Elementary math teachers need to understand math better in order to teach effectively, concludes a new study by the National Council on Teacher Quality.
With some exceptions, elementary education programs spend too little time on elementary math topics, the report concluded. Teacher candidates don’t really understand why arithmetic and multiplication work.
In addition, ed schools take candidates with very weak reading, writing and math skills.
“Almost anyone can get in. Compared to the admissions standards found in other countries, American education schools set exceedingly low expectations for the mathematics knowledge that aspiring teachers must demonstrate,” said the report.
State certification tests typically produce an average score: A prospective teacher who flunks math but does well in other areas can earn a passing score.
Kate Walsh, president of NCTQ stated, “As a nation, our dislike and discomfort with math is so endemic that we do not even find it troubling when elementary teachers admit to their own weaknesses in basic mathematics. Not only are our education schools not tackling these weaknesses, they accommodate them with low expectations and insufficient content.
I’ve met many elementary teachers who say quite cheerfully that they don’t like math. They believe that a second-grade teacher who knows second-grade math can teach the subject well enough. A few elementary schools hire math-science specialists to avoid this.
“I’ve met many elementary teachers who say quite cheerfully that they don’t like math.” These teachers then cheerfully pass along this attitude to their students. Who usually aren’t so cheerful in their dislike of mathematics.
I am good a math. I am planning on being an elementary school teacher after I retire.
My interest in education was spurred when my oldest daughter struggled in 6th grade math because she had never been taught the multiplication facts to mastery.
Rory
“State certification tests typically produce an average score: A prospective teacher who flunks math but does well in other areas can earn a passing score.”
That kind of inappropriate averaging pops up in a lot of places. Marksmanship tests (called “qualifications”) have a single score added over a lot of exercises. Someone who can’t shoot adequately at 25 yards may be able to make up for it by being careful at closer ranges.
This is the problem with education programs: sure, they churn out plenty of teachers who know HOW to teach, but they fail to address one little tiny problem: they have to teach a subject, and in order to do so, it stands to reason that they should know the subject COLD. But this apparently isn’t demanded of many teachers.
For those who do know the subject cold, ed schools make sure that the subject is taught poorly, relying on discovery/inquiry-based approaches and assuming that if children are told something directly, that’s tantamount to cheating and that kids won’t learn the subject that way.
I gave up on my local public school when my daughter’s fourth grade teacher cheerfully admitted that balancing her checkbook was a challenge for her. Apparently adding and subtracting all those pesky decimals was more than she could handle…yet she was supposed to teach my child to manipulate fractions, percents and ratios in preparation for higher math.
We are now very happy with homeschooling.
“ed schools take candidates with very weak reading, writing and math skills”
Sad to say, but many of the struggling students in my university’s junior-level statistics courses are…math ed majors, who can’t do calculus.
Catch 33, Yep, they should know math cold. They should also know grammar cold, kiddie lit cold, earth, physical and life sciences cold, spelling cold, state and national history cold, all the rules for kickball cold. They should be on top of all the allergies, all the IEP’s, all the 504’s. They should be able to figure out how to give eleven kids preferential seating.
Hey,I’m dancing as fast as I can.
Atlas
It appears that not only do some elementary math teachers not understand elementary math, they also are not willing to learn from their students who do. My daughter’s 5th grade teacher misgraded correct math answers. When my courageous 10 year old politely tried to explain why she answered the questions way she did, the teacher refused to change the grade. Some of the things the 5th grade teacher did not know - alternate names for geometric shapes and the mathematical notation for repeating decimals. Curriculum beyond 5th grade perhaps, but certainly not beyond some 5th graders.
So for students of teachers who have already graduated from ed school who will not benefit from the NCTQ report, schools need to assess which staff knows what and supplement where needed with specialists, allow students in different classrooms to rotate to the teachers who get math, or put students online and let the computer do the teacher’s work.
With all the reports on why math is so important to students and our country, schools need to be more creative with how they teach it.
Catch 33, Yep, they should know math cold. They should also know grammar cold, kiddie lit cold, earth, physical and life sciences cold, spelling cold, state and national history cold, all the rules for kickball cold. They should be on top of all the allergies, all the IEP’s, all the 504’s. They should be able to figure out how to give eleven kids preferential seating.
Hey,I’m dancing as fast as I can.
