I really like our late start; why the hell are so many school districts kicking off in early August? (They want higher test scores, Ed.)
Anyway, I’m teaching trigonometry for the first time. In every course, I assess my kids on algebra I, varying the difficulty of the approach based on the level of math. What to do with trig? My precalc assessment was too hard, my normal algebra assessment too easy—or was it? I didn’t want to discourage them on the first day, but I also didn’t want to give a test that gave them the wrong idea about the class’s difficulty level. After much internal debate, I created a simplified version of an early algebra 2/trig quiz. I dropped the quadratics (we only had 45 minutes). Then, just to be safe, I made backup copies of my algebra pre-assessment. If the kids squawked and gave too much of the “this is too hard” whine, I’d be ready.
And so in they came, 23 guys, many of them burly, a few of them black, none of them both, and 11 girls. Fully half the students I’d taught before, two of them I was teaching for the third time. (one poor junior has only had one high school math teacher.) Perhaps their familiarity with me helped, but for whatever reason they charged right in and demonstrated understanding of linear equations, systems, a shaky understanding of inequalities, and willingness to think through a simple word problem. Good enough. Great class—rambunctious, enthusiastic, way too talkative, but mostly getting the job done.
I’m still not much of a planner, which is why I gave no thought to my trig sequencing until I saw how they did with the assessments. If they’d tanked, I would have done a simple geometry activity to give me time to regroup, start after the weekend with some algebra. But they didn’t tank, so how did I want to start?
Special Rights. Definitely. I would use special rights to lead to right triangle trig. All clear. But how to get to special rights? Algebraic proof of the ratios. But why special rights? It seems random to start there. As long as I’m going to be random, and since trigonometry has something to do around the edges with right triangles, why not start with right triangles? At that moment, this image popped into my head:
Hey. One step back to geometric mean, and I’ve got a nice intro unit all set up.
So the next day, I started with this:
Note: I told them the questions were separate—that is, the square was equal only to the area in #1 and only to the perimeter in #2.
I wasn’t happy with the questions. They gave too much away. But every rewrite I tried was even more confusing, and in a couple cases I wasn’t sure it was an accurate question. Besides, on the second day of school, you want to release to something achievable. Better too straightforward than have the kids feel helpless this early.
And it went great. Top kids finished in under five minutes; I had them test out the process for cubes vs rectangular prisms. All the rest completed the work in 15 minutes or less, with some needing a bit of reassurance.
I had to prompt them to recognize that the perimeter to side relationship is the “average” algorithm (that is, the arithmetic mean). “If I add two numbers and divide by 2, what is the result?” I think I noodged for a few minutes before someone ventured a guess.
I followed with a brief description of geometric mean, reminded them of the various measures of central tendencies, pointed out that now they all knew why the SAT followed “average” with arithmetic mean. Finished up with practice problems.
I was stumped briefly when a student noticed that the arithmetic mean always seemed larger. Argghh, I’d mean to look that up. I told them I’d look up the answer and get back to them. Meanwhile, I wondered, could the two means ever be equal? I made the stronger kids do some algebra, and let the others just talk it through.
Great lesson, not so much from the content, but from the energy. Look, I was winging it. I do that when I have a good idea that isn’t fully fleshed out. I cut back goals, keep things very simple, and watch for opportunities. I always advise new teachers to avoid mapping things out—they are often wasting time, because things will go off the rails early in some cases. Keep it broad, tell the kids that you’ll adjust if needed, and go.
The rest of the opening “unit”: a brief review of similarity and then use of geometric means in right triangles, leading to my favorite of the Pythagorean proofs. Then onto special right triangles, deriving the ratios algebraically. This puts things nicely in position for introduction of right triangle trig and I can drop in a quiz. Well, I’ll probably put in a day of word problems first.
After school today I ran into a group of football players waiting for practice to start, many of them previous students and two of them currently in that trig class. After hearing what they were all up to, how their summers had panned out, what the team’s chances were, Ronnie, one of the two current students, said, “I’m glad I have you; I would hate to be dumped for low grades my senior year.”
“Ah, yes, that’s my claim to fame. I’m not a great teacher, but by golly, I give passing grades.”
Shoney, the other of the two, a big, burly, not black senior, was laying along a school bench calmly watching the conversation, and spoke for the first time.
“You know. Trig was….fun today. It really was.”
The point is not oh, gosh, Ed is a fabulous teacher who makes kids love math. That’s never my goal, and it’s not what Shoney meant.
Recently, Steve Sailer writes that “school teaching can be thought of as a very unglamorous form of show biz, which involves stand-up performers (teachers) trying to make powerful connections with their audiences (students)”. He’s right. Education and entertainment are both, ultimately, forms of information transmission.
