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Sensenbrenner on Connected Math



Running some searches recently, I came across this April, 2004 article by Lee Sensenbrenner on Connected Math. The words remain timely more than two years later:

A seventh-grader at a Madison middle school is posed with the following situation: A gas station sells soda in three sizes. A 20-ounce cup costs 80 cents, a 32-ounce cup is 90 cents and a 64-ouncer goes for $1.25.
The first question, which appeared in similar form on a recent exam, is as traditional as any mathematical story problem: What size offers the most soda for the money?
But the second question carries the spirit of the Connected Math Program, which has developed strong undercurrents of controversy – both here and nationally – and plays prominently in one of the Madison School Board races Tuesday.
This question asks: If the gas station were to offer an 84-ounce Mega Swig, what would you expect to pay for it?
There’s really no concrete answer. A student, for instance, could argue that the 84-ouncer would cost what the 20-ounce and 64-ounce cups cost together. Another student could say that soda gets cheaper with volume, and then choose an answer based on some per-ounce price slightly less than what was given for the 64-ounce drink.
For the people fighting an impassioned battle over Connected Math, the differences between question number one and question number two are not subtle or inconsequential.
On one side, those who support Connected Math say that engaging students by presenting problems as real-life scenarios – often with no absolute solution or single path to arrive at an answer – fosters innovation and forces students to explain and defend their reasoning as they discover mathematical concepts.
The other side says the approach trades the clear, fundamental concepts of math, distilled through thousands of years of logical reasoning, for verbiage and vagary that may help students learn to debate but will not give them the foundation they need for more advanced mathematical study.

Many links and articles on math can be found here. The recent Math Forum is also worth checking out, along with a discussion of the District’s math performance.

I’m told that the MMSD’s math curriculum will be getting some attention this fall. We’ll see (35 of 37 UW Math Faculty Open Letter on Math).

My largest concern with Connected Math – having read some of the books is that we’re training the students to be consumers, not creative types (figure out the phone bill, count the cheerios, buy a soda, etc.). TeacherL made a great point recently: We can choose to be consumers or we can choose to be citizens. I know which one I think will provide the stronger future for our country.”




Analysis of Connected Math and Core Plus Textbooks



A reader deep into math issues emailed these two reviews of curriculum currently used within the Madison School District:

  • Connected Math (Middle School); R. James Milgram:

    The philosophy used throughout the program is that the students should entirely construct their own knowledge and that calculators are to always be available for calculation. This means that

    • standard algorithms are never introduced, not even for adding, subtracting, multiplying and dividing fractions
    • precise definitions are never given
    • repetitive practice for developing skills, such as basic manipulative skills is never given. Consequently, in the seventh and eighth grade booklets on algebra, there is no development of the standard skills needed to solve linear equations, no practice with simplifying polynomials or quotients of polynomials, no discussion of things as basic as the standard exponent rules
    • throughout the booklets, topics are introduced, usually in a single problem and almost always indirectly — topics which, in traditional texts are basic and will have an entire chapter devoted to them — and then are dropped, never to be mentioned again. (Examples will be given throughout the detailed analysis which follows.)
    • in the booklets on probability and data analysis a huge amount of time is spent learning rather esoteric methods for representing data, such as stem and leaf plots, and very little attention is paid to topics like the use and misuse of statistics. Statistics, in and of itself, is not that important in terms of mathematical development. The main reason it is in the curriculum is to provide students with the means to understand common uses of statistics and to be able to understand when statistical arguments are being used correctly.

  • Core Plus (some high schools); R. James Milgram and Kim Mackey:

    In a recent issue of the NCTM Dialogues, Prof. R. Askey comments on a particular and remarkably inept misunderstanding in CorePlus, of some basic methods in probability Prof. R. Askey’s comments on a problem with Core Plus.
    Recently, Core Plus has begun to appear in the Minnesota High Schools, with the usual results, including servere questions from parents and the withdrawal of a significant number of students from the school system. This has also prompted a number of independent analyses of the program by other professional mathematicians. Here are the comments of Larry Gray, a Professor of Mathematics at the University of Minnesota. A Sample List of Mathematical Errors in the Core Plus program.




Madison Superintendent Search Commentary; Groundhog Day, in some ways



Negassi Tesfamichael:

“I think the most important quality we are looking for in an interim superintendent is stability,” School Board member Cris Carusi said. “I don’t think it really matters as much if it’s an internal or external candidate … we’re going to want someone who can provide stability.”

Carusi noted that she hopes the board can engage in an open process when selecting a new superintendent.

“I really hope we have a transparent, public process for choosing a new superintendent where we are able to get input from our staff and our community,” Carusi said. “We absolutely have to do that for our superintendent process and I think on some level for the interim selection process as well.”

Will the interim superintendent eventually be hired as permanent superintendent?

Rainwater was hired as an interim superintendent before the board voted to hire him after conducting its search process. However, whether to have an interim superintendent considered for a long-term post is something the School Board will have to decide as it crafts the characteristics of who it wants to hire as the new district leader.

“When we did our search, we didn’t want the interim to be a person to be considered for the full job,” Howard said. “That’s something the board will have to decide. When we did it six years ago, we determined we didn’t want that person to be in consideration for the job, but that does not have to be the case this time.”

