## Saturday, December 29, 2007

### Math 1010

### Never been tagged before...

1. Quit smoking about three years ago, cold turkey. Speaking of which I believe I only ate turkey once shortly before becoming vegetarian (don't think two were related). Quitting smoking and eating meat are both surprising if you know anything about country I come from: Bosnia and Herzegovina. Still drink coffee, though.

2. I've started many a thing in which I lost interest shortly thereafter. It worries me still. I wonder what I else I will give up.

3. I've twirled my hair since I had it, is what my parents say. It is so me, that I haven't even noticed that my husband, then boyfriend, was doing it as well until our parents cracked up about it. My hair is now less than an inch short which makes twirling really hard. I steal his now and then for twirling purposes.

4. I don't understand people's obsession with procreating.

5. I used to be tolerant of people's religious beliefs. I still think to each their own, but I am not very concerned with not being perceived as offensive. I realize that I do not respect nor tolerate ignorance, nor unfounded statements in any other realm of life, so I don't see why I should when it comes to religion. And I don't mind saying it.

6. I have never been afraid of flying. Well, never until two years ago. Particularly turbulent flight from Zagreb to Sarajevo has made me really nervous about flying. I've been trying to ask as many questions as I can about planes and flying. I am particularly sad that I hadn't been paying attention in my physics classes. I just realized that I forgot to ask if a wing can fall off and what would happen then.

7. I can talk pretty much with anybody about pretty much anything. Except for my dad. He has a particular gift of upsetting me almost as soon as he opens his mouth. All right, a slight exaggeration, but only slight. My sister says that I am much more critical of my parents than of other people. I think I ought to be. They are my parents.

Here are the rules:

- Link to the person that tagged you and post the rules on your blog.

- Share 7 random and or weird things about yourself.

- Tag 7 random people at the end of your post and include links to their blogs.

- Let each person know that they have been tagged by leaving a comment on their blog.

Tagging 7 other people would be hard. I'm afraid the meme dies here.

## Monday, December 3, 2007

### Safe on internet, at home?

e: Sweetie, I just got a bit worried. I did hand a key to our house to a person we don't know!

**

m: Don't worry about it. It will be fine. Besides, what are they going to do? Steal all my photo shit in the basement?

**

e: She told me she used to dog sit for people in park city and how nuts they all are :)

**

**

m: Going to bed now. What are you up to?

**

e: Grading! Is there anything else? You don't think she'll come back and kill me?

**

m: Sweetie! The homework will get you first!

**

e: Are you sure? I feel like I may be on fox news tomorrow "a gullible math geek hands the keys of her house to a known criminal. Stay tuned, more after the weather"

**

m: Sweetie, don't be ridiculous. They always show the weather last :)

## Tuesday, November 20, 2007

### Mondays are hard

## Thursday, November 15, 2007

### ADHD

## Wednesday, November 7, 2007

### Vouchers, again

More to follow.

## Saturday, November 3, 2007

### Chalk?

On a different note, I asked my students "If you had to think of something that is as different from mathematics as possible what would it be?" I got a fair number of "I can't think of anything different".... What would be your answer?

And something well, maybe not as unrelated as it may appear. The other day (10/18 show) I listened to The Bryant Park Project and they had two people who were going to some sort of right conference. They were asked for three most important issues that would decide who they would vote for. The answers were, in this order: the abortion issue, the marriage issue, and the judges that the candidate would appoint. When asked "Why these?" the woman answered "I'm a mother of two children, and I'm concerned about their future." So am I.

## Wednesday, October 24, 2007

## Monday, October 22, 2007

### Vouchers

Eligible private schools:

....

(g) employ or contract with teachers who:

(i) hold baccalaureate or higher degrees;or

(ii) have special skills, knowledge, or expertise that qualifies them to provide instruction in the subjects taught;

(h) provide to parents the teaching credentials of the school's teachers; and

(i) provide, upon request to any person, a statement indicating which,if any,

organizations have accredited the private school.

...

The scholarship application form shall contain the following statement:

"I acknowledge that:

(1) A private schoolmay notprovide the same level of services that are provided in a public school.

(2) The private school in which I have chosen to enroll my child has disclosed to me

the teaching credentials of the school's teachers and the school's accreditation status.

(3) I will assume full financial responsibility for the education of my scholarship

student if I accept this scholarship.

(4) Acceptance of this scholarship has the same effect as aparental refusal to consent to services pursuant to Section 614(a)(1) of the Individuals with Disabilities Education Act, 20 U.S.C. Sec. 1400 et seq."

The polls seem to be saying that the vouchers will be voted down. I hope they are right.

