Obituary: Richard Allen “Dick” Askey, of Madison, passed away on Oct. 9, 2019, at age 86. He was born to Philip E. Askey and Bessie May Askey on June 4, 1933, in St. Louis, Mo. Dick devoted his life’s work to mathematics and improving K-12 math education. He joined the University of Wisconsin Mathematics department … Continue reading Richard Askey
Richard Askey on 12th Grade NAEP Results.
http://www.math.wisc.edu/~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 … Continue reading K-12 Math Curriculum: A Visit With UW Math Professor Dick Askey
UW’s Dick Askey emailed links to two of his papers on Elementary Math Curriculum: Good Intentions Are Not Enough (PDF) While there was a need to do something to improve school mathematics education, NCTM did not face up to the most critical problem, the lack of firm content knowledge of far too many teachers. There … Continue reading Askey on Elementary Math Curriculum: “Good Intentions Are Not Enough”
Wall Street Journal So much for Pennsylvania Gov. Josh Shapiro’s gutsy support for school choice. After backing a Senate proposal for school vouchers for K-12 students—one of his 2022 campaign promises—the Democratic Governor caved this week to his party and the unions and will nix the scholarships from the state budget.
G. S. Carr, M.A. (“The Textbook that Unleashed Ramanujan’s Genius”) THE work, of which the part now issued is a first instalment, has been compiled from notes made at various periods of the last fourteen years, and chiefly during the engagements of teaching. Many of the abbroviated methods and mnemonic rules are in the form … Continue reading A Synopsis of Elementary Results in Pure Mathematics
Stephen Askey: Once we were mighty. Once we were legion. Once we reigned over colleges and universities like demigods. Well, OK, we English majors were never that important, except maybe in our own eyes. According to a report in the New York Times, degrees awarded in English at American universities fell from seven point six … Continue reading The reality and mythology of an English major
American Academy of Arts & Sciences, via Richard Askey
Quora, via a kind Richard Askey email: You are in Mordor now and way closer to Mount Doom. There is suddenly so much less free time and everyone including the aunt of your neighbor kid’s cousin start to ask you how many years you have till “High School Entrance Exam”. Now the main subjects are: … Continue reading How is/was the education system in your country?
Richard Askey, Ryota Matsuura, and Sarah Sword (PDF): Given three numbers a, b, and c, we can find their mean (or average) as (a + b + c)/3. More precisely, this expression yields the arithmetic mean of a, b, and c. A different kind of mean, however, uses the product of these numbers instead of … Continue reading The Inequality of Arithmetic and Geometric Means from Multiple Perspectives
Scott Mahaskey: The Navajo reservation that stretches across vast swaths of desert in northern Arizona and New Mexico is home to 66 schools run by the Bureau of Indian Education. The landscape might be breathtaking, but the dilapidated condition of the schools is eye-popping for another reason. Despite well-documented needs for renovations, the schools linger … Continue reading Life At an Indian School
Randall Munroe, via a kind Richard Askey email: There once was a doctor with cool white hair. He was well known because he came up with some important ideas. He didn’t grow the cool hair until after he was done figuring that stuff out, but by the time everyone realized how good his ideas were, … Continue reading The Space Doctor’s Big Idea
The Lincoln Project (PDF): Measured in inflation-adjusted dollars per full-time equiv- alent (fte) student, states have been cutting this support for well over a decade, and spending cuts accelerated in response to the Great Recession. Between 2008 and 2013, states cut appropriation support per fte student in the median public research university by more than … Continue reading Public Research Universities: Changes in State Funding – Note Healthcare & K-12 Tax & Spending Growth
American Academy of Arts & Sciences (PDF), via a kind Richard Askey email: The Academy is also working with the university community to identify steps that could be taken on campuses across America to advance the recommendations from Restoring the Foundation. Com- mittee member Venkatesh Narayanamurti (Harvard University) presented the report at the November 2014 … Continue reading Academy Report Stresses Importance of Science and Engineering Research for American Prosperity and Competitiveness
Ronald E. LaPorte, via a kind Richard Askey email: Dear Friends, Ebola is frightening. Most information from TV, Facebook, and from our governments is poor. We want to change this by providing to you the best possible scientific information about Ebola from leading scientists from Nigeria, Africa, the Library of Alexandria and experts world wide. … Continue reading MYTHS AND REALITIES OF EBOLA VIRUS DISEASE in English and other languages
cspan 3 via Richard Askey: Amanda Ripley talked about her book, The Smartest Kids in the World: And How They Got That Way. In her book she followed three American high-school students who each spent a year in a high-scoring foreign school system, in Finland, South Korea, and Poland. She spoke in the Science Pavilion … Continue reading Book Discussion on The Smartest Kids in the World
Sarah Blaskey and Phil Gasper:
MADISON, WIS., has a reputation as one of the most liberal cities in the country. It is also possibly the most racially unequal.
In early October, Race to Equity–a Madison-based initiative started by the Wisconsin Council on Children and Families–released a report detailing racial disparities in Madison, and more broadly in Dane County, Wis. The findings are staggering.
The Race to Equity researchers expected the numbers compiled for racial disparities in Dane County to be similar or slightly better than the national averages. After all, Madison has long prided itself on having quality public education, good jobs, access to health care and human services programs, a relatively high standard of living and, in general, a progressive outlook on social, economic and political questions.
But while living standards for the white population in Dane County are higher than the national average, for the Black population, the opposite is true. On every indicator, with only two exceptions out of 40 measures, statistics collected in Dane County demonstrated equal or higher racial disparities between whites and Blacks than the national averages.
Related: The failed battle over the proposed Madison Preparatory Academy IB charter school and our disastrous reading scores.
We Californians like to think our state is the national leader in policy change and innovation, that new ideas are born here and other states follow our lead.
In one area, I am sad to say, that is not the case.
California is short-selling too many of its public school students because of education programs that inadequately prepare the next generation of teachers. A new review from the National Council on Teacher Quality that evaluates educational institutions, state by state, produced some sobering results for anyone who cares about what’s going on inside California schools of education.
Among the more disturbing findings from the institutions that provided data:
- Half of 72 programs for elementary school preparation failed the evaluation, a higher failure rate than programs in any other state.
- California’s secondary certification structure combined with inadequate coursework requirements, particularly in the sciences and social sciences, showed that only 17 percent of programs adequately prepared secondary teaching candidates in core subjects. That compared with 34 percent nationally.
- Coursework in a majority (63 percent) of California elementary programs did not mention a single strategy for teaching reading to English language learners.
- Of the 139 elementary and secondary programs that were evaluated on a four-star rating system, 33 programs earned no stars and only three earned as many as three. Not a single program earned four stars.
Related: Richard Askey: Examinations for Teachers Past and Present:
I have written about the problem in mathematics and hope that some others will use the resouces which exist to write about similar problems in other areas.
In his American Educational Research Association Presidential Address, which was published in Educational Researcher in 1986, Lee Shulman introduced the phrase “pedagogical content knowledge”. This is a mixture of content and knowing how to teach this content and is the one thing from his speech which has been picked up by the education community. However, there are a number of other points which he made which are important. Here is an early paragraph from this speech:
WGBH Nova, via a kind Richard Askey email:
In 1900, a storm blew a boatload of sponge divers off course and forced them to take shelter by the tiny Mediterranean island of Antikythera. Diving the next day, they discovered a 2,000 year-old Greek shipwreck. Among the ship’s cargo they hauled up was an unimpressive green lump of corroded bronze. Rusted remnants of gear wheels could be seen on its surface, suggesting some kind of intricate mechanism. The first X-ray studies confirmed that idea, but how it worked and what it was for puzzled scientists for decades. Recently, hi-tech imaging has revealed the extraordinary truth: this unique clockwork machine was the world’s first computer. An array of 30 intricate bronze gear wheels, originally housed in a shoebox-size wooden case, was designed to predict the dates of lunar and solar eclipses, track the Moon’s subtle motions through the sky, and calculate the dates of significant events such as the Olympic Games.
