America’s future math teachers aren’t as prepared as future teachers in other countries, concludes the Teacher Education Study conducted by William Schmidt, a Michigan State education professor.

In the study, a representative sample of 3,300 future math teachers nearing the end of their teacher training at 81 colleges and universities in the United States were given a 90-minute test covering their knowledge of math concepts as well as their understanding of how to teach the subject.

On the elementary test, future teachers from Singapore, Switzerland and Taiwan scored much higher than those in the U.S., Germany, Norway, the Russian Federation and Thailand; Botswana, Chile, Georgia, Malaysia, the Philippines, Poland and Spain scored well below.

On the middle school test, American students outscored students in Botswana, Chile, Georgia, Malaysia, Norway, Oman, the Philippines and Thailand, the study found.

The study found considerable variation in the math knowledge attained at different American colleges, with students at some scoring, on average, at the level of students in Botswana, the study said.

Hank Kepner, professor of mathematics education at the University of Wisconsin, Milwaukee, who is president of the National Council of Teachers of Mathematics, was happy for mediocrity. “We show up pretty well here, right in the middle of the pack.”

Schmidt wasn’t so optimistic:

“A weak K-12 mathematics curriculum in the U.S., taught by teachers with an inadequate mathematics background, produces high school graduates who are at a disadvantage. When some of these students become future teachers and are not given a strong background in mathematics during teacher preparation, the cycle continues.”

In releasing the Breaking the Cycle report, Schmidt said that more rigorous common core standards “will require U.S. math teachers to be even more knowledgeable.”

His study found that while nearly all future middle-school teachers in the top-achieving countries took courses in linear algebra and basic calculus, only about half of U.S. future teachers took the fundamental courses.

Schmidt called for recruiting teachers with stronger math backgrounds, raising state certification requirements and requiring more advanced math courses in teacher preparation programs.

“Intensive, state-of-the art” training for middle-school math teachers didn’t raise student achievement, concludes the “Middle School Mathematics Professional Development Impact Study,” by the U.S. Department of Education. In 2008, a two-year study of training for reading teachers also found no gains notes Ed Week’s Debra Viadero.

The results are already providing some intellectual ammunition for finding better ways to select and retain effective teachers—and shedding those who are ineffective—as the best way to improve instructional quality in schools.

In both cases, the training “spanned months and included summer institutes, follow-up seminars, and, in some cases, in-classroom coaching.” Participants received 55 more hours of training than teachers in the control group.

By the end of the school year, participants didn’t do significantly better on a test of math knowledge than the control group. Their teaching changed: They “were more likely to try to draw out students’ thinking by asking students whether they agreed with a classmate’s response, or inviting them to share their mathematical strategies.” But that did not lead to gains in student learning.

“And to suggest that you can’t be a good middle school math teacher unless you’ve taken calculus is a leap, because calculus isn’t taught in middle school,” said Kingsbury, a senior research fellow.

Ridiculous. Calculus is the first college-level class. The first one. There are no college-level math classes below calculus. Bright students take calculus as high school seniors. Exceptionally bright math students take it as ninth or tenth graders. If a potential teacher can’t even manage the first college math class, how can she teach the subject? If she knows so little about math that she won’t be able to answer questions from bright, inquisitive students thinking a little ahead, she has no business in the math classroom.

Cardinal Fang,

I tend to agree with you that students would receive better Math instruction from teachers with degrees which require some Math beyond the material we cover in Alg II and Trig, but I would mot be so sure that Calc I is the requisite qualification. Calculus happens to occupy a gate-keeper position, but that seems arbitrary to me. Most of the interesting questions that a bright student will ask about Math before s/he experiences Calc I come from Logic or deep questions about Arithmetic (What is a variable? Is the additive identity unique in any group? Why is negative times negative positive?). Although you can explain this to a bright 4th grader (I have), I learned to ask and answer these questions in 400-level college Alg and Logic classes. No calculus logically required.

All that said, I see criticism of subject-area expertise from Professors of Education as self-interested defence of the (implied) alternative: coursework in pedagogy.

