“It always baffles me how people, and this includes most teachers, have no problem claiming an ignorance of math.”

I think this is partly because it is much easier to get by without math than without reading.

As a former linguistics professor, I have spent most of my life learning and analyzing languages, but it doesn’t upset me at all when American admit they don’t know any foreign languages. I don’t expect everyone to be like me, particularly when they don’t need to be. Monolingualism is not a fatal handicap in America.

I agree that one of our very basic problems with math education is the large lack of knowledge of math by most teachers, particularly in the elementary grades. I know from my perspective that being aware of what students will be facing in the future (algebra, geometry, trig, calculus) allows me to give them a better understanding of the topics that we are currently working on. I can help them make connections that they would not see otherwise. I can explain to them (age-appropriately, of course) why they need to understand certain things and that they are not just a “waste of time”.

It always baffles me how people, and this includes most teachers, have no problem claiming an ignorance of math. “I just don’t get math. I never have!” is oftentimes said with a perverse kind of pride. I have often been tempted to stand up in a faculty meeting and say “Well, I just never learned how to read. I don’t get words at all!”

“…we are introducing more sophisticated math concepts at an earlier age, and progressing through them more quickly than was the norm when I was in school.”

Yes, knowledge a mile wide and an inch deep.

To take a trivial example, compare Kiselev’s Planimetry with any standard U. S. geometry text, say Larson for example. Look at the spare elegance of the Kiselev proofs, and then look at the innumerable postulates, theorems and corollaries in Larson; the vast majority could and should have been derived from first principles, preferable as exercises. Absolute crap!

To claim that the U.S. is doing well when compared to the rest of the world is indefensible. One has only to look at the TIMSS results.

I also think that part of the problem with teacher training is that the profession as a whole is torn between the dueling concepts of teaching is an art/teaching is a science. Good teaching involves both. You need to track both objective (homework and test scores) and subjective (observational and intuitive) information on each student to measure the progress of the student throughout the school year. Unfortunately, more weight is given to the objective data than the subjective data, and sometimes that objective data makes a student appear more competent than that student really is.

Let me explain. As a special education teacher, I do some aspects of my own diagnostic assessments (the academic pieces, not the cognitive). I take detailed notes and make observations of student test performance as I administer the test one-on-one. I have observed that some students I test perform better on diagnostic tests than they do in the classroom. Factors involved may include the one-on-one nature of the test, freedom from distractions, test pacing, the type of task performed on the diagnostic test as opposed to the classroom test, or even a preference for the test administrator rather than the classroom teacher. Determining what these factors may be is heavily dependent upon subjective data gathering rather than objective data gathering. However, the greater weight is frequently given to the objective data.

Anyway. I’m falling prey to sped geekery here. The point I want to make is that education schools focus heavily upon the objective pieces, and don’t really know how to transmit the subjective pieces short of forcing Parker Palmer and “reflections! reflect! reflect!” down the throats of their students. Most education school professors are either into methodology research, or left the K-12 classroom after the requisite years of experience because they burned out. One of the best profs I had still taught K-12 students on an occasional basis–and she taught one of the “Math for Educators” classes (and, ironically, was disliked by many students).

Learning to observe the learning process, come to a conclusion about how it is progressing, and formulating an individual response is part of the art of teaching. It’s not a skill which is easily taught, and in many cases, may only come about through becoming a learner yourself and observing your own learning process in non-academic areas(training a horse and learning to ski have both been useful to me in my progress as a teacher because both activities are about the learning process). We are much further along in figuring out how to effectively teach reading (even though we don’t always want to know the answers) than we are in math, especially given the modern desire for accelerated math learning (and we won’t talk about the mess which is writing instruction!). But until we swing the pendulum back from only giving strong credence to objective measurement of student progress, and readmit the understanding of teaching as an art, we’re going to struggle (and then we’ll probably dump objectivity in a mud puddle and fall into yet another mess because we dumped it!).

Just in case you are curious, I have always held a writing utensil with all fingers except the pinky. I used to use the pinky until I got tired of using it and taught myself to not use it. This infuriated many elementary school teachers I ran into, many of whom went through extraordinary lengths to break me of this. (All except my beloved fourth grade teacher, who was by far the best I had in elementary school.) They would ALL be furious if they found out that I write the same way to this day and that I have a B.A. in a writing intensive subject!!!

My father was even concerned about my handwriting until he met a one-star general who held his pen exactly as I did. Once he saw that, he stopped worrying about it.

To save server space I won’t go further, but the good teachers I have run into: those who at least pretended to care, those who challenged me, those who really wanted to teach, were all very rare. By and large I have run into a mess of very mediocre ones. And unfortunately, more than my fair share of incompetents and bozos were also encountered.

As a college math teacher I see plenty of evidence that things are not right in the teaching of math. Joycem says, “we are introducing more sophisticated math concepts at an earlier age”. I think that is true, and I think it is a mistake. Teaching “critical thinking” is an admirable goal, but how do we get there? I have become more and more aware as time goes by that many students come to my college algebra classes with a weak grasp of fractions. Some of those students may get a decent grade in my class, but I am suspecting more and more that that can be misleading. Some of those students may pass college algebra without the understanding that I want a grade of C or better to signify. Certainly I may be critized for that, and I’ve been giving it a lot of thought lately. But I am not supposed to teach them arithmetic, and I am not supposed to read their minds. Their grade comes from demonstrating on tests that they can do algebra problems. But maybe they can learn to do those problems and still not understand fractions. So when they become elementary school teachers they will not do a good job in teaching fractions, and the cycle keeps repeating. How did we get into this situation, and how do we get out of it?

