Friday, December 18, 2009

Thursday, December 17, 2009

Researchers Offer Dueling Views on Tracking

As the anti reformists continue their rhetoric that detracking is evil and hurts gifted children (the only one the anti-reformists ever write about), several dueling reports have been released about tracking. Of course, each report draws different conclusions. See here for both and send the one to your colleagues that supports your opinion like the anti-reformists do. I, however, choose to give both sides of the research.

Wednesday, December 16, 2009

Controlling a classroom isn't as easy as ABC --

Controlling a classroom isn't as easy as ABC --

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High School Exit Exam

One of my senior math majors at Rowan has compiled links to all 5o states high school exit exams in mathematics. It is interesting to see the requirements and content of the different exams in all 50 states. You can access the links here.

Thursday, December 10, 2009

Asian Nations

What is that high-performing Asian nations get right, when it comes to math teaching? A pair of researchers have explored that question in a new study, which examines the standards of Singapore, Hong Kong, and South Korea by creating a "composite" of their expectations in that subject.

Wednesday, December 9, 2009

Dont Let Washington Become NJ

Guest Columnist: Speaking math to the lay public By Bill Marsh
A well intentioned, partially informed and very political group of Washington citizens has convinced our Legislature to implement a 19th century mathematics curriculum in our schools. Since they believe that the half-century of work in mathematics education that started when Sputnik went up in 1957 was almost entirely misguided, they undervalue the ideas and research of the people who, in my lifetime, have worked hardest to better our children's learning of mathematics. Conversely, they tout the opinions of some of the louder research mathematicians who share their traditional views.

I am a mathematician with different views. I favor many progressive and reform ideas in mathematics education. But I am well aware that, as in other difficult areas of research and scholarship, mistakes are made, and ideas and opinions have to be abandoned or changed -- including some I once held.

Statements by practicing mathematicians should of course be taken seriously in mathematics education. Any reasonable person who has learned from mathematicians that there are an infinite number of primes would reject out of hand a fourth-grade curriculum built on a finite number of primes. The Washington State Board of Education would be justified in rejecting any curriculum that introduces real numbers in second grade, given that the mathematician it hired to review our state's standards has told them: "The point is that fractions are an essential intermediary step between whole number and real numbers." And since a renowned mathematician on the National Mathematics Advisory Panel recently convened by President Bush tells us that " must know what fractions are and how to add fractions before a decimal can be defined," surely no one should consider a curriculum that introduces decimals before fractions.

These two prominent mathematicians are honest, hard working scholars speaking the truth as they see it as a public service. Unfortunately, they often make statements about or in mathematics education and public policy in a manner that suggests these statements are mathematically certain. The two statements just quoted sound as if they are statements in mathematics. But they are not certain. In fact, they are not true.

There is a "naming trick" based on iterated halving with which second graders can understand and use real numbers, which they can call "measuring numbers," as "good names for dots on number lines." A six-year-old, who may or may not know what a tenth is, explains the trick in six minutes at
The idea behind this trick can be extended to decimals in third and fourth grades, before students have to face the horrors of fractions.

Mathematicians, it seems to me, have a special responsibility to be careful in how they speak to the lay public. Everybody knows that even the best knowledge in other fields is subject to revision, but that mathematics is different. I was told in high school chemistry 50 years ago that inert elements did not form compounds. Then along came xenon difluoride. I'm sure that our two mathematicians would agree that statements in mathematics education, including their own, have to be viewed and held more tentatively than those in chemistry.
Bill Marsh lives in Port Angeles. He taught in several secondary schools and colleges. He testified last year before K-12 education committees in the Legislature.

Tuesday, December 8, 2009

NJ to apply for federal stimulus money afterall

The Corzine administration reversed course Monday and said it would apply in January for the first round of competition for federal stimulus money that could bring more than $200 million to New Jersey’s public schools.

Saturday, December 5, 2009

Feedback on Common Core Released

Summary of Public Feedback on the Draft College- and Career- Readiness Standards

for English-Language Arts and Mathematics has released. Click here.

Thursday, December 3, 2009

Education Week: PTA Launches Campaign Backing Common Standards

Education Week: PTA Launches Campaign Backing Common Standards
and NJ is one of the states involved.
Note the anti-reformists comments at the end.

Tuesday, December 1, 2009

Business leaders in control - please no

Why Business Leaders Should Not Be in the Driver's Seat

Click here for full article

Yet now, we live in an age when it is the custom to bash the public schools, not to thank them for helping to build our nation. It has become commonplace for the president, the secretary of education, and the leaders of the business community to lament the terrible state of our schools and to demand radical, one might even say revolutionary, changes. We live in an age of data, and the data (they say) are awful. They look at NAEP test scores, international test scores, graduation rates, and anything else that is measurable, and they demand solutions, now.