Oh, the places we go: Madison Superintendents (2012):

Assistant superintendent Art Rainwater was elevated (no one else applied) to Superintendent when Cheryl Wilhoyte was pushed out. Perhaps Madison will think different this time and look outside the traditional, credentialed Superintendent candidates. The District has much work to do – quickly – on the basics, reading/writing, math and science. A steady diet of reading recovery and connected math along with above average spending of nearly $15k/student per year has not changed student achievement.

“The data clearly indicate that being able to read is not a requirement for graduation at (Madison) East, especially if you are black or Hispanic”

2005 (!): When all third graders read at grade level or beyond by the end of the year, the achievement gap will be closed…and not before: :

On November 7, Superintendent Art Rainwater made his annual report to the Board of Education on progress toward meeting the district’s student achievement goal in reading. As he did last fall, the superintendent made some interesting claims about the district’s success in closing the academic achievement gap “based on race”.

According to Mr. Rainwater, the place to look for evidence of a closing achievement gap is the comparison of the percentage of African American third graders who score at the lowest level of performance on statewide tests and the percentage of other racial groups scoring at that level. He says that, after accounting for income differences, there is no gap associated with race at the lowest level of achievement in reading. He made the same claim last year, telling the Wisconsin State Journal on September 24, 2004, “for those kids for whom an ability to read would prevent them from being successful, we’ve reduced that percentage very substantially, and basically, for all practical purposes, closed the gap”. Last Monday, he stated that the gap between percentages scoring at the lowest level “is the original gap” that the board set out to close.

Unfortunately, that is not the achievement gap that the board aimed to close.




The man who studies the spread of ignorance



Georgina Kenyon:

Proctor found that ignorance spreads when firstly, many people do not understand a concept or fact and secondly, when special interest groups – like a commercial firm or a political group – then work hard to create confusion about an issue. In the case of ignorance about tobacco and climate change, a scientifically illiterate society will probably be more susceptible to the tactics used by those wishing to confuse and cloud the truth.

Related: Connected Math and Reading Recovery.




Tyrany of Low Expectations: Will lowered test scores bring about broader change in Madison schools?



Chris Rickert via several kind readers:

Wisconsin has a “long way to go in all our racial/ethnic groups,” said Adam Gamoran, director of the Wisconsin Center for Education Research at UW-Madison.
My hope is that, given Wisconsin’s overwhelmingly white population, proficiency problems among white students will spur more people to push for policies inside and outside of school that help children — all children — learn.
“I hate to look at it that way, but I think you’re absolutely right,” said Kaleem Caire, president and CEO of the Urban League of Greater Madison. “The low performance of white students in our state may just lead to the type and level of change that’s necessary in public education for black and other students of color to succeed as well.”
Indeed, Gamoran said Massachusetts’ implementation of an evaluation system similar to the one Wisconsin is adopting now has been correlated with gains in reading and math proficiency and a narrowing of the racial achievement gap in math. But he emphasized that student achievement is more than just the schools’ responsibility.
Madison has known for a while that its schools are not meeting the needs of too many students of color.

The issue of low expectations and reduced academic standards is not a new one. A few worthwhile, related links:




A $30 Million Puzzle ‘Solution’? What We Have Here Is a Failure to Communicate



Like many citizens, journalists, and some of my fellow board members, I have been struggling to make sense of the projected $30 million budget or tax gap. Like others who have tried to understand how we got to the number “$30,” I have tried several approaches to see if I could come to the same conclusion. Some of them focused on an unexpected major rise in spending, or, an unexpected or unexplained loss of revenue beyond the $17 million in state cuts. (See Susan Troller’s Madison School’s ‘Budget Gap’ is Really a Tax Gap, for example.)
The answers for the portion of the gap that I could not understand or explain kept coming back to the tax levy. District staff were patient and helpful in trying to answer my questions, but we still didn’t understand each other. The shortest version of the tax levy explanation comes from the district’s Budget Questions and Answers handout.
To recap, the MMSD $30 million budget gap has been explained thusly by
administration. There are two parts to the gap, $1.2 million in expenses that cannot be met, and $28.6 million shortfall from a combination of state funding cuts and tax levy. To date, administration has explained the gap thusly:
This gap is $28.6 million. This total is composed of three parts:
* $9.2 million cut in state aid the MMSD sustained this year;
* $7.8 million cut in state aid the district will sustain next year;
* $11.6 million of increased costs that come with levying authority – broken out in two parts:
— $7.6 million of increased costs in order to deliver the same services next year that the MMSD is delivering this year, and which the state funding formula allows;
— $4.0 million of increased costs and with levying authority from the approved 2008 referendum)
$28.6 million Tax Shortfall Total
For me, and for others, the sticking point has been the idea that additional levying authority through the referendum and the state funding formula, would add to the shortfall in funds to run our schools. That is, how could more funds turn into a funding loss? Or, put in mathematical terms, how could -17 + 11.6 become -28.6? My math is rusty, and I don’t understand connected math, but it did seem to me that it was unlikely that a negative number would get larger after adding a positive number to it.
Full post on-line at lucymathiak.blogspot.com




