Thanks much for taking the time from your busy schedule to respond to our letter below. I am delighted to note your serious interest in the topic of how to obtain middle school teachers who are highly qualified to teach mathematics to the MMSD’s students so that all might succeed. We are all in agreement with the District’s laudable goal of having all students complete algebra I/geometry or integrated algebra I/geometry by the end of 10th grade. One essential component necessary for achieving this goal is having teachers who are highly competent to teach 6th- through 8th-grade mathematics to our students so they will be well prepared for high school-level mathematics when they arrive in high school.

The primary point on which we seem to disagree is how best to obtain such highly qualified middle school math teachers. It is my strong belief that the MMSD will never succeed in fully staffing all of our middle schools with excellent math teachers, especially in a timely manner, if the primary mechanism for doing so is to provide additional, voluntary math ed opportunities to the District’s K-8 generalists who are currently teaching mathematics in our middle schools. The District currently has a small number of math-certified middle school teachers. It undoubtedly has some additional K-8 generalists who already are or could readily become terrific middle school math teachers with a couple of hundred hours of additional math ed training. However, I sincerely doubt we could ever train dozens of additional K-8 generalists to the level of content knowledge necessary to be outstanding middle school math teachers so that ALL of our middle school students could be taught mathematics by such teachers.

Part of our disagreement centers around differing views regarding the math content knowledge one needs to be a highly-qualified middle school math teacher. As a scientist married to a mathematician, I don’t believe that taking a couple of math ed courses on how to teach the content of middle school mathematics provides sufficient knowledge of mathematics to be a truly effective teacher of the subject. Our middle school foreign language teachers didn’t simply take a couple of ed courses in how to teach their subject at the middle school level; rather, most of them also MAJORED or, at least, minored in the subject in college. Why aren’t we requiring the same breathe and depth of content knowledge for our middle school mathematics teachers? Do you really believe mastery of the middle school mathematics curriculum and how to teach it is sufficient content knowledge for teachers teaching math? What happens when students ask questions that aren’t answered in the teachers’ manual? What happens when students desire to know how the material they are studying relates to higher-level mathematics and other subjects such as science and engineering?

The MMSD has been waiting a long time already to have math-qualified teachers teaching mathematics in our middle schools. Many countries around the world whose students outperform US students in mathematics only hire teachers who majored in the subject to teach it. Other school districts in the US are taking advantage of the current recession with high unemployment to hire and train people who know and love mathematics, but don’t yet know how to teach it to others. For example, see

http://www.reuters.com/article/domesticNews/idUSTRE54L2W120090522

If Madison continues to wait, we will miss out on this opportunity and yet another generation of middle schoolers will be struggling to success in high school.

The MMSD has a long history of taking many, many year to resolve most issues. For example, the issue of students receiving high school credit for non-MMSD courses has been waiting 8 years and counting! It has taken multiple years for the District’s math task force to be formed, meet, write its report, and have its recommendations discussed. For the sake of the District’s students, we need many more math-qualified middle school teachers NOW. Please act ASAP, giving serious consideration to our proposal below. Thanks.

## 20 thoughts on “An Email to Madison Superintendent Dan Nerad on Math Teacher Hiring Criteria”

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Dr. Mertz,

“As a scientist married to a mathematician, I don’t believe that taking a couple of math ed courses on how to teach the content of middle school mathematics provides sufficient knowledge of mathematics to be a truly effective teacher of the subject. ”

Why do you believe that? I would agree that all teachers who teach math should be “numerate” (to use John Paulos’ term), and likely a few math ed courses won’t do the trick. But, that’s not quite the same as demanding a major in college-level mathematics.

I may be wrong, and maybe it’s just a terminology issue, but I don’t see the goals of K-8 learning of mathematics to be much more than facility in basic arithmetic — and even the standard math coursework at the high school level is not all that complex.

Clearly, a teacher needs to know how to think “like a mathematician”, otherwise they would not able to transmit the (many) correct thought processes.

I don’t know what coursework might be required to become “numerate”, but I don’t believe a major in math is that coursework.

