Equation Image Hacks

Here's a version of SteveH's equation that I built in Photoshop Elements. (If you don't have that, and don't want to buy it, I recommend that you take a look at GIMP, which is free and very capable. The tools and menu options in the instruction below are probably a bit different in GIMP.)

To create the image, do the following:

1. Open a new, blank document in your image program. Choose your image size appropriately, both in image size and resolution. (The base image here is actually too large, as you'll see if you click on it. I should have chosen a smaller upload size.)
   
2. Open a word-processor document. (I used OpenOffice Writer, but Word can work also.)
3. For each special character, use the Insert Special Character menu option to find and insert the special character in the word processor. Note: In this equation the apposite special characters were the capital sigma and the not-equals symbol.
   
4. Using the text tool, enter each of the elements of the equation in a separate layer. (For this image, I used five layers: Sigma, main equation, subscript, lower limit, upper limit.) When necessary, copy the special characters and paste them into the image editor. It is not important at this point to place the image elements precisely, we'll move them in the next step, but it is much easier if you choose your sizes appropriately.
   
5. Using the Move Tool, move each element to the place you want it to be in the final image.
6. Crop the image to remove most white space around the live part of the image.

Let me know in comments if you have any questions about this procedure.

we did it

I was just sitting at the picnic table outside the kitchen, going over C's math homework, when I realized: we did it.

Christopher is taking algebra in the 8th grade.

I started this whole thing, back in June 2004, with that goal in mind: algebra in 8th grade. (You may have to hit refresh a couple of times.)

And now here we are.

Testing Equations

I hope this equation appears OK. I created it with Microsoft Word Equation editor and then had to use a screen capture to put it into a jpeg file for uploading. It seems too small and fuzzy in Preview mode. The jpeg looked fine.

Catherine here --

Steve, I went into the html window and put in random numbers for width and height...which isn't getting rid of blurriness, obviously, but is making the image larger.

I frequently have this problem, and often I can make images larger by making the measurement figures larger -- usually without horribly distorting the image.

Flickr works pretty well, btw. The nouvel Obs cover is a flickr image from a scan of the cover.

Miss Malaprop explains the world to you

C. just said, "M. and J. have Ms. Apocalypto for ELA."

I'm sure that's not right.

you wouldn't shouldn't do it

Dyslexie, vraiment?

De plus en plus d’enfants en seraient atteints. Vraie pathologie ou effet néfaste des methods?

Il y a trente ans, les orthophonistes attendaient le client. Aujourd'hui, ils refusent du monde », constate Colette Ouzilou, orthophoniste d’experience. Auteur d’un ouvrage virulent sur le sujet (1), elle accuse les methodes d’apprentissage globales ou semi-globales, qui demandent a l’enfant de construire seul son savoir et de devenir le sense de mots. « La lecture et l’ecriture sont des codes. Il faut les enseigner. » Dans les années 1960, la plupart de ses patients souffraient de bégaiement, d’aphasie, bref, de réels troubles du langage. À partir des années 1970, elle a vu apparaître, en même temps que les nouvelles méthodes d’enseignement de la lecture, une première vague de lecteurs défaillants. Aujourd’hui, la quasi-totalité des enfants consulte pour des problèmes d’écriture. D’après elle, sure les 10% d’élèves qui arrivent en consultation, 1% a peine souffrirait de réelle pathologie. Les autres ? Des élèves « dysorthographiques » auxquels il manque des bases. Bien sûr, la plupart des pédagogues s’insurgent, rétorquant que le pourcentage de dyslexiques est le même dans la plupart des pays. Selon eux, cette « épidémie » serait due, pour l’essential, a la pauvreté du langage de certains enfants. « Pour les enseignants, c’est une manière de se fausser, pour les parents, de s rassurer, constate un instituteur de CP. «Du coup, tout le monde en redemande. »
Natacha Tatu

(1) « Dyslexie : une vraie-fausse épidémie », Presses de la Renaissance, 212 p., 15,10 euros, 2001.


le nouvel Observateurs
N^° 2235 du Au 12 Septembre 2007, p. 12

......................................

translation:

Is it really dyslexia?

More and more children are being affected. True pathology or harmful effects of teaching methods?