Response to the Madison School District’s Math Task Force Recommendations



To: comment@madison.k12.wi.us
Cc: askey@math.wisc.edu
There are a number of points in the Summary of Administrative Response to MMSD Mathematics Task Force Recommendations which should be made. As a mathematician, let me just comment on comments on Recommendation 11. There are other comments which could be made, but I have a limited amount of time at present.
The first question I have is in the first paragraph. “One aspect of the balanced approach is represented in the four block approach to structuring mathematics lessons. The four blocks include Problem Solving, Number Work, Fluency and Maintenance and Inspecting Equations.” There is a missing comma, since it is not clear whether Maintenance goes with the previous word or the last two. However, in either case, “Inspecting Equations” is a strange phrase to use. I am not sure what it means, and when a mathematician who has read extensively in school mathematics does not understand a phrase, something is wrong. You might ask Brian Sniff, who seems to have written this report based on one comment he made at the Monday meeting, what he means by this.
In the next paragraph, there are the following statements about the math program used in MMSD. “The new edition [of Connected Math Project] includes a greater emphasis on practice problems similar to those in traditional middle and high school textbooks. The new edition still remains focused on problem-centered instruction that promotes deep conceptual understanding.” First, I dislike inflated language. It usually is an illustration of a lack of knowledge. We cannot hope for “deep conceptual understanding”, in school mathematics, and Connected Math falls far short of what we want students to learn and understand in many ways. There are many examples which could be given and a few are mentioned in a letter I sent to the chair of a committee which gave an award to two of the developers of Connected Mathematics Project. Much of my letter to Phil Daro is given below.
The final paragraph for Recommendation 11 deals with high school mathematics. When asked about the state standards, Brian Sniff remarked that they were being rewritten, but that the changes seem to be minimal. He is on the high school rewrite committee, and I hope he is incorrect about the changes since significant changes should be made. We now have a serious report from the National Mathematics Advisory Panel which was asked to report on algebra. In addition to comments on what is needed to prepare students for algebra, which should have an impact on both elementary and middle school mathematics, there is a good description of what algebra in high school should contain. Some of the books used in MMSD do not have the needed algebra. In addition, the National Council of Teachers of Mathematics has published Curriculum Focal Points for grades PK-8 which should be used for further details in these grades. Neither of these reports was mentioned in the response you were sent.

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Madison Math Task Force Public Session Wednesday Evening 1/14/2009



The public is invited to attend the Cherokee Middle School PTO’s meeting this Wednesday, January 14, 2009. The Madison School District will present it’s recent Math Task Force findings at 7:00p.m. in the Library.
Cherokee Middle School
4301 Cherokee Dr
Madison, WI 53711
(608) 204-1240

Notes, audio and links from a recent meeting can be found here.
A few notes from Wednesday evening’s meeting:

  • A participant asked why the report focused on Middle Schools. The impetus behind the effort was the ongoing controversy over the Madison School District’s use of Connected Math.
  • Madison’s math coordinator, Brian Sniff, mentioned that the District sought a “neutral group, people not very vocal one end or the other”. Terry Millar, while not officially part of the task force, has been very involved in the District’s use of reform math programs (Connected Math) for a number of years and was present at the meeting. The 2003, $200,000 SCALE (System-Wide Change for All Learners and Educators” (Award # EHR-0227016 (Clusty Search), CFDA # 47.076 (Clusty Search)), from the National Science Foundation) agreement between the UW School of Education (Wisconsin Center for Education Research) names Terry as the principal investigator [340K PDF]. The SCALE project has continued each year, since 2003. Interestingly, the 2008 SCALE agreement ([315K PDF] page 6) references the controversial “standards based report cards” as a deliverable by June, 2008, small learning communities (page 3) and “Science Standards Based Differentiated Assessments for Connected Math” (page 6). The document also references a budget increase to $812,336. (additional SCALE agreements, subsequent to 2003: two, three, four)
  • Task force member Dr. Mitchell Nathan is Director of AWAKEN [1.1MB PDF]:

    Agreement for Releasing Data and Conducting Research for
    AWAKEN Project in Madison Metropolitan School District
    The Aligning Educational Experiences with Ways of Knowing Engineering (AWAKEN) Project (NSF giant #EEC-0648267 (Clusty search)) aims to contribute to the long-term goal of fostering a larger, more diverse and more able pool of engineers in the United States. We propose to do so by looking at engineering education as a system or continuous developmental experience from secondary education through professional practice….
    In collaboration with the Madison Metropolitan School District (MMSD), AWAKEN researchers from the Wisconsin Center for Educational Research (WCER) will study and report on science, mathematics, and Career and Technical Education (specifically Project Lead The Way) curricula in the district.

  • Task force member David Griffeath, a UW-Madison math professor provided $6,000 worth of consulting services to the District.
  • Former Madison Superintendent Art Rainwater is now working in the UW-Madison School of Education. He appointed (and the board approved) the members of the Math Task Force.

Madison School Board Vice President Lucy Mathiak recently said that the “conversation about math is far from over”. It will be interesting to see how this plays out.
I am particularly interested in what the ties between the UW-Madison School of Education and the Madison School District mean for the upcoming “Strategic Planning Process” [49K PDF]. The presence of the term “standards based report cards” and “small learning communities” within one of the SCALE agreements makes me wonder who is actually driving the District. In other words, are the grants driving decision making?
Finally, it is worth reviewing the audio, notes and links from the 2005 Math Forum, including UW-Madison math professor emeritus Dick Askey’s look at the School District’s data.
Related: The Politics of K-12 Math and Academic Rigor.