Ummm, Atlas, for the “academic” subjects like math if you’re a 4th grade teacher you only need to master these to probably the 6th grade level (just to be on the safe side, certainly not algebra or higher level math). As for the other aspects of your profession, like managing IEP’s, I have a question for you; Do you think that professionals like physicians, lawyers or public administrators have fewer varients? I don’t think so. You’re not a short order cook, being a professional actually demands knowledge, skills and adaptability.
Instead of dancing faster, maybe you need to learn an new dance.
Atlas, said, “Catch 33, Yep, they should know math cold. They should also know grammar cold, kiddie lit cold, earth, physical and life sciences cold, spelling cold, state and national history cold, all the rules for kickball cold. They should be on top of all the allergies, all the IEP’s, all the 504’s. They should be able to figure out how to give eleven kids preferential seating.”
No, Atlas, an applicant to any teacher education program should have average or better basic academic skills in reading, writing, math, and spelling. In far too many cases, they don’t even possess these basic skills. In the teacher education program at my university, the passing requirements for Praxis I reading, math, and writing scores is set below the 35th percentile. If a student does not achieve these scors, the department chair waives the requirement. The average ACT score of students in the teacher ed program here is 19. Math is by far the lowest ACT score of these students. But, the average graduating GPA of students in the program is 3.5. In the one math course the teacher ed students have to take, they sit in the class and play with blocks and “manipulatives” for 15 weeks. In three of the four courses on reading they have to take, they learn about whole language and social justice. In their “methods” and ed psych courses, they learn how to run a “constructivist” classroom. In the special ed program, they learn about laws and rules and IEPs, but they have to take only one course on how to teach reading and writing and no courses on how to teach math.
That’s why people complain about the skills of too many teachers.
Indeed. That’s why on any university campus, the ed school and its students are a joke. When even folklore faculty sneer at you, well, there’s a problem.
>Yep, they should know math cold. They should also know grammar cold,
>kiddie lit cold, earth, physical and life sciences cold, spelling
>cold, state and national history cold, all the rules for kickball cold.
I’m assuming this is sarcasm over the idea that anyone could be so smart as to know all of these things, but it misses the mark. We don’t expect elementary school teachers to be able to solve Fermat’s last theorem, but we do expect them to have arithmetic down “cold”. Similarly, they need to be able to spell every single word in the vocabulary of a ten year old and they should have a high-school-level understanding of history, literature, geography, science and so on.
I would not only ask this of every elementary school teacher, but of every one else. These are the building blocks of civilization.
anon 6:33 — The horrible classes that make up most Ed programs are part of the reason more smart people don’t BECOME teachers….
If you’ve just survived 12 years of boring easy classes and are now on a college campus where you can take all sorts of interesting things, WHY would you major in education?
I seriously looked into a MAT program at one point… then I saw the books I’d have to read, the classes I’d have to take, the professors I’d have to deal with, and the projects I’d have to do.
I felt brain-dead just looking at the syllabus.
Unless someone has such an intense drive to become a teacher that they’re willing to suffer years of boredem so they can get into a classroom, they’re not going to get an ed degree– they’ll go for computers, or Greek, or even Folklore, because they want to be engaged in the classroom, not bored to death…..
This is also why those alternative certification programs (the ones that get the teachers into the classroom and cover methodology on weekends) are awesome.
I want to second Rob’s point. It’s not so much that I don’t understand how people who don’t know how arithmetic works don’t teach well, I don’t understand how they get through life well. The checkbook example is exactly the kind of thing I mean. And, per Rob, I don’t expect a working knowledge of differential equations, abstract algebra, or even calculus. Arithmetic, however, seems to be a basic requirement just to get by in our technological society.
Amen, Deirdre. And, ed schools–like government schools–will NOT change because they have no reason to do so. They have a monopoly because state departments of education give it to them. Ed schools–and the teachers’ unions–work hard to limit alternative certification programs because they threaten the monopoly. When parents and employers find out that one doesn’t need to graduate from an ed school to teach, that is dangerous to the folks who work in government schools and run ed schools.
I say again and again–a teacher needs a license like a fish needs a bicycle. A teacher needs knowledge like a fish needs water.
One of the best books on the topic of elementary teachers and math is Liping Ma’s Knowing and Teaching Elementary Mathematics.