“Thirty years ago, speech therapists didn’t have enough clients. Today they are are turning people away,” says Colette Ouzilou, an experienced orthophonist. The author of a fiercely critical work on the subject, she condemns the whole language or balanced literacy teaching methods, which require the child to construct knowledge and tease out the meaning of words on his own. “Reading and writing are codes. You have to teach them.” In the 1960s, most of her patients suffered from stuttering, aphasia, in short, real language problems. Beginning in the 1970s, at the same time as new methods of teaching reading came into being, she began to see a first wave of failing readers. Today almost all kids consult her for problems of writing. According to her, of the 10% of all students who have speech therapy, only 1% [of that 10%] have a real pathological condition. As for the others, those diagnosed with reading dysfunction, their real problem is a lack of the basics. Of course, it goes without saying that most teachers disagree with this analysis, replying that almost all countries have the same percentage of dyslexics as we do. According to them this “epidemic” is due in essence to the poor language environment of certain children. “For the teachers, this explanation is a way to absolve themselves of responsibility. For the parents, this is a way of reassuring themselves. Everyone asks for more of the same. [not sure about this last sentence]


Le scandale de l'illetrrisme (nouvel obs: the scandal of illiteracy)
dyslexie, vraiment? ) (nouvel obs: true dyslexia?)
Comment en est-on arrivé là? (nouvel obs: How did we get here?)
French spelling

Why English speaking children can't read

Lucy Calkins on teaching children to write
Becky C on starting at the top

instructional casualties in America
curriculum casualties: figures
forcing hearing children to learn as deaf children must
Rory: I frickin' hate whole language!

thank you, whole language

Lucy Calkins, Lucy Calkins, part 2

Children can begin writing the first day they enter Kindergarten and they can learn to write in the same way they learn to talk.

- Lucy Calkins

.................................


I've cited a secondary source. It's possible Calkins did not say this.

If I had to bet, I'd bet she did.

But just so you know.


Le scandale de l'illetrrisme (nouvel obs: the scandal of illiteracy)
dyslexie, vraiment? ) (nouvel obs: true dyslexia?)
Lucy Calkins on teaching children to write

instructional casualties in America
curriculum casualties: figures
forcing hearing children to learn as deaf children must

Le scandale de l'illettrisme

check it out

whole language, "French across the curriculum," constructivism -- it's all here

I will type it up, Ed's will translate, I will post.

Starting with the sudden epidemic of dyslexia amongst French children after schools abandoned phonics in favor of whole language, aka balanced literacy.



Le scandale de l'illettrisme (nouvel obs: the scandal of illiteracy)
dyslexie, vraiment? ) (nouvel obs: true dyslexia?)
Comment en est-on arrivé là? (nouvel obs: How did we get here?)

Lucy Calkins on teaching children to write

instructional casualties in America
curriculum casualties: figures
forcing hearing children to learn as deaf children must
Rory: I frickin' hate whole language!

thank you, whole language

What Kitchen Table Math Means To Me

I decided to write a reflective post on what KTM means to me. I first discovered KTM several years ago while trying to track down the state cutoff scores for the PSAT. During this process, I remember somehow discovering Number 2 Pencil, which led me to KTM. I started to read some of the posts and comments and in very short order, just had the feeling that I had "come home."

Several years previous to that, I had fought my own version of the Math Wars. Our junior high did eventually return to a more traditional approach to math, but the elementary school was using a spiraling, non teach to mastery textbook (I have no idea what it was), and as a result, we took our younger daughter to Kumon for 2 1/2 years.

But, in the truest sense of the word, I think KTM represents a "community of learners." (See, I can throw that eduspeak around with the best of them.) But it is a community that is genuinely interested in education, and not just the education of their own children, but in the education of all children. Catherine is the professor, as she is constantly presenting us with information and challenging us to think, really think, about important issues. The commenters (except for the occasional comments from Anonymous), are amazing. I feel like I learn something new every day, and not just about learning theory, but about math and other subjects as well.

KTM has also caused me to think about my own teaching style and methods--am I presenting information in the most direct way possible? Am I constantly on the lookout for the gaps in their learning? Are my instructions as clear and unambiguous as possible? And so on. . .