Madison Math Task Force Minutes



March 7, 2008 Meeting [rtf / pdf]. Well worth reading for those interested in the use of Connected Math and Core Plus, among others, in our schools.
A few interesting items:

  • Mitchell Nathan proposed a change to the name of the Work Group to more authentically describe its intent. There was consensus to accept the change in designation for the Work Group from “Curriculum Review and Research Findings” to “Learning from Curricula.”
  • “Addresses the misconception that there is one curriculum. There are a number of curricula at play, with the exception of the narrowing down at the middle school level, but teachers are also drawing from supplementary materials. There are a range of pathways for math experiences. The work plan would give an overview by level of program of what exists. “
  • “Could say that variety is good for children to have places to plug into. Could expand on the normative idea of purchasing commercial curricula vs. richer, in-house materials. Standards tell the teachers what needs to be taught. Published materials often are missing some aspect of the standards. District tries to define core resources; guides that help people with classroom organization.” Fascinating, given the move toward one size fits all in high school, such as English 9 and 10.
  • “Want to include a summary of the NRC report that came out in favor of Connected Math but was not conclusive—cannot control for teacher effects, positive effects of all curricula, etc. “
  • “Would like to give some portrayal of the opportunities for accelerated performance — want to document informal ways things are made available for differentiation. “
  • “Include elementary math targeted at middle school, e.g., Math Masters. There is information out there to address the Math Masters program and its effect on student achievement.”
  • “Data are available to conclude that there is equity in terms of resources”
  • “District will have trend data, including the period when Connected Math was implemented, and control for changes in demographics and see if there was a change. No way to link students who took the WKCE with a particular curriculum experience (ed: some years ago, I recall a teacher asked Administration at a PTO meeting whether they would track students who took Singapore Math at the Elementary level: “No”). That kind of data table has to be built, including controls and something to match teacher quality. May recommend that not worth looking at WKCE scores of CM (Connected Math) student or a case study is worth doing. “
  • The Parent Survey will be mailed to the homes of 1500 parents of students across all grades currently enrolled in MMSD math classes. The Teacher Survey will be conducted via the district’s web site using the Infinite Campus System.
  • MMSD Math Task Force website

Math Forum audio / video and links.




“American Education Fails Because It Isn’t Education”



Tom DeWeese:

Perhaps the most bizarre of all of the school restructuring programs is mathematics. Math is an exact science, loaded with absolutes. There can be no way to question that certain numbers add up to specific totals. Geometric statements and reasons must lead to absolute conclusions. Instead, today we get “fuzzy” Math. Of course they don’t call it that.
As ED Watch explains, “Fuzzy” math’s names are Everyday Math, Connected Math, Integrated Math, Math Expressions, Constructive Math, NCTM Math, Standards-based Math, Chicago Math, and Investigations, to name a few. Fuzzy Math means students won’t master math: addition, subtraction, multiplications and division.
Instead, Fuzzy Math teaches students to “appreciate” math, but they can’t solve the problems. Instead, they are to come up with their own ideas about how to compute.
Here’s how nuts it can get. A parent wrote the following letter to explain the everyday horrors of “Everyday Math.” “Everyday Math was being used in our school district. My son brought home a multiplication worksheet on estimating. He had ‘estimated’ that 9×9=81, and the teacher marked it wrong. I met with her and defended my child’s answer.
The teacher opened her book and read to me that the purpose of the exercise was not to get the right answer, but was to teach the kids to estimate. The correct answer was 100: kids were to round each 9 up to a 10. (The teacher did not seem to know that 81 was the product, as her answer book did not state the same.)”
Social, political, multicultural and especially environmental issues are rampant in the new math programs and textbooks. One such math text is blatant. Dispersed throughout the eighth grade textbooks are short, half page blocks of text under the heading “SAVE PLANT EARTH.” One of the sections describes the benefits of recycling aluminum cans and tells students, “how you can help.”
In many of these textbooks there is literally no math. Instead there are lessons asking children to list “threats to animals,” including destruction of habitat, poisons and hunting. The book contains short lessons in multiculturalism under the recurring heading “Cultural Kaleidoscope.” These things are simply political propaganda and are there for one purpose – behavior modification. It’s not Math. Parents are now paying outside tutors to teach their children real Math – after they have been forced to sit in classrooms for eight hours a day being force-fed someone’s political agenda.




Columbia (Missouri) Parents for Real Math



Math Excellence in Columbia Missouri Public Schools:

To: Columbia Public Schools Board of Education and Superintendent Phyllis Chase
An increasing number of parents and community leaders have expressed concern about the various math curricula currently used in the Columbia Public Schools (CPS). These experimental math programs go by the names of Investigations (TERC), Connected Math (CMP) and Integrated Math (Core Plus) and they emphasize “self-discovery” over mathematical competency. We are concerned because these curricula have been discredited and abandoned in other regions of the country after they failed to deliver demonstrable results. The failed curricula are currently the only method of instruction in the elementary grades and middle schools. At higher grade levels, CPS has actively discouraged students from enrolling in math courses that place more emphasis on widely accepted standard methods. And, while implementing and evaluating these programs, the Columbia School District did not provide open access to meetings or adequately consider the concerns of professional mathematicians, parents and community leaders.
Therefore, we, the undersigned, would like to express our deep concern with the following issues and to propose that the Columbia School District adopt the following goals:
1. Protect the right of students to become computationally fluent in mathematics. We expect students to receive direct instruction in standard algorithms of all mathematical operations and laws of arithmetic so that they can master the skills that allow fast, accurate calculation of basic problems. This goal cannot be met with the current Investigations/TERC math curriculum for lower grade levels.
2. Ensure that math instruction is flexible enough to allow for various learning styles and is age and grade-level appropriate. The elementary level should focus on math standards that will build a solid base of mathematical skills for ALL students. Middle school curricula should build a bridge between the fundamental arithmetic learned in elementary school and the more abstract concepts taught in high school. At both the elementary and middle school levels the curricula should allow teachers the flexibility to meet the needs of all types of learners. This goal cannot be met with the Connected Math program currently used in middle and junior high schools.

