Math teaching without the math

“Math educators” have dumbed down math content in a vain effort to “engage” low achievers, charges Sandra Stotsky in City Journal.

National Council of Teachers of Mathematics (NCTM) 1989 standards lead to “trendy, though empirically unsupported, pedagogical and organizational methods that essentially dumb down math content.”

Stotsky suggests emulating high-math-achieving countries, which “teach arithmetic in the elementary grades in a coherent curriculum leading, step by step, to formal algebra and geometry in middle school.”

Stotsky served on the National Mathematics Advisory Panel, formed in 2006, which looked at how best to prepare students for Algebra 1, “the gateway course to higher mathematics and advanced science.”

The panel found little if any credible evidence supporting the teaching philosophy and practices that math educators have promoted in their ed-school courses and embedded in textbooks for almost two decades. It did find evidence for the effectiveness of a highly structured approach to teaching computational skills, called Team Assisted Individualization; of formative assessment, which entails ongoing monitoring of student learning to inform instruction; of the use of high-quality technology for drilling and practicing; and of explicit systematic instruction for students with learning disabilities and other learning problems.

Stotsky was the chief writer of Massachusetts’ highly regarded standards.

Reporter Beth Fertig of WNYC  is following the fortunes of remedial math students at a New York City community college. Most hope that more education will qualify them for better jobs: 10 of 28 students passed the first quiz.

Also check out Math Matters by the Hechinger Institute. While written as a guide for education writers, it offers a useful perspective on the math wars.

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  1. Stotsky is right on target in her analysis of mathematics education and the current Common Core Standards Initiative.

    As a high school math teacher, I look forward to the day that the public demands real math content at all levels in our schools. Don’t be fooled by so-called “higher-order thinking skills” or an “inquiry” approach. Look at the simplistic types of problems presented. The junk has GOT to go!

    Thank you, Sandra, for your honesty!

  2. Student of History says:

    Every mathematician who’s reviewed the CCSI is telling me the same thing. CCSI is requiring little more than a level of math knowledge we associate with Algebra 1. For states like California, Massachusetts, and even Georgia that have rigorous or somewhat demanding math standards, it appears to be a step backwards.

    We’re about to have national math standards imposed as states and local school districts commit to adopting them without scrutiny so they might get a share of the massive Race to the Top grant money.

    That’s right. Let’s commit to these unknown but for many weaker math standards so we might be able to get a grant that will be full of binding commitments on the states and local districts. Reading through the RttT regulations over the weekend and the valid concerns rejected summarily, it’s hard to believe that this is really about effective educational reform.

    I am sure the Chinese will not mind funding our deficit spending for these RttT grants if they bind this nation’s academically promising public school graduates to low levels of math literacy.

    Is closing the achievement gap to be the only goal of American education?

  3. Barry Garelick says:

    Excellent article by Stotsky; hits the nail on the head.

    If the CCSSI standards get adopted as currently written, math requirements would extend only a little beyond algebra 1 by end of high school. Unfortunately, most 4-year colleges in the US require at least three years of math, of which students should have had Algebra 1 and 2, and Geometry. Thus, blind adoption of CCSSI’s standards in order to get the RtT money could result in many students not meeting entrance requirements for 4-year universities regardless of what the student wants to major in. Was the goal of the CCSSI standards “community college for all with no math remediation?”

    As for STEM majors, CCSSI openly admits that the college readiness standards do not address students pursuing such fields. Why not? Wasn’t that the whole point?

    Meanwhile, we have the Hechinger Institute advising reporters how to write about math education. Some tips for reporters when visiting classrooms. See if the students are engaged: “Are
    students following what’s going on? If kids are going to be learning math, they need to be working on math in the class, and if they are not, then they are just pushing pencils, and that is really unfortunate.” Yes, very true. And how do reporters ascertain that a classful of students working at their desks are just “pushing pencils”. A class that is using Connected Math will reveal students rushing around doing lots of activities, working in groups. They won’t be learning much math, but to the average reporter, it appears as if they are “working on math in the class”.

  4. If you go back to a previous article in which 90 percent of CUNY freshmen could not solve a simple algebra equation (say 4x = 8 – 3x), and one third of them could not convert a decimal to a fraction, and vice versa, you’ll see the extent of the problem.

    I remember the endless drills in math classes of the 1970’s, so that when we reached high school, we were well versed in the skills that are needed to handle algebra I, geometry, algebra II/trig.

    Most students today don’t know the multiplication table, long division, percentages, decimals, and fractions (which are all concepts that one should have learned by the time they reach 6th grade in the United States).

    I believe it was Dr. Seaborg (1951 Nobel Prize in physics) who once stated in the landmark education report “A Nation At Risk”:

    That we were being engulfed by a rising tide of mediocrity, and if another nation did to us what we are doing to ourselves we would consider it an act of war.

    I would happen to agree with this statement, due to the complete failure of our schools and colleges over the last 20 years to produce individuals who can problem solve, critically think and analyze, and communicate effectively.