“Clearly, a teacher needs to know how to think “like a mathematician”, otherwise they would not able to transmit the (many) correct thought processes.”

I agree that we desire our math teachers to be able to think like a mathematician, not necessarily have completed all of the coursework required for a college major in mathematics. That is why I am proposing that folks who minored in mathematics or majored in related fields (i.e., computer science, economics, physics, engineering) be considered as well. The problem the MMSD currently faces is that most of its middle school teachers who are currently teaching mathematics are K-8 generalists who never majored or minored in a math-related field. Having them take a couple of math ed courses on how to teach middle school math is not going to teach them how to think like a mathematician. Thus, these teachers still would lack the deeper understanding of mathematics needed to be able to “think like a mathematician”.

Janet Mertz

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I agree that students need to possess a strong Math foundation before reaching High School. This foundation needs to start being built at the Elementary level. There is much room for improvement there, also. There are too many teachers that lack the knowledge they need to be effective, at all grade levels. Additional education may help some. However, MMSD needs to be more selective in their hiring and renewing the contracts of ineffective teachers. Frankly the majority of teachers my kids have had, either didn’t understand the material themselves or just didn’t want to make the effort to teach their class. One even told the class that they could teach themselves!

You know, it would be nice if every middle school teacher specialized in a subject area and taught only that subject area. However, fiscal reality dictates otherwise. That’s why we have generalists with specific interests. There are exceptions, and we’ve had a few of these fine souls. First and foremost, the best math teachers are also great teachers. Yes, they have the knowledge base specific to math, but they also have the knowledge base specific to teaching. I think it’s a complete crap shoot to take people who simply love mathematics and train them to be teachers. They have to have the desire to be teachers first, and math teachers second- otherwise they’ll flounder when the going gets tough because they “always wanted to be a ______”, but took a teaching job instead.

Your point is well taken, David. However, this was not a fiscal decision. It has been on-going MMSD policy for some time regardless of fiscal realities.

As for crap shoots, the idea that a teaching certificate guarantees either quality teaching or content proficiency needs better scrutiny. I’ve experienced both of the following types of teachers and,if given a choice between someone who had tons of pedagogical training and little content background, or someone with tons of content background and little pedagogical training, I would choose the one with more content.

Simply put, you cannot teach what you do not know. It feels pretty irresponsible to imagine that it helps our students to have teachers who are learning the content as they teach. (And don’t get me started on learning to write through “self-assessment.”)

But I also confess that I am old school and believe that we cannot afford to ignore the world that our students will enter when they leave our schools. It is highly competitive and not terribly forgiving of people who don’t lack the basic skills to move on to the next level.

For example, the fastest growing majors and job fields are heavily weighted towards math and science competence. Students who place at remedial or lower levels when they enter college have a much harder time getting into and successfully completing majors in those fields. It is one thing when the low skill levels are the result of poor student choices. It is quite another when a student’s low skill levels are the product of poor school system choices about the skill levels expected of teachers and/or the willingness to embrace a narrow curricular selection without being able to demonstrate its efficacy.

We will see how all of this pans out when MMSD looks at the math placement test results for its graduates. (I would welcome a related analysis of how many students engaged in math education, enrichment, or other activities through private vendors vs. relying solely on MMSD curriculum.) I may be dead wrong on my expectations. And I will be delighted if, indeed, our students are demonstrating that my reservations are misplaced.

David Cohen:

Your comments reflect the root of the issue here, it seems to me. I’m struck, in debates about how to get good teachers into classrooms, how the two (or more…) sides in this debate appear to be speaking entirely different languages to each other. One side (A) argues (generalizing here): Teaching is akin to the medical field, and what’s first and foremost of importance is getting people well-trained in the field of teaching. The other side (B) argues:No, what’s really important is content mastery, and training in the field/subject/content area that’s being taught. Side A proponents tend to argue that “teaching” is the fundamental skill, and that content can be learned through a few college courses, or summer workshops. Side B argues that “content” is key, and that the “skill” of teaching is something that can be learned in a few courses or workshops.

Ideally, you’d like to have both — well-trained teachers deeply knowledgeable in their subject matter. But that’s not often the case, particularly in hard-to-place areas like math and science (a far more competitive position for principals to fill than, say, 4th grade teachers).