Note that they never speak of the state of learning, nor even the state of education, because those words connote many intangibles that cannot be measured and converted into data. The politicians and business leaders do not speak about whether young people read in their spare time, whether their reading consists of good literature and non-fiction, whether they know how to write an engaging essay or a well-constructed research paper, whether they can engage in an informed discussion of history, whether they are knowledgeable about our governmental system, whether they perform volunteer service in their community, whether they leave high school prepared to serve on a jury and vote thoughtfully.

No, instead what we now hear from our business leaders is that the schools must be redesigned to function like business. They conveniently overlook the fact that business practices and the ruthless pursuit of a competitive edge nearly destroyed our national economy a year ago.

Wednesday, November 18, 2009

Lame Duck Commissioner Acts

New Jersey's lame duck education commissioner, Lucille Davy, released the following statement this week:

In May 2010, all students enrolled in an Algebra I course will take the Algebra I End of Course (EOC) Assessment. This administration will act as a formative assessment in preparation for the spring 2011 administration when passing the Algebra I EOC will be a graduation requirement. We have examined the results of the May, 2009 administration and are very concerned about the performance of the students on this assessment.

Thus she has single handedly confused the entire NJ mathematics education community and the students of NJ as on one hand she has committed the state to the Achieve Benchmarks and the Algebra I exam and on the other hand she has committed to the Common Core Standards. Thus, schools will have to change curricula now to meet the first and then change again later to meet the second.

Friday, November 13, 2009

Race to the Top

With the Race to the Top (federal education stimulus money) about to begin. It is interesting to see the huge contrast between Pennsylvania (who will compete for the funds) and New Jersey (who needs to read it). Quotes (Philadelphia Inquirer - Nov 13th) from each top education official are below.

Pennsylvania Education Secretary Gerald Zahorchak said he welcomed the competition.

The availability of Race to the Top funds presents a tremendous opportunity for all Pennsylvania's schools to build on our academic gains, and we are poised to compete vigorously for these funds," Zahorchak said in a statement. Zahorchak said Pennsylvania was on track to be "one of the first" states to apply for Race to the Top money, he said. The deadline for the first round of applications is in January.

In contrast, New Jersey Education Secretary Lucille Davy said her department had just received the 200-page application and wanted to review it before commenting.

Education Week: Funding for Common Assessments Poses Challenge

Education Week: Funding for Common Assessments Poses Challenge

Wednesday, November 11, 2009

K-12 common core writers

The K-12 common core standards writing group has been released.
Click here to see the list

Tuesday, November 10, 2009

Education Week: Will Science and Engineering Now Be a Good Career?

Education Week: Will Science and Engineering Now Be a Good Career?

Great article that refutes the false rhetoric that America's K-12 and colleges have a shortage of scientists and engineers

Thursday, November 5, 2009

Draft K-12 Standards Expected by Mid-December

Draft K-12 Standards Expected by Mid-December

Those of you who've been wondering when the next round of common, multistate standards would appear may want to clear some time in mid-December. That's when the first draft of K-12 standards are likely to be unveiled, says one of the officials leading that process.

Education Week: When Teachers Are the Experts

Education Week: When Teachers Are the Experts

Saturday, October 31, 2009

Faith in Common Standards Not Enough

To summarize, we found no association between state scores on the National Assessment of Educational Progress (NAEP) and ratings of the quality of state standards. We also drew attention to a little noticed finding from a recent federal study: weak to no association between state performance on NAEP and the stringency of performance standards for state assessments. In other words, when indexed by NAEP scores, differences among states in academic achievement do not seem to be related to differences in the quality of state content standards or the difficulty of passing the state assessment.

Monday, October 26, 2009

Ted Sizer dies

The Forum Mourns the Loss of Convener and Mentor Ted Sizer

It is with great sadness that we at The Forum share with you the news of the death of our friend and mentor, Ted Sizer. Ted lost his battle with cancer on Wednesday while at home with his family.

Monday, October 19, 2009

State of Mind

Two out of five of America’s 4 million K-12 teachers appear disheartened and disappointed about their jobs, while others express a variety of reasons for contentment with teaching and their current school environments, new research by Public Agenda and Learning Point Associates shows.

Wednesday, October 14, 2009

2009 NAEP

The 2009 NAEP Math scores were released today. Download the full report here.
Summary is below:
Highlights of the national results show that gains in overall average scores seen in earlier years did not continue at grade 4 but did continue at grade 8. While still higher than the scores in the six assessment years from 1990 to 2005, the overall average score for fourth-graders in 2009 was unchanged from the score in 2007. The upward trend seen in earlier assessments for eighth-graders continued with a 2-point increase from 2007 to 2009. There were no significant changes from 2007 to 2009 in the score gaps between White and Black students or between White and Hispanic students at either grade 4 or grade 8. State results for grade 4 show score increases since 2007 in 8 states and decreases in 4 states and jurisdictions. At grade 8, scores were higher in 2009 than in 2007 in 15 states and jurisdictions, and no states showed a decline.