Ed school ideology says we don’t have to teach directly. Rather we can have activities and group projects. I think that is a mistake. Ed school ideology says we don’t have to practice. They call it “drill and kill”. I think that’s a very big mistake. (Here’s a link to my expanded thoughts on that – http://www.brianrude.com/disagr.htm ) Ed school says a lot of other things that I think are misguided, at best. They may be well intentioned, in some ways, at least, but if they don’t work, or just plain wrong, then who cares about good intentions?

Here is another mistake I think I see happening at times. A teacher comes out of ed school with the usual attitude critical of ed school. That person learns to teach well on the job and rises in the hierarchy. After some years that person starts to defend ed school. They start to talk like they learned in ed school. That is very understandable. But I would ask anyone in that situation to be very careful. Ed school primarily has an ideology, not a body of explicit, verbalized, analytic, tested knowledge about teaching and learning. Now I’m not going to say ideology is not important. Ideology includes values, and values are always important. But the nuts and bolts of teaching and learning are also important. Students in the fifth grade don’t learn to add fractions because their teacher tries to boost their self esteem, or to improve their social skills by assigning group projects. Students in the fifth grade learn to add fractions because the teacher carefully explains how it works and why it works, and then assigns the right amount of practice with the right kind of problems, and gives appropriate feedback and repeats the whole process until the job is done. And to do that she has to keep order in the class. And ed school is no help there either.

I think many successful teachers come to sound like education professors because that is the only language and vocabulary they have learned to talk about teaching and learning. They probably don’t want to sound like they’re just talking at the lunch table. But that’s probably another mistake. You are probably most helpful when you’re talking like you talk with colleagues at the lunch table. I would ask all successful teachers to try to verbalize, in concrete terms just what really goes on in your class, what you do and why you do it. That is no easy task.

As it is, it’s hardly impressive to read a rant about teachers who can’t balance their checkbooks when there’s a few spelling errors as well as a couple of grammar errors.

And yes, there’s more than a couple folks here who fall into that category.

Atlas, I’m very impressed by your history. I’ve not been teaching that long, but my mother’s teaching career started before WWII. One of the things she shared with me is that every ten years, “reform” sweeps through the whole system. She was an old-time one-room schoolteacher who retired in the mid-70s–and threatened to come back and haunt me if I ever went into teaching myself–unless it was in special ed.

Given that perspective, and the experience of my old-timer colleagues, I’m inclined to look at reports of the educational sky falling in with a jaundiced eye. My own observations from both my own child’s progress through the school system and what I see now in the school systems is that we are introducing more sophisticated math concepts at an earlier age, and progressing through them more quickly than was the norm when I was in school.

…or students with disabilities–which is even scarier.

I”m not at all put off by your insistence that teachers should know their subject matter. Every teacher that I know agrees on that. We all grind our teeth about the few slackers we have. But teachers don’t hire or fire anyone, we just do our jobs.

Now on the checkbook thing. If the person is teaching anything remotely related to math of course they should be facile in math. If they are teaching middle school english, who cares? I myself can’t remember at the moment who is Secretary of the Interior. But if I were teaching American Government I should know.

I”d love to hear the gory details of your awful school experiences. How was it bad, why was it bad, what would have helped? Are there bright spots to remember?

On the point of education degrees. No primary teacher (you spoke of first grade) needs a major in a subject matter. They need most is to understand the process of brain development, know learning takes place, how to spot developmental problems, how to construct situations that foster future enjoyment of learning. That is supposed to be what happens in education classes. Whether or not that happens depends on the university.

By the way, I’m a science specialist for fourth and fifth graders, best job in the world.

atlas

Good point! And quite true. ALL teachers should have a major in a subject area. But, they do NOT need to have an education minor. In fact, they should not have to take any education courses in college. The only reason they must do so now is that the state extends the monopoly on licensing teachers to ed schools. Anyone who wants to teach should be hired by a school district or a private school. The district or the private school can provide “training” to the new teachers for those skills the district wants them to have in order to teach students.

I’ll use the teaching of reading as an example. The typical teacher graduates from ed school with no idea how children learn to read, how to teach reading, and knowledge about the structure of the English language. (All of the whole language professors make certain that they do not have these essential skills.) If a college graduate who majored in psychology (or anything else for that matter) wants to teach the first grade, s/he can be taught the aforementioned skills by the school district. I and my wife spend a great deal of time doing this for school districts in our area. The difference is that all of the folks we are teaching now are teachers with undergraduate and graduate degrees from ed schools. Many of them have been teaching for 5-20 years. We have been hired by the districts because their teachers do not know how to teach reading. They didn’t learn how to do that in ed school.

Take look at the recent studies on the teaching of reading and math that were published by the National Council on Teacher Quality (www.nctq.org). They are an eye opener!