What has struck me about this debate is how (there really is no other word for it) dogmatic the teaching profession tends to be about arguing in favor of Side A. Measures and ideas such as alternative licensing; short (as in, over the course of one summer), intense licensing institutes; and or even allowing non-licensed teachers in the classroom, tend to go nowhere, or get little support, because of the arguments made by Side A proponents.

I think there are(and have actually talked to quite a few) potentially huge numbers of talented teachers out there — now studying to be engineers, actuaries, lab researchers — who otherwise would like to teach but find the hurdles implied in Side A to be so onerous as to dissuade them from pursuing teaching as a profession.

Spend some time down at the UW-Madison engineering school, or at the biochem/chemistry/biology buildings (populated by some of this state’s brightest high school grads), and ask how many plan to become public-school teachers. Not too many, I’d bet, and that’s a real loss for our schools.

Again, with my UW hat on, I find it interesting that many of our science outreach efforts, including the Wonders of Physics and Chemistry Camp, rely heavily on people who major in the content but not in teaching. And yet they are some of our most effective outreach and public education tools….and WAY COOL too!

The problem with the debate on pedagogy vs content is the abstract nature of the dialog. Kept abstract and policy oriented, the results of this debate are irrelevant.

Let me take on elementary math. Question: Isn’t the math that should be taught and learned in grades 1 through 5 within the knowledge of all teachers? One needs to be specific in defining what content is in K-5 that is beyond even the least capable teacher.

In middle school, is there any math to be taught or learned in grades 6 through 8, that isn’t known to anyone, certainly with a college education? When I reviewed the math material my daughter brought home, the content was fairly easy — my disagreement with it was the poor way the books presented and explained the material — not the math content.

If there are teachers in K-8 who are unable to competently teach K-8 math, isn’t there something more seriously wrong? Won’t it mean that some teachers do not have an 8th grade education?

As a relevant aside, this is how math is organized, by teacher/grade level, in our middle school: 6th grade math is taught by a generalist who teaches science, social studies or language arts as well. 6th grade math is, by and large, designed to review elementary concepts the first semester, then forge onward second semester. 7th grade math (pre-algebra) is taught by a math specialist who only teaches pre-algebra. 8th grade math(either pre-algebra continued or accelerated algebra) is also taught by a math specialist. So, at least in our middle school, by 7th grade, you get a math specialist. As far as I know, only the 8th grade math specialist has the special certification, but I could be wrong (the 7th grade math teacher is top notch, I just don’t know her as well). To put the math teachers in perspective with the rest of the faculty, all the 6th grade teachers are generalists in practice, while all the 7th and 8th grade teachers are specialists in science, math, social studies or language arts, and the kids rotate through each specialty. Of course, there is an exception here and there (a 6th grade team teacher that only teaches language arts, or science, for example).

David, the current reality is that the MMSD has very few math-certified teachers currently teaching in the District’s middle schools. I don’t know the exact current number. A few years ago it was 6-8, meaning some of our middle schools didn’t even have 1 math-certified teacher in the entire building. Thus, most 7th and 8th graders in the MMSD are NOT currently being taught mathematics by math-certified teachers. It should be noted that even math certification is a pretty minimal requirement that does not require anything close to the equivalent of a college minor in mathematics.

Larry, most of the District’s K – 8 generalists do not have the math content knowledge to teach middle school mathematics. While most students need to pass at least “college algebra” (=11th grade math) to obtain a college diploma, elementary education majors at UW-Madison are exempt from this requirement. Instead, they are permitted to substitute courses in elementary math ed. The result is that many of our elementary ed teachers do not truly understand math concepts such as fractions, percentages, and factoring, concepts essential to master in middle school for success in algebra I and beyond.

Janet,

I may be missing the bigger issues, but it seems to me that person having taken middle school math, and earned a high school diploma, with whatever math is required in high school, then earned a college diploma (regardless of the courses taken), has to know middle school math, otherwise that person didn’t really EARN his/her high school diploma, should never have been accepted into college, and should never have been granted a college diploma.