Tuesday, October 13, 2009

Project MIND

Nice article in South Carolina newspaper
Once a child has a command of numbers, they can play around with them and find many ways of solving math problems, according to Su, who emphasizes teaching math concepts rather than the traditional use of teaching rules by rote memory.

“Unfortunately, that’s happening in our schools too often,” Su said. “They are just teaching rules after rules, and children are just learning rules without understanding math.”

Friday, October 9, 2009

Education Week: Standards Aren't Enough

Education Week: Standards Aren't Enough

Great article about common core and how revised curriculum and assessment must follow the standards.

Thursday, October 8, 2009

Education Week: 'Common Core' Standards Earn a B From Think Tank

Education Week: 'Common Core' Standards Earn a B From Think Tank

Note that this is the same neo-conservative group that gave NJ a "D" on our math standards and California an "A". Note also that those grades are the complete opposite of the performance of NJ and CA students on the NAEP assessments.

Tuesday, October 6, 2009

Focus in High School Mathematics: Reasoning and Sense Making

Today, NCTM announced the publication of NCTM’s Focus in High School Mathematics: Reasoning and Sense Making. This landmark book addresses high school mathematics by focusing on students’ reasoning and sense making, which are at the core of all mathematical learning and understanding.

Go online to learn more about Focus in High School Mathematics.
A set of Q&As and the news release are also posted online. You can purchase the book in print or electronic form, view sample pages, and download the Executive Summary as well as outreach brochures for teachers, administrators, policymakers, and families.

The first in a series of companion books will be published later this month. This book, Focus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability, will be followed soon by books that offer examples of ways to make reasoning and sense making central in algebra and geometry.

Monday, October 5, 2009


Jo Boaler, Marie Curie Professor, University of Sussex (England), formerly of Stanford, writes in the Fall 2009 NCSM Newsletter.

Antireformists have worked actively, effectively, and in some cases unethically to oppose any changes to math teaching, but how wide is their influence? I now believe the groups have not only organized campaigns against change, they have also created a fiction around their own importance and they do not well represent the public. Those of us who work as educators and know about children’s learning of mathematics need to question how groups who oppose change have managed to have such influence, we also need to be outraged by what they have done and continue to do.

Dr. Boaler’s sentiments above are very true especially with respect to the current issues in NJ. We have a small group of antireformists that we should be outraged by. I encourage all to read Dr. Boaler’s work and her new book, What’s Math Got to Do with It? I even mailed a copy to the Commissioner to read. I have several copies in my office. If you want one at no cost, just send me an email.

Friday, October 2, 2009

J.A. Paulos

"Mathematics is no more computation than typing is literature."

John Allen Paulos

Thursday, October 1, 2009

Economic competitiveness

As the antireformists ramp up their rhetoric about American lack of economic competitiveness, I refer to a quote by Lawrence Arthur Cremin in Popular Education and its Discontents pp. 102-103.

"American economic competitiveness with Japan and other nations is to a considerable degree a function of monetary, trade, and industrial policy, and of decisions made by the President and Congress, the Federal Reserve Board, and the Federal Departments of the Treasury, Commerce, and Labor. Therefore, to conclude that problems of international competitiveness can be solved by educational reform, especially educational reform defined solely as school reform, is not merely utopian and millennialist, it is at best a foolish and at worst a crass effort to direct attention away from those truly responsible for doing something about competitiveness and to lay the burden instead on the schools. It is a device that has been used repeatedly in the history of American education."

Education Week: Algebra 2 Test Yields Poor Results in Year II

Education Week: Algebra 2 Test Yields Poor Results in Year II

States that voluntarily took part in a demanding test of advanced algebra skills, given for a second straight year, again saw large proportions of their students struggle with that math content. At least 80 percent of students in all 13 states that participated in the exam this spring failed to meet the test’s threshold for being repared for entry-level college math. That poor showing mirrored the results from last year, when the Algebra 2 test was first piloted. Four states also took part in a separate Algebra 1 test this year, and the scores were also weak.

Thursday, September 24, 2009

Calculator Ban on NJASK

Commissioner Davy has released a memo today (September 24) changing the use of calculators on the NJASK 3-8. The memo can be read here. She has unilaterally (with little to no consultation from the field and ignoring current research) banned calculator use on all parts (except one section) of the NJASK grades 3 and 4. In grades 5-8, there will be an approximately 50/50 balance on calculator and non calculator items, which is appropriate (in my opinion) and was the recommendation of the math task force.

With this swift ban, there will be open ended (extended constructed response items) that will NOT allow a calculator in all grades. In fact, some ECR will allow a calculator and others will not. Moreover, the majority of items have NEVER been field tested without calculators but still will be operational without calculators this spring.

