# What to do about math

Only 39 percent of fourth graders and 34 percent of eighth graders test as “proficient” on the NAEP exam.  The NY Times’ Room for Debate blog asks researchers and advocates how to improve math scores.

Education Professor Bruce Fuller says the flat scores show NAEP has failed.

Lance T. Izumi of Pacific Research Institute warns, “Don’t shoot the messenger.”

Holly Tsakiris Horrigan, a parent of public school children, says the problem is with trendy but “nonsensical” math curricula, not with testing.

These curricula substitute writing, drawing and calculator usage for solid math content, leaving children unprepared for more advanced math topics.

Affluent parents send their children to tutoring centers to learn what’s not taught in school, she writes. But most parents can’t afford that.

Barry Garelick of U.S. Coalition for World Class Math agrees that students need to learn math content.

Students don’t need skills-free math and “real world” problems, they need to learn the skills and concepts necessary to solve challenging problems.

Richard Bisk, math professor and adviser to the Massachusetts Education Department, calls for giving students “a firm foundation” starting in the elementary grades.

.  . . a substantial improvement in elementary teachers’ knowledge of mathematics; a more focused curriculum that emphasize core concepts and skills; and more challenging textbooks that teach for mastery and not just exposure.

NAEP scores tell us nothing about what policies work, argues Cato’s Neil McCluskey. He provides a lesson in how to read the numbers in very different ways.

For advanced statistical hokum, by the way, Gotham Schools explains how New York City counts class sizes: If one teacher is teaching 37 students in the same room at the same time, pretend they’re in two not-so-large classes. See? You can use math in real life!

1. The NAEP categories, “basic”, “proficient”, “advanced” mean little. What qualifies as “basic”? Relative rank means something. In 1996, the Singapore 8th grade TIMSS Math 5th percentile score was higher than the US 50th percentile score. Several years ago, I used NAEP 4th and 8th grade Reading and Math percentile scores, proficiency scores, mean scores, and mean scores by parents’ race and level of education to rank States, and then to relate scores to various variables (per-pupil budget, district size, age (start) of compulsory attendance, percent of districts requiring PRAXIS for teacher applicants).

In brief:

1) Money makes no difference.
2) Smaller is better.
3) Later is better.
4) No credential test is better.

“What works?” is an empirical question which only a competitive market or numerous small policy experiments (e.g., small school districts) can answer.

If we disagree about a matter of taste, a market in services allows for the satisfaction of varied tastes, while the contest for control of polioy in a State-monopoly provider must create unhappy losers. If we disagree about a matter of fact, numerous independent providers of goods and services or numerous small government providers (Federalism) will provide more information than will a State-monopoly enterprise. A State-monopoly enterprise is like an experiment with one treatment and no controls; a retarded experimental design.

2. Or you could just look at the GAO’s and National Academy of Science’s evaluation of NAEP test scores, reach the enlightened opinion they’re all a load of crap, and turn your attention to something else.

3. As a very concerned parent running for a position on a local school board it is important to know what does work and what does not. How much longer are we to sit and watch stagnant test scores and false answers with delusional characteristics.

Karin Chenoweth, in “Successful schools avoid false choices” appearing in this week’s Ed Weekly, comments on how some local school boards do get it right. She champions the responsible evaluation and implementation of programs and notes several successes.

Recently, Secretary of Education Arne Duncan made it clear his favorable position on mayoral control of our schools. NYC comes to mind and that alone should serve as a reminder that as Mr. Kilpatrick points out, that the local government may provide us with the best information.

And, let us not forget the numerous expert math parents, serving on the front line, offer the most practical advice.

4. Laura,

If you are elected to the school board here is the advice I would give you. Don’t listen to outside consultants; they are there for one thing, to push their product. Once they get their foot in the door they will swear their product is the ONE AND ONLY thing your district needs.

Talk to the actual teachers instead.

5. tim-10-ber says:

Mike in Texas — good advice except some (many?) of the math teachers are pitiful as they do not know their subject either. Damn if you do damn if you don’t…neither choice is very good…

Laura…two cents says look at the research, who did (who funded it) and understand what it says before choosing a program. Look at other countries and see what they use and how well their students do, how well their teachers know the subject matter and how effective they are as teachers of their subject matter. Include in your conversations the most effective math teachers in your district as well as parents, too. Best of luck and thanks for getting involved.

6. Tim-10-ber,

There are some very good practices in other countries that are being ignored b/c they won’t make Pearson or McGraw-Hill money.

Teachers in Japan spend nearly half their day planning and collaborating, while their students are getting a rich and varied curriculum. When I suggested this here I was accused of being a lazy incompetent.

7. Mike,
You write

1) “Or you could just look up the GAO’s and the National Academy of Science’s evaluation…”

“Or” is a conjunction. A OR B. What is the “A”? Was this in response to Joanne or me?

2) “Don’t listen to outside consultants; they are there for one thing, to push their product.Once they get their foot in the door they will swear their product is the ONE AND ONLY thing your district needs.”

Insiders are just as self-interested as “outside comsultants”. Defenders of the NEA/AFT/AFSCME cartel’s exclusive position in receipt of the taxpayers’ K-12 education subsidy insist (against abundant evidence) that their product deserves this exclusive position.

8. anon says:

Yes, leave it to an Edyookashun perfesser to say that the test has failed instead of admitting that he and his minions have failed.

9. Malcolm,

Both the General Accounting Office and the National Academy of Science have determined the NAEP cutoff levels to be worthless.