Related: Columbia Parents’ blog site, which offers a number of useful posts. [RSS]
Math Forum Audio / Video.
Via a reader.




MMSD Math Review Task Force Introduction and Discussion



The Madison School District’s Math Task Force was introduced to the School Board last night. Watch the video or listen to the mp3 audio.
Background Links:


6th Grade Textbooks: Connected (left) and Singapore Math.
UPDATE: A reader emailed this:

I noticed that there were 10 student books in the 6th grade pile for CMP. That was surprising since there are only 8 in publication. Then I looked at the teacher editions and noticed there were 10 as well. There are two copies of both How Likely is It? and Covering and Surrounding.
The statement, “A quick look at the size of the Connected Math textbooks compared to the equivalent Singapore Math course materials illustrates the publisher and author interests in selling these large volumes irrespective of curriculum quality and rigor (not to mention the much larger potential for errors or the lost trees….)” is following the picture in one of the discussions. Taking a look at the Singapore Math website It appears that in addition to the 2 textbooks pictured and student workbooks pictured, there are Intensive Practice books, Extra Practice Books, and Challenging Word Problems books, as well as other resources. Also, the white book on the bottom of the pile appears to be an answer key. There are also teacher guides for 6A and 6B that are not in the picture.
I’m not suggesting the statement above is false, I would just like to point out that the picture being used is not an accurate comparison. I hope you find this information valuable.




New Math Curriculum Draws Complaints




Connected Math textbooks for one year and the equivalent Singapore Math version.
Brandon Lorenz:

A recent meeting at Central Middle School attracted about 50 people to discuss concerns with the district’s Connected Mathematics Project, a new constructivist approach that was introduced in sixth, seventh and eighth grades this year.
Another meeting for parents is scheduled for Dec. 13 at Horning Middle School.
Such new math programs rely on more hands-on activities and problem-solving skills than traditional programs.
Speaking with Zaborowski, Lynn Kucek said she was worried the math program would make it more difficult for her daughter, who does well in other subjects, to get into college.

More on Connected Math and the recent Math Forum.




“Too Little Math in Math?”



Lynn Thompson:

But they strongly believe that their math textbooks should include actual math.
Donald’s “Connected Mathematics” book at Harbour Pointe Middle School in Mukilteo asks him to arrange a list of 20 cities in order of their populations, all in the tens of millions.
Yes, he concedes, he must recognize differences among numbers, but it’s a pretty low-level task for a bright sixth-grader, about as challenging as alphabetizing words.
But check out the next activity: Locate the cities on a map.
“That’s not math,” Donald protests. “That’s geography.”
The Chacon-Taylor children and their parents, Hugh Taylor and Monique Chacon-Taylor, are among Snohomish County families raising questions about the effectiveness of widely used math textbooks that encourage discovery and writing about math, but de-emphasize basics such as multiplication and long division.
They’ve joined other Washington parents in an organization called Where’s the Math? that’s calling on the state Office of Superintendent of Public Instruction (OSPI) to rewrite its K-12 math standards, select more effective textbooks and re-examine the math content of the Washington Assessment of Student Learning (WASL)
The calls for rethinking the state’s math education come amid signs that the present system is failing large numbers of students. Just 51 percent of 10th-graders and 59 percent of fourth-graders passed the math section of the WASL in the spring. About 29,000 juniors haven’t passed the WASL math test, which they must do to graduate in spring 2008..

The Madison School District uses Connected Math in middle school. Many links and notes on math, including the recent Math Forum audio/video.




School math books, nonsense, and the National Science Foundation



David Klein:

Problem: Find the slope and y-intercept of the equation 10 = x – 2.5.
Solution: The equation 10 = x – 2.5 is a specific case of the equation y = x – 2.5, which has a slope of 1 and a y-intercept of –2.5.
This problem comes from a 7th grade math quiz that accompanies a widely used textbook series for grades 6 to 8 called Connected Mathematics Program or CMP.[1] The solution appears in the CMP Teacher’s Guide and is supported by a discussion of sample student work.
Richard Askey, a mathematician at the University of Wisconsin at Madison, reported, “I was told about this problem by a parent whose child took this quiz. The marking was exactly as in the text.”[2] Students instructed and graded in this way learn incorrect mathematics, and teachers who know better may be undermined by their less informed peers, armed with the “solution.” This example is far from the only failing of CMP. Among other shortcomings, there is no instruction on division of fractions in the entire three year CMP series, and the other parts of fraction arithmetic are treated poorly.[3]
Is CMP just an anomaly? Unfortunately not. CMP is only one of more than a dozen defective K-12 math programs funded by the National Science Foundation. More specifically, the NSF programs were created and distributed through grants from the Education and Human Resources (EHR) Division within the NSF. In contrast to the NSF’s admirable and important role in supporting fundamental scientific research, the EHR has caused, and continues to cause, damage to K-12 mathematics education.

Notes and links on math curriculum. Audio / Video from the recent math forum.
Connected Math is widely used within the Madison School District resulting in no small amount of supplementing by teachers, students and parents.