Instead of a clear strategy that would field test non calculator items and not allow calculator on computational items only, the commissioner has rushed to make a harmful decision to the students of NJ.

Sunday, September 6, 2009


"If a doctor, lawyer, or dentist had 40 people in his/her office at one time, all of whom had different needs, and some of whom didn't want to be there and were causing trouble, and the doctor, lawyer, or dentist, without assistance, had to treat them all with professional excellence for nine months, then he might have some conception of the classroom teacher's job."

(Donald D. Quinn)

Thursday, August 13, 2009

Editorial: Different animals

Editorial: Different animals
Policy makers shouldn't confuse schools with businesses 

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Wednesday, August 12, 2009

Incorrect facts

Very interesting article by Cognitive psychologist Gordon H. Bower of Stanford University who looks at: Why is it hard to "unlearn" an incorrect fact?

Building on the correct information can help you learn new associations to it: add something to change how you retrieve the item from your memory. You might replace your question “Name of John’s wife?” with “Name of John’s second wife?”; or use an elaboration that contains the accurate information, such as “We are weird” or “My niece is nice”; or convert 7 X 9 into 7 X (10 – 1) = 70 – 7 = 63. As you practice the elaborated association, the simpler direct association (7 X 9 = 63) eventually replaces the earlier one, which weakens without rehearsals. Labeling and rehearsing the wrong association (for example, saying to yourself, “7 X 9 is not 63”), however, are distinctly counterproductive.

Monday, August 10, 2009

Next Draft of Common Standards Due in Early September

Next Draft of Common Standards Due in Early September

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Schools Need Teachers Like Me. I Just Can't Stay

A wonderful article in the Aug 9 Washington Post by Sarah Pine entitled: Schools Need Teachers Like Me. I Just Can't Stay. She list several factors why she left teaching – one particular factor is below:
There is yet another factor that played a part in my choice, something that I rarely mention. It has to do with the way that some people, mostly nonteachers, talk about the profession.

Thursday, August 6, 2009

Education Week: Experts Hope Federal Funds Lead to Better Tests

Education Week: Experts Hope Federal Funds Lead to Better Tests

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The anti-reformists often demand that probability and statistics be removed from state standards.  They ignore the vital place that statistics plays in today's world.   An article by Steve Lohr in the August 5th edition of the NY Times entitled:  "For Today’s Graduate, Just One Word: Statistics" discusses the great need for Statistics in today's curriculum.  
“I keep saying that the sexy job in the next 10 years will be statisticians,” said Hal Varian, chief economist at Google. “And I’m not kidding.”

Sunday, August 2, 2009

Common Core & Federal Dollars LInked?

An interesting editorial in the NY Times (July 30th).  It clearly linked states' adoption of the Common Core Standards to Federal Government funds.  See below:

The president and the secretary are rightly interested in replacing a wild patchwork of standards with coherent common standards and tests that would allow parents to compare their schools with others. The government cannot and should not write those standards.  But states that have committed to joining, say, the standards consortium started by the National Governors Association will be favored in the funding competition over states that have not. More consideration will eventually be given to states that develop plans for adopting internationally benchmarked K-through-12 standards that build toward college and career readiness.

Wednesday, July 29, 2009

Common Core, the anti-reformists, and Connected Mathematics

The Common Core Standards are getting tons of press in the blogs, websites, and media.  It is interesting to read the opinions of many.  It is clear to me that the anti-reformists are aligned against the common core no matter what the core content is.  They clearly have their own agenda and compromise is not in their vocabulary.  

What is the anti-reformist's agenda?  Rid all schools of any NSF program and rid schools of inquiry driven pedagogy.  In particular, Connected Math and Everyday Mathematics are especially evil.  Thus, I post new research about Connected Math below.   The study is THE EFFECTS OF CONNECTED MATHEMATICS PROJECT 2 ON STUDENT PERFORMANCE: RANDOMIZED CONTROL TRIAL.  The results are summarized below:

Those using CMP2 and those using another curriculum scored comparably on standardized mathematics assessments, however, less conservative tests comparing CMP2 and non-CMP2 students indicated that CMP2 students significantly outperformed control students on the Balanced Assessment that reflects mathematical reasoning, problem solving and communication. In this study, it is clear that implementation of the CMP2 curriculum varied greatly across study sites and teachers despite the extensive professional development teachers received prior to implementing the program in their classrooms. However, we suspect that the level of implementation in the classroom, and consequently, teachers’ efficacy, may play a role in the extent to which students might be successful in using CMP2. A second year study will be conducted to investigate this hypothesis and determine more precisely whet her or not t he CMP2 curriculum is superior for students in comparison to alternative mathematics curricula. Student attitudes and achievement are better for those student s in CMP2 classrooms with higher levels of implementation, and consequently, it is expected that teachers implementing CMP2 for a second year would have greater fidelity of implementation as compared to their first year of using the curriculum. Comparing performance of students and teachers in a second year of implementation is a fairer test of the efficacy of the curriculum than the model used in the current study.