## Saturday, October 20, 2007

### Further development with unsatisfied students

I was going to tell you more about these two students. We have a 2 hour class, so I usually try to give them a break half way through, so we can all take a breather. Well, on Monday these two students left during the break, without telling me that they would, what is what most students do if they need to leave. So I sent them a message that said something like "I noticed you left, I hope everything is ok, and that you'll be able to catch up. Let me know if I can do anything." Only one of them bothered to respond, and said something to the effect that she doesn't feel comfortable in the classroom, that assigned groups make her feel irresponsible and she already has issues with group work. "The main reason I left was simply becuase of this discomfort. I know you are trying to get us to work with other people, but there are more effective ways to achieve this goal." Of course I emailed back and said that I feel saddened by this and that we should meet in person and talk. I also asked about these more effective ways. She responded only to tell me that she can't make it before class because she had another class right before and not a word about the more effective ways. I responded that she should name any time and I'll meet with her. Hadn't heard back.

Anyway, it appears that they since emailed the chair of the department to say that nothing has been done about this and to complain some more. The chair politely directed them back to the associate chair whom they had spoken to already. The thing is that it is not clear what it is that they would like to happen. Would they like me fired? Would they like to get a new instructor? Would they like me to let them do whatever they want? What is it that I am supposed to do? There are 2 students who are fuming, out of 43. Do I ignore them? What would you do?

Funny thing: Another student came by to talk to me and told me that a while back some sort of petition had been written, and that he had signed, but under pressure, and that if anybody ever mentions it he would gladly go talk to them on my behalf. I have no idea what they asked for in the petition. The funny thing is that the student who started the petition apparently decided to take the sequel of this course next semester. From me.

## Monday, October 15, 2007

### First time for everything

## Tuesday, October 2, 2007

### Opposite of recruiting?

## Friday, September 28, 2007

### Hurt feelings

## Tuesday, September 18, 2007

### Division

## Thursday, September 6, 2007

### Insane

So, we've been going for almost three weeks now. Apart from feeling like there should be 36 hours in a day, I'm enjoying both my classes a lot. Since I have some grading to do and I have to get ready for tomorrow's class I'll only write two observations.

El. math teachers course: From what I can observe (and this class isn't exception, I don't think) my students believe that in order to learn mathematics they only need to solve problems. But how can you find a complement of a set if you don't know what a complement of a set is. It is hard work to make them learn definitions. Or even to see the value of definitions.

Secondary: There was a homework problem that I assigned that asked "How would you want your students to respond to question: Explain why the sum of the digits of any multiple of 3 is itself divisible by 3." The question came form Principles and Standards, so one might imagine that this is material that these students will be expected to teach once they become teachers. I wonder what response you think I got. I'll tell you about three that I found most surprising: they said that they wouldn't expect their students to know the answer since they themselves don't know it. What was surprising, or rather what made me sad, was the fact that not only did they not know, but they didn't express any desire to find out. They didn't say "We'll look it up" nor "Can you tell us?", and they definitely didn't say "I'll work it out." I guess it's only a beginning of the semester :) Maybe we'll see some improvements as the class goes on.

## Sunday, August 19, 2007

### New school year

I almost forgot. Mark and I were looking for dual flush toilets. As a friend of our would say "a peepee and a poopoo". We went all over the place looking and asking and we happened to be in Lowe's for something else, so I decided to see what they can order. The man in the plumbing was most helpful. He was looking them up and we ran into one made by kohler, I think, and it read 1.4/1 gpf. He read "This one uses one and a quarter gallons and one gallon per flush".

## Thursday, July 5, 2007

### Long time no write

Then PCMI started at Park City. I have expected a lot more from it, and am rather disappointed. PCMI organizes a three week event that is supposed to do what administration thinks is vertical integration. There are several programs running at the same time, and people are supposed to interact and learn. There is usually a mathematics topic around which the whole program is structured. This year it is statistical mechanics. There are research program, graduate seminar, undergraduate seminar, mathematics education research seminar, secondary school teacher prof. development, and professional developers' seminar. I am there as a part of prof. development program, but that only meets about 1hr a day. The rest we hang out with high school teachers and observe what they do. The teachers' schedule is something like this:

8:20-8:45 there is one or the other administrative thing that needs to be addressed.

8:45-11 teachers work in groups on some math problems, statistics and probability. Good idea, but I think poor implementation and not great problems.

11-12 research teaching topics. This as far as I can tell was just a disaster. We were given a choice of several topics, groups were formed based on a topic, we got a list of few research articles that we were supposed to read and write a little report about. However, at least in my group there wasn't much discussion. We each wrote up a blurb on the article we read, but when the time was to write it up, they had the prof. development session running parallel, and I think half of us were gone. I think I am likely to miss tomorrow's presentations.

