- 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 (MMSD Parent and a UW Math Department Lecturer)
- Dr. Terry Millar of the Wisconsin Center for Education Research
The conversation, including audience questions was lively.
The discussion continues with these notes and links from the audience and participants:
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 office to phase out our “accelerated” course offerings beginning next year. Rather than addressing the problems of equity and closing the gap by identifying minority math talent earlier, and fostering minority participation in the accelerated programs, our administration wants to take the cheaper way out by forcing all kids into a one-size-fits-all curriculum.
It seems the administration and our school board have re-defined “success” as merely producing “fewer failures.” Astonishingly, excellence in student achievement is visited by some school district administrators with apathy at best, and with contempt at worst. But, while raising low achievers is a laudable goal, it is woefully short-sighted and, ironically, racist in the most insidious way. Somehow, limiting opportunities for excellence has become the definition of providing equity! Could there be a greater insult to the minority community?
Learning from Teaching: Exploring the Relationship between Reform Curriculum and Equity, Jo Boaler, Stanford University [110K pdf]:
Some researches have expressed doubts about the potential of reform-oriented curricula to promote equity. This article considers this important issue and argues that investigations into equitable teaching must pay attention to the particular practices of teaching and learning that are enacted in the classrooms. Data are presented from two studies which middle school and high school using reform-oriented mathematics curricula achived a reduction in linquistic, ethnic, and class inequalities in their schools. The teaching and learnign practices that these teachers employed were central to the attainment of equality, suggesting that it is critical that relational analyses of equity go beyond the curriculum to include the teacher and training.
The Real Story Behind Story Problems: Effects of Representations on Quantitative Reasoning Kenneth R. Koedinger, Human–Computer Interaction Institute Carnegie Mellon University; Mitchell J. Nathan, School of Education, University of Colorado [677K PDF]:
This article explores how differences in problem representations change both the performance and underlying cognitive processes of beginning algebra students engaged in quantitative reasoning. Contrary to beliefs held by practitioners and researchers in mathematics education, students were more successful solving simple algebra story problems than solving mathematically equivalent equations. Contrary to some views of situated cognition, this result is not simply a consequence of situated world knowledge facilitating problem-solving performance, but rather a consequence of student difficulties with comprehending the formal symbolic representation of quantitative relations. We draw on analyses of students’ strategies and errors as th ebasis for a cognitive process explanation of when, why, and how differences in problem representation affect problem solving. We conclude that differences in external represen-
tations can affect performance and learning when one representation is easier to comprehend than another or when one representation elicits more reliable and meaningful solution strategies than another.
NAEP 2005 data for US, Wisconsin, Minnesota, and Texas
US WI MN TX
All students 237 241 246 242
White 246 247 251 254
African-American 220 210 219 228
Hispanic 225 224 223 235
All students 278 285 290 281
White 288 291 296 295
African-American 254 246 251 264
Hispanic 261 265 263 271
Wisconsin Center for Education Research:
Attached is the powerpoint presentation [820K pdf | html (click the slide to advance to the next screen)] that Linda, Faye, and I used.
I also have cc’d UW-Madison Curriculum and Instruction Professor Victoria Hand who spoke from the audience Wednesday evening. You might contact her about contacts in the School of Education with expertise on the science of testing, or for research in math education. Dr. Norman Webb is one such person, and therefore I have copied him also. As I said that evening, Connected Math will be releasing a report sometime in March that has a lot of information about implementation of Connected Math nationwide. Their url is
I found the forum interesting – thanks for arranging it.
Last night was a display of statistics that 3 of the 4 professors shot holes in quickly. I really don’t care what the statistics show — I’m NOT happy with the math curriculum. And, as a taxpayer, I should have a say, and I do, but I am not heard — as evidenced last night, where I felt I was dismissed when I went to speak to one of the MMSD panelists.
We have to reinforce fractions and teach percentages, decimals, etc at home because the basic building blocks are not being addressed in the classroom. Ridiculous. As parents, we should not have to do the job ourselves — support the job done at school, YES. But, do the job ourselves, NO. And, my sense is the teachers agree with us — two or three with whom I have spoken at Thoreau would love direction to switch to Singapore. It’s logical, sequential, and text-book based, as opposed to all these loose sheets that come home, which do not seem to build on anything.
Madison Parent and UW Math Professor:
Good meeting last night.
But, whenever data or statistics or testing was mentioned, the conversation was redirected.
There seems to be little understanding of testing, what each test means, what each kind of test tests; characteristics of norm referenced tests (NRT), of criterion referenced tests with their cut scores, achievement tests, predictive tests, how test items are chosen, the specific characteristics of WKCE, NAEP, TIMSS, PISA, ACT, SAT, GRE, LSAT, MCAT, etc.
Statistics is not understood, and how it is reflected in the testing, and testing wars. Classics such as Huff’s How to Lie With Statistics, and more currently, Best’s two books “Damn Lies and Statistics”, and “More Damn Lies and Statistics”. Seems to me these books are the bibles of the advocates.
Prof Askey mentioned the NAEP as the key indicator of student success, but the National Academy of Science, as cited approvingly by NCES, “NAEP’s current achievement level setting procedures remain fundamentally flawed. The judgment tasks are difficult and confusing; raters’ judgments of different item types are internally inconsistent; appropriate validity evidence for the cut scores is lacking; and the process has produced unreasonable results.”
What I am seeing is purposeful misrepresentation in the schooling wars, each side conveniently hiding flaws and inconsistency in their reasoning and data. All smoke and little light.
I would like to suggest a forum to discuss the “science” of testing to help remove the smoke.
