Saturday, December 26, 2015

The New Math Wars

by James Tanton

Monday, December 21, 2015


Just a quick question ...

With everything that goes on in a public school these days, why has actual teaching been shuffled so far down the list of priorities, behind:
  • Fire Drill/Police Dog Drug Search
  • Professional Development
  • Addressing Damage in the Bathrooms
  • Sports in all its forms (mostly afternoon disruptions, but we're coming up on skiing and snowboard season, and spring has golf ... 8am meets and competitions are the norm.
  • "Pardon the interruption for this announcement."
  • Service Organizations.
  • Class Fundraising going door-to-door.
  • Class Meetings 
  • Pep Rallies
  • Anti-Bad Things Assemblies
  • Teacher Education/School Visits/conferences/workshops
  • Principal doing Teacher Evaluations (Major disruption when he sits clicking his laptop)
  • Anything the Administration finds on their calendars.
  • Send the kids to the office if they're late ... to get a pass and come back to class.
  • Talk to the kid in trouble, set up a detention ... for missing class.
  • Meeting with the State College Scholarship rep who tells them they need to be sure they're attending class. Said meeting happens during class.
  • Anti-Drug counselor pulls them to have them sit in her comfy chair and eat cookies.
  • Volunteer Fire Department Rescue calls.
  • Field Trips for non-academic things.
  • Family vacations and appointments.
  • Illnesses that mysteriously occur on test days.
  • Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice. Inservice.
"Give them the assignment so they can make up the work. We'll be out all week."

"This is the only time we could schedule 'Bodybuilders Against Drugs' and I didn't want to let the opportunity pass by."

"I think everyone in the department should attend this workshop."

You might point out that teacher education and workshops and school visits are intended to improve the overall teaching and improve the school. I worry that the professional development is explicitly expected to take a couple of years to come to full fruition ... and this is the only education these kids will get.

Sure, I can take the long view, but what of that senior?  What will replace this year for her if we continually mess with it? It's part of what lead to my previous rant about research.  I WANT to use the best ideas, but I don't care to spend a lot of time trying to winnow out the chaff and uncover the lone jewel of future glory at the expense of the students I already have.

I'm expressly NOT wishing for repetitive, boring, lock-step, soul-crushing monotony. This isn't a prison and can't be run like one. That's not what this is about. It's about predictability and finding security in knowing what's coming and when, and that school, unlike many of their homes, is about habits of mind and habits of behavior and learning everything you can while it's still free.

You might think it silly, but knowing that "Every Friday is a quiz in History" is actually comforting to a majority of students. The worst thing in a high school is to change everything suddenly. When you call "everyone out to the courtyard for an impromptu dance to relieve stress", you frustrate everyone who was just about to get to work, you get the ADHD kids going on something new at the exact wrong time, and you raise the anxiety levels of everyone.

It's easy to sit in an office and look at a shiny new workshop proposal and find a blank day on the calendar to schedule it in isolation, but that's messing with the rhythm of the school. When there's no rhythm in a school, there's no soul and no quiet confidence.

When did teaching move so far down the list of priorities?

Sunday, December 20, 2015

Hey Researchers!

Hey researchers. you know what would be cool?

How about if you settle some questions for us?  I've been in education a long time and I've heard what seems like infinite variations on the same questions, along with what seems like infinite new thoughts that came out of the blue.  Every time our principal or superintendent goes to a conference or a workshop, it seems they bring back a new idea, a new structure, a new way of doing things that "research has shown" to be the shiny new penny of educational thought.

When you look a little deeper, you find it was done on 65 elementary students in NYC ... and you're supposed to try and develop curricula for your 10th grade math classes that follows this brand spanking new paradigm.

Answers are NOT overrated. The whole point of research is to answer a question, either to prove or disprove it. Research that is only about finding something new is exploration, and while it does have it's purpose, it's not what we need in this country at this time in this industry.

We have lots of new ideas. I, for one, am sick of all of them. What we don't need is more new ideas to be trotted out, forced on the students and faculty, only to be replaced when the fashion statement of the month changes.

What we do need is to weed out the bad ideas, the bad policies, and the bad science that we already are following, used to follow and are considering going back to, or that we might consider in the future.

If you simply MUST develop new ideas and new ways of doing things, please in the name of anything you find holy, write the results down and save them for the next round of research on that topic.  

Researchers!  Instead of thinking of brand new things, how about you settle a few debates?

I know. It's boring.  You want to be "Fresh!" and "New!" and "Creative!" and here I'm asking you to determine the pros and cons of Semester Block vs 4x4 Block vs 40 min (8periods) vs 50 minutes (7periods).

That would be helpful.