As always: “What works?” is an empirical question which only a competitive market in goods and services can answer. A State-monopoly enterprise (e.g., the US government-operated school system) is like an experiment with one treatment and no controls, a retarded experimental design.

Malcolm,

Cardinal didn’t suggest that CalcI was ‘the’ qualification but objected to the claim that because it’s not part of the middle school curriculum it shouldn’t be *a* qualification. Aside from the fact that the objection was primarily to the reasoning rather than the conclusion, I would argue that in fact some understanding of several higher level topics in the subject area should be prerequisite to the teaching of any level of any subject.

What I found interesting in the teacher report are charts of “institution level knowledge” on pages 31-32. At elementary level it shows Singapore, with its single institution, at the high end of the US distribution. Interestingly, at the middle school level Singapore drops lower and the US distribution reaches much higher, so Singapore is just mediocre as compared to the US institutions at this level.

Yet it seems because their elementary students benefited so much in the early grades, they outpace the rest of the world even at the middle school level on TIMSS. Despite the unimpressive achievement of their teachers at that level.

This seems to support the point that our problem is not in needing more/better algebra teachers for middle schools. Our problem is in needing more competent teachers at the elementary level.

And the charts also clearly make the obvious point that it is much easier to control teacher quality in a single institution as Singapore does, than in a large country with hundreds or thousands of them.

There are no college-level math classes below calculus.You don’t know what you’re talking about. Besides, at most UCs, you can get a degree without taking a single math course.

It’s rare for anyone below the level of junior to take calculus, although not impossible. But teaching extremely advanced math students is not a problem we have.

There’s a serious flaw in this study as far as California goes–namely, in order to teach middle school math you have to be qualified as a single subject math teacher. That means taking the single subject CSET, which means that most new middle school math teachers in California are qualified to teach high school math, and do in fact know calculus. However, I very much doubt that this study included those teachers, but rather teachers that passed the much less rigorous MSUB.

Hank Kepner, professor of mathematics education at the University of Wisconsin, Milwaukee, who is president of the National Council of Teachers of Mathematics, was happy for mediocrity. “We show up pretty well here, right in the middle of the pack.”

Yep, we’re mediocre and we’re satisfied. Like the IRA that has destroyed reading instruction and the NCTE that has destroyed the teaching of English at all levels of American education, the NCTM has destroyed the teaching of mathematics in the US.

Folks, as long as ed schools have control of training teachers and the government has control of schools, it isn’t going to get any better and it’s going to become even worse over time than it is now. Abolish ed schools, abolish teacher licensure, and take away government control of schools and watch them flourish over time.

Mr. Kirkpatrick:

My experience is that the primary problem people have with calculus is a lack of facility with algebra. In that sense, Cardinal Fang is right: we would likely be better-served if all would-be math teachers had to take calculus. While other forms of higher mathematics would also be beneficial, they don’t reinforce a working (practical) knowledge of algebra like calculus does.

Cal:

I suspect you and Cardinal Fang are working with different definitions of college-level. It is true that a lot of students come to college and are not ready to take calculus. I’d probably differ from both of you and state that the first college-level math course is pre-calculus- everything below is remedial. It isn’t unsusual (let alone rare) for science and engineering students to take calculus in their first year (or even test out of it); since it’s a prerequisite for physics, which is prerequisite for a number of other classes, it needs to be taken before the junior year.

Is it really true that one can avoid any math course at all? Most schools require some level of mathematical reasoning course: sometimes a “Statistics for Social Scientists” course or a symbolic logic (philosophy department) course satisfies this requirement. I would hope, however, that any teaching degree- particularly for anyone hoping to teach junior-high or higher mathematics- would require more than that.

I can’t remember how many times I’ve heard el ed students and teachers say they don’t like or don’t understand math or that they wouldn’t have become teachers if they had to take math classes. I’ve heard and read many similar comments from others so I’m thinking it’s possible that el ed students are not all required to take math.

For elementary teachers at the local state school near me there are several options to fulfill the Math Requirement. One is College Algebra. There are other classes that seem easier based on the title.