Madison Parent and UW Math Lecturer
Good evening, I am Gabriele Meyer and I am a lecturer in the Math dept at
UW Madison. Through my son, Walter, I first encountered Connected Math.
Here is what I found:
on a practical level:
- the material covered in Connected Math is insufficient in depth and structure and even in scope, e.g. it doesn’t explicitly cover double fractions and even though it is excessively wordy, it doesn’t cover multistep word problems.
- The way material is covered does not stress the connections within math, i.e. the mathematical structures and rules, which to a large extent are the beauty of the field
- there are way too few exercises to firm up the concept in the learner.
- It takes a very good teacher to achieve a good outcome given these flaws. In particular, the teacher would have to supplement with other material and modify lesson plans. This is inefficient and prone to great inequities in teaching performance.
on a philosophical level:
Math was discovered over thousands of years and represents the
distillate of the efforts of its many practitioners. The next step can
only be comprehended if the previous one has been understood.
The investigative/discovery method, while very enjoyable, makes the
student to reinvent the wheel, without the benefit of the rules already
discovered. 12 years of math education are simply too short to have
students discover their way to calculus, a path that took humanity from
prehistory to the 16 hundreds.
What can be done?
On a general note, any teaching philosophy elevated to the level of dogma is bad. Good teachers usually use a mix of techniques. We should not completely discard the investigative approach, but we should look at what others, also in other countries, do better.
For uniform Math instruction at the Middle school level, I personally, would use Singapore Math. It worked for our son, with Discovery/Connected Math as a backup and supplement. This ensures that the benchmarks (arithmetic with whole numbers and fractions, some geometry) are met and the kids can go on to geometry and algebra in high school.
If there are to be different Math class styles in middle school, then the choice of which class to attend should be left to the parents/children with the understanding that in some classes more homework is required to keep up.
Also, it should be clear that certain types of math are terminal in the sense that they do not prepare for the next level. For example, to a very large extent Discovery type math throughout high school does not prepare for the rigors of Calculus, as is needed for the sciences and engineering. It costs time and money to make up for this in college.
I think it is especially important that *Public Schools* provide a solid math curriculum for the sake of economically and socially disadvantaged youths. They can’t get it anywhere else.
Mike and Kristin Jenkins:
Chapel Hill, NC
We feel your pain, and have left Madison to live in an area that “gets it”. Our 6th grade son is now enrolled in a racially diverse public school program and studying among other things the quadratic equation and Shakespeare. In addition to this our property taxes are about half what they were in Madison. A short description of the program is below. UW is just as good (probably better) as UNC and I expect this could be put together in Wisconsin. We would move back in a minute if a “LEAP like” program was available in Wisconsin. Wisconsin spends lots of money on challenged folks who need help…gifted kids need help too…as your dropout rates indicate. I have no doubt in my mind that my son would not have made it through public school in Wisconsin.
Tar Heel Education: Something For The Gifted
In the schools of the college town of Chapel Hill, North Carolina, kids who score above the 97th percentile in reading and math are invited to participate in a program that is designed to meet their needs:
Carol Horne, gifted program curriculum coordinator for Chapel Hill-Carrboro City Schools, explained in a presentation Tuesday night at Smith Middle School the logistics of LEAP. [ Learning Environment for Advanced Programming]
The program is geared toward kids who have “demonstrated extraordinary levels of intellectual potential and academic achievement found in the top 1 percent of the national population in reading and math,” according to Horne’s presentation.
Previously offered only to fourth- and fifth-graders, the program now is available at Smith to all eligible district students in sixth- and seventh-grades. And by the 2006-07 school year, eighth-graders will get their chance to prove their skills.
Ed Holub, whose child participates in the program, said he is pleased with the program and emphasized its necessity.
“It’s hard to operate with a wide range of students in the class,” he said. “It fulfills the district’s mission of meeting each child’s potential in every classroom.”
Holub said it is almost impossible for teachers to instruct each student at his or her own proficiency level in a class, and that LEAP provides an efficient way of teaching the most talented kids.
Tuesday’s information session focused on availability and which children qualify for the program. Horne explained that a committee decides entrance based on aptitude or achievement — students take the Naglieri Non-Verbal Aptitude Test as one indicator.
Only those who score in the 97th percentile or higher on both the reading and math portions of the test are eligible for the program.
Horne said many parents who have children who qualified for the program might choose not to leave their individual school, adding that each system school had a “thriving, excellent gifted program.”
One concern about LEAP is that students might be isolated from the rest of the school population, which might prove detrimental.
But Valerie Reinhardt, principal at Smith, said no such problem exists.
Students in the program have homeroom and four core sections with their LEAP classmates but attend three electives that allow them to follow an avenue of learning of their choice, she added.
“Above all, they are Smith students, not LEAP students,” she said.
Boyd Blackburn, a math and social studies teacher in the program, agreed.
“In the middle school, they aren’t isolated,” he said. “It’s a good mix. I would not describe them as isolated, and I don’t think they feel isolated either.”
So far, Reinhardt said the installation of the program into middle school has progressed smoothly.
“There’s a lot of healthy learning,” she said. “There were a couple of bumps in the beginning, but the kids and parents are pleased.”
Holub admitted how satisfied he was with the program so far.
“I think the district did an outstanding job of recruiting teachers and putting together a curriculum,” he said. “They are very committed to making the entire LEAP program a success.”
It is a most unfortunate fact that in many American schools bright and highly-motivated children are often “picked-on” by students who think that school is not a place to work and learn but a place to play and waste time.
It is even more unfortunate that in many cases, the schools permit this to continue.