The U.S. public education system is trying any number of techniques–from charter schools to presidential initiatives to oil-company-run teacher academies–to catch up to countries like Finland and South Korea in math and science education. But policymakers seem to be overlooking one simple solution: requiring math and science teachers to progress further up the educational ladder before they teach those subjects to kids.
The map above shows the minimum level of education each country requires teachers to obtain before working at the upper-secondary level. The map, based on data collected by Jody Heymann and the World Policy Analysis Center and subsequently published in Children’s Chances: How Countries Can Move from Surviving to Thriving, illustrates that the United States lags behind most other countries in its requirements.
Many U.S. school systems defer to teachers with higher degrees when they hire faculty, and teachers are required to have some kind of state certification along with a bachelor’s degree. However, the precise certification requirements vary, depending on how a teacher enters the profession and what state they teach in. The traditional route to becoming a teacher in the United States usually involves a bachelor’s or master’s degree in education along with a standardized test and other state-specific requirements. But most states have some form of an alternative route, usually involving a bachelor’s degree and completion of an alternate certification program while a person simultaneously teaches full-time. There is no federal mandate for teacher education requirements, according to the World Policy Analysis Center. The federal Improving Teacher Quality State Grants program rewards states with funds when they meet the “highly qualified teacher” requirement set forth in the No Child Left Behind Act.
Related: When A Stands for Average: Students at the UW-Madison School of Education Receive Sky-High Grades. How Smart is That?
and,
Examinations for Teachers Past and Present by Dr. Richard Askey.
WU Yingkan, via a kind Richard Askey email (PDF):
xamination is a critical issue in education system in China. Zhongkao is a kind of graduation examination of junior high school, and at the same time, the entrance examination to senior high school. This paper describes the structure, features and changes in zhongkao mathematics in China based on a detailed analysis of 48 selected zhongkao mathematics papers from eight regions in recent six years. Examples of examination items are given to illustrate the identified features and changes. Zhongkao Mathematics, examination, features, changes, junior high school graduates
INTRODUCTION
China is the birthplace of examination system. The imperial examination was started in 597 during the Sui Dynasty, and was banned in 1905 during the Qing dynasty (Li & Dai, 2009; Zhang, 1996). It lasted for about 1300 years. With the influence of the long existence of the imperial examination system, examination is of great importance in China. It attracts attention from parents, educators, teachers, students, policy makers and so on. It is a big issue in education.
There are two significant examinations for students in school education in China, which are called “zhongkao” and “gaokao”. Figure 1 shows the school education system in China. Students start their nine-year compulsory education usually at six years old. Most of them stay at elementary school for six years, and junior high school for three years. In some districts like Shanghai, students stay at elementary schools for five years and junior high school for four years. At the end of Grade Nine, all students take zhongkao, which is summative assessment of the nine-year compulsory education, and more importantly, the entrance examination to senior high school. Nearly 90% of junior high school graduates continue their study. About half of them go to senior high schools, and the other half enter secondary vocational schools (Ministry of education of China, 2010a). The results of zhongkao decide whether students go to key senior high school, ordinary senior high school or vocational school. At the end of three-year senior high school study, students take gaokao, which is the entrance examination to universities. About 80% senior high school graduates are promoted to tertiary education (Ministry of education of China, 2010a). The results of gaokao decide whether senior high school graduates go to key university, ordinary university, college, or other high education institutes.
Rick Hess, via a kind reader’s email:
You didn’t think the ferment around Common Core could keep building? Hah! Prepare for several more years of increasing wackiness. In the middle of it all is Jazon Zimba, founding principal of Student Achievement Partners (SAP) and the man who is leading SAP after David Coleman went off to head up the College Board. SAP is a major player in Common Core implementation, especially with the aid of $18 million in support from the GE Foundation. Zimba was the lead writer on the Common Core mathematics standards. He earned his doctorate in mathematical physics from Berkeley, co-founded the Grow Network with Coleman, and previously taught physics and math at Bennington College. He’s a private dude who lives up in New England and has not been part of the Beltway policy conversation. I’d never met Zimba, until we had the chance to sit down last week.
Now, I think readers know that I’m of two minds when it comes to the Common Core. On the one hand, it does have the potential to bring coherence to the education space, shed light on who’s doing what, raise the bar for instructional materials and teacher prep, and so forth. On the other, there are about 5,000 ways the whole thing could go south or turn into a stifling bureaucratic monstrosity-and one rarely goes wrong when betting against our ability to do massive, complex edu-reforms well. Given all this, like many of you, I’m carefully watching how all this is playing out. In that spirit, I enjoyed meeting Zimba; found him smart and engaging; and thought you all might be equally interested in hearing from him. In particular, I’d love to hear how much Zimba’s responses do or don’t assuage various concerns about the Common Core. Here’s what he had to say (in an email interview that followed our conversation):
…..
RH: How confident are you that teacher preparation programs are ready and able to alter their practice in light of the Common Core?
JZ: There is a long tradition of mathematicians partnering with education schools and local districts to enhance the mathematical education of teachers. The first thing I ever read about this was Richard Askey’s 1999 article in American Educator. The National Math Panel also made recommendations to improve teacher preparation in mathematics. But the fact that mathematicians have been working on the mathematical preparation of teachers for so long is really a good-news/bad-news story. The Common Core could bring some much-needed scale and impetus for change here.
I’ve heard about some of the alternative certification programs basing their training on the Common Core, and that makes sense because these programs tend to have national reach. As for traditional universities, I assume change will happen faster in some places but slowly in most. I would love to see some creative thinking about this from the universities themselves, but also from the states and districts who are their clients.
Dr. Richard Askey, via a kind email (PDF):
TIMSS is an international set of tests on mathematics and science which is given every four years in grades 4 and 8 to a sample of students, and occasionally for a sample of students taking advanced mathematics and physics in their last year in high school. All of these will be given in 2015.
The following useful link gives access to the released TIMSS-2011 items and the scores different countries made on these items.
…………
One interesting fact is that among the 42 countries which tested 8th grade students, Finland had the highest percent of students who picked answer A and the third lowest percent correct, Chile had 11.7and Sweden had 14.4 percent. The Finnish result is likely a surprise to the people who have praised the Finnish school system for their results on another international test, PISA. However, one group which would not be surprised are university and technical college mathematics faculty in Finland. See an article signed by over 200 of them which is on the web at:
http://solmu.math.helsinki.fi/2005/erik/PisaEng.html
Dr. Alfred S. Posamentier (PDF), via a kind Richard Askey email:
We have come a long way since the 1960s, when a plane ride to Europe from the United States required a fueling stop in Gander, Newfoundland. Today we can reach airports in far-off Asia in a single flight. Combine this ease of travel with the technology-facilitated communication afforded us through e-mail and the Internet, and clearly the world has shrunk in the past few decades. Correspondingly, at all levels of education it is our responsibility to help our students appreciate their place as citizens of the world by giving them the most enriched view of the global environ- ment in which we study, work and live.
Australian Mathematical Sciences Institute via a kind Richard Askey email:
These modules are prepared by AMSI as part of The Improving Mathematics Education in Schools (TIMES) Project.
The modules are organised under the strand titles of the Australian Curriculum
- Number and Algebra
- Measurement and Geometry
- Statistics and Probability
The modules are written for teachers. Each module contains a discussion of a component of the mathematics curriculum from early primary up to the end of Year 10. There are exercises that teachers may wish to undertake – answers are given at the end of the module and often screencasts giving a solution are linked and indicated by an icon.