12-1 lunch

1-3 working group. I went to geometry, but that too was rather disappointing. It mostly appears to be Geometer's Sketchpad advertisement.

3:15-4:15 cross program. This is where we listen to talks whether they're given by research mathematicians, high school teachers, math ed people.... or there is nothing.

4:30-5:30, 6 is when prof. development group meets and so far this mostly consisted of them giving us math problems to work on. Hello! Half the people have Ph.D. is math. It just seemed like not a good use of time.

In the meantime, my preparation for my classes has stalled. My preparation for the session of ThEMaT has stalled as well, and I am supposed to be presenting it in less than three weeks (this is another potential PD that involves geometry). Also, since I am back in the most fun Salt Lake there are plenty of things to do that do not involve sitting at a computer. However, if the temperatures continue the current trend I may be writing more :)

## Wednesday, June 27, 2007

## Friday, June 1, 2007

### Small world

But to go back to my title. Half way through the day I ran into Yvonne (you will have to pardon the lack of linkage in this post), a graduate student from UCD whom I met at some math conferences couple of years ago. Turns out she's organizing Math Circles in Davis, and I will be helping with Teacher's Circles in Salt Lake City. She and her friend Brandy went out to dinner with us. Brandy turns out to be a grad student at UCD as well, but in math biology. So I mention that I know a professor there who is math bio, and she immediately tells me a name of another professor who used to be in Salt Lake when I was a grad student there who I remember moved to Canada. I guess it was too cold up there for him. With us at dinner were Sendhil, a math teacher, and John, a former high school math teacher who is now with Math for America, both from NYC. Sendhil was at the Math and Social Justice conference about which I first read at mrc's blog. Then we started talking about blogging teachers, so I mentioned Jonathan. Do I have to say that John knew him? Sendhil knew about Darren's class blogs. The world is small.

## Wednesday, May 30, 2007

### math-mathed conference

## Wednesday, May 16, 2007

### Feel good story

## Friday, May 4, 2007

### No time

As for the pledge: they recited it in a middle school I visited as well. And I talked to a friend's mom who is a second grade teacher. She says that she makes her students stand. She gave three reasons: to keep them form making noise and fuss during, to teach them that they should be grateful for living in the us (as opposed to unlucky kids without freedom that we enjoy here) and, if I remember correctly, to teach them respect. I am fairly certain that all of those things could be done without standing and reciting the pledge of allegiance. I am surprised that this is still going on and that people are not complaining.

## Wednesday, April 18, 2007

### Pledge of Allegiance

Next observation is that fair number of kids did not bother to stand up and recite. I wonder how many had reasons other than laziness.

## Friday, April 13, 2007

### Equity in the classroom

## Thursday, April 12, 2007

### Electronic portfolios?

## Thursday, March 29, 2007

### What is mathematics education?

*"Mathematics education is mathematical engineering".*From what I understand he views engineering as

*a discipline that customizes abstract notions so that they are usable by wide populations*. Therefore mathematics educations should be taking mathematics and turning it into a user-friendly product, i.e. into a product usable by a population under consideration. I thought this was an interesting way to look at it. Otherwise, what I learned is this: this nation is in crisis, W. is the best president as far as the education goes, it is against constitution to have national curriculum (I asked about this), in 2007 mathematical engineering urgently needs close collaborations of mathematicians and educators, there are no mathematical engineers yet. Few of these, I must say, came as a huge surprise to me. But let's not dwell on the politics. After the talk a smaller group retired to a smaller room to talk to the speaker some more. As people would walk in they wold introduce themselves and inevitably would say "I'm from the math department". It felt as if this was a secret handshake, or a a secret club. They were surprised to hear that I was as well. The comment I got was "You were laying so hard that we thought you were from the education side". Needless to say that nobody from education side was there, in this smaller, more intimate setting. Anyhow, I've heard, yet again, what I heard from teachers: It is all somebody else's fault. These future teachers don't know enough math, they don't want to learn, it's high school fault, it's their old teacher's fault... Maybe, just maybe, we aren't doing a good job either! How novel idea. I asked about NMAP, what the goal is, and what he though of the panel's composition. The goal is apparently to make recommendations about algebra. And the panel could be better, but it could be worse. Couple of us agreed that that seemed like a fairly lame answer, and since he thought it was perfectly fine, I decided to ask what he thought in particular of the fact that there is only ONE mathematics teacher on the panel. He agreed that that was a shame. I asked why they didn't ask that that be changed. He said that these things don't work that way. I think my words were:"I thought your job was to make recommendations. Couldn't you have made a recommendation to add a teacher to the Panel?" He said no. But here is the kicker: apparently they've just added three new members: one mathematician, one cognitive psychologist and mathematics education researcher (elementary math), I believe.