  5. Regardless of the standards, we’ll never have the outcome Asian countries do on standardized math tests until our students are as hard working and competitive. And until they value the educational opportunities our free public education offers – which will be never. The difference between American and Asian educational outcomes aren’t caused by the standards or even the instruction – correlation not causation – it’s the culture they exist in.

  6. Andrew Bell says:

    I have a hard time believing that the problem is as bad as Bill describes with CUNY students, but he has the statistics and I don’t. In any case, Bill and Stacy are talking about different things, I think. You don’t have to have super-competition to be able to deal with a little algebra and some fractions by the time you get to college.

    Although I love math and think it has a lot to offer beyond solving some equations, EVERYTHING that is taught in school seems to be disposable. You would think that writing would be necessary for most people in their lives, but I would be that it is not. Most of us tend to be specialists, and we don’t use or remember most of the material we learn in school, which is why I’d love to see schools focus on things that we hope would make student’s lives more fulfilled, regardless of their future calling.

  7. barry garelick says:

    I’d love to see schools focus on things that we hope would make student’s lives more fulfilled, regardless of their future calling.

    School is about opening doors, not slamming them shut. If schools choose not to prepare students for math beyond algebra 1, then the choice of going into the STEM fields is out of the question. Making students’ lives more fulfilling should not come at the expense of choices that the edu-collective decides to make.

  8. I just administered a 10 problem arithmetic quiz to 55 Ed school majors that consisted of borrowing, long multiplication and long division, the four computational processes with fractions, multiplication and division of decimals, and percent of a whole number. The students could not use a calculator and had unlimited time to complete the quiz. All of the students had taken Algebra I and II and Geometry in high school and at least one college level math course. Many of the students had taken 3-4 math courses in college. Only two of the students had failed the college’s math placement test and had been required to take a so-called remedial math course.

    The average score of the 55 students was 42.6% Four students scored 0% and no student scored 100%. Then, I administered the quiz to our two department assistants, both of who are 50 years old and have been out of high school for some time. One scored 100% and the other scored 90%.

    The evidence has been clear for some time that U.S. students are generally abysmal failures in not only mathematics but also basic arithmetic computation. They are being taught by teachers who themselves are generally taken from the bottom of the math barrel. Enough said.

  9. Anon, it’s true that the current crop of educators seems to be weak at what they’re supposed to teach (my history colleagues know little about history). And I fear that the NEXT generation of teachers will know even less. We’re in a negative spiral now. However, civilizations can lift themselves up by the bootstraps. My colleagues are not dumb, just poorly educated. If they WILL to be smarter, they can start to reverse the tide of dumbing-down by learning more and raising the bar for their students. The problem I see is that teachers, and many Americans, lack the WILL to be intellectual. School, for so many Americans, is about social work and socializing; making kids feel good, talking about their problems, etc.

  10. A common thread between this dumbing down of mathematics education and the earlier movement from phonics to “whole language” reading programs is that Schools of Education advocated these programs, which are “trendy, though empirically unsupported.”

    I bugs the hell out of me the “educators” are willing to adopt these unproven programs. The cost is a generation or two of students who receive inferior education and a society with diminished intellectual capacity and diminished economic productivity.

    The benefits? First, I suppose the educators who originate these programs get their 15 minutes of fame at the time the programs are adopted. By the time the mistake is recognized and corrected, the originators have long since moved on to another area of research or have retired completely, and thus avoid any negative spotlight that may be shone upon the fiasco. Second, we prevent a generation of dull and/or lazy students from having their precious self-esteem bruised because they never have to confront their failure to learn a higher level of mathematics.

  11. Anon,

    If you gave a 10 question test to 55 takers, you have a total of 550 questions. If 234 questions were answered correctly, the average would have been 42.5%. If 235 questions were answered correctly, the average would have been 42.7%.

    How could the average be 42.6 percent?

  12. Deirdre Mundy says:

    Anon– another thing to remember–arithmatic skills fade into sloppiness if people don’t practice them.

    Some of the worst arithmaticians I know are MATHEMETICIANS. Why? Because they never have to deal with any numbers bigger than n, n+1, n-1, 2n and n/2….. Math and Computation are two different skill sets.

    That (IMO) is one of the problems with Chicago Math — Paul Sally wanted a program to teach kids to think like Mathematicians… but what MOST people want out of Elem. School math is to learn basic computational skills…..

  13. Stotsky’s article is good. A few years ago I wrote up some of my thoughts on the 2000 Standards published by the NCTM. In particular the standards do not address the importance of practice in learning any subject. Indeed there is much in the standards that can easily be interpreted as disparaging practice. Here are links., and

  14. John Drake says:

    Schools of Education, following postmodern dictum, do not believe in empirical evidence, Two Tone.

    Now stop oppressing me with your evil Enlightenment ideals.

  15. x = 8/7 ?


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