Zeit Online, via a kind Richard Askey email:
How do families live these days? OECD’s comprehensive world education ranking report, PISA 2009, was published in December of 2010. All participants of the test (fifteen-year-old pupils) completed a questionnaire about their living situation at home. ZEIT ONLINE analyzed and visualized this data to provide you with a unique way of comparing standards of living in different countries. Click on any icon to see further details.
Olli Martio – University of Helsinki, Marticulation Board in Finland
olli.martio@helsinki.fi, via a kind Richard Askey email:
Curricula changes in the Finnish school system have taken place in 8-10 year intervals. They have been recorded in the official curricula for schools by the Finnish Ministry of Education. However, these texts do not provide a complete picture since they are rather short of details. Schools can freely choose their textbooks and there is neither an official inspection nor an official approval for the textbooks. The system is based on the free market principle. Because of this textbooks, and the practice of teaching, should also be studied in order to understand the Finnish mathematics curriculum. A similar situation prevails in many other countries.
The leading ideas, from the point of view of people working in pedagogy, from 1960 on were “New Math” (1960-1970), “Back to Basics” (1968-80) and “Problem Solving”(1978- ), see [M1] and [PAL]. These trends have appeared in many other countries as well. However, these key words do not give a proper picture what really happened in the mathematics curriculum and education.
In Finland these trends had the following effects on the mathematics curriculum.
- Mathematics at school became descriptive – exact definitions and proofs were largely omitted.
- Geometry and trigonometry were neglected.
- Computations were performed by calculators and numbers and not on a more advanced level.
“Problem Solving” and putting emphasis on calculators have taken time from explaining the basic principles and ideas in mathematics. It should be also remembered that with the invention of calculators and computers the pressure to traditional mathematics teaching increased enormously since a general believe in 1960-70 was that all the mathematical problems can be solved by computers and hence the traditional school mathematics is useless. This criticism did not come from ordinary laymen only but from well known scientists as well and this attitude was very much adopted by people working in education and didactics. These ideas had a profound effect on the changes in the Finnish school curriculum.
Erin Loury, via a kind Richard Askey email:
Monkeys banging on typewriters might never reproduce the works of Shakespeare, but they may be closer to reading Hamlet than we thought. Scientists have trained baboons to distinguish English words from similar-looking nonsense words by recognizing common arrangements of letters. The findings indicate that visual word recognition, the most basic step of reading, can be learned without any knowledge of spoken language.
The study builds on the idea that when humans read, our brains first have to recognize individual letters, as well as their order. “We’re actually reading words much like we identify any kind of visual object, like we identify chairs and tables,” says study author Jonathan Grainger, a cognitive psychologist at France’s National Center for Scientific Research, and Aix-Marseille University in Marseille, France. Our brains construct words from an assembly of letters like they recognize tables as a surface connected to four legs, Grainger says.
Much of the current reading research has stressed that readers first need to have familiarity with spoken language, so they can connect sounds (or hand signs for the hearing-impaired) with the letters they see. Grainger and his colleagues wanted to test whether it’s possible to learn the letter patterns of words without any idea of what they mean or how they sound–that is, whether a monkey could do it.
Nancy Kober and Alexandra Usher:
The 2012 Public Education Primer highlights important and sometimes little-known facts concerning the U.S. education system, how things have changed over time, and how they may change in the future. Together these facts provide a comprehensive picture of the nation’s public schools, including data about students, teachers, funding, achievement, management, and non-academic services.
John Witte & Barbara Wolfe, via a kind Richard Askey email:
There is considerable concern in Wisconsin and other states that accessibility to colleges and universities is becoming more elite; that due to rising costs of education and rising standards for admission universities are increasingly serving only those from higher income families. For example an article in the Christian Sciences Monitor in August of this year entitled “Too Few low income students?” stated that “about 50 percent of low-income students enroll in college right after high school, compared with 80 percent of high income students” and go on to state that the rate of high achieving low income students is about that of high income students that have far lower achievement scores1. William Bowen, Martin Kurzwell and Eugene Tobin note in their book that students in the bottom quartile of family income make up only 11 percent of elite college enrollment and receive no advantage from college admission programs; they call for an affirmative action program directed at low income applicants to promote equal opportunity and increase economic growth2. In this paper we use family income of University of Wisconsin- Madison applicants and those admitted over more than three decades to shed light on whether there has been a decline of opportunity to attend elite institutions among those with limited family incomes. As the premier public university in the state, this profile can serve more generally to provide insight on the issue of increasing elitism of premier public universities.
How accessible are the best public institutions to students from different socioeconomic groups? And, given the debates about financial aid that have been occurring at both the national and state, it is important to know: (a) How has access to the University of Wisconsin-Madison changed in terms of family income during the last three decades? (b) Are the patterns different for those within the state compared to those from outside the state? (c) Is there an income difference between those admitted and rejected for admission? And (d) What is the trend in the rate of applicants being admitted? This study addresses these questions.
Data on family income of applicants to specific colleges and universities are difficult to acquire. The most common sources are the income questions that students answer when completing ACT or SAT examinations. For a number of reasons these responses are probably woefully inaccurate. There is evidence from other studies that students simply do not have accurate information on family income. Universities could include income information on application forms, but most do not (including UW-Madison). Detailed income and asset data are included on the federal financial aid application form (FAFSA), but only students applying for financial aid complete those forms.
A controversy broke out on Twitter earlier this week about an article in the Times Educational Supplement in which a teacher called Jonny Griffiths describes a conversation with a bright sixth-former who’s worried about his exam results. “Apart from you, Michael, who cares what you get in your A-levels?” he says. “What is better: to go to Cambridge with three As and hate it or go to Bangor with three Cs and love it?”
The controversy was not about whether the teacher was right to discourage his student to apply to Cambridge – no one thought that, obviously – but whether the article was genuine. Was Jonny Griffiths a real teacher or the fictional creation of a brilliant Tory satirist? Most people found it hard to believe that a teacher who didn’t want his pupils to do well could be in gainful employment.
Alas, Mr Griffiths is all too real. Since 2009, when I first mooted the idea of setting up a free school devoted to academic excellence, I’ve come across dozens of examples of the same attitude, all equally jaw-dropping.
We’ve certainly seen such initiatives locally. They include English 10, Connected Math and the ongoing use of Reading Recovery.
Perhaps Wisconsin’s Read to Lead initiative offers some hope with its proposal to tie teacher licensing to teacher content knowledge.
Related: Examinations for teachers, past and present.
There are certainly many parents who make sure that their children learn what is necessary through tutors, third parties, personal involement, camps, or online services. However, what about the children who don’t have such family resources and/or awareness?
Texas Hispanic and African-American students rank
second on eighth-grade NAEP math test
Texas Education Agency:
Texas Hispanic and African-American students earned the second highest score among their peer groups on the 2011 eighth-grade National Assessment of Educational Progress (NAEP) mathematics test. The state’s white eighth grade students ranked fourth, missing out on the second place position themselves by less than one point.
Only Hispanic students in Montana earned a higher scale score on the math test than did eighth-grade Hispanic Texans. Only African-American students in Hawaii earned a higher average score than did their counterparts in Texas.
White students in the District of Columbia earned an average scale score of 319, the highest score for that ethnic group. Texas students ranked fourth, with less than a fraction of a point separating this group from students in Massachusetts and New Jersey. Massachusetts students had the second highest scale score at 304.2876, while Texas received an average score of 303.5460.
Overall, the state ranked 10th among the states with an average scale score of 290, substantially above the national average score of 283.
NAEP math on upward trend, state reading results stable
Wisconsin DPI:
Wisconsin’s biennial mathematics and reading results held steady on the 2011 National Assessment of Educational Progress (NAEP), also known as the Nation’s Report Card. The state’s overall trend in mathematics is improving.