Thursday, July 23, 2009

Education Week: Draft Content Standards Elicit Mixed Reviews

Education Week: Draft Content Standards Elicit Mixed Reviews

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More on Common Standards

Draft Common Standards Hit the Internet
We're getting a peek at the draft academic standards that a work group is putting together.
Core Knowledge, an advocacy group that calls for giving students deep grounding in content across subjects, has posted a draft copy of the common, multistate standards on its Web site—and it argues that the document completely misses the mark.
The draft document represents the first step in an effort being led by the National Governors Association and the Council of Chief State School Officers to create common academic standards across states. Achieve, the ACT, and the College Board are also working on the project. The first set of standards, which the organizations have said they hoped to have completed by the end of this month, focuses on the standards for college and career readiness in language arts and math. Copies of the draft document had been circulating among some organizations for review, Robert Pondiscio, the communications director at Core Knowledge, wrote on the blog entry. His group decided to post them, because they saw no restrictions on doing so, he said.
The organization's view of the draft document is highly negative. Here's a piece from the online blog entry:
"The draft insists that the voluntary standards be 'coherent' but defines coherence to mean they 'should convey a unified vision of the big ideas and supporting concepts within a discipline and reflect a progression of learning that is meaningful and appropriate.' Framed as a series of benchmarks students must reach 'to be college and career ready,' the draft enumerates standards such as the ability to 'determine what text says explicitly and use evidence within text to infer what is implied by or follows logically from the text.'
"To put this as blandly as possible, this is neither a revelatory insight nor a meaningful standard. Educators hoping for guidance on what particular texts are expected to be taught, or how to get students to reach the bland and obvious standards will be disappointed."

Obviously, Core Knowledge has its own view of what should go into academic standards, and others reviewing the document will have their own. After you've had a look, give me your opinion.

UPDATE from guest blogger Catherine Gewertz: Gene Wilhoit of the CCSSO and Dane Linn of the NGA said it's too early to draw conclusions about the draft, since it lacks the feedback from working groups tasked to review it, and from governors and state chiefs. Once all that feedback is in, a revised draft—with evidence supporting each standard—will be available online, in mid-August, for further public comment. Wilhoit and Linn's overall message? That this draft represents just the first step in a much longer process.

Common Core Standards

Common Core Standards have been leaked today and they look DOA.
You can see them here

Monday, July 20, 2009

Some Interesting Questions

Some interesting questions appear at the EduWonk Blog below.    As the common standards are about to be released, please keep these questions in mind.

When people talk about “what (students) know and are able to do” they seem to mean: what they learn in school. Does anyone study the knowledge and skills young people actually have; look at what’s been learned outside school? Have a look at this to get a sense for how much more there is.

Are there to be consequences, ‘high stakes’, for a student not meeting standards? If so, then the standards will be fairly low, won’t they? The politics of this public institution mean that K-12 realistically can’t deny success to more than a small proportion of students. (Probably this explains the interest now in ‘benchmarking’, which lets everyone see performance compared to others while imposing no sanction.)

Is there a concept of achievement, then, above the standards? Surely high achievement (as in the STEM areas) must be important, especially for the country’s economic success. Where and how is that assessed? Who works to encourage high achievement?

Beyond a ‘basic’ level is it essential that all students achieve the same thing? Why are standards set in terms of exit from high school rather than in terms of entrance into what a young person wants to do next? Would it be OK to differentiate ‘achievement’ for different groups of students; for individual students? Might that diversification better serve to produce the breadth of accomplishment the country needs?

Is it really important for all students to master algebra? What fraction of the occupations actually require knowledge of Algebra II? Might it be better to try to get students to understand something of statistics: probability, risk, rates, proportions and such?

Do schools achieve — or is it only students who achieve? Is the students’ achievement the school’s achievement? Or is Professor Raudenbush correct that one cannot properly use measures of student proficiency to draw conclusions about school performance?

Should achievement be treated as something adults do? That seems implied when we talk of education being ‘delivered’. But in the end who does determine what a student knows and is able to do?

Tuesday, July 14, 2009

NJDOE Math Task Force Update

Nearly two months after the last NJDOE math task force meeting, NJDOE has found the time to issue the following statement:

TO:     Members of the Math Standards Task Force
FROM:   Willa Spicer, Deputy Commissioner & Sandra M. Alberti, Director, Office of Math and Science Education
DATE:   July 10, 2009
RE:   Update on New Jersey Math Standards

It has been well over a month since the last time we all formally gathered as a task force.  Certainly, a lot has happened during that time.  Attached please find a document that captures the products of our discussions and work together as a task force as well as a brief update regarding the common core initiative. Our intention in bringing this group together was to address many of the issues being debated regarding the math standards. We are very pleased with the commitment of task force members to grapple with these issues as a group. We believe that this experience was valuable to our staff as well as to many of the participants.