The requirements for secondary math endorsement include quite a bit more math including several semesters of Calculus.

Middle school teachers can have a k-8 math endorsement that requires 6 math classes over several areas (Algebra, Geometry, Number Theory, Measurement, Computer Programming and Statistics), but does not require Calculus.

“I would hope, however, that any teaching degree- particularly for anyone hoping to teach junior-high or higher mathematics- would require more than that.”

“I’ve heard and read many similar comments from others so I’m thinking it’s possible that el ed students are not all required to take math.”

At my little (private) college, prospective teachers must take two courses in math. The courses purport to teach algebra and geometry. In reality, the two courses allow the students to play with calculators, blocks, and cut out shapes most of the semester. The students get an A or B and everyone is happy. The courses teach little or no math because to quote the Chair of the Math Dept: “They would never pass a real algebra or geometry course.” But, the Chair added: “The students in other majors are just as bad.” In my little corner of the higher ed world, our math dept has been required by the college over the last several years to create separate math courses for each of several majors (e.g., Math for Business), including education, because the students cannot pass real algebra and geometry courses. Calculus? Furgiddaboutit.

Cal, I know perfectly well that there are math classes below the level of calculus that are taught at colleges. But teaching eighth-grade algebra to college students doesn’t make remedial algebra a college level class. A rule of thumb: if it’s got “college” in the name, it’s not a college-level class. College Writing, College Algebra- those are remedial classes.

There are some other math classes at the same, introductory level as calculus: Modern Algebra (not the same as middle school/high school algebra, despite the name) and Discrete Math, for example. But aspiring middle school math teachers aren’t taking those classes either.

In engineering schools, calculus is a 100-level course. It is freshman material. Any applicant with less than a command of algebra/trig is going to take remedial courses or flunk out.

Cynical,

I believe that Cal was talking about it being rare for anyone below the level of a junior in *HIGH SCHOOL* to take calculus. As you say, for engineering schools (and, I suspect, most/all hard sciences — chemistry, physics, bio at least — and mathematics) calculus in college is a freshman level course.

-Mark Roulo

I’d probably differ from both of you and state that the first college-level math course is pre-calculus- everything below is remedial.Not from me. That’s exactly right. However, it’s also true that at most UCs, you can get a humanities degree without taking a single math course if you got a 600 or higher on the SAT math section.

I believe that Cal was talking about it being rare for anyone below the level of a junior in *HIGH SCHOOL* to take calculus.Which, one would think, was completely obvious from context.

You may be able to get a humanities degree at most UCs without taking any math classes, but that doesn’t mean you should then be allowed to teach math to middle school kids.

As a 20 year veteran high school math teacher who teaches Calculus and trains teachers to prepare students for college math, here is my take on all this…

First of all, ALL middle school and high school teachers should be required to take Calculus. One of the main questions students ask when they take a class above Algebra is “When are we ever going to use this?” Having a knowledge of how the high school level courses all fit together to prepare the kids for Calculus and beyond is a wonderful tool for the math teacher’s toolbelt.

Second, ALL elementary school teachers who teach math should have a much better foundation in the math that they teach. They should be comfortable in mathematics up through high school Algebra and Geometry, for the same reason I mentioned earlier. I also want to stop the myriad of “educators” who come up with these crazy new ways to do math, like long division by guessing and checking. These methods they tout don’t work with all math problems and just confuse the kids when they get to middle and high school. Elementary schools also need to pitch out discovery learning and go back to drill and practice without a calculator. It may be boring, but the kids who don’t know their addition and multiplication facts crash and burn when they get to Algebra.

Okay, I’m getting off of my soapbox now…

Jill,

Please stay on your soapbox a little longer. My oldest started on guess and check until I realized what that was. I then talked to her teacher about it. I didn’t understand why the kids couldn’t learn to solve the problem correctly. His response was that just because my kid might be able to figure out the solution to the problem without guess and check, the other kids couldn’t and they needed guess and check to be able to score high on the state tests.

He had NO clue that the kids needed to learn their math facts to automaticity to have any hope of a STEM major in college.