For fourth-grade mathematics, the state’s 2011 scale score was 245, up one point but statistically the same as in 2009, compared to the national scale score of 240, a one-point increase from 2009. Wisconsin results for fourth-grade math are significantly higher than in 2003 when the average scale score was 237. At eighth grade, the Wisconsin scale score for mathematics was 289,
the same as in 2009 and up five points from 2003, which is statistically significant. For the nation, the 2011 mathematics scale score was 283, up one-point from 2009. State average scale scores in mathematics at both grade levels were statistically higher than the national score.
Average scores for fourth grade
| All | White | Black | Hispanic | Asian Amer-Pac.Island | Native Amer | |
|---|---|---|---|---|---|---|
| US | 240 | 249 | 224 | 229 | 256 | 227 |
| Texas | 241 | 253 | 232 | 235 | 263 | *** |
| Wisconsin | 245 | 251 | 217 | 228 | 242 | 231 |
| Average scores for eighth grade | ||||||
| US | 283 | 293 | 262 | 269 | 302 | 266 |
| Texas | 290 | 304 | 277 | 283 | 316 | *** |
| Wisconsin | 289 | 295 | 256 | 270 | 290 | *** |
via a kind Richard Askey email.
Erin Richards has more on Wisconsin’s results.
Steve Dykstra’s comments on Wisconsin’s NAEP reading scores.
Related: Madison and College Station, TX.
Hung-Hsi Wu, via Richard Askey:
Many sets of state and national mathematics stan- dards have come and gone in the past two decades. The Common Core State Mathematics Standards (CCSMS), which were released in June of 2010,*have been adopted by almost all states and will be phased in across the nation in 2014. Will this be another forgettable stan- dards document like the overwhelming majority of the others?
Perhaps. But unlike the others, it will be a travesty if this one is forgotten. The main difference between these standards and most of the others is that the CCSMS are mathematically very sound overall. They could serve–at long last–as the foundation for creating proper school mathematics textbooks and dramatically better teacher preparation.
Before the CCSMS came along, America long resisted the idea of commonality of standards and curriculum–but it did not resist such commonality in actual classrooms. Despite some politicians’ rhetoric extolling the virtues of local control, there has been a de facto national mathematics curriculum for decades: the curriculum defined by the school mathematics textbooks. There are several widely used textbooks, but mathe- matically they are very much alike. Let’s call this de facto math- ematics curriculum Textbook School Mathematics (TSM).1
edweek, via a kind Richard Askey email:
This interactive timeline digs deep into the Education Week archives to tell the story of U.S. education and the changing policies, theories, and perspectives that have influenced it since 1981, the year the publication began.
Joe Resmovits, via a Richard Askey email:
Three years ago, Heather Vogell, an investigative reporter at the Atlanta Journal Constitution, sat down with a data analyst to crunch some numbers.
She had just received the latest crop of scores for the CRCT, a state standardized test. Curiously, Vogell noted, several schools statewide had changed in status between the spring 2008 administration of the test and the summer retest in 2008, going from not meeting Adequate Yearly Progress rates, a calculation set by federal legislation that determines the fates of individual schools, to meeting the measure.
“We saw there were a lot more schools that met AYP than we had expected. It was a larger shift,” Vogell told The Huffington Post.
Like any intrepid reporter, she had some questions. “We were poking around. We saw some schools that had very hard to believe gains, just looking with the naked eye,” she said.
A high school in Lancaster, Pennsylvania, is defending its decision to segregate its students by race and gender.
The scheme, at McCaskey East High School, separates black students from the rest of the school body, and then further breaks it down into black females and black males.
The separation is only for a short period – six minutes each day and 20 minutes twice a month – but it naturally drew criticism for bringing back the awful memory of racial segregation.
Today the school’s principal defended its policy.
Gary W. Phillips, Ph.D., via a Richard Askey email
It is worth looking at the data to see how Wisconsin compares with some other states. Here is the mathematics comparison with Minnesota.
The “state” results are the percent of students ranked as proficient on the state test with the current cut scores being used. The international percent was obtained by using the state results on NAEP (National Assessment of Educational Progress) and this was mapped by comparing levels of problems to the level on TIMSS, (Trends in Mathematics and Science Study).
Grade 4 Mathematics Percent proficient
State International
Wisconsin 74 45
Minnesota 68 55
Massachusetts 49 63
Grade 8 Mathematics
Wisconsin 73 33
Minnesota 56 41
Massachusetts 46 52
No, the Massachusetts scores were not reversed here. Their cut score levels are set higher than the TIMSS levels.
It is time for the Wisconsin Department of Public Instruction to redo the cut score levels to make them realistic. Parents in Wisconsin are mature enough to be told the truth about how well their children are doing.
Paul Barton & Richard Coley, via a Richard Askey email:
There is widespread awareness that there is a very substantial gap between the educational achievement of the White and the Black population in our nation, and that the gap is as old as the nation itself.
This report is about changes in the size of that gap, beginning with the first signs of a narrowing that occurred at the start of the last century, and continuing on to the end of the first decade of the present century. In tracking the gap in test scores, the report begins with the 1970s and 1980s, when the new National Assessment of Educational Progress began to give us our first national data on student achievement.
That period is important because it witnessed a substantial narrowing of the gap in the subjects of reading and mathematics. This period of progress in closing the achievement gap received much attention from some of the nation’s top researchers, driven by the idea that perhaps we could learn some lessons that
could be repeated.
Next, there are the decades since the late 1980s, in which there has been no clear trend in the gap, or sustained period of change in the gap, one way or another. While there has been considerable investigation of the gap that remained, little advance in knowledge has occurred as attention was directed to alternating small declines and small gains, interspersed with periods of no change.
Paul Barton and Richard Coley drop back in time to the beginning of the 20th century when the gap in educational attainment started to narrow, and bring us to the startling and ironic conclusion that progress generally halted for those born around the mid-1960s, a time when landmark legislative victories heralded an end to racial discrimination. Had those things that were helping to close the gap stopped, or had they been overshadowed by new adversities that were not remedied by gaining equality before the law? Unfortunately, no comprehensive modeling by researchers is available that might identify and quantify the culprits, nor is it likely that there will ever be. The authors draw on the knowledge base that is available, from whatever schools of scholarship that have made relevant investigations, whether they be historians, or sociologists, or economists, or practitioners. Barton and Coley explore topics that remain sensitive in public discussion in their search for answers.
A lot of suspects are rounded up, and their pictures are posted for public view. Ultimately, readers will have to turn to their own good judgment. The report informs the judgments that have to be made, for there is no escaping the fact that failure to re-start progress is an unacceptable and dangerous prospect for the nation.
Michael T. Nettles.
Senior Vice President .
Policy Evaluation and Research Center
The nation’s attention has been — and remains — riveted on the persistent Black-White gap in the achievement of our elementary and secondary school students. Each year when the National Assessment of Educational Progress (NAEP) releases “the nation’s report card,” the front-page news focuses on whether scores are rising or falling and whether the achievement gap is changing. Speculation is rife as to whether any change is some indication of either the success or failure of the No Child Left Behind (NCLB) Act and other efforts in our local-state-federal education system.
The nation’s efforts to address the achievement gap have a long history. Expectations increased with the Brown v. Board of Education desegregation decision in 1954 and with passage of the Elementary and Secondary Education Act (ESEA) in 1965, which focused on the inequality of school resources. The Civil Rights Act of 1964 spiked optimism for progress in education and in society at large. And most recently, NCLB was purposeful in its requirement to “disaggregate” the average achievement scores of state accountability programs to expose the inequality that had to be addressed.