In moving forward, we will first consider the documents that come from the common core initiative. We look forward to sharing the drafts with you as well as larger stakeholder groups throughout the state. Our collective work that is represented in this packet, as well as the resources that each of you brought to this work, will certainly help to inform this process. Please accept our sincere gratitude and appreciation for your dedication and commitment to mathematics education in New Jersey. We look forward to more opportunities to work together in the future as we continue our work.

Notice, in particular, the words "we will first consider the documents that come from the common core initiative".  I will share some insight about the common core initiative in the next post.  Full memo from the NJDOE.

Thursday, July 2, 2009

Common Core State Standards Development Work Group and Feedback Group Announced

Common Core State Standards Development Work Group and Feedback Group Announced
NGA Center, CCSSO Unveil New Web site
Outline Process to Develop Common English-language Arts and Mathematics Standards

Monday, June 29, 2009

NJDOE Math Task Force Dies without DOE Action

The NJDOE convened a math task force which met for 4 full days and to date, DOE, has ignored the task force and has not released one iota of information from the task force.  Thus, I wrote the following letter to DOE:

Now that the Math Standards Task Force has completed its work, a number of us want to address the issue of what will happen next.  For the Department of Education to develop a set of math standards that will provide teachers, schools, and districts with the guidance that they need to enable our students to achieve high expectations in mathematics, it is critical that the next steps, following the efforts of the Department’s Task Force, build on the good work already done and involve people who are best able to craft the standards New Jersey deserves.

Concurrent with the Department’s Task Force, the New Jersey Mathematics and Science Education Coalition convened a working group of experienced math educators to take the two early versions of the standards, the December version prepared by the Department of Education’s writing team and the February version prepared by the Department of Education’s staff, and develop a set of recommendations that combines the best of them.  That document came to be valued and used by a number of members of the Task Force as it deliberated; it should be integral to any subsequent development of the math standards.

There are many people who can examine and critique individual indicators in the standards, including many of the members of the Task Force.   But only those with a more intimate knowledge of the curriculum, such as math supervisors and curriculum specialists, are able to see the standards as a whole, so that an individual indicator is not only analyzed in itself, but also in regard to how it fits in the K-12 flow within its standard and how it fits it with indicators in other standards at its and nearby grade levels.  Those are the people who should be called upon to provide advice on the content of the standards.

Writing standards requires a team whose members:

ª have a deep understanding of mathematics and of the PreK-12 mathematics curriculum

ª understand the curricular consequences of what might appear to be a modest change of language

ª can write concisely and clearly

ª understand assessment and have experience with a wide range of types of questions including multiple-choice and extended response

ª have knowledge of a wide variety of curricula in order to ensure that appropriate, high-quality instructional materials are available

ª have knowledge of the psychology of learning mathematics so that content is developmentally appropriate.

Even those who have experience with the content cannot necessarily translate their recommendations into the language of standards.  The people in New Jersey who have the greatest experience and expertise in doing that are Janet Caldwell, Warren Crown, Bob Riehs, Joe Rosenstein, and Bill Smith (Crown and Smith are now retired and may therefore not be available).  In addition to and because of their qualifications, they have the trust of their colleagues across the state. They should be key players in the further development of math standards which are both credible to the field and of the highest quality.

Friday, June 26, 2009

Big News at Rowan

With the stroke of a pen, Gov. Jon S. Corzine Thursday changed the landscape of higher education and health care in South Jersey.  Through an executive reorganization plan submitted by the governor to the state Legislature on Thursday, Corzine requested the creation of a four-year allopathic medical school on Broadway in Camden that would combine the resources of Cooper University Hospital and Rowan University. The result would be the fourth medical school in New Jersey, and the only one not to be affiliated with the University of Medicine and Dentistry of New Jersey.

Saturday, June 20, 2009

The Structure of Educational Revolutions

In his widely influential book, The Structure of Scientific Revolutions [7], Thomas Kuhn argued that, while science usually proceeds by taking small steps based on the accepted paradigm at the time  ("normal science"), occasionally it is recognized that the current paradigm is incapable of solving important problems and what is needed is a new paradigm (a "paradigm shift") One example is the Copernican revolution in the 16-17th centuries where the paradigm of a geocentric universe was gradually replaced by that of a heliocentric universe.  A second example is the chemical revolution caused by Lavoisier's discovery of oxygen that replaced the phlogiston theory that posited that all flammable substances contain a material ("phlogiston") that enables them to burn.  A third example is the Einsteinian revolution that made Newtonian mechanics a limiting case of relativistic mechanics for small velocities.

