On September 19, 2012 I hit a wall. Having been inspired by Dan Meyer, I had set out to teach magnificently, using ideas and tools found on math-teacher-blogs, and resented that those supposed-to-be-brilliant ideas and tools did not always work as expected. I wrote an email to Mr. Meyer that I tried to make measured and professional, but which was really bursting with distress and anger.
I remember reading in one of your posts that you wondered whether it’s possible to shorten the amount of time it takes for new teachers to start doing things better. My two cents: shortening the improvement period makes it tumultuous and unreliable. I work at a small school with a weak math program and a student body made up entirely of students with IEPs. I blog, read blogs, and talk to teachers outside my discipline to enhance the instruction I give. My pie in the sky was to reduce the amount of time it takes me to get better to zero. That was obviously a long shot.
I crave the opportunity to work closely with an expert teacher, to observe and be mentored by him/her, but instead I engage in a constant trial-and-error method of implementing the ideas I find in blogs while crossing my fingers that I understood what the blogger intended and that the ideas are transferable to my unique student population. I guess the trial and error aspect would stick around even with an expert mentor teacher, but at least I’d have a leg up.
You spent two years (or so) establishing yourself as a teacher before you branched away from familiar methods. My situation tells me that those two years were invaluable to your success upon branching away. I don’t want to wait two years but I don’t especially enjoy the alternative.
Unguided trial and error succeed in making me (a newbie) a better teacher on some days and advances me toward being a consistently better teacher in the future, but the overall immediate effect is that my approach is inconsistent and unsure. Oh, I don’t like that feeling. I’m not sure it benefits my students either. So my working conclusion is that reducing the time it takes to get better can only be done by increasing the badness of the intervening time.
Have you found something different to be true among the teachers you know?
Mr. Meyer responded considerately, and I sought support from colleagues at my school. This isn’t the end of the story. Just a snapshot.
Last June I wrote oh so enthusiastically about the homework policy I planned to implement in trig this year, which I had borrowed from one of my college math professors. It was going to basically change the world. Until I abandoned it only a few weeks into the school year. Wisely.
This year was funny that way. So many of my theoretically solid plans turned out to be worth bupkis in actual practice and had to be tossed. But, also in practice, I picked up ideas, plans, strategies worth far more than anything I thought I had before.
I haven’t posted here since September, partly because of time, priorities, stress, etc., and partly because it was then that I bore the heaviest load of inadequacy awareness. I had learned just enough to know that my “insights” into teaching could well turn out to be that much rubbish, and it seemed that my options for publishing posts were to either pretend to greater wisdom than I had or fill them with nauseating angst.
But here I am in May! With a list of things I’d like to reflect on in writing! And enough objectivity, despite my still-new-ness, to give it all, I think, a fair shake! Expect to hear more.
I’m about five weeks into the school year, so for about five weeks now, whenever I have a really good day in class I tell myself, “Jeepers, I’m pretty remarkable. I guess I’ve hit my stride as a math teacher now and am going to keep being remarkable from here on out.”
Then, the next time I have a doldrum-y day, I worry and fuss over what went wrong, what I need to do differently. And at some point I reassure myself that “I’m still settling into the role, the new students, the odd classroom situation, etc. But I’ve got really good stuff coming up, so don’t worry — I’m gonna hit my stride and start bringing the house down with my general excellence.”
I’ve been devotedly trying out ideas I get from esteemed math teacher-bloggers, but there’s a limit to how effectively I can implement methods born of experience when I have very little. I still want to try them. I just flounder a bit as I do.
My Trig-ers are preparing for their second test of the year. I accidentally did something funky with this unit, which has complicated the test prep process for them. It’s possible that it could improve their long-term info retention, but I’ll have to see whether the improvement is worth doing it this way again.
I began teaching the first unit (a review of the final material from their last math class) overestimating the amount they’d remember from last year, underestimating the difficulty of schoolwork re-entry, and not realizing that the previous trig teacher (whose reviews and tests I’m using) split this unit in two.
That last error led me to push the students through the entire unit before telling them to go back and review only the first half of what we covered. After reviewing and being tested on that half, they began reviewing the second half, which is recent enough that instruction about it is now boring, but distant enough that they were all relatively lost. I gave a valiant effort at stepping them back through the material, but observed that even the most diligent among them were intellectually zonked out. So I stopped, and set them loose on some review problems.
Cons: the class seems unorganized and confusing. Possible pros: hitting the material twice, with a bit of a break between, could improve their long-term retention. Their test is on Monday and I wish them the very best.
I’m doing some things in my trig class differently from what my students are used to. For example, instead of showing them how to multiply a trinomial and a binomial, I reviewed how to multiply two binomials and then asked them to figure out how do it with a trinomial. I answered questions and gave support but did not give instructions. I did this for two reasons: first, it’s important for students to view math as a way of figuring things out, not a list of disjointed procedures. Second, in Brain Rules by John Medina, which all teachers at my school read over the summer, Medina explains that simple things are actually harder to remember, while complex things (like applying a concept to a new situation without comprehensive directions) are actually easier to remember.
Some students (I’m thinking of one in particular) are unexpectedly thriving in this new atmosphere and love the change. Others are ambivalent. Others (again, I’m thinking of one in particular) seem frustrated that the familiar math class landscape has changed, leaving them uncertain of how to proceed.
I’m crossing my fingers that I can help them appreciate this more meaningful challenge.