This report is about understanding the periods of progress and the periods of stagnation in changes in the achievement gap that have occurred over the past several decades. We try to understand what might have contributed to the progress as well as probe the reasons that may account for the progress halting, in the hope of finding some clues and possible directions for moving forward in narrowing the achievement gap.
Mark H. Ingraham Dean Emeritus, College of Letters & Science, University of Wisconsin
Professor Emeritus of Mathematics, University of Wisconsin [Click to view this 23MB PDF “book”]:
Contents
Preface
Part I Liberal Education
The Omnivorous Mind 3
Given May 16, 1962, to the University of Wisconsin Chapter of Phi Beta Kappa. Republished from The Speech Teacher of September 1962.
Truth-An Insufficient Goal 17
The Keniston Lecture for 1964 at the University of Michi- gan; March 17, 1964. Republished from the Michigan Quarterly Review of July 1964.
On the Adjective “Common” 31
An editorial for the February 1967 Review of the Wisconsin Academy of Arts, Letters, and Sciences, February 23, 1967.
Part II Educational Policy
Super Sleep-A Form of Academic Somnambulism 37
First given as retiring address as President of A.A. U.P . This much revised version was given to the Madison Literary Club, March 12, 1940.
No, We Can’t; He Has a Committee Meeting 57
Madison Literary Club; May 11, 1953.
Is There a Heaven and a Hell for Colleges? 70
Commencement address, Hiram College; June 8, 1958.
The College of Letters and Science 79
Talk given to the Board of Regents of the University of Wisconsin, May 3, 1958.
Some Half Truths About the American Undergraduate 84
Orientation conference for Whitney-Fulbright Visiting Scholars. Sarah Lawrence College, September 6, 1962.
Maps Versus Blueprints 94
Honors Convocation, University of Wisconsin, May 18, 1973.
Part III To Students
A Talk to Freshmen 103
University of Wisconsin; September 18, 1951
Choice: The Limitation and the Expression of Freedom 112
Honors Convocation, University of Wisconsin; June 17, 1955. Republished from the Wisconsin Alumnus.
“The Good is Oft Interred with Their Bones” 121
Commencement, University of Wisconsin-Oshkosh; Janu- ary 19, 1968.
Talk at Honors Convocation at Ripon College
Talk at Honors Convocation at Ripon College 129
April 9, 1969
The Framework of Opportunity 136
Thanksgiving Address, University of Wisconsin; November, 1947
Part IV A Little Fun
Food from a Masculine Point of View 149
Madison Literary Club; November 11, 1946
On Telling and Reading Stories to Children 165
Attic Angel Tower, Madison, Wisconsin; March 6, 1978
Three Limericks 179
Fragments 181
a. From an address given to the University oF Wyoming Chapter of Phi Beta Kappa, April 26, 1965
b. A comment
Part V Somewhat Personal
Letter of Resignation from Deanship 185
April 5, 1961
Retirement Dinner Talk 188
May 24, 1966
Thanks to Richard Askey for extensive assistance with this digitized book. Clusty Search Mark Ingraham.
The mathematics committee of the junior high schools of Madison has been meeting regularly for four rears with one intention in mind — to improve the mathematics program of the junior high school. After experimenting with three programs in the 7th grade, the Seeing Through Mathematics series, Books 1 and 2, were recommended for adoption and approved in May of 1963.
The committee continued its leadership role in implementing the new program and began evaluation of the 9th grade textbooks available. The committee recommended the adoption of Seeing Through Mathematics, Book 3, published by Scott, Foresman and Company, and Algebra: Its Element and Structure, Book 1, published by Webster Division, McGraw-Hill Book Company, and the Board of Education adopted them on May 3, 1965.
A number of objections to the Seeing Through Mathematics textbooks were made by various University of Wisconsin professors. Dr. R. C. Buck, chairman of the University of Wisconsin Mathematics Department strongly criticized the series. A public objection to the adoption was made at the Board of Education meeting by Dr. Richard Askey of the University Mathematics Department. Later, a formal petition of protest against the adoption of Seeing Through Mathematics, Book 3, was sent to committee members. [related: 2006 Open Letter from 35 UW-Madison Math Professors about the Madison School District’s Math Coordinator position]
The sincerity of the eminently qualified professional mathematicians under Dr. Buck’s chairmanship was recognized by both the administration and the committee as calling for reconsideration of the committee’s decisions over the past three years relative to the choice of Seeing Through Mathematics 1, 2 and 3.
Conversely, the support of the Scott, Foresman and. Company mathematics program and its instruction philosophy, as evidenced by numerous adoptions throughout the country and the pilot studies carried out in the Madison Public Schoolsvindicated that equitable treatment of those holding diametric viewpoints should be given. It was decided that the interests of the students to be taught would be best served through a hearing of both sides before reconsideration.
A special meeting of the Junior High School. Mathematics committee was held on June 10, 1965.
Meeting 1. Presentations were made by Dr. R. C. Buck, Dr. Richard Askey, and Dr. Walter Rudin of the University of Wisconsin Mathematics Department, and Dr. J. B. Rosen, chairman-elect of the University of Wisconsin Computer Sciences Department.
The presentations emphasized the speakers’ major criticism of the Seeing Through Mathematics series — “that these books completely distort the ideas and spirit of modern mathematics, and do not give students a good preparation for future mathematics courses. Examples were used to show that from the speakers’ points of view the emphasis in Seeing Through Mathematics is wrong. They indicated they felt the language overly pedantic, and the mathematics of the textbooks was described as pseudo-mathematics. However, it was pointed out that the choice of topics was good the content was acceptable (except for individual instances), and the treatment was consistent. A question and answer session tollowed the presentations.
……….
After careful consideration of all points of view, the committee unanimously recommended:
- that the University of Wisconsin Mathematics and Education Departments be invited to participate with our Curriculum Department in developing end carrying out a program to evaluate the effectiveness of the Seeing Through Mathematics series and, if possible, other “modern” mathematics series in Madison and other school districts in Wisconsin;
- that the committee reaffirm its decision to recommend the use of Seeing Through Mathematics, Book 3, and Algebra: Its Elements and structure, Book 1, in grade nine with Seeing Through Mathematics, Book 1 and 2 in grades seven and eight, and that the Department of Curriculum Developnent of the Madison Public Schools continue its study, its evaluation, and its revision of the mathematics curriculum; and
- that en in-service program be requested for all junior high school mathematics teachers. (Details to follow in a later bulletin).
Related: The recent Madison School District Math Task Force.
Britannica on deja vu.
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.
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:
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.
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.
Nineteen years ago, Jennifer Courter set out on a career path that has since provided her with a steady stream of lucrative, low-stress jobs. Now, her occupation — mathematician — has landed at the top spot on a new study ranking the best and worst jobs in the U.S.
“It’s a lot more than just some boring subject that everybody has to take in school,” says Ms. Courter, a research mathematician at mental images Inc., a maker of 3D-visualization software in San Francisco. “It’s the science of problem-solving.”
The study, to be released Tuesday from CareerCast.com, a new job site, evaluates 200 professions to determine the best and worst according to five criteria inherent to every job: environment, income, employment outlook, physical demands and stress. (CareerCast.com is published by Adicio Inc., in which Wall Street Journal owner News Corp. holds a minority stake.)
The findings were compiled by Les Krantz, author of “Jobs Rated Almanac,” and are based on data from the U.S. Bureau of Labor Statistics and the Census Bureau, as well as studies from trade associations and Mr. Krantz’s own expertise.
According to the study, mathematicians fared best in part because they typically work in favorable conditions — indoors and in places free of toxic fumes or noise — unlike those toward the bottom of the list like sewage-plant operator, painter and bricklayer. They also aren’t expected to do any heavy lifting, crawling or crouching — attributes associated with occupations such as firefighter, auto mechanic and plumber.