His next paragraph is dead on, too:
We are not surprised that some entertainers are better than other entertainers, nor are we surprised that some entertainers connect best with certain audiences, nor that entertainers go in and out of fashion in terms of influencing audiences. Moreover, the performances are sensitive to all the supporting infrastructure that performers may or may not need, such as good scripts, good publicity, and general social attitudes about their kind of performance.
People tend to construe the “education as entertainment” paradigm as “show the kids movies all day” or “keep the kids laughing”, but just as all entertainment isn’t comedy and happy endings, so too is education more than just giving the kids what they want.
I’m a teacher. I create learning events. I convince my audience to suspend disbelief, to engage. Learning happens in that moment. Some of the knowledge sticks. Other times, only the memory of learning remains, and I’m starting to count that as a win.
And so the year begins.
August 29th, 2014 at 1:01 pm
[…] Source: Education Realist […]
August 29th, 2014 at 3:18 pm
My mother is still thanked by former students (almost 50 years ago) who indicate that with her skills (particularly, emotional intelligence) they were able to succeed and move-on with their lives. She was their favorite, pivotal teacher.
She taught something akin to AP English…and always kept a discrete “open door” to understand when assignments were late or incomplete. Some of her students had dysfunctional parents…serious farm-work after school, poverty, neglect. She also discretely, gave away my father’s spare clothes/shoes. The “American” clothes were particularly appealing.
So, I would say she was entertaining (she said she was just very young and enthusiastic in front of the class) but, just as importantly, she was a great listener, and still is. She was not a big believer in homework (my sons love that when I told them this factoid,) and tended to give very specific, light home work. She wanted a few nuggets to be put on paper so she knew her students were also listening and grasping pertinent information from a 4′-11″ teacher (despite wearing high heels) since she wasn’t particularly funny, but was so, so sincere. She still blushes when her 55-65 year-old former students find her in town. So, yeah, listening AND being funny would be the ultimate combination.
August 30th, 2014 at 4:12 am
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August 30th, 2014 at 4:34 am
Weird. It was there before. I fixed it, or think I did.
August 30th, 2014 at 5:16 am
I’m working on getting students to work in teams and wrestle with challenging problems. It didn’t go too well with the first problem I gave them, and I’m teaching by guiding this year, or at least trying that. When I released the teams to work on the problem, I didn’t hear a single conversation for some time. So, I’ve got to figure out how to get the communication working.
They struggled with “If a woman buys three pieces of turkey that weigh 1/3 of a pound, and her diet allows her to eat 1/4 of a pound, how many slices can she eat?” I didn’t keep the frustration level low the first week of school, but one student yelled, “Now I get it!”
I also threw in a real problem where I hired a maid to clean my house for 6 hours @ $109.. When she showed up, she brought another person who worked alongside her and about half as hard. These two ended up working only three hours together and wanted the same price. I called the owner and mentioned that I expected one person to work six hours. My students saw the problem with two workers not working at the same speed, and I asked them to figure out what I should have paid.
Have a successful and fun time working with the kids this year.
August 31st, 2014 at 10:38 pm
[…] lesson would rarely be included in a typical trig class, whether reform or traditional. I described the thinking that led to the sequence. But it’s a good example of what I do. (Also, as many bloggers have […]
September 7th, 2014 at 4:35 am
So why do so many districts start in August instead of pushing later into June, when it’s not as hot? I asked a teacher friend of mine, and she said it’s because the Filipino families all travel during June, and the schools would lose too much money from absences if they made the school year later.
September 7th, 2014 at 4:38 am
No, I think it’s testing. Testing is usually in mid-April, so they want as much school time as possible.
September 11th, 2014 at 9:16 am
[…] Another entry in “teacher as entertainer”: […]
November 1st, 2015 at 9:03 am
[…] I am often somewhat ruthlessly focused on one objective. As I’ve said before, teaching is a performance art, and the act of engaging students to convince them to learn is often an arduous mental […]
February 8th, 2016 at 3:15 am
[…] performer in my trig class, convinced me to let him TA, and then another favorite football player, Ronnie, begged me for a chance. I figured I may as well spend time with students whose company I actually […]
May 6th, 2016 at 12:22 pm
[…] Anyway, the story goes on with a second great moment, but I’m getting better at chunking and this half had too many details I didn’t want to give up. I’ll stop here for dramatic effect. Because oh, lord, I was high as a kite in this moment, watching the room, realizing I was riding a tremendous wave of energy and excitement. Yeah. ME. On Stage. Making Drama. […]
May 20th, 2016 at 7:35 pm
[…] like math, isn’t aspirin. It’s not medicine. It’s not a cure. It is an art enhanced by skills appropriate to the situation and medium, that will achieve all outcomes […]
November 26th, 2016 at 11:38 pm
[…] and straight discussion lecture lies a lot of ground for productive, memorable teaching. In my opinion, good teachers don’t just transmit information, but create learning events, moments that […]