The Politics of K-12 Math and Academic Rigor



The Economist:

Look around the business world and two things stand out: the modern economy places an enormous premium on brainpower; and there is not enough to go round.
But education inevitably matters most. How can India talk about its IT economy lifting the country out of poverty when 40% of its population cannot read? [MMSD’s 10th Grade Reading Data] As for the richer world, it is hard to say which throw more talent away—America’s dire public schools or Europe’s dire universities. Both suffer from too little competition and what George Bush has called “the soft bigotry of low expectations”.

Thursday’s meeting between Madison School Superintendent Art Rainwater, the MMSD’s Brian Sniff and the UW Math department included two interesting guests: UW-Madison Chancellor John Wiley [useful math links via the Chancellor’s website] and the Dean of the UW-Madison Education School. Wiley and the Ed School Dean’s attendance reflects the political nature of K-12 curriculum, particularly math. I’m glad Chancellor Wiley took time from his busy schedule to attend and look forward to his support for substantial improvements in our local math program.

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Connected Math in Olympia, WA



Education Wonks:

After a number of parents and teachers objected, the school board of Olympia, Washington, has ignored an administrative recommendation to adopt a constructivist math program for their middle schoolers:

Connected Math and the Madison School District was discussed at a recent math forum (audio / video).
UW Emeritus Math Professor Dick Askey wrote a followup article on test scores and the local math curriculum.
The MMSD is currently looking for a “Coordinator of Mathematics“.
Clusty Connected Math Search.




State Test Scores Adjusted to Match Last Year



Sandy Cullen:

A new statewide assessment used to test the knowledge of Wisconsin students forced a lowering of the curve, a Madison school official said.
The results showed little change in the percentages of students scoring at proficient and advanced levels.
But that’s because this year’s Wisconsin Knowledge and Concepts Examinations- Criterion Referenced Tests proved harder for students than last year’s assessment, said Kurt Kiefer, director of research and evaluation for the Madison School District, prompting adjustments to the statewide cut-off scores for determining minimal, basic, proficient and advanced levels that were in line with last year’s percentages, Kiefer said.
“The intent was not to make a harder test,” Kiefer said, adding that the test was particularly more difficult at the eighth- and 10th-grade levels. “It had nothing to do with how smart the kids were.”
While scores can differ from district to district, Kiefer said, increases in students testing proficient and advanced are not as profound as districts might have hoped.

Kevin Carey recently wrote how states inflate their progress under NCLB:

But Wisconsin’s remarkable district success rate is mostly a function of the way it has used its flexibility under NCLB to manipulate the statistical underpinnings of the AYP formula.

I’m glad Sandy is taking a look at this.
UW Emeritus Math Professor Dick Askey mentioned changes in state testing during a recent Math Curriculum Forum:

We went from a district which was above the State average to one with scores at best at the State average. The State Test was changed from a nationally normed test to one written just for Wisconsin, and the different levels were set without a national norm. That is what caused the dramatic rise from February 2002 to November 2002. It was not that all of the Middle Schools were now using Connected Mathematics Project, which was the reason given at the meeting for these increases.

Alan Borsuk has more:

This year’s results also underscore a vexing question: Why does the percentage of students who are proficient or advanced drop from eighth to 10th grades? The decline was true almost across the board, including across ethnic groups, except in language arts. In reading statewide, the percentage of students who were advanced and proficient held close to steady from third through eighth grade and then dropped 10 points, from 84% to 74% for 10th grade. The decline was even steeper for black and Hispanic students – in each case, 17-point drops from eighth to 10th grade.
Overall, lower test scores at 10th grade are part of a broader picture of concern about how students are doing in high school that has put that level of education on the front burner nationwide, whether it is special programming from Oprah Winfrey or efforts by the National Governors Association, the Bill and Melinda Gates Foundation or others.
But assistant state schools superintendent Margaret Planner said one factor in the 10th-grade drop simply might be that many students at that level do not take the tests very seriously. Their own standing is not affected by how they do, although the status of their school could be affected seriously. She referred to the tests as “low stakes” for students and “high stakes” for schools under the federal education law.

Planner was most recently principal at Madison’s Thoreau Elementary School.
Madison Metrpolitan School District’s press release.




Better MMSD budget process? Maybe next year.



The National School Board Association argues that local school boards exist to translate the community’s educational goals for its children into programs and to hold staff accountable for the quality and effectiveness of the programs:

Your school board sets the standard for achievement in your district, incorporating the community’s view of what students should know and be able to do at each grade level. Your school board also is responsible for working with the superintendent to establish a valid process for measuring student success and, when necessary, shifting resources to ensure that the district’s goals are achieved.