What does this have to do with mathematics education.  Well, read on...

Calculators and the Elementary School Mathematics Curriculum
Arithmetic has been at the heart of the elementary school mathematics curriculum for many centuries.   Since counting has been important for as long as there has been human civilization and since, except for geometry, there was - and still is - just about no other mathematics accessible to children of elementary school age, arithmetic has been and still is a crucial, indeed a dominant part of the elementary school mathematics curriculum.  And so, I believe, it should remain.  The relevant issue here is:  How should arithmetic be taught to students?

There is (almost?) no one who questions that an understanding of what addition, subtraction, multiplication and division are and an ability to discern when each of these operations is the appropriate one to use should be in every child's mathematical arsenal at some point in his/her elementary school career.  Neither is there any substantial disagreement among mathematicians or mathematics educators or anyone else that students need to achieve virtually instant recall of the addition and multiplication tables as early as possible in their educational careers.

For at least the past two centuries the heart of the elementary school arithmetic curriculum has been instruction in the pencil-and-paper algorithms (hereafter PPA) of addition, subtraction, multiplication and division that all readers of this article surely recall from their own schooldays.  Until the advent of the hand-held calculator these algorithms were of substantial practical value, being essentially the only way for almost everyone to add columns of figures, subtract one sizable number from another, multiply two multi-digit numbers or perform long division .  But now the practical value of these algorithms has all but disappeared.  The question is:  Are these algorithms still the best way to impart the understanding of arithmetic necessary to prepare students for the further study of mathematics?

The Math Wars

Mathematics education, particularly in the United States , has been a subject of controversy for some 40 years now since the time of the New Math in the 1960s.  Indeed, the New Math has been called the first of three "revolutions" in mathematics education [2], the other two being the back-to-basics reaction to the New Math and the changes wrought by the NCTM Standards (hereafter the Standards) [10].  The first two of these, however, whatever you may think of either, were not revolutions in the Kuhnian sense and the last, whatever the long term impact of the Standards, proposed only a modernization of school mathematics education rather than anything revolutionary.

One thing the Standards did do, however, was to spark the so-called Math Wars which for nearly 20 years now have pitted mainly research mathematicians but also some parents, business groups and teachers and others (Traditional Math Warriors - TMWs) against mainly mathematics educators but with significant support from some parents, teachers and others (Reform Math Warriors - RMWs) [5, 12].  At times these wars have led to acrimonious exchanges between the two sides; at other times the exchanges have been more genteel.  There have even been recent attempts at truces [3] and fudges [9].  But an end to the Math Wars is not in sight nor, I believe, should it be because the essential issues are too important and the essential positions of the two sides are so far from each other that what is needed is victory for one side, not a pale compromise that, in the long run, would not be good for anyone.

Calculator technology has been the catalyst for almost all the disputation in the Math Wars.  Since this technology almost wholly diminishes the practical value of PPA, it is essential to answer the question above about whether these algorithms are the best way, even an effective way to prepare students for further study of mathematics.  In one sense, the answer to this question is clearly, yes, since there is no alternative to these algorithms that has ever been tried in schools anywhere.

Some places, notably California, have, after some experiments with calculators in elementary school mathematics, returned to a "back-to-basics" curriculum in which calculators are effectively banned in the classroom through the sixth grade.  In many other places curricula are in use in which calculators are used in conjunction with traditional instruction in PPA.  There are lots of variations in these curricula.  Judging only by test results and anecdotal evidence, some of these curricula seem just as or more effective than traditional PPA curricula while others do not seem to perform very well.  In some partly-calculator curricula, the traditional algorithms for addition, subtraction and multiplication are taught but long division is no longer taught.  This is in line with a 25-year-old recommendation from Great Britain [4] that is, however, anathema to TMWs.

The More Distant Future

It is only reasonable to conclude this paper by asking the question:  If the computer revolution presages a paradigm shift in elementary school mathematics education, will there also be paradigm shifts in other aspects of mathematics education?

It is true today that essentially all the manipulations of mathematics taught not just to elementary school students but also to secondary school students and to university undergraduates can now be performed by hand-held devices and, in virtually all cases, more rapidly and accurately than (almost) any human can perform them.  What value then to teaching any of the old, almost entirely pencil-and-paper manipulations taught almost universally in secondary schools and universities?  The answer to this question is not so simple as I believe it to be in the case of elementary school arithmetic.  As with arithmetic, the practical valueof learning to do these manipulations is rapidly decreasing.  But it cannot be said, at least it cannot be said yet, that learning these manipulations is not the best way to understand the underlying mathematics and, therefore, the best way to proceed to the study of further mathematics.  Nevertheless, I would be surprised if more and more of the current secondary and university mathematics curricula were not replaced in coming decades by new curricula in which calculators and computers are fully integrated into them (mental algebra?  mental calculus?).

