Precise speech is critical in math.

Here something just posted on twitter:

My first grader's INSANE Common Core math problem that literally requires 48 steps!

Here's the picture:

 

Now, I know Jack Diddly about teaching kids that young, but I do know this: They're not stupid ... but every kid in the room will read that and struggle a bit on the vocabulary. The font choice will explode the dyslexics' minds (I can barely get "birthday", and "edch" took me a second because the ascender on "a" makes it look too similar to a "d". Yeah, that says "each".)

It's cuetsy and I guess that's okay for first graders.

BUT

When you say "12 classmates", you are directly, explicitly and literally saying that there are 12 other people in the room; Glenda is the 13th student.

Precision in your language is critical. Clear and correct problem statements are essential.  These kids are barely in their comfort zone and you're pitching curveballs and changing it up with high heat?

This is precisely where kids develop their fear of mathematics, where they learn that they don't know how to read it, and where they learn to dread trying word problems because the words don't mean what the kids think they mean.

The teacher doesn't have a clue as to how dangerous this little problem can be.

Kids get confused when they try to understand and keep getting corrected for something that is actually incorrectly stated. Kids get frustrated when you say "at least 10" when you mean "more than 10" and then you don't acknowledge that 10 is valid for one but not the other.

They wind up just getting by and letting the confusion (and the understanding) flow right on past and out the window. Too much of this and we will have lost another generation. It's the fault of this and the next five elementary-level math-phobic teachers.

Thanks for nothing.

Embedded Content and the Foreign Language Paradox

Bumped to the top from August of 2010:


Joanne Jacobs: Kids Don't Know Grammar. Although neither of those quoted (perhaps misquoted) can spell "embedding," their point is good. Embedded curriculum doesn't work.

Less than 10 percent of Robert Archer’s 10th graders know grammar. A 14-year veteran teacher in Spokane, Archer doesn’t blame middle-school teachers. He blames curriculum developers for “imbedding” grammar in the curriculum.

"in my experience, the term “imbedded” is nothing more than educationalese for “not ever specifically taught.” Somehow, this grammar-is-imbedded movement is supposed to help students naturally take in what proper grammar is (i.e., grammar by osmosis). It’s very much a hyper-constructivist approach to education; the students are supposed to “discover” proper grammar on their own as they read good pieces."

He's right. They don't pick up on the proper forms of grammar, nor do they pick up much of anything that isn't specifically presented and what is, doesn't last.

Maybe I'm an old-school fart but it seems to me that if the students really could do this type of learning by assimilation, they would be miles ahead of where they are now. I do SAT prep classes and the grammar skills are terrible -- except for the kids in Spanish or French III or IV.

I call this the "Foreign Language Paradox." When learning English in an English class, grammar and basic forms are not supposed to be explicitly taught. Literature reigns supreme and some limited essay forms are required. Grammar and proper sentence structure are supposedly understood as 5th graders. Then we are all surprised that no one seems to know them.

In any foreign language class on the other hand, noun and verb declensions, grammar and sentence structure are specifically taught; then drill, drill, drill. Every student learns through actual work and walks out with an understanding of the language and a better understanding of English, too. "I never understood the subjunctive mood until Señor told us." "Past, imperfect, pluperfect - wow! Then, a couple of present tenses and more than one future tense? Damn."

It's not just Latin that builds English skills, although Latin does have power in its rigid simplicity and endless lists and mnemonics. It's specifically teaching grammar to students when they are finally sophisticated enough to really understand and appreciate it in all its nuanced glory.

Hello? Is my curriculum coordinator listening?

Apparently not.

Joanne chimed in with her own anecdote:

On Back to School Night, my daughter’s eighth-grade English teacher told parents she was going to go off curriculum for two weeks to teach grammar and punctuation. She got a standing ovation.

It's not just English, but math as well. Bunches of my students go off to the tech center for a one or two year program and then return. They have me for algebra I and then go to forestry or woodworking or something. Invariably, I hear about the embedded math credit. They are then placed in the next class and have no clue about the missed material. What's worse is that they are in my class for the eleventh grade and thus on my roster for the NECAP tests in November. I think of myself as a good teacher, but that's just not fair to either of us.

Bottom line: No matter how smart, no matter how motivated, all kids need some instruction. Unless you are specifically making things clear, you are allowing kids to construct any old thing, and it's usually flawed.