But, perhaps the most important benefit is that I understand how important it is to not sit on the sidelines when I think there is a battle to be fought. In an earlier post, Catherine commented about the enormity of the battle, and wondered if all of her actions had made a difference, and concluded that they probably had. Maybe that's the message--we have to stay in the game. Spaced repetition of important messages, over and over. Ever vigilant.

stop the madness

over at Joannejacobs I find this quote from a teacher who has left her job because of NCLB:

“There are a lot of people living good lives in this country who aren’t able to write a cohesive paragraph and don’t know grammar,” Zunin said. “I’m more concerned about them being able to put themselves in someone else’s shoes — which is the essence of To Kill a Mockingbird. I’m more concerned with them being able to feel compassion and to question authority in a constructive way, which is the essence of Night. I’m more concerned with them looking at the nature of friendship, which is at the heart of Of Mice and Men. “

I've mentioned more than once that I don't have much policy sense, though I'd like to.

However, I do have a gut feeling about this. Normally, contemplating the train wreck that is U.S. public education, I don't have a gut feeling, just a kind of horror tempered by bewilderment. Or bewilderment tempered by horror, as the case may be.

So it's nice to have an actual, identifiable gut feeling about something educational.

My gut feeling is that this is the kind of thing that will steadily eat away at public support for public schools, and probably has been steadily eating away at public support for public schools for some time now.

The problem isn't just this teacher's open expression of disregard for grammar and the ability to write a cohesive paragraph, which is bad enough.

The problem is this teacher's open expression of disregard for parents and the broader public. She is talking about other people's children. She is saying that it doesn't matter to her what parents want for their children; it doesn't matter to her what the broader public wants.

What matters to her is what she wants, and she makes no bones about it. Teacher narcissism - not a pretty picture, and not the picture Americans carry in their hearts of the teachers they knew and loved growing up.

You hear this kind of thing a couple of thousand times and you start to think, Those homeschooling people might be on to something.

And, shortly after that, my taxes are way too high.


grammar in Irvington

I had a nice moment this summer that I've been meaning to write about.

It's not worth posting details, but after going over C's state ELA test, I realized that his grammar and usage are quite good - possibly close to excellent, and certainly proficient for his age - and he learned everything he knows about these subjects in our Irvington schools.

We have done essentially no supplementing, afterschooling, or direct instruction of any kind in written grammar, usage, and mechanics. None. Nor do I believe for a second that C. has done enough independent reading to have picked up what he knows incidentally.

I do think he's done enough independent reading to reinforce what he learned at school -- and that's great. He should be reading, and the school correctly, and properly, assumes that we'll make an effort to see that he does.

This comment from lu lu tells me that my own district is doing some things right:

I teach biology at a community college and am frequently amazed at the fact that my students can’t write a coherent sentence (including a subject and verb, even if their tenses don’t agree). Quotes from Ms. Zunin might explain why.

C. is far past this point, and has been for a number of years, I believe.

Thinking about this, I realized that the ability to write grammatically, with correct usage, is a skill C. will use nearly every day of his adult life.

And he's got it.

Pretty amazing.

when do students in Singapore begin algebra?

in the fourth grade:

...starting with volume 4A, which is used in the first half of 4th grade, algebra story problems begin to appear. Consider the following problems:

1. 300 children are divided into two groups. There are 50 more children in the first group than in the second group. How many children are there in the second group? (Primary Mathematics volume 4A, page 40, problem 8)

2. The difference between two numbers is 2184. If the bigger number is 3 times the smaller number, find the sum of the two numbers. (Primary Mathematics volume 4A, page 40, problem 9)

3. 3000 exercise books are arranged into 3 piles.
The fist pile has 10 more books than the second pile. The number of books in the second pile is twice the number of books in the third pile. How many books are there in the third pile? (Primary Mathematics volume 4A, page 41, problem 10)

source:
Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4-6 Texts Used in Singapore (pdf file)
Sybilla Beckmann

Used copies of the first edition of Beckmann's textbook are here. Dipping in and out of the book, I've found it somewhat difficult to understand. Not sure whether it would be easier if I sat down and worked straight through.

This isn't exactly a 'no' vote....I think the book is probably valuable.

But its look to me as if it may not serve well as a self-teaching text.

The Parker and Baldridge text may be better for that purpose, but I'm not sure. At the time I was working with Parker and Baldridge I was in desperate need of basic understanding of arithmetic, so I was highly committed to getting through that book. And, in fact, I didn't get through it; I made it through only 50 pages....which may tell me that Parker & Baldridge is no more accessible to the self-teacher than Beckmann's work appears to be.

I ended up doing best just teaching myself math out of math textbooks.

I'm going to give Parker & Baldridge another go.