Thursday, June 18, 2009

Wolfram|Alpha Search Engine

Sum Help: New Search Engine for Mathletes

Wolfram Alpha Site Automates Arithmetic Drudgery for Students, but Teachers Worry It Does Homework, Too

I bet the anti-reformists want this "banned" from schools too.

Wednesday, June 17, 2009

STEM Careers

A previous post referred to an article by Gerald Bracey in Phi Delta Kappan (March 2008) entitled "On the Shortage of Scientists and Engineers".  The full article can be found here.

Education Week: Subject-Matter Groups Want Voice in Standards

Education Week: Subject-Matter Groups Want Voice in Standards

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Tuesday, June 16, 2009

Abolish Paper & Pencil Arithmetic

Let's Abolish Pencil-and-Paper Arithmetic by Anthony Ralston (Imperial College, London).  The paper appeared in Volume 18, Number 2, pp. 173-194 (1999) of the Journal of Computers in Mathematics and Science Teaching.  (The anti-reformists will love this article!)  The article proposes that paper-and-pencil arithmetic no longer be taught in elementary school and that it be replaced by a curriculum which emphasizes mental arithmetic much more than at present and in which calculators are used for instructional purposes in all grades including kindergarten. The article analyzes and refutes the arguments made by "back-to-basics" proponents against the use of calculators and for traditional instruction in the algorithms of pencil-and-paper arithmetic. The value of mental arithmetic in achieving all the aims - and more - of the traditional curriculum is argued. Also considered is the outline of an elementary school mathematics curriculum without pencil-and-paper arithmetic. As well, the impact of such a curriculum on secondary school and college mathematics is discussed. Finally, the barriers to achieving what the article advocates are assessed.  To read the full article, click here.

Monday, June 15, 2009

On the shortage of scientists and engineers

The anti-reformists have continued their rhetoric with respect to the failures of the US in math and science.  
Gerald Bracey in Phi Delta Kappan (March 2008) does a wonderful job of responding to them. 
His article, On the shortage of scientists and engineers, touches on many aspects.
He response to the U.S. TIMSS data is below:
While the U.S. is middling in ranks in math and science assessments, the differences among countries in terms of scores are often quite small. The most extreme occurrence of this phenomenon was in the eighth-grade science assessment for the 1995 TIMSS (Third International Mathematics and Science Study). American students got 58% of the items correct, compared to 56% for the international average. This ranked them 19th among the 49 participating nations. Middling performance, no? Had they gotten a mere 5% more correct answers, they would have ranked fifth, and had they gotten 5% fewer correct, they'd have slumped to 30th.
He also points out two other major fallacies of the anti-reformists:

1. The U.S. suffers serious shortfalls or shortages of scientists and engineers, and this bodes ill for both creativity and international competitiveness.
RESPONSE: There is no shortage. Several RAND Corporation studies found surpluses. There might be shortages in some new fields or fields growing explosively, but not overall.
2. The number of newly educated scientists and engineers is insufficient to fulfill employer needs. Thus the need to hire from   overseas.
RESPONSE: There are substantially more scientists and engineers graduating from U.S. universities than can find attractive career openings in S & E fields. Indeed, the S & E opportunities seem unattractive to many holders of S & E degrees. "Into the Eye of the Storm" (no doubt a pot shot at the National Academies), a paper by Lindsay Lowell of Georgetown University and Harold Salzman of the Urban Institute, found roughly three S & E graduates for every new S & E job (not counting openings created by retirements). They also found that two years after graduation from S & E programs, 20% of the grads with bachelor's degrees were in school but not in S & E programs and 45% were in the work force but not in S & E jobs. The attrition rate for that time period for those with master's degrees was about 38%. One can only imagine how critics would howl if education lost 65% of its work force in just two years!

Nor are fewer students following S & E paths in universities. From 1977 to 2002, the number of citizens and permanent residents earning bachelor's degrees in S & E grew from about 300,000 to about 400,000, those earning master's degrees increased from about 60,000 to about 70,000, and those earning doctorates held steady at about 20,000.

Other studies have concluded that the decline in the pool of citizens and permanent residents with S & E credentials may reflect a weakening demand, a comparative decline in S & E wages, and market signals to students about low relative wages in S & E. I'm not sure exactly what the "market signals" are, but real wages for S & E workers have declined over a 20-year period. And students can see older scientists spending more time writing grant applications, getting fewer of them funded, and having a tougher time getting tenure. They can see the post-doc headed for what science writer Dan Greenberg calls the newest title: post-doc emeritus. And students, not surprisingly, head to greener fields.

Finally, there is some evidence that the nature of the engineering profession has become less appealing. Lowell and Salzman observe that projects today are often larger team efforts that require more coordination and management. In their interviews, engineers often commented that the field was not as challenging as it once was because it contains less "real" engineering.