Why Johnny Can't Write a Term Paper.

Bumped to the top of the queue from July 2010:

Joanne Jacobs passes on a Jay Matthews article about kids not ready for college writing because they have never written long papers.

Now, when nearly every student is expected to go to college, they spend more time writing personal essays in journals than they learning how to research and write a college-level paper.

I see the same thing up here in the mountains. I'm not sure that it's laziness or reluctance on the part of the teachers - grading a fifteen-page paper is actually much easier than grading ten page-and-a-half short ones.

I think part of the reason may lie in the detail-oriented, bite-sized education our State DOE is pushing. Standards list the many things those English faculty should be doing. There is emphasis on touching every kind of writing instead of trying to master any one long-form type. We have "writing across the curriculum" which strives to get every teacher writing in their curricular area.

Calvin has a piece of it, too. Some teachers are too full of themselves to do something as pedestrian as a research paper. I won't even discuss the puerile drivel of a book report.

What of the rest of the building? What of Literacy across the Curriculum?

Math teachers (Hi!) try to avoid set pieces and stick to paragraph-sized explanations. If you push us (and many principals do), we'll do the useless 1-page biography of a math person. Since we're not comfortable grading such, the students aren't pushing their envelope and it's a useless exercise. I try to do 30-word abstracts of Scientific American articles - that's tough - but it's not research. I don't have time to divert them from parabolas to writing papers. Besides, I want them to write Math, not words.

History teachers are doing 1- to 2-page factual "research papers" at the longest. Answer this question or explain that, but not much more. Science teachers are doing lab reports, lazy science teachers have them fill out pre-printed ones.The music teacher has them writing, too ... on staff paper.

Because the non-fiction is being done elsewhere, I think the English teachers are pushing short essays and creative writing. If they go anywhere else, it's journalism.

Is this wrong? I don't think so. We're being increasingly held to these standards that do not address long-form writing.  No one should be surprised that English teachers are ignoring it. 

I think the only way to really bring out the research paper is to put it alongside senior English ... and call it "Research Seminar" or something.

Years ago, my school had a "Senior Seminar" class that consisted of SAT/English prep first trimester, college essay and application writing second trimester and, for the third trimester, a 30-page research paper. This seminar was a graduation requirement in addition to 12th grade English. I've been trying to get it implemented at my current school, but no dice.

My thought today, mirroring the school's thinking then, is that the process can't be relegated to a single week of an otherwise busy English class. There is too much to be done for it to be anything less than the sole point of 3 months of class. Notes, research, outlines, drafts, false starts and restarts, time management.

In the incarnation of twenty years ago, the teacher had a list of topics from which to choose, already had a (minimal) list of books that would be appropriate, and basically knew the topics well enough to recognize cheating and/or plagiarism. She didn't just drop them in the deep end and cackle evilly, she had the time and the resources to work through the whole process. Even the ESL kids here on I20 visas, the remedial kids who read very slowly, and the the lazy kids, all had enough teacher time to do it right.

Added from my later comment:

You can call it an English elective. One research paper is not enough for a whole credit so make part of the class into SAT or PSAT prep (or NECAP or whatever) focusing on vocabulary and basic grammar and sentence formation because you know they probably still don't have that quite right.  (Read Embedded content and the Foreign Language Paradox for more on grammar.) 

Spend time with the computers and formatting and MLA and footnoting and all the stuff.

Then patiently start the process of research and reading and library search and proper Internet research. This will take a month in itself. Outlines, note-taking using Keynote or something similar, such as, *gasp* note-cards.

Diagrams and images and photoshop. Spend a few days with the AP stylebook and reading "Eats, Shoots and Leaves."  Can they make proper footnotes in their Word Processor of Choice? Bibliography? Pull-out quotes? Binding allowances? Hell, you can even get the damn thing published and sold through Amazon.com or Lulu with a print-to-order option if the student really wanted to shine.

Open your imagination - what would you do if you had a group of kids whose sole focus was on writing a long-form research paper without ANY references to standards, no limitations or requirements to teach "The Lottery" and no literature to read because that's happening somewhere else?

What if your graduation requirements included "Four years of English" and "Senior Research Paper"?

Stop drooling.  You can thank me later.