I’d point you to the GAO report but it was removed about a year ago from the US govt. websites. The report was PEMD-93-12. You may also want to check:

Linn, R. L (1998) Standards-Based Accountability: Ten Suggestions. Policy Paper. Center for Research in Evaluation, Standards and Student Testing, General Accounting Office,

Educational Achievement Standards: NAGB’s Approach Yields Misleading Interpretations. (1993). Washington, DC: Author, June, Report GAO/PEMD-93-12; National Academy of Sciences,

Grading the Nation’s Report Card: Evaluating NAEP and Transforming the Assessment of Educational Progress. (1999). Washington, DC: National Academy Press.

Jones, L.V. (1997) National Tests of Educational Reform: Are They Compatible? Princeton, NJ: Policy Information Center, Educational Testing Service.

10. Malcolm,

My comment was intended for Joanne.

BTW, this is what the GAO report says”

A General Accounting Office review of the NAEP proficiency levels was prompted by a report of a
small group of scholars who labeled the National Assessment Governing Board (NAGB)—the body that sets the proficiency levels — as “incompetent” and the levels themselves as “ridiculous.” The GAO review concluded: “NAGB’s… approach was inherently flawed, both conceptually and procedurally, …the approach [should] not be used further until a thorough review could be completed… These weaknesses are not trivial; reliance on NAGB’s results could have serious consequences.”
(p. 38) (GAO (U.S. General Accounting Office). 1993. Educational Achievement Standards. NAGB’s Approach Yields Misleading Interpretations. GAO/PEMD 93-12. Washington, D.C.: General Accounting Office.

In addition, the NAGB chair was none other that that “reform” crowd darling, Checker Finn.

11. Mike,

Thanks. I do not know enough about the qualifications of the NAGB to express any opinion on their mathematical competence. I agree that the proficiency levels are nonsense. That does not make them useless as relative measures of school effectiveness. By analogy, suppose someone sets arbitrary levels of health, as measured by resting pulse rate. Set “athletic” at 55 bpm, “fit” at 70 bpm, and “at risk” at 85 bpm. State-by-State comparisons of “population below (i.e., better than) athletic” or “population above (worse than) at-risk” could provide a lot of information, when correlated with diet, daily sun exposure, etc. even if the cut-off points are arbitraty and subject to exceptions.

12. Malcolm,

If the achievement levels are nonsense what makes you think it would be a valid measurement of anything.

13. (Mike): “If the achievement levels are nonsense what makes you think it would be a valid measurement of anything.”

The levels (cut-off points) are arbitrary, and the definitions of “advanced”, “proficient”, and “basic” may be dubious, but the tests measure Reading or Math ability (not perfectly, but nothing’s perfect). The measures themselves can be correlated with institutional variables to generate useful information.

14. SteveH says:

Are you as dumb as our fourth graders? Try for yourself.

http://nationsreportcard.gov/math_2007/m0017.asp

It makes you wonder how bad “Basic” is.

Here is one of the fourth grade questions. Only 55% got this correct.

14, 26, 38, ______ , ______

The numbers in the pattern above are increasing by 12. Which of these numbers is part of the pattern?

A. 52
B. 58
C. 60
D. 62

They GIVE you the pattern, even after all of the effort they put in on emphasizing patterns.

It must be the 7th grade reading level. That’s it. Let’s see if we can get kids to tie their shoes by the end of 3rd grade. Gee, I don’t know. There must be something mysterious about it. This is not about discovery, direct instruction, or teaching with hand puppets. It’s about expecting any level of accountability from our schools.

15. SteveH,

Did you fail to notice I was mentioning the “READING” test, not the Math? Was my writing on too high a level for you?

Is this a valid skill to expect 4th graders to know? Is skip counting by 12s part of the curriculum standards for every state? If not the kids may have never seen a problem like this before and not know how to solve it.

16. SteveH says:

The thread is about math, if you didn’t know. Now you are saying that you were off topic and your comment had nothing to do with math? I see you are still an apologist for low expectations. Everyone should go to the web site and see how low they are. They have some reading examples there too. Judge for yourself.

17. Laura,

Thanks for the kind words. Good luck to you.

Here are my recommedations (in increasing level of difficulty):
1) Use no US Math textbooks. They are all gaudy, ponderous, overpriced crap. Use Singapore Math (textbooks are available) or the Hong Kong, Russian, Hungarian, or Czech equivalent.
2) Abandon College of Education course requirements (hire anyone with a Math-oriented degree, like Math, Physics, Chemistry, Economics).
3) Replace probationary status with a two-year stint as teacher’s aide, department gofer, and in-house substitute. Hire those who work out.

18. Steve H,

I see you failed to answer any of my questions. Is this a reasonable expectation that a child in the 4th grade will know how to do this? Is it a standard they have been taught?

BTW, while the problem may seem simple to you remember that your typical 4th grader is 9 years old. In effect this problem asks them to do a multi-step process to arrive at the correct answer. Were YOU capable of doing that when you were 9 years old.

As a 4th grade math teacher I say it’s a poorly written question. If you want them them

19. Mike in Texas
From the CA state standards(Which are considered reasonable)

“Find the sum or difference of two whole numbers between 0 and 10,000.”

“Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.”

“Determine when and how to break a problem into simpler parts.”

The problem would probably be considered 3rd grade level under CA standards.

14 + 12 = 26
26 + 12 = 38
38 + 12 = ?