The study also considers pay, which was determined by measuring each job’s median income and growth potential. Mathematicians’ annual income was pegged at $94,160, but Ms. Courter, 38, says her salary exceeds that amount.
Related:
Parents and citizens have another opportunity to provide input on this matter when Brian Sniff, Madison’s Math Coordinator and Lisa Wachtel, Director of Madison’s Teaching & Learning discuss the Math Report at a Cherokee Middle School PTO meeting on January 14, 2009 at 7:00p.m.
In the comments on TIMSS-07 math scores, one important aspect
has not been mentioned.
| Grade 8 | US | Minn. | Korea | Singapore |
| Number | 510 | 537 | 583 | 597 |
| Algebra | 501 | 515 | 596 | 579 |
| Geometry | 480 | 505 | 587 | 578 |
| Data and Chance | 531 | 560 | 580 | 574 |
Korea and Singapore have balanced scores, the US and Minnesota do not. The first three areas are the core areas of mathematics on which otherthings are built. We have to improve on them.
Dick Askey
John Hechinger has more:
U.S. fourth- and eighth-graders improved their math scores in a closely watched international test, but continued to lag well behind peers from top-performing Asian countries. U.S. students also failed to show measurable gains in science.
The U.S. and other governments on Tuesday released the results of the test, Trends in International Mathematics and Science Study, the world’s largest assessment of international achievement. Some 425,000 students in almost 60 countries took the exam, administered every four years, starting in 1995.
To Jay Matthews:
Let me suggest that Gerald Bracey is not an appropriate person to quote when dealing with mathematics education. First, it was TIMSS in 1995 rather than 1999 when students in the last year of high school were tested. Second, while some of our students who took the advanced math test had only had precalculus, all of them had studied geometry and we did worse in geometry than we did in calculus. Bracey never mentions this. Check the figures yourself to see the disastrous results in geometry.
We had 14% of our students take this test so the fact that some other countries did not test students in vocational tracts is irrelevant since they have a much larger fraction of their students in academic programs than 14%, as we do. About the ETS restudy, while they claim that the original sample was not comparable with other countries, their population was also not comparable with that of other countries. When you take the top say 7% of our students, judged by the courses they take which is not a perfect match but
not bad, and compare them with the top say 20% of the students in another country, that is not the same as comparing them with the top 7% in another country. ETS never mentions this in their press releases on this study.
Richard Askey
A Math book for “High Schools and Normal Schools by S.Y. Gillan [9.6MB PDF]:
Arithmetic can be so taught as to make the pupil familiar with thc fact that we may use a number in a problem without knowing what particular number it is. Some of the fundamentals of algebra may thus be taught along with arithmetic. But, as a rule, whenever any attempt is made to do this the work soon develops or degenerates into formal algebra, with a full quota of symbolism, generalization and formulae — matter which is not wholesome pabulum for a child’s mind and the result has been that teachers have given up the effort and have returned to the use of standardized knowledge put up in separate packages like baled hay, one bale labeled “arithmetic,” another “algebra,” etc.
Every problem in arithmetic calls for two distinct and widely different kinds of work: first, the solution, which involves a comprehension of the conditions of the problem and their relation to one another; second, the operation. First we
decide what to do; this requires reasoning. Then we do the work; this is a merely mechanical process, and the more mechanical the better. A calculating machine, too stupid to make a mistake, will do the work more accurately than a
skillful accountant. Adding, subtracting, multiplying and dividing do not train the power to reason, but deciding in a given set of conditions which of these operations to use and why, is the feature of arithmetic which requires reasoning.
The problems offered here will furnish material to promote thinking; and a few minutes daily used in this kind of work will greatly strengthen the pupils’ power to deal with the problems given in the textbook.
After consultation with teachers, the author decided to print the problems without regard to classification. They range all the way from very simple work suitable for beginners up to a standard adapted to the needs of eighth grade pupils. As a review in high school and normal school classes the problems may be taken in order as they come, and will be found Interesting and stimulating. For pupils in the grades, the teacher will Indicate which ones to omit; this discrimination will be a valuable exercise for the teacher.
A few “catch problems” are put in to entrap the unwary. To stumble occasionally into a pitfall makes a pupil more watchful of his steps and gives invigorating exercise in regaining his footing. The groove runner thus learns to use his wits and see the difference between a legitimate problem and an absurdity.
It is recommended that these exercises be used as sight work, the pupils having the book in hand and the teacher designating the problems to be solved without previous preparation.
S. Y. GILLAN.
Milwaukee, Wisconsin, May 21, 1910.
Many thanks to Dick Askey for providing a copy (the!) of this book.
From the book:
To answer in good, concise English, affords an excellent drill in clear thinking and accurate expression. This one is suitable for high school, normal school and university students, some of whom will flounder in a most ludicrous fashion when they first attempt to give a clear-cut answer conforming to the demands of mathematics and good English.
224. After a certain battle the surgeon sawed off several wagon loads of legs. If you are told the number of legs in each load and the .price of a cork leg, how can you find the expense of supplying these men with artificial legs? Writeout a list of twenty other expense items incurred in the fighting of a battle.
225. The American people spend each year for war much more than for education. If you know the total amount spent for each purpose, how can you find the per capita expense for war and for schools?
227. A boy travels from Boston to Seattle in a week. Every day at noon he meets a mail train going east on which he mails a letter to his mother in Boston. If there is no delay, how frequently should she receive his letters?
Well worth reading [1.2MB PDF]:
rivulet: A small stream or brook. The ancient rivulet was conducted according to customs that were centuries old. The children enjoyed wading in the rivulet. The manuscript needed only minor rivulets before publication. A pleasant rivulet trickled through the fields.
firth: A narrow inlet or arm of the sea. (A firth may refer to any narrow arm of the sea or more particular to the opening of a river into the sea. Because the coast of Scotland is dotted with so many firths, the word has come to be associated with that country.) The soldier explored the firths that cut into the coastline. The young child was severely reprimanded for having committed the firth. After swimming across the firth, he was completely exhausted. The coast was cut with many narrow firths, which were ideal hideouts for smugglers.
Related: Dick Askey: Content Knowledge Examinations for Teachers Past and Present and NAEP writing scores – 2007 along with an article by Alan Borsuk. A Touch of Greatness:
You won’t find ten-year old children reciting Shakespeare soliloquies, acting out the Cuban Missile Crisis or performing Sophocles plays in most American classrooms today. But Albert Cullum’s elementary school students did all this and more. Combining interviews with Cullum and his former students with stunning archival footage filmed by director Robert Downey, Sr., A TOUCH OF GREATNESS documents the extraordinary work of this maverick public school teacher who embraced creativity, motivation and self-esteem in the classroom through the use of poetry, drama and imaginative play.
Regarded by academics as one of the most influential educators of the 1960s and ‘70s, Cullum championed what is, by today’s standards, an unorthodox educational philosophy: the belief that the only way teachers can be successful with children is to speak directly to their hearts and to their instinctive and largely ignored capacity to quickly understand and identify with the great personalities, ideas and emotions found in classical literature. To that end, Cullum regularly taught his elementary school children literary masterpieces, exposed them to great works of art and engaged them in the events of world history. Without leaving the classroom, his students visited King Tut’s tomb, attended joint sessions of the U.S. Congress, operated on “bleeding” nouns in his “grammar hospital,” and clamored to play the timeless roles of Julius Caesar, Lady Macbeth and Hamlet.
When Cullum was an elementary school teacher in the New York City suburbs during the 1960s, his friend Robert Downey helped film several student plays and classroom events. In A TOUCH OF GREATNESS, these lush black and white films, with original music created by Tom O’Horgan, capture the work of this radical teacher and his students’ love of learning.