PEMDAS is unfair? I can't believe I read that.

On a blog which ordinarily doesn't have much silliness, I read the following

You can explain the truly arbitrary elements of PEMDAS (the left to right of AS and MD) through an experiment. Allow students, independently, to do these two problems any way they want, ignoring any stupid arbitrary rule they might have previously memorized:

Include here a few order of operations-type problems.

Enter the Stupid Arbitrary Rule (SAR).
Because we need to all come up with the same answer, we need a rule to follow. Really, it can be any stupid arbitrary rule (SAR). But we agreed, at some point in history, to all follow the “left to right” thing once we were down to addition & subtraction or multiplication & division.

While I agree that it is an arbitrary rule, it's far from stupid and, for me, it highlights one of the reasons why schools exist; that is, telling kids how the world they are about to enter works and what its rules are. But then I get this:

It’s important to note that kids didn’t get to be part of that agreement we made. Just like they don’t get to vote in elections. Is it fair? Probably not. They would probably do a better job of choosing leaders as well as determining the order of operations. But that’s the way things likes SARs work.

You have to stop that crap right at the source. How can anyone say "that agreement we made" and conclude that it probably wasn't fair that kids can't be part of that decision?

First, of course, is the "we" thing. There is no "we" and "they" here and nobody waved their scepter around declaring that henceforth All Students Will Do It This Way. The order of operations didn't exist at some point in time, but then neither did algebraic notation. There weren't exponents until fairly recently (they were written words), someone had to have been the first to use a zero and place value ... you can go on. The point is that someone started using a notation, explained what it meant and how it worked and others decided it was easier and fell in with the crowd.

Enter the modern student, spoiled silly and clutching his cellphone and fantasies of being a "Digital Native" who can multitask and has no use for That Boring Crap.

What has "fair" got to do with it? Why is this pubescent psycho-babble coming from the only adult in the room?

And when he says students would probably do a better job of electing leaders, you have just heard the sound of a deluded mind. It's typical in education, echoing the "noble savage" mentality. So many teachers harbor this idea that kids know so much more than we stupid adults, that if we only took off the restraints, they'd be teaching themselves calculus in no time. They're better than we were, smarter than we were, and by golly just look at how responsible they'd be.

This is a huge disservice and only feeds the disillusionment with school and learning - "Why are you screwing me over? This is so UNFAIR."

And to then make up new rules for mathematics, post them in the classroom and keep using them? You've just gotten through telling them that all the rules are stupid and arbitrary and you want to have them invent, and then use, more stupid and arbitrary ones?

I'll stick with the valuable, useful and arbitrary ones and I'm always looking for a new way to demonstrate them ... like this image I found (might be Dy/Dan's):

Now, that's education.

I don't DO math.

This article:

Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence.

Confusing Stats

On the other blog, matharguments180.blogspot.com, there is exactly one post and a confusing number of pageviews:

Maybe this should be Day 2.

Yo, IT Department.

Just some notes for any IT personnel who may be reading:

1. If the accounts at a school aren't consistent -- the account names are different for network log on, powerschool log on, and email -- teachers are not going to be happy. Having mcurmudgeon as my powerschool account, curmudgeonm as my school computer account and math.curmudgeon@vtsch.net as my email is stupid. Do your job - fix that.
2. Changing the domain three times in one year is stupid. Expecting anyone to be happy when you're changing over all of the Google accounts and all of that stored class information from one domain to another should have happened over the summer, not a month into the year.
3. Training is not something you can throw together in two minutes. 



It's called a computer lab. Surely you've heard of that?

4. When conducting software training, it helps if the teachers can be logged in to a computer and can see what you're talking about. Waving your hands dramatically isn't a good way to convey the use of the four level tab and pull down menu structure.
5. Showing a random video to a roomful of teachers isn't software training.
6. Making a 100+ character link available on the school webpage works much better than attempting to relate it verbally to the group.
7. Your job is to make the technology work for the teachers and staff. Period. You have no other purpose.
8. My job is to teach. It does not include teaching myself how to use all this technology so that I can teach the rest of the faculty because you're an incompetent ass.

Have a nice day.

I'm tired of Twitter and Mindless Slogans.

