Unnumbered

Peter Wood

American students don’t do well in math, but things could be worse. And apparently will be very soon.

For that we can thank the National Research Council (NRC) and its new 280-page Framework for K-12 Science Education, released on July 19. The framework comes with an illustrious pedigree. The National Research Council is an arm of the National Academies (Science-NAS; Engineering-NAE; and the Institute of Medicine). It appointed an 18-member committee of “experts in education and scientists” to draft the framework, and then shopped the draft to the members of the National Science Teachers Association, the American Association for the Advancement of Science, and the Council of State Science Supervisors. It released a public draft July a year ago.

With all that, one might think we would have a pretty good framework for K-12 science education. Indeed the framework comes packaged in some inspiring language. It depicts a future in which “Students, over multiple years of school, [will] actively engage in science and engineering practices and apply crosscutting concepts to deepen their understanding of each fields’ disciplinary core ideas.” This emphasis on depth comes in contrast to what the NRC laments is the current superficiality of K-12 science education which is “not organized systematically across multiple years of school, emphasizes discrete facts with a focus on breadth over depth, and does not provide students with engaging opportunities to experience how science is actually done.”

We’ve been here before. I grew up in the post-Sputnik era in which science education was the vital center of public schooling, and at least in my corner of Pittsburgh, there was nothing superficial about it. It had breadth and depth, and some capacity to inspire. I went to school in a pretty modest district, but it took science education seriously. There was something for everyone and the more capable students could finish high school with a solid grounding in lab-based physics, chemistry, biology, astronomy, and geology. And indeed math, without which one could make only limited headway in the other fields.

A New Kind of Quantitative Easing

But that seems to be the Achilles heel of new NRC framework. Perhaps the teachers on that 18-member commission prevailed with the counsel that our students just can’t be expected to master the quantitative side of things. As Ze’ev Wurman, a Palo Alto software engineer who has been a frequent critic of the “Common Core” standards in mathematics, puts it, the NRC “framework does not expect students to use any kind of analytical mathematics while studying science.” Wurman observes that the Framework for K-12 Science Education is thick with rhetoric praising the importance of mathematics but when it comes to expectations of students achieving some measure of actual competence, the drafters of the document turn tender:

…it only expects students by grade 12 to be competent in “recognizing,” “expressing,” and “using simple … mathematical expressions … to see if they make sense,” but not in actually solving science problems using mathematics. Its other suggestions include the use of computer programs and simulations, ability to analyze data using computer tools and spreadsheets, modeling, and describing systems using charts and graphs. But there is nothing about actually being able to model a system by its equations, or solve it using mathematical techniques. The framework also includes as one of its Cross Cutting Concepts something it calls Systems and System Models (p. 4-7), but there, yet again, it does not expect students to use mathematics for that modeling. Its models “can range in complexity from lists and simple sketches to detailed computer simulations or functioning prototypes,” but mathematics is left behind.

Zurman’s critique is unnerving. The NRC apparently thinks “algebra” lies beyond the intellectual horizon of most American students. The word occurs only once in those 280 pages and that in the context of a tiny-steps-for-baby-feet injunction that students should learn how to take equalities expressed in words and express them in “algebraic symbols—for example, shifting from distance traveled =  velocity multiplied by time elapsed to s = vt.” And, alas, as Zurman adds, “This is the single equation in the whole 280 pages of the science framework.”

Countdown

What in the world is going on? I’ve had the experience as a college provost of discovering that a high percentage of my otherwise bright and ambitious undergraduate students were functionally math illiterates. The New York Times reported earlier this month that this year only “57 percent of students in third through eighth grade in [New York] city passed the statewide math tests.” Nationwide, the statistics look a little better. The National Center for Education Statistics reports on the last (2009) National Assessment of Educational Progress (NAEP) scores in math that 26 percent of 12th graders (49,000 were tested) rated “proficient,” or better, and 64 percent achieved “basic” or above. These were slight improvements over the 2005 levels. (The “advanced” level was attained by 3 percent of the tested students.) Interestingly, the percentage of students who took relatively advanced high-school mathematics courses is significantly higher than those who achieved “proficiency.” Some 24 percent of students took pre-calculus and another 18 percent took calculus. That in itself testifies to something amiss:  students ambitious enough to take and pass pre-calculus should surely be able to achieve the NAEP’s not very strenuous definition of mathematical “proficiency”—

Twelfth-grade students performing at the Proficient level should be able to recognize when particular concepts, procedures, and strategies are appropriate, and to select, integrate, and apply them to solve problems. They should also be able to test and validate geometric and algebraic conjectures using a variety of methods, including deductive reasoning and counterexamples.

The “Nation’s Report Card” gives examples of the kinds of questions on the math part of NAEP. They are not especially taxing.

Of course all of this has been widely reported and prompts episodic hand-wringing. We will get another bout of that this fall when the 2011 NAEP results are released.

Excuses

As if in anticipation of the bad news, stories about “dyscalculia” seem to be getting much more play. Dyscalculia is the “neurocognitive disorder” that “inhibits the acquisition of basic numerical and arithmetic concepts,” as Science Daily recently put it. Let me tread lightly here. Surely mathematical ability lies on a spectrum. Most are not born with the mind for numbers that will produce a Euler or a Gauss. But very few people are altogether bereft of numerical sense. How few? Four to six percent according to dyscalculiaforum.com. “At least five percent,” according to Dr. Brian Butterworth, a cognitive neuropsychologist speaking on NPR’s “Science Friday” earlier this year. “Up to 7% of the population,” says the Science Daily article I quoted. I’ve heard estimates as high as 10 percent.