The race to the bottom

So, you think your fancy suburban school is doing a good job educating your little darling based on those high proficiency numbers your school spits out every year? Think again.

This recent study, Mapping 2005 State Proficiency Standards Onto the NAEP Scales, might give you some reason to question that assumption.

The NAEP sets the achievement bar pretty low; but wait until you see how much lower states have set the proficiency levels of their own tests compared to NAEP.

Here's the comparison for 4th grade reading.



Not surprisingly, no state has set its proficency level above the NAEP Proficient level. That would be political suidice. But, notice how 75% of the states that participate in NAEP have set their own proficiency levels below NAEP's Basic level.

I knew Basic was the new Proficient, but this is ridiculous.

Here's the graph for 4th grade math.



Better than Reading, but not by much.

Can Johnny read and do simple math? Maybe he can and maybe he can't. but, don't think your state test is going to shed any light. It is a race to the bottom.

Speaking of pundits

Speaking of pundits, I find it revealing that none of them appears to have picked up on the fact that, in math, KIPP is blowing "high-performing" suburban schools out of the water.

The only people I've seen talking about this issue are Bill Sanders, who invented value-added measurement, and Ted Hershberg, also an academic.

Do we have any pundits using the phrase slide and glide?

I'm thinking we don't.


Bill Sanders, interview
Bill Sanders, statement before the Committee on Education and the Workforce
Hershberg articles & presentations
Hershberg clips
march of the pundits, part 1
speaking of pundits
march of the pundits, part 2
how to change the system
parents need a union
Independent George on the pundits and their ways
one is a nutjob, twenty five are powerful
first person

March of the pundits

OK, I have just spent 5 minutes of my life listening to Fordham's weekly podcast.

Subject:
suburban schools

Question:
Suburban schools are doing "fine" (or some such) teaching their white kids.
They are failing to teach their black kids.
Should we or should we not, as a matter of law, insist they teach their black kids, too?

Number one, how is this even a question?

Yes, I understand politics are involved: white parents, the middle class voter, blah blah blah.

What I don't understand: How is this even a question?

Suburban schools should teach all children attending suburban schools.


the white kids aren't doing "fine"

Number two, suburban schools are not doing fine teaching their white kids.

Suburban tutors and parents are doing fine teaching their white kids.

Scratch that.

Surburban tutors and parents are not doing fine, either. Many of us are merely hanging on, averting complete disaster.

This is why we have a Math War. We have a Math War because parents are aware they can't make up for the lousy math education their child is receiving at school.

If it were easy just to teach great math at home, we'd do it and forget about the math war. Or, rather, some of us would forget about the math war. I'd probably join the Math War for the same reason people climb Mt. Everest, because it's there. But that's me.


why don't we have a Spelling War?

If pundits wanted to know why "high-performing" schools are failing to teach disadvantaged students, which they apparently do not, they might ask themselves why we have a Math War in the first place.

Why don't we have, say, a Spelling War?

My own school has failed to teach C. how to spell. When I asked his 3rd grade teacher— a terrific teacher in every other respect, a woman who taught him 3rd grade fractions and made it stick—about his spelling, she laughed and said, "He's not very good, is he?"

Then she said she couldn't spell, either.

When we asked his 4th grade teacher, also an excellent teacher, she shared with us the method she'd ended up using to teach her own kids to spell. (As I recall, she had them write each spelling word 20 times.)

Then his 7th grade teacher told us: "I always tell the kids, if you can't write well nobody's going to care if you can spell,'" or something along those lines. (She, too, was a terrific teacher, an opinion I can probably document. C.'s grammar and usage in written work are very good for his age, and he didn't learn either at home.)

My email to the assistant superintendent in charge of instruction on the subject of a spelling curriculum for middle schoolers went unaddressed.

So: not only did my district not teach C. how to spell, my district routinely conveyed to us the attitude that if we wanted our child to spell, it was up to us.

Question: Do you see me waging a Spelling War here in my district?

Writing a blog about spelling?

Answer: No. You do not.

The reason I am not engaged in a Spelling War is that, as it happens, it has turned out to be possible to teach spelling here at home. I spent a couple of weeks of my life Googling the known universe, trying to figure out what spelling actually was and why people can't do it; I bought a couple of books on the subject, which I have yet to read beyond the first chapter; then I cruised the available textbooks and lit upon Megawords.

