## Tuesday, February 05, 2008

### Limitless Inability

Is it possible that there are math teachers out there that do not know math? The shocking answer to this question is YES! I 'm not talking about not knowing advanced math or even high school calculus, I'm talking about geometry, intermediate algebra and trigonometry. My AP said the new geometry course is going to be a problem because most of the teachers in my department don't know the subject and can't teach it. Little by little the old timers are retiring and those left behind are a sad bunch. (Not all new teachers are this uneducated in math, but lots of the ones in my school fall into this category.)

One of the young ones who will be around for a long time (and probably become an administrator) told me that if an answer is 3/2 and a kid writes 1 1/2, she marks it wrong. I tried to explain to her that she couldn't do that, the answers were equivalent. Her reply was, "my students know what I want and that is what they will give me." She taught the probability of picking a red and a blue marble from a bag of marbles and refused to recognize the answer had to be the probability of red and blue plus the probability of blue and red. It's her way or no way. My AP loves her. Even if he knew, he would probably not say anything.

There are teachers that go to the library for their C-6 tutoring assignment but who cannot help the kids with any math past the Math A regents. Even that is too hard for some of them. One teacher had to teach an SAT course over the summer and refused to learn the math. I have no idea what she taught but she will freely admit that she did not know the material and did not bother with it. The administration was just glad to have a body in the room and to be able to say the course was being offered.

A few weeks ago, my chairman brough a large part of the department in to watch one of the young ones teaching factoring. Her lesson consisted of doing the same exact problem (slightly different numbers) over and over. She never introduced coefficients higher than or lower than one or exponents higher than two. Don't get me wrong, she was excellent, but she doesn't know how to progress and there is no one to show her. She's a teaching fellow and her math education is limited.

My school is a good school. Attracting quality teachers should not be a problem. But, in a system that does not value senior teachers this does not happen. Seniority transfers are no longer available. Administrators want the newbies who take a much lower salary than the experienced teacher and jump to follow all their directives. Experienced teachers in the schools already are being harassed and told to transfer (as if some other school would take them.) Only the young are valued.

When I started teaching there were many experienced teachers around. I needed to learn and they were around to help. Sadly, this is no longer true. Sadly, even the older teachers still around are so overwhelmed with work that there is no time to help the new ones. Soon the only teachers left will be the ones who don't know the material and can't teach. These teachers will embrace the horse shoe seating arrangement and they will embrace group work so my guess is they will be embraced by the administration.

17 (really 15) more years said...

For all their talk of "Children First", it seems that that most favored teachers are those that know (and get paid) the least, and suck up the most.

mathmom said...

One of the young ones who will be around for a long time (and probably become an administrator) told me that if an answer is 3/2 and a kid writes 1 1/2, she marks it wrong. I tried to explain to her that she couldn't do that, the answers were equivalent. Her reply was, "my students know what I want and that is what they will give me."

Minor point, but this is actually a standard MATHCOUNTS Rule. They generally ask for answers in the form of a "common fraction" which according to their rules is "a fraction in the form +/- a/b where a and be are natural numbers, and GCF(a,b)=1." They go on to clarify that if the answer is 3/2 then the answer 1 1/2 is unacceptable. So... if a math teacher wants to clearly specify the form of answer she requires, I think that's reasonable. (You could argue that she also "has to" accept 6/4 since it too is equivalent, but most math teachers wouldn't accept that.)

I don't really mean to nitpick, since I do agree with everything else you are saying, and especially with how big a problem it is. In my opinion, the fact that we don't pay teachers enough results in few people with good math skills (who can chose from among many professions) choosing to teach math.

This issue with not wanting to pay senior teachers is also a big one. sigh.

jose said...

Interestingly enough, the math fellows I graduated with came out of the program knowing math 6-12 grades, like they're licensed to. Maybe she wasn't a math fellow herself or maybe she was just nervous and wanted her lesson to go well. My retraining went rather well for me during the nyctf program. Then again, what do I know? Good entry ...

Pissed Off said...

Math mom--I would have no problem with her answer if she specified what she wants, which she does not. Fractions do not have to be in lowest terms unless that is also specified. In my higher level courses, I tell the kids not to reduce. They waste time and risk careless mistakes.