**Update**A friend of mine emailed and was asking "What's up with tallying mathematicians?" Once again, I fail make myself clear (or clear enough in a single post). I have talked about this before: it's not the lack of mathematicians that I find troubling as is the lack of mathematics teachers.

## Monday, March 26, 2007

### news and blogs

## Monday, March 19, 2007

### Really cool

*We take any Euclidean line, mark point 0 on it, choose a unit length and mark point 1, and then the non-negative "numbers" are associated (identified) with all the points on the ray from 0 through 1in the usual way. The negative numbers are then identified with the remaining points on the opposite ray in the usual way so that we have now a Cartesian coordinate number line L. Now choose a second line M through 0 and mark a 1 on it at the same unit distance as we used on L, and complete this so M is also a Cartesian coordinate line. Now for any number b (point) on L, and any nonzero number c on M, the product point b*c can be found: let J be the line from 1 on L to c on M, and K the line parallel to J through b on L, then b*c is the intersection of K and M.*

Here is a picture that shows L as x-axis, M as y-axis, and we are looking for 4*3.

The only problem with this explanation is that the students need to know about similar triangles! Regardless, this was way cool. If I had thought about this on time, I would have given it to my students on their final that had them think about similar triangles. Next time!

## Saturday, March 17, 2007

### If I can't be an actor

*I'll go to LA to go to college to become an actor. If the whole actor thing doesn't pan out, I can always be a math teacher,*

said one of the boys from the movie.

**New:**Coincidentally, I just saw this article in NY Times:

*A scathing 18-month evaluation of California’s public schools has concluded that the state’s educational system is “broken,” crippled by a complex bureaucracy, flawed teacher policies and misspent school money, leaving it in need of sweeping reforms that could cost billions of dollars.*

## Sunday, March 11, 2007

### Assigning unworked problems?

P.S. Jonathan, you still didn't tell me why you hate teaching geometry :)

## Friday, March 9, 2007

### Back in town

## Tuesday, February 27, 2007

### Mistakes

*Solve and graph each compound inequality*

The teachers solves 4 problems, during which time the students are reminded that the compound inequality means that both inequalities need to be satisfied (not in those words), how to graph solutions on the number line, various notation, and so forth. They arrive at problem numbered 4 that reads:

While working out the problem the teacher says: "Now listen very carefully. We have to pay attention to our signs". They arrive at the following:

and proceed to graph it:

Students make no comment, they copy down the solution and the class proceeds to the next problem. A conversation similar to this happens as the next problem is being solved:

Student: "So, if the bigger one is on the left then they go out, and if it's on the right then they go in?"

Teacher: "That's right"

After the class, I brought problem number 4 to the teacher's attention and got the following response:

Teacher: "I realized it as I was writing it down. I'll fix it by the fifth hour. I didn't want to confuse them."

I, dumbfounded: "?!"

How and when do we teach our teachers that making a mistake in front of the classroom happens, and is not something we should hide and sweep under the carpet. I remember making mistakes in classes I teach; we all do, sooner or later. I apologize every time I do as if I had wasted their time, and not taught them something of value. We make mistakes, but we need to deal with them in a responsible manner. Go back, fix them, show your students that even when you know something it is not shameful to make a mistake, but it is to hide it. Show your students that we are learning all the time. And that we should not think that we ever learned it all. I think I wrote about this before, but it seems that our teachers think that there is nothing more they need to learn once they have their teaching certificate. They are ready. Are we really?

## Wednesday, February 21, 2007

### Mental?

I am still observing. Yesterday and today I saw something that seems recurrent, so I have to comment/ask. In a process of solving a problem my teacher gets to:

She writes

Or, let's have even simpler example:

She proceeds to multiply 6 and 50, and then divide by 3. I saw identical process in the first classroom that I observed. In fact, kids (9 grade, I believe, possibly even 10) there couldn't do things like -4-2 or 7*3 without a calculator (the latter we figured out, and then two minutes later we had 8*3 in a problem and the student couldn't do it even after I reminded her that she knew 7*3). The teacher there said "Their mental math skills are terrible"?! I wouldn't call that mental math. Should I? Regardless of what we may call it though, I was terrified. I still am.

Back to my examples, I can understand using the long process when teaching it, but this was not an introductory lesson. Why do the teachers not use the "shortcuts"? Is it out of some consideration for the students? Do they think the students can't handle it? Or they'd be confused? Or is there some other explanation?

Tags: shortcuts+math

## Sunday, February 18, 2007

### Mathematics and lyrics

I just saw this on Darren's blog, and just in case there are people here who read my blog, I had to put it here. I would have anyways, because it's awesome. And, yes, I guess I'm a nerd. For this kids out there who may think that's bad: It's not really! Enjoy:

I have to say it all sounds sligthly less impressive when you know that the leader was a math graduate student , who in the mean time finished his PhD, but still. Pretty neat. I have to go continue investigation, and enjoy my nerdom.