Greg Barlow, an Air Force officer in the defense secretary’s office at the Pentagon, was helping his 8-year-old son, Christian, one recent night with a vexing problem: What is 674 plus 249?
The Prince William County third-grader did not stack the numbers and carry digits from one column to the next, the way generations have learned. Applying lessons from his school’s new math textbook, “Investigations in Number, Data, and Space,” Christian tried breaking the problem into easier-to-digest numbers.
But after several seconds, he got stumped. He drew lines connecting digits, and his computation amounted to an upside-down pyramid with numbers at the bottom. His father, in a teacherly tone, nudged him toward the old-fashioned method. “How would you do that another way?” Barlow asked.
In Prince William and elsewhere in the country, a math textbook series has fomented upheaval among some parents and teachers who say its methods are convoluted and fail to help children master basic math skills and facts. Educators who favor the series say it helps young students learn math in a deeper way as they prepare for the rigors of algebra.
The debate over “Investigations in Number, Data, and Space,” a Pearson School series used in thousands of elementary classrooms, including some in Arlington, Fairfax, Loudoun and Howard counties, is one of the newer fronts in the math wars. Such battles over textbooks and teaching methods are fueled in part by the anxieties of parents who often feel powerless over their children’s education, especially in subjects they know.
The curriculum, introduced in the 1990s and updated in a second edition issued last fall, offers one answer to the nation’s increasingly urgent quest for stronger elementary math education. The nonprofit organization TERC, based in Cambridge, Mass., developed “Investigations” with support from the National Science Foundation.
Related Links:
Susan Troller on retiring Madison Superintendent Art Rainwater:
Later this month, a new contract between Dr. Daniel Nerad and the Madison Metropolitan School District will signal the end of an era. For over a decade, Art Rainwater has been at the helm of Madison’s public schools, guiding the district during a period of rapid demographic change and increasingly painful budget cutting. Both admirers and critics believe Rainwater has had a profound impact on the district.
Retiring Madison schools superintendent Art Rainwater may have the name of a poet, but his first ambition was to be a high school football coach.
“I grew up loving football — still do — especially the intellectual challenge of the game. I was obsessed with it,” Rainwater explained in a recent interview.
In fact, during his early years as an educator, Rainwater was so consumed by his football duties for a Catholic high school in Texas he eventually switched from coaching to school administration for the sake of his family.
In some ways, Rainwater has been an unusual person to lead Madison’s school district — an assertive personality in a town notorious for talking issues to death. His management style grows out of his coaching background — he’s been willing to make unpopular decisions, takes personal responsibility for success or failure, puts a premium on loyalty and hard work and is not swayed by armchair quarterbacks.
A few related links:
Much more on Art here. Like or loath him, Art certainly poured a huge amount of his life into what is a very difficult job. I was always amazed at the early morning emails, then, later, seeing him at an evening event. Best wishes to Art as he moves on.
David Klein, a mathematics professor at California State University at Northridge, says he was pleased to review Advanced Placement and International Baccalaureate math courses for the Thomas B. Fordham Institute. He respects institute President Chester E. “Checker” Finn Jr., a longtime leader in the movement to improve U.S. schools. Among the views Klein shares with Finn is that overuse of calculators can interfere with students’ mastery of analytical skills.
But their collaboration on Fordham’s analysis of AP and IB did not turn out the way either of them hoped.
On June 4, Klein submitted his report on two courses, AP Calculus AB and IB Mathematics SL. Klein’s analysis of AP and IB math was more negative and his grades lower than what the experts on AP and IB English, history and biology courses submitted to Fordham. He would have given the AP math course a C-plus and the IB math course a C-minus. The other reviewers thought none of the courses they looked at deserved anything less than a B-minus.
Still, Klein says, he got no indication from the Fordham staff of any problems until the edited version of his material came back to him for review on Sept. 28, a week before the deadline for completing the report. Many of what he considered his strongest points, he discovered, had been deleted. He had Fordham remove his name as a co-author of the report, “Advanced Placement and International Baccalaureate: Do They Deserve Gold Star Status?” which was released Nov. 14.
After agreeing to the name removal, Finn told Klein in an e-mail: “I imagine we’ll also reduce your overemphasis on calculator use and probably change the grades (upward). Thanks, tho, for your help.” Klein’s grade of C-plus for AP was not changed, but his grade of C-minus for IB got a big jump to a B-minus, meaning the report was saying that IB math was better than AP math, the opposite of what Klein had said.
Related:
Click to view MMSD Accounting Details. A number of questions have been raised over the past few years regarding the Madison School District’s math curriculum: West High Math Teachers: Moreover, parents of future West High students should take notice: As you read this, our department is under pressure from the administration and the math coordinator’s … Continue reading MMSD Paid Math Consultant on Math Task Force
Andy Hall: Wisconsin students’ performances improved in math and held steady in reading, language arts, science and social studies, according to annual test data released today. Dane County students generally matched or exceeded state averages and paralleled the state’s rising math scores, although test results in Madison slipped slightly on some measures of reading, language … Continue reading Wisconsin State Student Test Scores Released
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: Madison School Board Discusses Independent Math Review: Audio / Video. Math Forum Audio / Video UW Math Professor Dick Askey on the MMSD’s math scores; related: State test scores … Continue reading MMSD Math Review Task Force Introduction and Discussion
2.1MB PDF First, a disclaimer. I am far from an expert on most of the topics which will be illustrated by questions. One of my aims in giving this talk is to let others know about a serious problem which exists beyond the problem of mathematical knowledge of teachers. I have written about the problem … Continue reading Madison Literary Club Talk: Examinations for Teachers Past and Present
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 … Continue reading School math books, nonsense, and the National Science Foundation
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? … Continue reading The Politics of K-12 Math and Academic Rigor
Critics of “Fuzzy” Methods Cheer Educators’ Findings; Drills Without Calculators. Taking Cues from Singapore. John Hechinger: The nation’s math teachers, on the front lines of a 17-year curriculum war, are getting some new marching orders: Make sure students learn the basics. In a report to be released today, the National Council of Teachers of Mathematics, … Continue reading Return to Basics in Teaching Math
The issue of curriculum quality and rigor continues to generate attention. P-I:
The good news is that the high school class of 2006 posted the biggest nationwide average score increase on the ACT college entrance exam in 20 years and recorded the highest scores of any class since 1991.
The bad news is that only 21 percent of the students got a passing grade in all four subject areas, including algebra and social science.
“The ACT findings clearly point to the need for high schools to require a rigorous, four-year core curriculum and to offer Advanced Placement classes so that our graduates are prepared to compete and succeed in both college and the work force,” Education Secretary Margaret Spellings said in Washington, D.C.
Alan Borsuk has more:
Wisconsin high school graduates are better prepared to succeed in college than students nationwide – but that means only that more than 70% of state students are at risk of having trouble in one or more freshman-level subjects while the national figure is almost 80%, according to ACT, the college testing company.
The message still isn’t getting across,” Ferguson said in a telephone news conference. If students want to go to college and do well, they have to take high school seriously and take challenging courses, he said.
ACT results showed that students who took at least four years of English and three years each of math, science and social studies in high school did substantially better on the tests (22.9 in Wisconsin, 22.0 nationwide) than those who took lighter loads in those core areas (21.0 and 19.7, respectively).
Elizabeth Burmaster, Wisconsin’s superintendent of public instruction, said she believes that if schools in Wisconsin stay focused on efforts such as early childhood education and small class sizes in the early grades, combined with strong academic programs in middle school and high school, achievement will go up and racial and ethnic gaps will close.
Individual state data is available here.