Do a lot of research on it. Use a lot of schools and do it with HS students.  Settle the debate we're having at every goddamned school in the country and settle it so definitively that we can all tell our principals to go pound sand if they say something stupid. And make the research available so we can actually read it?

That would be helpful.

How about Proficiency-Based Grading and Graduation Requirements?  Do they work? If so, what did they look like when they did work and when they didn't? Is this just Standards Based Grading updated with a shiny new name for the new decade or is there really something good here?

How about getting into whether we should be taking statewide tests or home-grown final exams?

How about the use of technology in the early grades; in middle grades; in high school?

Don't tell me about your cutting edge research if it doesn't involve multiple grades and a full range of socio-economic levels encompassing thousands of students taking all the courses. (At least tell me what those grades are, in a font just as large as the headline.)

Don't tell me that research has shown that you shouldn't teach the subtraction algorithm ... unless you also tell me that the research was done exclusively on k-4th graders and was somewhat inconclusive.

Why not?  If you remember, I don't teach k-4 grades and my classes really should know the algorithm.

Hattie does this kind of thing all the time and my principals eat it up. Hattie puts out results with this really precise measurement that isn't very accurate. Why is nearly all of Hattie the stuff of nightmares for HS teachers?

Because our principals can't read. They see a big shiny number and say "We should do that, too."

They don't take the time to delve into the conditions of the research and merely assume that we should be changing RIGHT NOW so they can retain their jobs.

My district has gone to a half-day inservice every week to develop new initiatives .. and that's messing up the students something fierce.  We faculty, in the meantime, are going nowhere fast, wandering through tedious and worthless makework that the curriculum coordinator dreams up. Ill-defined terms, vague promises that "This will all make sense" and exercises that belong in a 6th grade classroom the day before Christmas break, all combine to make us want to tear our hair out.

Show me something that WORKED and let me build from that.  If it doesn't work, we need to have some way of reporting that back to the same researchers so others won't have to go through the same disruption and failure.

EVERY school that tries your new idea is now part of the research; all data should be kept. It never is ... in fact education is the only field where all of the research is case-control, the selection bias is ignored, the publication bias is widespread, and the results don't ever seem to matter ... all while the subjects of the research suffer through another set of changes and failures in the vague hope by the administrators that "Someday, we get it right." I'm here to tell you that "Someday" hasn't arrived yet.

My only consolation is that we're not experimenting on my kids.

"But it's backed by research!"

Yeah, show me. Prove it.

In the meantime, I've got to get back to work.

Sunday, December 13, 2015

Foolish Consistency

A discussion with a student at the end of a calculus class began with her saying "I feel that I didn't learn my fractions AT ALL in middle school and elementary school." It made me laugh a little because she was, in the same breath, saying how confident she felt about them now.

And we all know where the errors in calculus are ...

But, her next comment nestled in nicely with something that's been festering in my brain for a while. "My teacher last year had us use calculators way more than you do. He wanted decimal answers instead of √2, decimals instead of fractions. I think I like fractions better than decimals now." (I'm paraphrasing, here.)

Coincidentally, I had had a discussion with him the previous day about why I had given an online quiz on simplifying radical expressions like √300 = 10√3. He didn't see the point while I feel that it's a good thing for algebra 2 students to understand and certainly within their wheelhouse. It helps build the understandings that I feel are important.  Additionally, it's on the SAT, ACT, AP.

His point, equally valid, is that the RealWorldtm is increasingly going digital, demanding numerical answers and using computers to run simulations and solve problems. The diagonal of a square is going to be measured as 14.14 feet, not 10√2 feet.

In reply to my student, I said "We're different ... we focus on slightly different things and both are necessary.  Neither is a better teacher and neither has all the answers, but by having had both you can now apply either approach as appropriate and as suits you.  It would be terrible if you always had the same teacher for your entire career and never saw another point of view, another frame of reference."

Why do I mention this now?

Her comment had resonated with me because we're currently in the process of converting the grading system to Proficiency-Based Grading, and Carnegie Units to Proficiency-Based Graduation Requirements.

Transformations this extensive require long and elaborate discussions about how we measure, about what we measure, about how we justify our decisions to parents and colleges, and about how, whether, and when we teachers will measure.

Because our supervisory district administration aren't really teachers, and our curriculum coordinator used to teach elementary school and some MS social studies, everything must have a rubric or it isn't proper.  As well, everything we used to do was BAD and must be changed.

"We can't use the word 'Proficient' because it's not a growth word."
We're being asked, "Do we use a rubric?  Since your answer should be 'yes', which one of these four is the one you're all going to use?"

The fact that we spent nearly an hour discussing whether to use the word "proficient", "competent", or "skilled", and whether the top level would be modified with "highly", "advanced", or "with distinction" should give you a good idea of how divorced this all was from real students and real teaching. We never did finish that conversation, but we did begin to spend time arguing over whether the four levels should be considered five if there was a checkbox labelled "Not Enough Data to Measure" in addition to Highly 'word', 'word', Nearly 'word', Beginning 'word'.