Tags: math+lyrics

## Tuesday, February 6, 2007

### Geometry teachers out there?

*Prove that the midpoint quadrilateral (a quadrialteral obtained by connecting consecutive midpoints of sides) of an isosceles trapezoid is a rhombus.*

I know of three different proofs. Would love to know if there are more.

**Update**Here is one remaining proof that I know of. Well, sort of proof :) more of an idea.

### Funding for what?

The budget would add about $1 billion for the education law, most of it directed toward high schools to help pay for a proposed expansion of testing and other programs.

This reminded me of somebody's comment about testing agencies and how they might be profiting from NCLB (can't find the actual comment now) that I read while following the discussion on Dan Meyer's blog about NCLB.

## Wednesday, January 31, 2007

### Amateur survey of mathematics teachers

- Do you think that mathematics courses you took as part of your preparation program (whether it be undergraduate, or certification, or anything else) are relevant to what you do in the classroom? In other words, do you think that what you learned there is directly or indirectly applicable to your profession?
- Same questions about methods courses you my have taken.
- In light of your experience in the classroom, if you had a say in what should be taught to future teachers as a part of their preparation, what would it be? Or, what do you wish you learned before you started teaching?

It is possible that I am asking wrong questions. If you think that is the case, then offer your own questions. And answers :)

### Doing the steps and not going anywhere

I don't see them learning, I just see them stepping. Everything is done for them and when they make mistakes and do procedure incorrectly, she says "Oh, you just forgot to ______________". No, they didn't forget. In order to forget, you must have known it at some point.

It seems to be a common practice to have students work on their homework in class. This, I believe, is an American construct. I find it useless, but people feel attached to it (also, which part of the word homework says that the work is supposed to be done in class?). I saw a teacher give kids and upward of 20 minutes to do their homework. About 75% of the students, if they even bother to attempt the homework, are out of their seats and ready to head out the door within 5 minutes. Now, there is all this talk about not having enough time to go through the material that one is required to cover, but there seem to be so much wasted time. Am I observing an extreme case, or is this practice common? Here is a questions for all the teachers out there: How do you feel about homework time, how much do you give and is it really beneficial?

## Sunday, January 28, 2007

### Research vs. Practice

I don't think I made this clear so far, but I am in between two worlds right now: mathematics and mathematics education. I feel I'm in a no man's land, and there aren't too many of us hanging out there (or we just don't know each other?). Until a year ago I was a semihappy postdoc working on my own little projects, proving my little lemmas, was happy and felt guilty when I taught. Why semihappy? I guess I didn't feel that my contributions to the field or the world at large would be big enough to justify spending my life picking at the mathematics pie and hanging out with people who think that what they do is earth shattering (especially since most of the time I disagreed). Where I did think I could be more useful was with my teaching. I like to think that I am a pretty good teacher, I certainly love doing it, although I may not see myself in an objective light (see the post and post below, and I plan on revisiting this later). In any event, I taught a course for teachers this past semester, and as I was getting ready for it, I started realizing that I don't really know much about teaching, or methods, or pedagogy, or anything really. I decided I ought to learn and started talking to people over in education. It didn't take me too long to realize that they are more similar to mathematicians than either group would like to admit. It seems to be a widespread opinion, especially in education circles, that mathematicians don't care about teaching. That may be, but I would venture to claim that education faculty do not care about teaching any more than mathematicians do. This may need clarification, apart from the one where I say that I haven't actually conducted any research on this and everything I say are observations only and the samples aren't too huge :)

Educators as well as mathematicians largely think that teaching takes the time away from scholarly work. From the professional development programs that I saw, I can not claim that I am convinced that the benefits for teachers are what is on the education faculty's mind, but rather data that they may collect along the way. There also seem to be a big issue of who teaches content courses. Education stance: people who teach it (a.k.a. mathematicians) know the content, but not in the way that is relevant to teachers, so it should be taught by education people. Mathematics stance: the teachers need to know lots more content than they do, and all they get from them (a.k.a. math educators) is this touchy-feely, hold each other hand and reflect nonsense, and consequently they should never be allowed to teach the content courses. Am I exaggerating? Maybe, but only slightly. So what is is missing in this picture? Could it be

**conversation**? But who is to start it when everybody is busy with their research??? The obvious answer to me is the people who do not want to do research, but want to practice. If they are diplomatic enough (hmm, guess that rules me out) they could bridge the divide between the two worlds. Mathematicians who are also knowledgeable about results of research by mathematics educators (slight misnomer: mathematics education researchers would be more precise) seem to be a natural choice. So, if you are out there, and are reading this, or know somebody who is, let me know.