Burmaster’s statement, along with the ACT information will increase the attention paid to curriculum issues, such as the ongoing questions over the Madison School District’s math program (See UW Math professor Dick Askey’s statement on the MMSD’s interpration and reporting of math scores). Will we stick with the “same service” approach? This very important issue will be on voters minds in November (referendum) and again in April, 2007 when 3 board seats are up for election. See also the West High School Math Faculty letter and a recent open letter to the Madison School District Board and Administration from 35 of the 37 UW Math Department faculty members. Vaishali Honawar has more.
The Madison School District issued a press release on the recent ACT scores (68% of Wisconsin high school graduates took the ACT – I don’t know what the MMSD’s percentage is):
Madison students who took the 2006 ACT college entrance exam continued to outperform their state and national peers by a wide margin, and the scores of Madison’s African-American test takers increased significantly. Madison students’ composite score of 24.2 (scale of 1 to 36) was higher for the 12th straight year than the composite scores of Wisconsin students and those across the nation (see table below). District students outscored their state peers by 9% (24.2 vs. 22.2,) and their national peers by 15% (24.2 vs. 21.1).
Compared to the previous year, the average ACT composite score among the district’s African-American students increased 6% — 18.8 vs. 17.7 last year. The gap between district African-American and white student ACT scores decreased this year. The relative difference this year was 24% (18.8 vs. 24.8) compared to 30% last year.
Scores also increased this year for the district’s Asian students (22.1 to 23.0) and Hispanic students (21.5 to 21.8).
The Madison School District recently published this summary of student performance vs other similar sized and nearby districts (AP, ACT and WKCE) here. Madison’s individual high schools scored as follows: East 22.9, LaFollette 22.1, Memorial 25.1 and West 25.5. I don’t have the % of students who took the ACT.
I checked with Edgewood High School and they have the following information: “almost all students take the ACT” and their composite score is “24.4”. Lakeside in Lake Mills averaged 24.6. Middleton High School’s was 25 in 2005. Verona High School’s numbers:
222 students took the ACT in 2005-2006.
Our composite score was 23.6 compared to the state at 22.2
87% of test takers proved college ready in English Composition (vs. 77%)
66% of test takers proved college ready in College Algebra (vs. 52%)
77% of test takers proved college ready in Social Science (vs. 61%)
45% of test takers proved college ready in Biology (vs. 35%)
37% of test takers proved college ready in all four areas (vs. 28%)
(#) as compared to the state %
Waunakee High School:
Score HS Mean (Core/Non-Core)
Composite 23.3 (24.3/21.5)
English 22.5 (23.9/19.5)
Mathematics 23.2 (24.2/21.8)
Reading 23.3 (24.1/21.5)
Science 23.7 (24.4/22.7)
McFarland High School’s 2006 Composite average was 23.7. 110 students were tested.
UPDATE: A few emails regarding these results:
In the Waunakee information I sent to Jim Z, our mean for the Class of 2006 comes first, followed by the core/non-core in parentheses. So, our mean composite score for our 157 seniors who sat for the ACT was 23.3, the mean composite for those completing the ACT suggested core was 24.3, the mean composite for those who did not complete the core was 21.5.
With ACT profile reports, the student information is self-reported. It’s reasonably accurate, but some students don’t fill in information about course patterns and demographics if it is not required.
Please let me know if there are any other questions.
It appears that Jim Z’s chart comparing scores uses Waunakee’s “Core score” as opposed to the average composite that the other schools (at
least McFaland) gave to Jim Z.. If Jim Z. wishes to report average “Core” for McFarland it is 24.5. Our non-core is 22.2 with our average composite 23.7.
Probably everyone is familiar with the ACT definition of core, but it’s 4 years of English, and three years each of math, science, and social studies. ACT is refining their position on what course patterns best position a student for undergraduate success, however.
Additional comments, data and links here
NY Times Editorial: Many of the nations that have left the United States behind in math and science have ministries of education with clear mandates when it comes to educational quality control. The American system, by contrast, celebrates local autonomy for its schools. When Congress passed the No Child Left Behind Act, it tried to … Continue reading The School Testing Dodge
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 thatstandard … Continue reading Analysis of Connected Math and Core Plus Textbooks
OPEN LETTER: Dear Members of the School Board, dear Superintendent Rainwater, We are writing to strongly urge that the new Coordinator of Mathematics have the depth of knowledge of mathematics that we believe is essential for the position. While we are obviously concerned about the preparation of students entering the University, our concerns are much … Continue reading Open letter about Math Coordinator position at MMSD
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 … Continue reading Connected Math in Olympia, WA
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 … Continue reading State Test Scores Adjusted to Match Last Year
Education & Academia: he District of Columbia spends far more money per student in its public elementary and secondary schools each year than the tuition costs at many private elementary schools, or even college-preparatory secondary schools. Yet, District 8th-graders ranked dead last in 2005 in national reading and math tests. Not one U.S. state can … Continue reading “D.C.’s Distinction: $16,344 Per Student, But Only 12% Read Proficiently”
Will the Madison district sink or swim? April 4th elections could prove pivotal At the end of an especially divisive Madison school board meeting, Annette Montegomery took to the microphone and laid bare her frustrations with the seven elected citizens who govern Madison schools. “I don’t understand why it takes so long to get anything … Continue reading The fate of the schools
Eduwonk: Most everyone in the political and policy world was fixated on all the “what does it mean” questions about Sunday’s NYT Mag story on Mark Warner. But there was also some chattering about the Outlook spread on No Child Left Behind in the Wash. Post. It was well done including reactions from DC-area principals, … Continue reading What’s an AYP Rating? And Why it Matters
The Education Trust [full report:
Michele Besso & Cecilia Le: The study raised questions about the rigor of state tests and standards because of the large disparity in student performance between state and federal standardized tests. While most states report high proficiency rates on their own tests, just 29 percent of the nation’s eighth-graders did well in reading and math … Continue reading More on Local/State vs. National Tests
Justin Ware: “And that’s what’s so exciting about the program for the kids,” said Luke Felker, Madison Country Day School, “is that through some solid work at the beginning, they begin to realize that they can do a lot of this in their heads.” Felker says the program also focuses more on depth, than it … Continue reading Singapore Math Program Used In Madison
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 … Continue reading Madison and Wisconsin Math Data, 8th Grade
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: Dick Askey (UW Math Professor) Faye Hilgart, Madison Metropolitan School District Steffen Lempp (MMSD Parent and UW Math Professor) Linda McQuillen, Madison Metropolitan School District Gabriele Meyer … Continue reading Math Forum Audio / Video and Links
There’s been no shortage of discusion regarding math curriculum. Rafael Gomez’s latest event, this Wednesday’s Math Forum should prove quite interesting. The event will be at the Doyle Administration Building (McDaniels Auditorium) [Map] from 7:00 to 8:00p.m. Participants include: Dick Askey (UW Math Professor) Faye Hilgart, Madison Metropolitan School District Steffen Lempp (MMSD Parent and … Continue reading Math Forum: Wednesday 2.22.2006 7:00p.m.
Hamilton Middle School [Map] is hosting a Math Night, Wednesday, February 8, 2006 at 7:00p.m., evidently designed for parents of children attending that school this fall. Rafael Gomez is organizing a Forum on Middle School Math Curriculum Wednesday evening, February 22, 2006 at the Doyle Administration Building (McDaniels Auditorium) [Map] from 7:00 to 8:00p.m. Participants … Continue reading February Math Events
Jason Shepherd recently wrote an article on the Madison School District’s Affiliated Alternatives Program. This differentiated program supports about 150 students: Many of the school’s students have multiple problems, from severe learning deficits to turmoil at home. A countywide survey found they use alchol and marijuana at three times the rate of other students in … Continue reading A Different Approach: Affiliated Alternatives
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 … Continue reading A Few Notes on the Superintendent’s Evaluation & Curriculum
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 … Continue reading Math Curriculum: Textbook Photos