Jose, she might have been nervous, but she was following her lesson. Her background is Spanish and jouralism. She really was excellent, she just needs some guidance and that is what is lacking.

Anonymous said...

I am from Sweden so I am supprised to what you write. Dont you need to major in math at college to become a highschool math teacher? I have studied 2 years of math and 2 years of physics and 1 year wasted to teachers ed before i became a teacher. How does the US system work?

/Per

JUSTICE not "just us" said...

Hey Sweden:

You wouldn't beleive how the American system works or does not work!

Great entry.

I have a stories about teachers teaching Spanish whithout knowledge of it and Social Studies too.

Mrs. T said...

This whole nonsense of teachers teaching without actually being licensed in something is troubling. Our district is pretty strict about teachers teaching only what they are qualified to teach. That being said, there are plenty of people who have a minor in something or have enough hours to be licensed in a subject, but really shouldn't be teaching in that area.

Lsquared said...

I find the comment that there is no one who feels qualified to teach geometry very discouraging. I teach the geometry (University) that the pre-teachers take, and I find that although a lot of my students come in thinking that they can do geometry proofs, they really can't. Pretty much the ones who pass can do them by the end, though. I sometimes think geometry is becoming a lost art.

So, I'm curious--what should they have learned about geometry that they haven't? Any suggestions will be thoughtfully considered for inclusion in next year's course!

Pissed Off said...

I was pretty discouraged when I heard his comment also. I also know that kids come for tutoring and there are teachers in my department that cannot do the math the kids are doing.

Most of these teachers are recertified from other areas. One is a change of career person. These people took the inimum requirement to get certification. Some had to take the licensing exam more than once. The thing all these people have is a shared vision with my AP and principal.

J said...

See, I feel exactly the same way about English teachers who can't spell! No one would tolerate a teacher whose artifacts had incorrect math facts, but I can't even count the number of spelling or grammar errors I've seen in English classrooms. All of this just means that the kids will turn out the same way--not knowing what they need to know.

Anonymous said...

P-O T:

the geometry issue is going to be enormous. We've been talking about it for over a year, but I am just hearing whispers from other schools.

Think about this: most NY State 25 year olds will have had a small taste of proof in Course II (and a bit in Course III) and that's it.

How qualified will they be to teach the new geometry course if they barely know more than the course material?

Jonathan

Pissed Off said...

Actually I just finished a whole term of proofs with my Math B kids. I do realize that my school does a lot more of them than most schools.

Anonymous said...

A full term? Bravo!

There are not many schools with math departments that are that committed to proof... And, there are not that many teachers left who can pull it off. A bunch of recent retired geometry teachers could form some sort of consulting business. Seriously.

Our school does straight-up geometry, and we are looking for a replacement for the Fall, and it's hard, though we'll see what the Open Market brings in. Who still knows the stuff?

I like it. Inequality and indirect proof this week... next up? circles... heavy on the constructions...

Jonathan

Allison said...

Professor Wu in the math department at UC Berkeley has been sounding the alarm about geometry in high school for quite some time (as well as fractions in grammar school, etc.) He spends his time trying to teach math to grammar school and high school math teachers at various seminars, summer institutes, etc. His papers on the problems that he sees are quite informative on just where the knowledge is and isn't.

You can read his papers here:
http://math.berkeley.edu/~wu

Pissed Off said...

Thanks--I will look at some of his work.

Anonymous said...

"I sometimes think geometry is becoming a lost art."

I think this might be something we could reasonably expect. The 1989 NCTM 'Curriculum and Evaluation
Standards for School Mathematics' document (several hundred pages ... I have a copy) recommend less time spent on:

- Euclidean geometry as a complete axiomatic system
- Proofs of incidence and betweenness theorems
- Geometry from a synthetic viewpoint
- Two-column proofs (p127)

I'm not clear what all of these are, but it seems like a general call for less time on 'formal' geometry. Given this, I'd expect less geometry knowledge (certainly less *formal* geometry knowledge) from students. The standards are almost 20 years old, so I'd expect that most new teachers had high school math curricula influenced by them.

-Mark Roulo