## Monday, January 22, 2007

### Too much information?

“I’m only here,” Esquith announces at the outset, “to share some of the ideas I have found useful.” But most of the things he shares aren’t all that useful and barely qualify as ideas.

The rest follows similar pattern. I have to admit that most of the time I don't doubt NPR much, so this came as a surprise. I decided to look some more. Next was a blog entry , and I list it only because it pointed me to Washington Post's article America's best classroom teacher ?! Its first sentence could not be further from the above quote:

Rafe Esquith is the most interesting and influential classroom teacher in the country, but he is not getting nearly as much glory as he deserves.

I read Washington Post regularly. Along with NPR and BBC, it's one of my favorite news sources. I expect more from them than just stating that somebody is

*the most interesting and influential classroom teacher in the country*. What is the criterion for "interesting teacher"? Or "influential"? Have they visited every single classroom in the country? How many people have participated in determining that he should get the title?

I suppose after seeing such opposite opinions there is no other option but to read the book myself, and make my own judgment. I was going to say that I'd prefer my news to be less grandiose and more specific, but after paying little more attention to where this article appeared, I realize that it was written in a weekly education column Class struggle, so I guess there is no reason to complain.

## Friday, January 19, 2007

### Observations cont'd

One of the things that bothers me and seem to be common across the board: each class was interrupted by something/somebody from the outside anywhere between one time and three times during the class. I am not talking here about student's random talking, but PA/phone/students walking in or out/student council announcements/teacher aids.... This is something I do not remember ever being done when I went to high school. I don't even know if we had AP!

## Friday, January 12, 2007

### Observations

*Doctors don't try to figure out a new technique or procedure for every patient who comes into their office; they begin by using the standard techniques and procedures based on the experience of many doctors over the years. Nobody considers this a way of doctor-proofing medicine, although they do have a name for the failure to use standard practices -- it's malpractice. The standard practices that doctors use contain the wisdom of the profession.*

Last few days I have been observing a class in a near by high school. In this country teachers are not often observed, and from what I can tell even when they are, they do not seem to consider it an opportunity to improve their teaching. I asked the teacher in question today whether she would like or mind me making a couple of comments about what I've seen. Her immediate reaction was less than welcoming and she told me that she gets little defensive about it. On one hand, I suppose there is really no reason for me to think that what I have to say would improve student learning or her teaching. On the other hand, if I were her, I would at least want to know, so that I can judge myself whether the comments were warranted or not.

Another thing that book mentions, and that I am becoming more and more aware of is the following. A lot of teachers can explain, in theory, how they should be teaching. They also may think that they are doing what they know they should be doing. However, their practice is far from their words. I guess what I am trying to say is that how can one expect teachers to apply their theoretical knowledge if they don't know what the application should look like.

Technorati tags: teaching, math, observation

## Sunday, January 7, 2007

### Over-achievers

Technorati tags: education, students, content quality

## Saturday, January 6, 2007

### Self-critisicm

*As researcher Catherine Lewis found, teacher collaboration can create a profound motivation to improve. A young teacher she interviewed recalled that after watching a lesson by her fellow first-grade teacher, she burst into tears: "I felt so sorry for my own students. I thought their lives would have been so much better if they'd been in the other teacher's class."*

Past semester it has become apparent to me that not only majority of people are not critical of themselves, but are not critical of others either. There is a constant fear of hurting other people's feelings. Criticism can be expressed in a manner that is not offensive (ok, maybe I am not the best example, but I am sure it can be done :) ), but rather constructive. Not to be blunt, but I'd rather have one person's feelings hurt, than thousands of children not learning what they are capable of.

In any event, this book is truly amazing, and I recommend it to everybody who aspires to be a teacher (or is one). One of the major points in my view is that majority of U.S. teachers believe that having finished their studies they are ready to teach and the only area in which they might seek improvement is in HOW they teach. But not in WHAT they teach.

Technorati tags: improvement, math, teaching

## Friday, January 5, 2007

### Michigan Radio and probability

Oh, and one more thing: Ann Arbor and Detroit are in southeast Michigan. No need to include them just for the weather report.

## Thursday, January 4, 2007

### More on typesetting

< img src="http://www.forkosh.com/mimetex.cgi?c=\sqrt{a^2+b^2}"

alt="" border=0 align=middle >

Unfortunately, I think one needs very light background, for these to be visible, so I need to make that happen (I'm guessing it'd be enough to make a white box around the gif). Maybe this'll work:

Gotta go walk the dogs. I'll try to make it work later :)

## Wednesday, January 3, 2007

### Gifted students

Technorati tags: elementary education, math, gifted

## Tuesday, January 2, 2007

### Frustrations with blogger

### The Teaching Gap

"There is no way my students could handle this."