C. started the Megawords series in the beginning of 5th grade.^*

He is now in 8th grade and is completing the 4th book in the series.

Last week I began testing him on all of the word lists contained in the first 3 books. Result: he's not bad.

"Not bad," in this context, is meaningful. Today his spelling errors are reasonable, as opposed to psychotic, which is what they were when he was 10.

For instance, when I asked him to spell badminton, he said b-a-d-m-i-t-t-e-n.

That is a correct guess.

I have now pulled out all of the words he missed from the first and second books (have yet to review Book 3), and will have him practice them sporadically as he works his way through Book 5. I'll do the same for Book 4 when we finish it this week.

It's clear now—even Ed says so—that by the time he graduates high school he will be proficient in spelling, or close enough.

This is why I am not engaged in a Spelling War. I think it's ridiculous my "high-performing," lavishly funded school district didn't teach my kid to spell.

I also know for a fact that some of the brainiest kids in the school can't spell worth a damn.

But I'm not having a Spelling War.

I'm having a Math War.

I'm having a Math War, not a Spelling War, because I can make up for lousy spelling instruction, but I can't make up for lousy math instruction.

Pundits appear to be singularly uninterested in the existence of a raging Math War across the land. If they spent 5 seconds paying attention to it, they'd realize their core premise where suburban schools are concerned is wrong.

Talk about the answer being right under your nose.


what does an achievement gap in a high-performing district tell you?

When you look at a suburban school and you see the white kids "doing fine," and the black kids not doing fine, what does that tell you about the school's curriculum, pedagogy, and accountability?

It tells you the school doesn't trouble itself with accountability.

The school does what it does; if the kids learn, great; if they don't, they're disadvantaged and what can you expect?

Humbug.


the slow girl track

This reminds me of a story I've probably told before. It appears in Ed's new book (not sure if it's out yet—I'll check).

The book is a collection of essays by French historians talking about why they became French historians.

In one of the stories, a historian who is.....in his 40s maybe?....writes that as a kid, he was a math hotshot here in the U.S. Then he went to France on a student-exchange program, and the French school put him in "the slow girl track."

Meaning: the track was the slowest the school had to offer and it was filled with girls. The slow boy track was faster than the slow girl track.

He was in the slow girl track.

I say: let's pick a high-performing suburban school district, do a student-body swap with a high performing school in Singapore, and see what happens.

Our kids are gonna get stashed in the slow girl track.

That's assuming Singapore even has a slow girl track.

Which it probably doesn't.


the physicist

Speaking of which, I sat by a former director of the Jet Propulsion Laboratory on my flight back from Illinois.

His daughter is now in graduate school, and he's still exercised about the low quality of U.S. public education.

He told me, flat out, that no parent can remediate a bad math education.^** He'd said this repeatedly to his own school board, to no avail.

He had actually said, to his school board, "You have them sequestered here 6 hours a day and you're not teaching them anything."

This is a physicist and former head of the JPL.

Saying no parent can remediate a bad math program.

Reasonable conclusion: if the head of JPL can't remediate his daughter's lousy math education, I can't, either.

I wish our pundits would get a clue.

^* The books are created to begin in 4th grade, continuing through 11th.
^** I think he extended this to reading and writing, but I don't remember what he said specifically.


march of the pundits, part 1
speaking of pundits
march of the pundits, part 2
how to change the system
parents need a union
Independent George on the pundits and their ways
one is a nutjob, twenty five are powerful
first person
#marchofthepundits

board meeting - much bettah!

Ed went to the board meeting last night and came home, for the first time in years, feeling encouraged.

The tone of the meetings is vastly improved; apparently the new board president conveys an attitude of respect and interest in what parents have to say. This really hasn't been the case for as long as I can remember, and I'm not the only person who feels this way. One parent told me, "Why go to these meetings and get condescended to?"

At one point, Ed asked a question she didn't want to address just then, and she said so in a friendly and courteous fashion, explaining that they would be getting to it soon.

Then, when they did get to it, she came back to Ed to answer the question of her own accord.

That is an enormous change, and so welcome.


more good news

And here is something wonderful.

For years the board has refused to allow board meetings to be televised. Years and years.

That will now change.

Even better, part of the reason it is changing is that the IEF -- the Irvington Education Foundation -- made a grant of $15,000 to purchase the necessary equipment.

God bless their hearts.