For me, the basic problem with Twitter is the all-too-common resort to pithy statements that fit the character count but don't make for a coherent conversation.  I don't really care what's been said about the Seattle-San Francisco game; that's not important enough that sound-bites and sloganeering detracts from the conversation.

I'm talking about education reform ... and that is a big problem when discussed on Twitter. Changes to standards-based grading is a big discussion currently, as is standardized testing. These broadsides are fired without really discussing nuance, and for me, nuance is necessary.

You can't standardize learning nor will a standardized test ever be able to report it #abed #edchat #bced #mathchat #onted #ableg
— D Martin (@d_martin05) January 20, 2014

Here's the thing ... that's not an argument. It's a statement unbounded by fact or reason.

There are plenty of situations in which standardized tests are important, mostly in those situations where you have a need to compare against a national standard such as SAT, ACT, AP, IB, A-levels, GRE, Bar Exam, Civil Service, Driver's License, et.al.

DMartin agreed with my sarcastic comment to eliminate all of the above testing with "Yeah all mc parts. I agree!! Great idea!!"

So now we've gone from being anti-testing to being anti-MC, as if MC is somehow flawed.  Again. I have to ask, what leads anyone to think that MC can never be useful?

Why is this such a necessary part of my online life?  (The answer: it isn't.) What part of reasoned and thoughtful commentary includes these random unproven factoids and false dichotomies?

I'll leave with another ...

No cell phones in class b/c they cause distractions well let's remove pencils they cause spelling mistakes 

Instead of Mindless Dichotomy, how about just removing or eliminating the distraction part of the cellphone?

It's not Psuedocontext, it's just wrong.

Credit for the Bad parts, too.

There are many errors in the packaged, bought and paid for, courses from Florida Online. Unfortunately, the "developers" seem to have taken that "Beta" software approach ... if it isn't "Threatening-the-President-bad", then we won't bother fixing it.

Take this problem, from the Semester Exam:

Triangle ABC is congruent to triangle DEF. In triangle ABC, side AB measures 9, side BC measures 3x+18, and side CA measures 7. In triangle DEF, side DE measures 9, side EF measures 2x+26, and side FD measures 7. What equation would help you to solve for the side length of BC and EF? Explain your reasoning using complete sentences. (10 points)

At first blush, you say "They're congruent. BC is congruent to EF, so 2x+26=3x+18. Done."

What's the big deal?

Solve it.

Pretty easy ... x = 8.  So the sides of a triangle are 9, 7, and 42. Shit.

Any student who takes that obvious next step, and thinks for more than a second about a different topic just studied, i.e. comparing sides of a triangle and scissors theorem, is now convinced he's done something wrong.

It's not Psuedocontext, it's just wrong.

Source of Puzzles

A reader asked the other day where I got some of the puzzles I put on here. (Okay, she asked about two weeks ago, but I don't check the email all that often.)

Many of the roughly pre-calculus level math questions come from the UVM Math Contest. The website has only the last dozen years but I have the Notebook that goes back to the 70s.

Some of the Old-Timey one are from Sam Loyd's Puzzle Encyclopedia. You can find many of them on Wikipedia but I downloaded the images of the original book from mathpuzzle.com/loyd or get the whole thing as a zip file.

Technology - Interactive with what?

Technology is great.

Technology is the wave of the future.
Technology is a tool, allowing us to do more.
But so far, technology doesn't seem to be helping with the whole "Interaction" thing.

We'll have to figure this thing out before it kills us.

Every kid, staring at a screen.

More staring ... but at least he's not letting his head fall over.

Ah, now the teacher is watching them stare at screens. So META.

Staring in a circle.

Seriously, Rocketship Academy? This is Edutopia? This cubicle-farm with rows of cells?

We have to do better.

Putting everything on wheels and moving them around daily so the "teacher doesn't even know where to stand" isn't going to improve things much.

Yeah. They get enough at home. Mindlessly fiddling with crap isn't education.

See, lecture isn't a bad thing, in moderation, and when done well. But changing to Khan Academy lectures on the computer to replace the teacher's lectures in the classrooms isn't much of a fundamental shift.

Your guidance counselor spent untold time arranging the schedule so you and your unique teacher skill-set could be present at the same time as the students who needed that exact same set of knowledge and ability. Use the time. Be the teacher.