"This is too hard for my students."

"Good luck teaching that. That's way above their heads."

If I complained that I didn't think that particular topics under discussion were that hard, I would get these answers:

"You don't have experience with (insert your favorite k-12 grade) students."

"You haven't been in our school."

These statements are correct. I do not have yet that much experience with K-12, but I am fairly positive that students respond to unstated expectations very well (and stated ones even better). What I mean by that is: if your students believe that you think they can not learn math or that the math is just too hard for them to grasp, then they do not have much incentive to prove you wrong. After all, you are the expert. However, if you set the bar high for them, their performance and in the process you let them know that YOU think they are able to become good in math, then they will try harder to prove you're right. I do think that the attitude teachers have influences greatly their students. The reason I am writing about this is the book I just started reading: The Teaching Gap by Stigler and Hiebert. I have a couple of quotes that I'd like to share:

One of the most striking impressions when watching the videotapes is that students in teh United States encounter a different kind of mathematics from that encountered by their peers in Germany and Japan. The content appears to be less advanced and is presented in a more piecemeal and prescriptive way.

As it turns out there were NO mathematical proofs in U.S. lessons. In contrast, there were proofs in 53 percent of Japanese lessons and 10 percent of German lessons.

Average percentage of topics in eight-grade mathematics lessons that contained topics that were DEVELOPED or STATED.

Percentage of lessons rated as having low, medium, and high quality of mathematical content (as rated by a team of mathematicians who did not know which lessons came from which countries).

Technorati tags: education, math, content quality

## Monday, January 1, 2007

### Typing mathematics in blogs

The character entities can all be invoked via their numeric or alphabetic names. For example, both

x ∈ A and x ∈ A

will display

x ∈ A

A radical can be done. The HTML

√<span style="text-decoration: overline">a + b</span>

will display as

√a + b

Below is a partial list of the character entities specificied in the W3C Character Entity References for HTML 4. It includes most of the characters of interest to the mathematician.

#### Generic Character Entities

# | alpha | sym | IE6 | FF | description |
---|---|---|---|---|---|

38 | amp | & | Y | Y | ampersand |

160 | nbsp | Y | Y | no-break space = non-breaking space | |

8194 | ensp | N | ? | en space | |

8195 | emsp | N | ? | em space | |

8201 | thinsp | N | ? | thin space | |

8204 | zwnj | | ? | ? | zero width non-joiner |

8205 | zwj | | ? | ? | zero width joiner |

8211 | ndash | – | Y | Y | en dash |

8212 | mdash | — | Y | Y | em dash |

8230 | hellip | … | Y | Y | horizontal ellipsis = three dot leader |

#### Mathematical Character Entities

# | alpha | sym | IE6 | FF | description |
---|---|---|---|---|---|

60 | lt | < | Y | Y | less-than sign |

62 | gt | > | Y | Y | greater-than sign |

176 | deg | ° | Y | Y | degree sign |

177 | plusmn | ± | Y | Y | plus-minus sign = plus-or-minus sign |

215 | times | × | Y | Y | multiplication sign |

216 | Oslash | Ø | Y | Y | latin capital letter O with stroke = latin capital letter O slash |