The funny part is the explicit statement is that we will use the same rubric throughout the building, that every teacher, in every course, for every student, for every transferable skill (the non-content skills), will use the same rubric to determine proficiency.  If any measurement does not use the rubric, it isn't measured properly and cannot be defended as fair and consistent across the board.

This is foolish. A foolish consistency adored by little statesmen.

or, in this case, by administrators.

There are differences between students just as there are differences between teachers.  We cannot maintain absolute control over 18 year-old seniors in the same way we do 10 year-old elementary students. 8th-grade Algebra 1 needs a different approach than 11th-grade Informal Geometry. Some kids thrive on general questions that allow them to explore while others need more algorithmic approaches. We must allow some teachers to holistically judge an essay while others are focused on grammatical issues along with the content.

It wasn't that long ago we were all assured that it was right and proper to be adjusting our teaching to the "learning styles" of the students. Whatever happened to that?

Well, now we are to be consistent. Consistent in our teaching, consistent in our grading, consistent in our departments, consistent between departments, consistent across high schools in the SU.  Everyone consistent. Everyone using the same rubric ... as if a rubric were the only way and that rubric the only acceptable one.

Friends, the pendulum has swung towards "ROBOT", the French army is nowhere near Toledo, and the Inquisition is still safe from its enemies. I'm used to this quinquennial flip-flopping but I don't have to like it.

The Inquisition Administration has looked at teaching and decided that everyone needs to be consistent.  That's pure, unadulterated, bull.

The only consistency we should expect should be within a course ... but even that is muddied by IEPs, behavior plans, 504s, and other, very necessary, adjustments.

Here's the important point: Differences are GOOD.

Diversity in background is GOOD. Differences in approach are GOOD. Sure, you need to have a progression through the department that includes everything you've deemed important, but you also need to have individuals and their strengths.

Way back in the depths of time, when I was in high school, Mr. Corbin would just look at my essay and declare it a "B".  I thought him harsh until I looked at everyone else's in our little complaint session afterwards ... lo and behold, that "B" paper of mine was not as well written as John's "A" paper and was better than Peter's "C" paper.

When it came time to take English from Mr. Clark, we knew the rules changed.  Every grammatical error, no matter how insignificant, meant a full letter grade down.  One spelling mistake turned an "A" paper to a "B" paper.   To add to our teenaged angst, it was timed and, while we knew what day we'd be doing this, we didn't know the topic.  We would walk into the class on Wednesday, see the topic on the board, and then have 45 minutes to produce a page-and-a-half essay. (college-ruled, of course -- not of that wide-lined crap.)

Oh, how we bitched about that ...

... but we did learn to write. 

Was Mr. Clark a better teacher?  I would argue that he was because of his amazing command of the topic and the stories he could tell and the standards he set, but part of what made him good was the preparation we all got from Corbin and the fact that the two men were different. Corbin introduced us to American Lit. Clark introduced us to writers; Thoreau, and Frost, and Jacob Bronowski.  Corbin didn't mark down for minor grammatical mistakes; Clark did. We were students; we adapted. That's what you do.

"Yes, you can borrow this copy of Robert Frost's poetry, but make sure you give it back ... he and I wrote to each other by sending this book back and forth and making margin notes. I'm fond of it."
Trying to impose consistency on these two gentlemen would have been foolish and counter-productive.

Trying to impose a common rubric for AP Calculus and 7th-grade civics is foolish and counter-productive.

Trying to impose consistency even within our department is foolish and counter-productive. He's a math major; I'm an engineer; of course we look at things differently.

He uses the calculators more than I do; I ask for more mental math than he does. "Who's better?" misses the point that, over the course of four years, students get both.

"Who's better?" Why would you even ask that question?

In the long run, I suppose, it doesn't really matter what gets decided in these silly little meetings.  I intend to use the AP scoring style for AP calculus, a variation of it for Algebra 2 and Pre-Calculus and I will probably do many of the same things that I've been doing for years ... the successful things, at least. I don't think I'll ever stop changing subtly.

And that's the point.  When I find something good, an idea from another math teacher or even one of the curriculum people, I insert it into the folder. As it becomes relevant, I work it into the daily routine or the once-a-week, or whatever.

When it comes time to taking advice on how to teach high school math, though, I don't have much tolerance for people who have never taught anyone older than 12 and who couldn't describe a data set graphically if I did it for them ... and they're going to tell me the words I must use and the forms I must use and the rubric I will use to declare proficiency in standards that we haven't even decided upon yet?

Thanks for Reading.
I've got to get back to work.