her article (When Politics Took the Place of Inquiry: A Response to the National Mathematics Advisory Panel’s Review of Instructional Practices) uncovers some of the politics behind the report. Boaler writes:
One of the most critical areas the panel chose to consider was the impact of different teaching approaches on student learning. In framing its review, the task group posed this question: “How effective is teacher-directed instruction in mathematics in comparison to student-centered approaches?” (Gersten et al., 2008, p. 12). The task group’s assertion that student-centered teaching involves teachers handing over the teaching of mathematics to the students is remarkable. Indeed the task group itself acknowledged that such definitions are “extreme” (Gersten et al., 2008, p. 30). The task group admits that it found no studies in which students were doing the teaching of mathematics, and it quotes from the National Research Council’s report Adding It Up(Kilpatrick et al., 2001), summarizing the different and complex forms of teaching in which student-centered teachers engage. The idea that showing and explaining would be absent from student-centered teachers’ pedagogy suggests that the task group members either held deep misunderstandings about student-centered teaching or that certain members of the group were engaged in a more politicized exercise. Even the strongest advocates of different teaching approaches would probably find the task group’s trivialized definitions of teaching to be inadequate, making any subsequent reviews of research redundant. The task group’s advocacy for an “extreme” and unrealistic definition of student-centered teaching was blamed on conversations held with teachers. This is particularly ironic given the Panel’s admonition to the readers of its report to recognize only experimental evidence.

Boaler continue her review of the report and its recommendation by stating:

More seriously perhaps, the National Mathematics Advisory Panel’s report presents a case of a government controlling not only the membership of a panel chosen to review research—a panel dominated by educational conservatives rather than mathematics researchers—but the forms of knowledge admissible in the public domain. In its adherence to government directions (Gersten et al., 2008, p. 213), resulting in the disregard of the field of mathematics education research, the Panel’s report communicates the view that the government, rather than academic researchers, should decide on the forms of knowledge that are legitimate in our pursuit of understandings about ways to help children learn (U.S. Department of Education et al., 2003). When governments step in to control research and knowledge production, limiting the methods used by researchers and the forms of knowledge acceptable, to the extent that a whole field of research is invalidated, then it is time to acknowledge that America’s celebrated freedom—of thought and inquiry—has been dealt a very serious blow.

If you want a copy of the full article, just send me an email and I will send you the file.

Monday, April 6, 2009


The Star Ledger ran an article on Sunday entitled: A new approach to an old math problem (The state looks to balance traditional and reform methods to improve learning). Once again the Commissioner was quoted as stating:
"I think there was a movement away from children mastering the basics of math -- the basics of division, multiplication, the basics around percentages. We began to rely on calculators," Davy said. "We need to wind up with a balance."
With all due respect, Mrs. Davy, movement away from mastering the basics? Where? I have visited hundreds and hundreds of classrooms across NJ and there is no elementary school teacher who has moved away from kids learning their basic facts. No where, no place. Such rhetoric is very disappointing and it shows a complete lack of reality of what is happening in the field. She also stated we began to rely on calculators? Who is the we? Do you blame the teachers of NJ? Do you blame their students? Calculator usage has always been balanced in the NJ standards. Always. It always seems to come back to calculators. That somehow these $1 tools cause students to not master their basic facts. It is such a sad and tired argument. Cathy Liebars, in contrast to the Commissioner, states:
"The traditional way of teaching math is to drill them until they memorize. That produced a lot of adults who hate math or don't understand math," said Cathy Liebars, a mathematician at the College of New Jersey and one of the founders of the Concerned Math Educators. "Kids don't just have to memorize things. They can learn basic facts while they are solving problems." And calculators help students "when the focus is not on doing the computing but on how to figure out how to solve the problem," Liebars said. "Teachers help them understand when it is appropriate."

I only wish the Commissioner was so eloquent.

Thursday, April 2, 2009

Algebra for All?

It is very easy for politicians and various parental groups to push for more algebra (algebra for all in 8th grade and algebra II for all in high school) and the rhetoric sounds so nice. But, the reality is much different. A March 2009 study in Education Week highlights this. The article: Algebra-for-All Policy Found to Raise Rates Of Failure in Chicago states:
The Chicago school district was at the forefront of that movement in 1997 when it instituted a mandate for 9th grade algebra as part of an overall effort to ensure that its high school students would be “college ready” upon graduation.
The policy change may have yielded unintended effects, according to researchers from the Consortium on Chicago School Research, based at the University of Chicago. While algebra enrollment increased across the district, the percentages of students failing math in 9th grade also rose after the new policy took effect.
By the same token, the researchers say, the change did not seem to lead to any significant test-score gains for students in math or in sizeable increases in the percentages of students who went on to take higher-level math courses later on in high school.
“This policy that Chicago tried in 1997 seems to be sweeping the country now and not a lot of thought is being given to how it really affects schools,” Elaine M. Allensworth, the lead researcher on the study, said in an interview.

The simplistic rhetoric of algebra for all and high standards for all does not address the mathematical readiness of students and the often irrelevant traditional algebra curricula. We must stop the rhetoric and discuss the real issues such as a curriculum that addresses the needs of the 21st Century (contextual application not rote drill) with the full integration of technology.

Wednesday, April 1, 2009

The evils of Technology

As I work on the draft of a white paper on calculators for the NJDOE math standards task force, I am reminding that the discussion about calculators can be extended to any technology including the Internet. Wired Magazine had a wonderful article: The Critics Need a Reboot. The Internet Hasn't Led Us Into a New Dark Age.
When in doubt, blame the latest technology. Socrates thought the advent of writing would wreak havoc on the powers of the mind.

I think Socrates was wrong and those who blame calculators ...