Leave the screen time for when you and the other kids aren't around each other. FLIPping the classroom is fine. Assigning the Khan for outside work is fine. Watching them day after day, huddled in their solitary confinement of a sensory-deprivation cubicle with walls to block sight of other students, headphones to block the sounds of other students, and a computer to overwhelm all thought ... isn't education and isn't an improvement.

No matter what Rocketship might say.

Maybe a quick glimpse of my road will calm us down so we can be objective about this.

Nice.

Smart is the New Invisible.

Actually, Smart kids have always been ignored in most schools.

Joanne Jacobs passes on this about Smart Kids:

Exceptionally smart students “are often invisible in the classroom, lacking the curricula, teacher input and external motivation to reach full potential,” writes Science Daily, citing a Vanderbilt study that followed gifted students for 30 years.  The 320 high-IQ students went on to become business leaders, software engineers, physicians, attorneys, and leaders in public policy, reports Who Rises to the Top?, published in Psychological Science.

Despite their remarkable success, researchers concluded that the profoundly gifted students had experienced roadblocks along the way that at times prevented them from achieving their full potential. Typical school settings were often unable to accommodate the rapid rate at which they learned and digested complex material. . . . This resulted in missed learning opportunities, frustration and underachievement, particularly for the exceptionally talented, the researchers suggest.

 This has been a constant irritant for me, for many years. We focus on the "bubble" kids, the weaker students who might pass if we give them a little more attention, and we tend to ignore the very weak as well  as the motivated and the smart.

"Heterogeneous classrooms" is the mantra where I teach, resulting in the kid up front twitching in boredom while the weaker students nod off, zone out, and then need the retakes and the constant nudge to hand in work, finish work, start work, etc.

Honors classes were replaced with CP "College Prep" because Everyone Must Go To College.


"That's the way those One-Room Schoolhouses did it. Why should we single out and spend more money on those kids? They'll be fine. They'll get their As."

It makes me cringe. Yes, they'll get a A, but the weaker kids don't get what they need, and neither do the strong. If you're going to have 5 sections of Algebra 2, why not simply let one of them be comprised of strong students?

Is it wrong of me to note that the people who ask why we should single out smart kids are invariably the parents of, or who were themselves, weak students?

Is it wrong of me to note that I haven't been able to get a whole class to participate in the Norwich Bridge Building Competition, only a few here and there?

"The smart kids can help the weaker kids ... collaboration is 21st Century teaching, you know, and it's the way the Real World works."

Let me channel my inner teenager ...

What if I don't want to do the teacher's job? What if I don't like many of my classmates. Why should I be forced to "teach" my classmates stuff they couldn't be bothered to learn in class the normal way?  Why should my grade depend on someone else's motivation?

Don't give me that "It's Real World" crap because I know that in the RealWorld, the dead-beats would be fired. No one pays people to sit around and wait for the one team member to do all the work. No one gets to wait until someone else is finished and lean over, "So, what did you get on number 1? And how about number 2?"

Tech's Magic Formula

Scott MacLeod:

Lack of vision + inadequate infrastructure + no training + poor implementation + insufficient ongoing support + refusal to change = tech success!
Does this sound like your wishful school or district? Hope not!

With our Highly Ineffective Principal (HIPster), we drew a Royal Flush on this one. It's all we can do to keep the one-to-one going despite the random flailings of the administration ... we being three of the teachers.

1. Lack of vision - If it hadn't been for one particular teacher getting the ball rolling and two other of us pushing, we'd still be without BYOD or any one-to-one program.
2. Inadequate infrastructure - don't get me started.
3. No training - Inservices revolve around the Curriculum Coordinator and his protocols for having discussions about "authentic" learning and teaching, protocols for having meetings, protocols for developing a single lesson plan that we'll test in a few months. That's right ... we're making a single lesson. Technology? Not so much.
4. Poor implementation - 
1. Kids are damaging their devices and no one has a plan for that. 
2. They don't charge the batteries ... "I can't hold class because they didn't bring it."
3. Leave it at home.
4. Some parents don't want their kids to have that much screen time and have asked that the kids NOT be given one.
5. Insufficient ongoing support - Crickets make more noise.
6. Refusal to change - This is the one part we do too much of. Change, change, change ... without ever looking back to see if the previous changes were effective or looking forward to see if we can predict and measure the effects of the present proposed change.

= tech success!