Get a copy on Amazon. You’ll be glad (or perhaps very sad, after reading it) you did.
Rob and Annoying Old Guy have it right.
For the life of me, I can’t understand how any college graduate should have problems with elementary school arithmetic, let alone the spelling and vocabulary words encountered up to the eighth grade level.
On the other hand, if the story about the elementary school teacher who could not balance her checkbook is not apochryphal…
Bill
Hey– I know MATHEMATICIANS who have trouble balancing a checkbook by hand….
mental arithmatic is like any other skill. If you don’t use it regularly, you get rusty. If you depend on calculators or spreadsheets and only work on projects that don’t require manipulation of numbers greater than two, you lose it.
(Kind of like how I used to be a top-notch speller until I got in the habit of using “autocorrect”……)
You don’t really NEED to balance your checkbook if you have excel…..
Bill, for what it’s worth, (and despite the fact that the plural of anecdote is not data), I can add that my sister-in-law is an elementary school teacher who is mystified by the process of calculating the tip at a restaurant. She’s not even embarrassed about it.
“Hey– I know MATHEMATICIANS who have trouble balancing a checkbook by hand….”
You excused from bookkeeping speed drills when you can prove the dominated convergence theorem.
As an outsider (no kids in school, gradutaed college when Moses was a small lad) I thought that in order to teach Subject X, you had to know Subject X. In math, not necessarily to the point where you win the Fields Medal, but enough to be able to answer your 6th-graders’ questions about why 6+4 = 4+6 and which triangle is isoceles and why logarithms are cool.
I sympathsize with atlas - but really, you don’t need to be a Michaelangelo and Florence Nightingale to run a classroom. Maybe a black belt, perhaps.
About that checkbook thing: the reason it’s so “hard” is that it’s tedious. Anyone can get Quicken, or even cobble up a spreadsheet and never have to worry about it again.
Math teachers do know how to use Excel, don’t they?
Darren: The Liping Ma book looks like a good resource. I’d recommend Diane Ravitch’s “Left Back”, a long, depressing look at education here in America, starting about John Dewey’s time. It’s been one failed experiment after another, mainly at the hands of teacher’s unions.
Another thing about math: students who are good at it will tend to go into other fields, like science or finance, where there’s a heck of a lot more money, and less irritation.
“About that checkbook thing: the reason it’s so ‘hard’ is that it’s tedious.”
Huh? Keeping track of your OWN money is “tedious”?
The credit card and loan companies love those people, and said companies hope said fools never grow up!
Bill
–Ummm, Atlas, for the “academic” subjects like math if you’re a 4th grade teacher you only need to master these to probably the 6th grade level (just to be on the safe side, certainly not algebra or higher level math).
No, this isn’t true. You need to know algebra. You need to know enough to understand abstraction. You need to understand why division of fractions works out to being “invert and multiply”–and you need to know it well enough to explain it, correctly, truthfully, and at a grade appropriate level.
that’s not as simple as you might think. It’s clearly over the heads of nearly all elementary school teachers.
Many of my children’s elementary school teachers had a firm grasp of the required math, however, we live in a desirable school district. Each open position receives multiple offers, from qualified candidates. Most school systems don’t have that luxury. It’s a question of supply and demand.
I propose a change in teacher licensing. As it stands now, the teachers who feel themselves to be weak in math have an enormous incentive to teach the youngest children.
Atlas, your whining impresses me little. As a logistics officer in the AF,I HAVE to know a hell of a lot more than logistics. I often wind up learning the jobs of those who I am working with because they understand so little of what I do.
I can’t imagine that this experience is that far removed from countless other professionals in the real world.
Indeed, you ought to learn a different, much more simple dance if all of that is too demanding for you. I really don’t think I am asking that much of teachers, who more often than not get paid by the taxpayers, to understand every subject they are expected to teach COLD, forwards and backwards and diagonally, before they set foot in the classroom.
Good grief 33, take a breath. I’ve been teaching since 1961, probably before you were born. Have a little respect for your elders.
I love the challenge and excitement of teaching. How in the world do you read my post as whining? Of course teachers should know their subject matter cold. I’m taught in five states, one territory and seen hundreds of elementary schools in my career. In my experience the vast majority of teachers are dedicated and competent. Let’s keep it in perspective.