247 | divide | ÷ | Y | Y | division sign |

8226 | bull | • | Y | Y | bullet = black small circle |

8465 | image | ℑ | N | Y | blackletter capital I = imaginary part |

8472 | weierp | ℘ | N | Y | script capital P = power set = Weierstrass p |

8476 | real | ℜ | N | Y | blackletter capital R = real part symbol |

8501 | alefsym | ℵ | N | Y | alef symbol = first transfinite cardinal |

8592 | larr | ← | Y | Y | leftwards arrow |

8593 | uarr | ↑ | Y | Y | upwards arrow |

8594 | rarr | → | Y | Y | rightwards arrow |

8595 | darr | ↓ | Y | Y | downwards arrow |

8596 | harr | ↔ | Y | Y | left right arrow |

8709 | empty | ∅ | N | Y | empty set = null set = diameter |

8711 | nabla | ∇ | Y | Y | nabla = backward difference |

8712 | isin | ∈ | Y | Y | element of |

8713 | notin | ∉ | N | Y | not an element of |

8715 | ni | ∋ | Y | Y | contains as member |

8719 | prod | ∏ | Y | Y | n-ary product = product sign |

8721 | sum | ∑ | Y | Y | n-ary sumation |

8722 | minus | − | Y | Y | minus sign |

8730 | radic | √ | Y | Y | square root = radical sign |

8734 | infin | ∞ | Y | Y | infinity |

8736 | ang | ∠ | Y | Y | angle |

8746 | cup | ∪ | Y | Y | union = cup |

8747 | int | ∫ | Y | Y | integral |

8764 | sim | ∼ | Y | Y | tilde operator = varies with = similar to |

8773 | cong | ≅ | N | Y | approximately equal to |

8776 | asymp | ≈ | Y | Y | almost equal to = asymptotic to |

8800 | ne | ≠ | Y | Y | not equal to |

8801 | equiv | ≡ | Y | Y | identical to |

8804 | le | ≤ | Y | Y | less-than or equal to |

8805 | ge | ≥ | Y | Y | greater-than or equal to |

8834 | sub | ⊂ | Y | Y | subset of |

8835 | sup | ⊃ | Y | Y | superset of |

8836 | nsub | ⊄ | N | Y | not a subset of |

8838 | sube | ⊆ | Y | Y | subset of or equal to |

8839 | supe | ⊇ | Y | Y | superset of or equal to |

8853 | oplus | ⊕ | Y | Y | circled plus = direct sum |

8855 | otimes | ⊗ | N | Y | circled times = vector product |

8869 | perp | ⊥ | Y | Y | up tack = orthogonal to = perpendicular |

8901 | sdot | ⋅ | N | Y | dot operator |

8968 | lceil | ⌈ | N | Y | left ceiling = apl upstile |

8969 | rceil | ⌉ | N | Y | right ceiling |

8970 | lfloor | ⌊ | N | Y | left floor = apl downstile |

8971 | rfloor | ⌋ | N | Y | right floor |

9001 | lang | 〈 | N | Y | left-pointing angle bracket = bra |

9002 | rang | 〉 | N | Y | right-pointing angle bracket = ket |

#### Greek Letter Character Entities

Both IE6 and Firefox implement all of these characters.

# | alpha | sym | description |
---|---|---|---|

913 | Alpha | Α | greek capital letter alpha |

914 | Beta | Β | greek capital letter beta |

915 | Gamma | Γ | greek capital letter gamma |

916 | Delta | Δ | greek capital letter delta |

917 | Epsilon | Ε | greek capital letter epsilon |

918 | Zeta | Ζ | greek capital letter zeta |

919 | Eta | Η | greek capital letter eta |

920 | Theta | Θ | greek capital letter theta |

921 | Iota | Ι | greek capital letter iota |

922 | Kappa | Κ | greek capital letter kappa |

923 | Lambda | Λ | greek capital letter lambda |

924 | Mu | Μ | greek capital letter mu |

925 | Nu | Ν | greek capital letter nu |

926 | Xi | Ξ | greek capital letter xi |

927 | Omicron | Ο | greek capital letter omicron |

928 | Pi | Π | greek capital letter pi |

929 | Rho | Ρ | greek capital letter rhothere is no Sigmaf, and no U+03A2 character either |

931 | Sigma | Σ | greek capital letter sigma |

932 | Tau | Τ | greek capital letter tau |

933 | Upsilon | Υ | greek capital letter upsilon |

934 | Phi | Φ | greek capital letter phi |

935 | Chi | Χ | greek capital letter chi |

936 | Psi | Ψ | greek capital letter psi |

937 | Omega | Ω | greek capital letter omega |

945 | alpha | α | greek small letter alpha |

946 | beta | β | greek small letter beta |

947 | gamma | γ | greek small letter gamma |

948 | delta | δ | greek small letter delta |

949 | epsilon | ε | greek small letter epsilon |

950 | zeta | ζ | greek small letter zeta |

951 | eta | η | greek small letter eta |

952 | theta | θ | greek small letter theta |

953 | iota | ι | greek small letter iota |

954 | kappa | κ | greek small letter kappa |

955 | lambda | λ | greek small letter lambda |

956 | mu | μ | greek small letter mu |

957 | nu | ν | greek small letter nu |

958 | xi | ξ | greek small letter xi |

959 | omicron | ο | greek small letter omicron |

960 | pi | π | greek small letter pi |

961 | rho | ρ | greek small letter rho |

962 | sigmaf | ς | greek small letter final sigma |

963 | sigma | σ | greek small letter sigma |

964 | tau | τ | greek small letter tau |

965 | upsilon | υ | greek small letter upsilon |

966 | phi | φ | greek small letter phi |

967 | chi | χ | greek small letter chi |

968 | psi | ψ | greek small letter psi |

969 | omega | ω | greek small letter omega |

Immediately after stealing all this code from Clark (thanks a bunch), I ran into Flip Tomato's Blog. This was an absolute gem, as it contained the following link: mimeTeX. Score! I better get this running on my computers. If anybody has better solutions, let me know.

Technorati tags: tex, math, type math