Last year I was sooooo fed up. I'd always contributed to the IEF; I'd always gone to their galas.

But last year I just couldn't. I couldn't raise money for a school that was failing to teach my child math (or spelling or handwriting or Spanish or writing), and treating so many parents as shabbily as it has done (and continues to do often enough -- more on that anon).

I was wrong.

I'll be at the gala this year; that's for sure.


board meeting
tone change

Fairfield, CT

Do we have readers (or commenters) from Fairfield, CT?

If so, and you feel like it, could you shoot me an email?

cijohn@verizon.net

Thanks!

for Paula

Trawling the web last night, I found a set of PowerPoint slides (pdf file) Thomas H. Parker used in two presentations to the Core Knowledge National Conference on March 5, 2004.

Here's what he had to say about place value, and in this color, too:

Place value causes MANY, MANY problems all through elementary school

Parker also has this to say:

This idea of using position to encode value is a secret code. Because this is second nature to adults, it is easy to overlook the fact that it is difficult to learn. It requires explicit teaching and must be repeatedly worked on. Place value ideas occur and present difficulties in topic after topic in elementary school.

I haven't read the slides yet, but they look helpful, and include place value exercises.

source:
Sequencing in Elementary Mathematics
Thomas H. Paker

High-Level Policy Guru Interviewed

Dave Marain posted Part One of an interview with Lynn Arthur Steen today at MathNotations. Vlorbik sez check it out.

six years out

I haven't wanted to think about 9/11 all day. I don't know why.

Ed reminded me, this morning, that today was 9/11. Then C. reminded me this afternoon, twice.

I'm sick as a dog; maybe that has something to do with it.

Because I do remember.

what is the opposite of a silver lining?

C's graphing calculator has surfaced.

It was in his locker, jammed between two notebooks.

That's a good thing.

Unfortunately, it is also a bad thing, because it means C. has a graphing calculator. Leafing through the many-colored spendor that is our new Glencoe Algebra textbook, New York Edition, I spy numerous graphing calculator exercises, lesson upon lesson culminating in graphing calculator "features" and the like.

This can't be good. Apparently, the kids are going to be poking away at their hundred-dollar graphing calculators during "math lab," an extra period of math the 8th graders attend every other school day. The math lab teacher has told the class they will "need" their graphing calculators for math lab.

Let us hope the math lab teacher misspoke.

The math lab was originally put into the schedule by our former principal, who had noticed long lines of students snaking out of the then-chair of the math department's office every morning, each awaiting his turn to receive "extra help." Since at that time the big tests happened in the 4th and 8th grades, he decided to add extra periods of math to the 8th grade schedule.

The new middle school principal, who is forging ahead with planning for the dreaded middle school model on orders from our superintendent, wants to get rid of the math lab, which will have the effect of rendering our middle school exemplary (very important!), because it will free up time in the schedule for Exploratory Programs on Darfur and the like. That was the example he gave, an exploratory program on Darfur.

Needless to say, Ed and I were counting on the extra math period to serve as catch-up time for C. As far as we are concerned, there should be NO graphing of functions on hundred-dollar calculators by a student who, exactly 8 weeks ago, did not know how to figure 10%.

There should be diagnostic assessment, and there should be remediation.

By remediation I mean formal remediation, remediation planned and overseen by actual math education professionals, not by me.

So.

I'll probably bug them about this.

Then I'll do it myself.


the good news

The good news is that C's math teacher is fantastic. That's the math teacher I'm talking about, not the math lab teacher.^*

He is a real, live teacher -- and a guy, to boot!

A guy who watches football, and roots for a particular team!

C. is in heaven.

His homework assignments, thus far, have been perfect.

I had heard good things about this teacher, but by the end of the summer I had been thinking we were beyond the point at which an effective teacher was going to make a difference one way or another. By now a lot of these kids -- by no means all, but a number of them -- are going to have math knowledge so riddled with gaps, holes, and yawning chasms that one teacher working alone isn't going to cut it.

But now I'm thinking.....perhaps all is not be lost.

More later.


TI 84 page on ebay
"instructional time issues"
hundred dollar calculator
178 days left 'til summer
email to the principal re: hundred dollar calculators
other people's money
what is the opposite of a silver lining?



^* The math lab teacher may be great, too; I've heard one report thus far, and it was glowing. I like glowing. My point is simply that the math teacher and the math lab teacher are two different people.