Don’t expect to see that kind of process as the Madison School Board adopts a $383.7M budget for 2006-07.
On April 24, 2006, Superintendent Art Rainwater presented his proposed budget for 2006-07 to the school board. MMSD Proposed Balanced Budget for 2006-07 To the credit of the administration, the documents are better organized and provide more detail than in recent years.
Nonetheless, the board’s adoption of next year’s budget will likely be an unsatisfying process for parents and the community. I say this because the Madison board has again skipped the decision-making steps that are necessary for budget decisions to occur within a framework that we can all understand and support.
Long before the school board tries to evaluate a budget, the board should have translated the community’s vision for the education of its children into specific, measurable goals for student achievement. Key Work of School Boards
We don’t have such goals except for third grade reading, completion of algebra and geometry and attendance. What kind of budget commitment should we make to offering a comprehensive high school program? We don’t know, because we have set no standards for the “challenging, contemporary curriculum” that we claim is a strategic priority for the district. What funds should we commit to fine arts education? We don’t know, because we have no achievement goals in the arts or any other curriculum area. Should we cease funding a “Race and Equity” position at the $100,000 a year level? We don’t know because we don’t have objectives for the position to accomplish.
The board should also have developed a shared understanding of how data will be used to evaluate the district’s progress toward meeting its goals.
We don’t determine which data will be used in decisions about educational programs or any other aspect of the budget. Should we cease the “same service” approach to the teaching of reading? Should we continue to invest in “instructional coaches” who teach teachers how to present the Connected Math program? Again, we don’t know. The administration claims that its curriculum decisions are data-driven. However, the administration does not share the student achievement data behind our “same service” approach or proposed new programs nor has the board agreed to rely on whatever data that the administration may use in its internal analysis.
As the result of the April elections, the board has two new members: Lucy Mathiak and Arlene Silveira. Both promised to focus on standards and accountability during their campaigns. Maybe next year will be better. That’s important because the fuss that occurs each spring as the board struggles to “restore” programs or staff that the superintendent has cut should not occur. We should not be on the defensive–always having to create our own individual rationales for replacing cut items or changing programs. We should be on the offensive—judging the superintendent’s budget against the goals that we have set for our programs and the measurements of effectiveness that we have agreed on.
Please stay tuned.
Ruth Robarts
Member, Madison School Board




Madison and Wisconsin Math Data, 8th Grade



At a meeting on February 22 (audio / video), representatives of the Madison Metropolitan School District presented some data [820K pdf | html (click the slide to advance to the next screen)] which they claimed showed that their middle school math series, Connected Mathematics Project, was responsible for some dramatic gains in student learning. There was data on the percent of students passing algebra by the end of ninth grade and data from the state eighth grade math test for eight years. Let us look at the test data in a bit more detail.

All that was presented was data from MMSD and there was a very sharp rise in the percent of students scoring at the advanced and proficient level in the last three years. To see if something was responsible for this other than an actual rise in scores consider not only the the Madison data but the corresponding data for the State of Wisconsin.

The numbers will be the percent of students who scored advanced or proficient by the criteria used that year. The numbers for Madison are slightly different than those presented since the total number of students who took the test was used to find the percent in the MMSD presented data, and what is given here is the percent of all students who reached these two levels. Since this is a comparative study, either way could have been used. I think it is unlikely that those not tested would have had the same overall results that those tested had, which is why I did not figure out the State results using this modification. When we get to scores by racial groups, the data presented by MMSD did not use the correction they did with all students ( All 8th grade students in both cases)

MMSD Wisconsin
Oct 97 40 30
Feb 99 45 42
Feb 00 47 42
Feb 01 44 39
Feb 02 48 44
Nov 02 72 73
Nov 03 60 65
Nov 04 71 72

This is not a picture of a program which is remarkably successful. We went from a district which was above the State average to one with scores at best at the State average. The State Test was changed from a nationally normed test to one written just for Wisconsin, and the different levels were set without a national norm. That is what caused the dramatic rise from February 2002 to November 2002. It was not that all of the Middle Schools were now using Connected Mathematics Project, which was the reason given at the meeting for these increases.

It is worth looking at a breakdown by racial groups to see if there is something going on there. The formats will be the same as above.

Hispanics
MMSD Wisconsin
Oct 97 19 11
Feb 99 25 17
Feb 00 29 18
Feb 01 21 15
Feb 02 25 17
Nov 02 48 46
Nov 03 37 38
Nov 04 50 49
Black (Not of Hispanic Origin)
MMSD Wisconsin
Oct 97 8 5
Feb 99 10 7
Feb 00 11 7
Feb 01 8 6
Feb 02 13 7
Nov 02 44 30
Nov 03 29 24
Nov 04 39 29
Asian
MMSD Wisconsin
Oct 97 25 22
Feb 99 36 31
Feb 00 35 33
Feb 01 36 29
Feb 02 41 31
Nov 02 65 68
Nov 03 55 53
Nov 04 73 77
White
MMSD Wisconsin
Oct 97 54 35
Feb 99 59 48
Feb 00 60 47
Feb 01 58 48
Feb 02 62 51
Nov 02 86 81
Nov 03 78 73
Nov 04 88 81

I see nothing in the demography by race which supports the claim that Connected Mathematics Project has been responsible for remarkable gains. I do see a lack of knowledge in how to read, understand and present data which should concern everyone in Madison who cares about public education. The School Board is owed an explanation for this misleading presentation. I wonder about the presentations to the School Board. Have they been as misleading as those given at this public meeting?

Richard Askey




Math Forum Audio / Video and Links



Video and audio from Wednesday’s Math Forum are now available [watch the 80 minute video] [mp3 audio file 1, file 2]. This rare event included the following participants:

The conversation, including audience questions was lively.

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“Less May be More with Math Curriculum”




Jamaal Abdul-Alim:

The books are distributed by an Oregon-based company known as SingaporeMath.com, which counts a private school in Madison as the first of its growing number of clients.
The biggest difference between math instruction in Singapore – a city-state with a population of about 4.4 million – and the United States is a simple premise: Less is more.
Students in Singapore are introduced to roughly half the number of new math topics a year as students in the United States are. Experts and policy analysts say Singapore’s emphasis on depth over breadth is a formula for success.
The thicker the textbooks and the greater the volume of math topics introduced a year, the less likely American students and teachers are to achieve similar results, says Alan Ginsburg, director of the policy and program studies service at the U.S. Department of Education.

More on the Connected Math / Singapore Math textbook photos.