Perhaps this is so, but I’m skeptical, especially since the publicity that dyscalculia has recently received has prompted so many self-diagnoses, such as that of the science blogger “Barbara” who has discovered that “genetics” has left her with “migraines, acid reflux, the color blindness gene, and dyscalculia.” Dyscalculia may as some believe reflect an organic condition, but it is surely becoming a social condition too, as a few minutes reading dyscalculiaforum.com will quickly show.

The medicalization of poor mathematical ability will save some from unwarranted intellectual embarrassment but it seems almost inevitable that dyscalculia will be grossly over-diagnosed and will become one more comfortable bench for those numerous students who have a perfectly good intraparietal sulcus but not much academic motivation. Meanwhile, some observers are beginning to think that the argument that lays most of the credit for math ability in the genes is due for revision.

Almost Half Prepared

The widespread failure of American primary and secondary schools to achieve anything like mass competency in mathematics, of course, bears directly on what American higher education can and cannot accomplish. It means that our commitment to mass higher education—the ethic of “send everyone to college”—commits most colleges to remedial and junior-high-school-level quantitative skills, and precludes the vast majority of American-educated students from pursuing majors in the hard sciences and engineering. Higher education gets the knock-on results of the failure of K-12 schools to teach math successfully.

We get frequent reminders, most recently from the 2011 ACT College Readiness Benchmarks, announced earlier this month. There we learned that “Twenty-five percent of the class of 2011 met the ACT College Readiness Benchmarks in math, science, English, and reading.” That is, 25 percent met all four benchmarks, but a great big 45 percent achieved college readiness in math. That’s interesting to contemplate, given that the NAEP result for 2009 was that only 26 percent of high school seniors achieved “proficiency.” Does this mean that “college readiness” in math no longer requires “proficiency?”

Inequalities

I began with the National Research Council’s well-intentioned effort to repair the dismal state of science education in the United States, and I mentioned along the way the haplessly anemic “Common Core” standards that the Obama administration is maneuvering into place behind the masquerade of an initiative of the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO). It is important to add that numerous philanthropic foundations are earnestly trying to “boost student achievement.” The Gates Foundation has been especially concerned about preparation in the sciences, but the William and Flora Hewlett Foundation, the Rockefeller Philanthropy Advisors, and others are grappling with this too.

I wish them all well, but I think Mr. Wurman has put his finger on the crux of the problem. We will make little progress in the sciences if we content ourselves with a standard of teaching students merely to “recognize” mathematical concepts and to set the bar at “using simple…mathematical expressions” on the order of distance = velocity X time. Zurman excoriates the NRC report for its frequent resort to the rhetoric of “appreciation,” as on its page one declaration that:

The overarching goal of our framework for K-12 science education is to ensure that by the end of 12th grade, all students have some appreciation of the beauty and wonder of science.

Wurman’s terse appraisal:

This framework simply teaches our students science appreciation, rather than science. It expects our students to become good consumers of science and technology, rather than prepare them to be the discoverers of science and creators of technology.

Appreciating something falls far short of knowing how, as anyone who has walked through an art museum, listened to a concert, or watched a professional athlete perform can attest. Maybe admiring a form of knowledge you do not yet possess spurs you to acquire it, but most “appreciation” stays at a pretty passive level. That, unfortunately, seems to be the highest standard the NRC thinks we can expect Americans to achieve.

Solving the Problem

I have a proposal that would in quick order solve the problem. Let me rephrase that. What I have is not exactly a proposal, but more like a thought experiment. What if Congress were to set aside all its efforts at curricular reform? Tell the Department of Education: Desist. Tell the states: Keep the Common Core if you like, but there will be no “Race to the Top” bonuses for adopting it. Say goodbye to “No Child Left Behind.” Tell NRC, thanks for the Framework, but we’re not in the market. Instead, Congress would pass and the President sign a bill declaring that in 2020, nine years from now, no student who scores less than “proficient” on the mathematics portion of the National Assessment of Education Progress will be eligible for a federal student grant or loan.

This would leave plenty of time for students who are now in school to work up to that standard. We might make provision for those who get test jitters—say, three chances to pass. Those who don’t meet the standard would, of course, be perfectly eligible to attend college, but without federal assistance.

My thought experiment comes with predictions:

  1. The rate of math “proficiency” would zoom, well before 2020.
  2. Educrats would do all in their power to dumb down the test and hollow out the meaning of “proficient.”
  3. Schools would declare the standard onerous and destructive; and then miraculously make it work.
  4. Colleges would find a large new source of students both capable of and eager to study the sciences.
  5. The incidence of “dyscalculia” would drop precipitously.

There could be other consequences that I suspect might happen but that I’d predict with less confidence:

  1. The racial achievement gap might narrow.
  2. The movement towards separating academically-oriented programs from career-oriented training might accelerate.

Of course, nothing like this proposal will happen. But that’s just a measure of how much we prefer not to trouble our children by giving them real intellectual choices.

This article origianlly appeared on August 24 in the Chronicle of Higher Education's Innovations blog.

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