The trig gears were grinding clumsily today. Disappointing after a smooth(ish) and ambitious start. My problem is two-fold and self-contradictory. I both over- and under-estimated my students. In the same lesson. Using the very same slides. Then I grew impatient.
Maybe I oughta get myself a ukelele (channeling Sarcasymptote) to help us all chill out a bit.
I actually had a great time in Algebra II, working with students, bringing the math out, and having a laugh, maybe because I was working with students I’ve already taught. But the trig flop is winning the battle for preeminence in my thoughts.
I came across this article on the Planet Money blog last week: “Why Einstein Was Not Qualified to Teach High-School Physics.” (The answer: because he didn’t hold the required teacher certifications.)
My initial reaction is, “Careful, now. Einstein was a legendary physicist, but I can’t say whether he would have made an effective high school physics teacher.” Then again, can I say that all those carrying secondary teaching certificates now make effective high school teachers? A perplexing issue, right? Do teaching certification requirements ensure quality classroom instruction, or prevent great teachers from entering the profession?
Here’s where I stand. Education about education is essential for those who teach, but school systems should be in the business of maximizing the ways that talented people can enter the field.
Here’s my bias: I’m one of those people benefiting from a non-traditional entrance into teaching. I’m not yet certified but have plans to change that, and am an enthusiastic advocate of replicating in public schools the apprenticeship style of entry I experienced at a private school. If schools want to gain access to a large demographic of ambitious adults seeking employment and eager to learn a profession, they need to create entry level positions that can be filled by young college grads looking for work, who are potentially interested in teaching but not ed majors. (For me this was the “support teacher” position.) Let them learn some of the tricks of the trade, work with teachers and students, and find out whether their interest is more than fleeting before they have to fully commit to the profession. Schools would benefit from the chance to observe some of their aptitudes on the job before making a full commitment as well.
As these employees acquired experience and skill, they would be promoted to increasingly responsible positions on the condition that they seek any necessary certifications. This would be a more organic entry into the profession and would better match much of the rest of the workforce, where you climb the ranks by showing that you’re good at your job.
The trig students gushed unforeseen excitement about seeing me derive the Law of Sines today. They loved it! My plain old plan for it had been this:
- Go through derivation clearly but quickly so students see a connection between SOHCAHTOA and sinA/a=sinB/b=sinC/c
- Demonstrate using the LoS to solve a triangle
- Have students practice solving a triangle using LoS (make sure they do the practice problem)
Little did I know that step one would be so energizing and fascinating to them! Although I told them they would not have to reproduce the derivation, students who normally forget the proper function of notebook paper were furiously copying down the steps, asking questions (“In the area equations, what represents the height?” “What’s the pattern of the letters in the different equations?” “Why is it that way?”), and answering other students’ questions.
My favorite moment was when I asked the class, “Does everyone understand how I went from this to this?” A pedagogically poor question, it has traditionally been answered by silence, a dull or uncertain “Yeah,” or even a perturbed “We get it.” Today in my class it was answered by, “Yeah, you broke off that part and everything cancelled out except the a on the bottom.” The language is not terribly specific or mathematical, but it’s far more so than any of the traditional replies.
I wonder whether all derivations would strike these students as forcefully, or whether this one was especially suited to the task. Either way, I slapped a sticky note down on my lesson plan to remind myself to hit it out of the park again next year.
Yesterday my trig class worked on a genuinely interesting problem, but as I described what we were trying to find, one student asked that hated question, “Why would anyone want to do that? They could just ________________[insert non-math route to the same information, perhaps reasonable, perhaps not].” In hindsight I see that the student was actually enjoying class, that he asked the question not from pure frustration, but playfully, hoping to elicit fun banter from myself and the other students. And yet. And yet it just plain irked me to have prepared and presented an intriguing problem only to encounter this response in the key of whine.
Tell me, how should I have responded? Should I welcome the question because it’s an opportunity to make the case for mathematics? Should I establish a class culture that eschews that question in favor of more productive ones? Or should I put up with the question, acknowledging that I work in a high school and must occasionally partake of the culture of complaint?
Along the same lines: As a support teacher I sometimes step in as a substitute, which I recently did in the geometry class I “support.” This time when I convened the group they were attentive and engaged rather than giving me the wake-me-when-we-have-a-real-teacher-again attitude I’ve received from them in the past. But almost instantly upon deciding they respect me, they delivered the question: “Why do we have to learn geometry?” which exploded into, “I don’t get why we have to learn history,” “Yeah, and why do we have to learn physical science?” Fortunately, one student held everyone at the level of a respectable discussion instead of descending into pure lamentation (oddly, the student who led the wake-me-when-we-have-a-real-teacher movement is the same one who led the come-on-guys-let’s-keep-this-respectable movement), but really? How do I defend the worth of their entire education to students (all of whom have some kind of learning disability, remember) when my only instructions were to review the triangle congruence postulates? Sincerely seeking input.
The goal of teaching LD students is to make information, etc., accessible, but there is a risk of becoming too eager to give “help” when these students struggle. The result is a cluster of students who plead for help even when they can succeed without it, who throw their hands up at the slightest sign of struggle, who demand assurance after every thought, who insist that the teacher stand beside them while they work, just in case.
Realizing that I could do more to discourage such dependency, I’ve adopted a new habit of stalling when certain students ask for help with their work. I protest that it will take me some time to finish what I’m doing and that they should solve the problem as best they can without me—even if they’re unsure—and that we’ll discuss how they solved it when I make my way over to them. Or, at the very least, that they should skip that problem and move on rather than sitting immobile, waiting for teacher.