Madison Country Day School was the first US school to purchase Singapore Math textbooks, in 1997, according to this article.




A Few Notes on the Superintendent’s Evaluation & Curriculum



Several writers have mentioned the positive news that the Madison Board of Education has reviewed Superintendent Art Rainwater for the first time since 2002. I agree that it is a step in the right direction.
In my view, the first responsibility of the Board and Administration, including the Superintendent is curriculum: Is the Madison School District using the most effective methods to prepare our children for the future?
There seems to be some question about this:

  • Language: The District has strongly embraced whole language (Troy Dassler notes in the comments that he has been trained in balanced literacy). I would certainly be interested in more comments on this (and other) point(s). [Ed Blume mentions that “”Balanced literacy” became the popular new term for whole language when whole language crumbled theoretically and scientifically.”] UW Professor Mark Seidenberg provides background on whole language and raises many useful questions about it. Related: The District has invested heavily in Reading Recovery. Ed Blume summarized 8 years of District reading scores and notes that Madison 3rd graders rank below state wide average for children children in the advanced and proficient categories. (Madison spends about 30% more than the state average per student)
  • Math: The District embraces Connected Math. UW Math Professor Dick Askey has raised a number of questions about this curriculum, not the least of which is whether our textbooks include all of the corrections. A quick look at the size of the Connected Math textbooks demonstrates that reading skills are critical to student achievement.
  • Sherman Middle School’s curriculum changes
  • West High School’s curriculum changes and families leaving
  • “Same Service Budget Approach“: I think the District’s annual same service approach reflects a general stagnation.

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Math Curriculum: Textbook Photos




A year’s worth of Connected Math textbooks and teacher guides are on the left while the equivalent Singapore Math texts are on the right.

Friedman’s latest ,where he demonstrates how other countries are “eating our kid’s lunch in math” is well worth reading, as are these www.schoolinfosystem.org math posts. UW Math Professor Dick Askey has much more to say on K-12 math curriculum.

A few observations from a layperson who couldn’t be farther from a math expert’s perspective on this (in other words, I’m not a math expert):

  • Children must be able to read effectively to use the voluminous Connected Math curriculum,
  • The Connected Math curriculum has very extensive teacher instructions, while the Singapore curriculum is rather thin in this area. Does it follow that teachers using Singapore Math have far more freedom with respect to their instruction methods, or is the intention to make sure that teachers teach Connected Math in a scripted way?
  • The Connected Math texts require more dead trees and I assume cost more than the Singapore texts directly and indirectly (transportation, packaging and the overhead of dealing with more pieces)
  • The voluminous Connected Math texts have far more opportunities for errors, simply based on the amount of text and illustrations included in the books.
  • Madison Country Day School uses Singapore Math.

There’s quite a bit of discussion on Connected Math and Singapore Math around the internet. Maybe it’s time to follow the www.heymath.net people (from India, China and Great Britain) and virtualize this while eliminating the textbooks?

Post your comments below.




PEOPLE Program: The Debate continues



(With apologies to readers – it is not possible to respond using the comments feature on the blog.)
Response to Lucy’s Post on PEOPLE program
JOAN: Tempting though it is to rebut your arguments tit for tat I am not sure it will necessarily be productive.
RESPONSE: I would be interested in a “tit for tat” response to my comments on the reasons why the PEOPLE program is needed.
JOAN: Let’s back up and look at the assumptions underlying this program. The first is that minority students are not getting adequate preparation in their home schools. You assert that this is true in the well-staffed, well-funded Madison school district because of institutional racism. You believe your visual review of a school proves your point. That’s not particularily strong evidence.
RESPONSE: I think you need to go back and read what I wrote. I said,

“All of the above examples are conditions that I have witnessed first hand or, in one or two cases, have heard of from other parents – including parents of white students. When the above conditions disappear and/or white students experience these same conditions, we can talk about equity.”

Nowhere did I say or imply that my comments were “based on a visual review of a school.” It is true that there is no systematic, methodologically defensible, study of how students of color and their parents fare in Madison’s schools. I would welcome a well-crafted study of this nature.

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K-12 Math Curriculum: A Visit With UW Math Professor Dick Askey



UW Math Professor Dick Askey kindly took the time to visit with a group of schoolinfosystem.org writers and friends recently. Dick discussed a variety of test results, books, articles and links with respect to K-12 math curriculum. Here are a few of them:

  • Test Results:

    Wisconsin is slipping relative to other states in every two year NAP (sp?) Math test (4th and 8th grade). In 1992, Wisconsin 4th graders were 10 points above the national average while in 2003 they were 4 points above. Wisconsin students are slipping between 4th and eighth grades. In fact, white and hispanic children are now performing equivalent to Texas students while Wisconsin black students are performing above Washington, DC and Arkansas (the two lowest performers). He mentioned that there is no serious concern about the slippage.

    30 years ago, the United States had the highest % of people graduating from High School of any OECD country. Today, we’re among the lowest. We also have a higher drop out rate than most OECD countries.

    Said that he has asked Madison Schools Superintendent Art Rainwater twice in the past five years if our District asked for and received corrections for the current connected Math textbooks.

    Mentioned that CorePlus is evidently being used at West High but not Memorial

    Asked why these math performance declines are happening, he mentioned several reasons; “tame mathemeticians”, declining teacher content knowledge (he mentioned the rigor of an 1870’s California Teacher exam) and those who are true believers in the rhetoric.

  • Books:

    Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States

    The Schools by Martin Mayer

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