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.
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 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.
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.