Am I being too harsh here? Given much of the curricula in elementary and middle school math, such persons may not be wholly at fault (their teachers and schools failed them); however, they should have realized the hole in their knowledge and taken corrective action.

Not knowing fractions, percentages, and factoring is the math equivalent of being illiterate.

The assertion that “many of our elementary ed teachers do not truly understand math concepts such as fractions, percentages, and factoring”…is that backed up by data, or just your opinion, Janet?

In reference to David Cohen’s post, there is no data on teachers’ comprehension of math concepts. We all know that. As a parent, I KNOW that there are some teachers that do not understand what they are teaching. I’ve experienced this in Elementary, Middle and High School. In defense of the teachers, part of the problem lies with MMSD’s curricula choices. The teachers figure out how to teach using one program; ie, Everyday Math, then it changes. This problem lies more with the Elementary Schools. In Middle and High School, I’ve seen that the problem is more comprehension on the teacher’s part. As I’ve posted before, sometimes the students are teaching the class in High School. Sometimes it is a case where the teacher doesn’t understand the material. Other times it is a matter of the teacher not wanting to make an effort. There are too many teachers that are burned out and some that just don’t care. Being a teacher in MMSD is unlike being employed by the private sector. The teachers are not “graded” based on student performance, whether they get along with their co-workers or get the job done. MMSD does have many good, caring, competent teachers. It is unfortunate that the ones that aren’t can’t be held accountable for their performance!

I’ve NEVER encountered a math teacher who didn’t comprehend the concepts they were teaching. Not in elementary school, not in middle school, not in high school. I have encountered math teachers who were very frustrated by the way that connected math forced them to teach certain concepts, and to a T, they would differentiate the methods by which the concepts were taught.

My previous post was not intended to be an attack on David Cohen’s June 9 remarks. Sorry if it appeared that way. If I was an outsider to MMSD, I would not believe that there are teachers that do not comprehend the subjects they are teaching. I have seen it first hand as a volunteer in the classrooms. Part of the problem is the teachers’ frustration with the curricula. Too often my kids have been taught at home because the teacher was unwilling or unable to teach them at school.

It’s certainly true that all of us have very different experiences within each of our various schools, so I’m not discounting Disappointed Parent’s experience…..However, Janet Mertz typically has strong data that backs up her assertions, which is why I asked.

It is true that we all have different experiences. We have our own opinions and ideas of what our schools should be like. We, should, all have the common goal of giving the students in our community a good education. An education that prepares them for each step along the way. For the most part, MMSD has been a disappointment from my point of view. I am hoping that with the new Administration and discussions about Math…it will get better.

David, Here are some data from published studies regarding the math competence of US versus Chinese elementary school teachers:

1. “When given a problem of division with fractions, for example, 1 3/4 divided by 1/2, and asked to make it meaningful to their students, 100% of Chinese teachers solved it correctly and 90% provided a story that was an accurate representation of the division. In contrast, only 43% of American teachers calculated the division correctly and a mere 4% provided an accurate story.”

2. “At the elementary school level (in the US), only 2% of public school teachers and 5% of private school teachers had majoring in mathematics or natural sciences as undergraduates.”

3. In China, applicants to college are required to choose an academic major – “education” is not a major. China has a demanding, rigorous national math curriculum. Compared with the SAT-Math, the mathematics section of the Chinese College Entrance Examination is much more difficult, containing many college-level mathematics questions.

The bottom line is that a majority of K-8 generalist teachers in the US really don’t understand middle school math. How can we expect our students to learn it from them? With socio-economically privileged students frequently learning this mathematics, instead, from their parents or tutors their parents hire, there is little hope of closing the math gap unless we have mathematics taught in our middle schools by teachers with solid math content knowledge through at least 11th grade algebra II, if not higher, as well as teaching skills. We don’t currently have that.

I understand the generalized data worldwide and nationally. Is there any data on our MMSD teachers?

Scheduling is a huge roadblock to this actually happening. It is difficult to hire people who are only certified in one subject area. This does not allow for flexibility for administrators in scheduling teaching teams. Very seldom does a person teach only one subject at the middle school level.