You know one of the first education related books I had to read in Ed 101 in 1957 was, Why Johnny Can’t Read. Every ten years or so since then there has been another book proclaiming that education is worse than it has ever been. Well if it was so horrible then and has gotten steadily worse for fifty years, we should be freezing in caves by now. This has not happened.
It has not happened because we have basically a good system. It works the great majority of the time. Most teachers are quite good at what they do, most teachers like kids, most school board members really do want the schools to do a good job, most parents are quite happy with their local school.
Oh, one more thing. I taught my first elementary class in a portable classroom, a 5/6 grade combination and had 35 kids. No specialists, no aides, no counselor, a nurse half day once a week, etc. Things have gotten a lot lot better. And so have our skills. We know a lot more about the learning process now. We do actually teach better now. I wouldn’t last a month now with what I knew about teaching in 1961.
OK, that’s it for this far reaching ramble, unless you want to hear my take on climate change.
atlas
You’ve been teaching before I was born? Well, I sure will sleep better at night knowing that. I can easily read your post as whining: whether you intended to or not, you seemed put off by my insistence that if a teacher was teaching (insert subject here), they should KNOW (insert subject here) better than the students they are teaching. And as for “having respect for your elders”: 1) your age is not easily discerned online, as mine is not and 2) my respect for the teaching profession has been on life support since about the age of six or so. I won’t bore you with the gory details of why and how.
When sending my children to school, I’d feel a lot more comfortable if the teacher who was going to teach my students math could balance their won checkbook if Quicken were not available, and/or (horrors!) were actually somewhat enthused about the subject, instead of seeing the children as a nuisance and a bother (as I have encountered too many times in my mandatory tour of he educational system).
I find it quite odd that teachers are required to have education degrees for the most part in order to teach instead of say an education minor and a major in the subject they intend to teach. An elementary school teacher isn’t going to teach first graders how to teach, are they?
Catch Thirty-Three siad, “I find it quite odd that teachers are required to have education degrees for the most part in order to teach instead of say an education minor and a major in the subject they intend to teach. An elementary school teacher isn’t going to teach first graders how to teach, are they?”
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!
33,I’m just being a little light hearted on the respect for elders thing. I know I’m quite the dinosaur in the profession. But that doesn’t give me any special reason for respect, just a perspective that most people don’t have. Respect is only earned.
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
“As it stands now, the teachers who feel themselves to be weak in math have an enormous incentive to teach the youngest children.”
…or students with disabilities–which is even scarier.
I’d consider the teacher critics here to be a bit more credible if their spelling and grammar were correct.
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.
I am in agreement with what atlas says to quite an extent. Most teachers are caring and competent. Most people get educated. The world keeps turning and we’re not freezing in caves. But still people may legitimately be concerned about many things in American education. I have been saying for some years now that the competence of teachers comes not from what they learn in ed school, but in spite of it. Atlas says teachers need to know how learning takes place. I agree, and I think teachers do know how learning takes place. However I think that knowledge is intuitive, operational, a result of experience, a result of common sense, and a result of imitating and learning from other teachers. Ed school does not have a body of knowledge about teaching and learning. It has an ideology, progressivism (though they don’t necessarily claim that name), and that is a very poor substitute. I developed this idea much more extensively in an article on my web site. Here’s a link.
http://www.brianrude.com/indict-ed.htm
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.
I’ll put it this way, atlas (please note I only skimmed your post as I am pressed for time): my first memory of being taught anything in school is having a pencil pried from my hands by a teacher, and her screaming at me “STOP THAT!!! HOLD YOUR PENCIL LIKE THE OTHER CHILDREN!!!” That’s just round one.
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.
Brian, you say a lot of good things here, and I agree with your statement that teaching the more abstract math concepts earlier on is a mistake. There are some kids who respond well to that method, but there are more who do not. I also think that the demise of the PeeChee with the times tables on the back flap might be an unidentified factor in the decline of student calculation skills (grin). Hey, that’s as viable a theory as any other (and that’s how I learned them, as well as weights and measures!)!
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!).
joycem said:
“…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 teach middle grades math and I came to this position with a science background, heavy with math courses. I am one of the fortunate “alternate certification” teachers. I say fortunate because I learned classroom management, methodology, and practice hands-on. I had the subject matter knowledge when I walked in the door.
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!”
Alt Cert in FL,
“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.