Tag Archives: teaching

What I Learned: Year 2

Year 2 was all algebra, all the time. Few things are as draining—or as revealing of the utter emptiness of our educational policy—as teaching algebra I in high school.

The epiphany moment: Realizing that kids could distribute and combine terms but lack the skills to work the steps in combination. I noted this in first year, and just the hint of its return in the fall led to the development of the Multi-Step Equation Drill Down and the mantra “Distribute-Combine-Isolate”.

Technically, this process is called a “reteach”, but another thing I learned that year is that done well, a reteach is much more than reviewing the same material. Once I realized, less than a month after covering equations, that most of the kids could solve 3(x+5)=18 but not 3x+2(x-7) + 6 = 6x – 2, I didn’t drop everything. I finished up with linear equations and considered the best way to move on this. The problem wasn’t the individual steps, but the confusion that resulted when using the processes in combination. So why reteach? Instead, I just explained to the kids where their confusion started, by using a problem set similar to the one above.

When done properly, the kids are totally on board. The minute I put the two problems up and demonstrated common mistakes, I had their attention because they were bothered by it, too. Which is a bit weird, because trust me, I can list a million things that kids don’t get about algebra. And yet, the kids know the difference between something they completely don’t understand and something they vaguely feel they should understand, but don’t. The confusion they felt during a complicated multistep equation fell firmly into the latter area.

I learned that even unmotivated students have this, dare I say, inchoate yearning to having confusing areas clarified. Spotting these areas and drilling down gives the students faith in their teacher. They can see the teacher is paying attention to mistakes, distinguishing between utter confusion and “man, I almost got this but sojmething’s wrong”.

And the performance pop from these clarifications is huge. The majority of mid-level ability kids never lost the DCI clarity. I attribute this to the time spent in the darkness, followed by the blazing light of knowledge. Or maybe I just pick my moments well.

Never fear, most of them still struggled with “is this slope negative or positive?” Alas, that confusion has nothing to do with procedural confusion.

Other things I learned:

  • Data Collection and Analysis: as a long-time analyst, I knew how to evaluate the data, but this was the first year I had the opportunity to gather and compare the data.
  • I always differentiate instruction, but in Year 2, I ran 4 different lesson plans at all times. This led me to realize that teachers can pick their discomfort. For me, watching kids be either lost or bored leads to far greater stress than the work involved in running four classes simultaneously.
  • Low ability students: In algebra I, you often get kids who literally do no work, or who scribble frantically but clearly have no clue. At the end of the first semester, I put them on a contract. I would pass them if they demonstrated competency in five high-leverage areas: linear equations, quadratics, multistep equations, and simple systems.

    I didn’t need to use it in Year 3, but I strongly recommend this approach. Motivation among my low ability kids increased dramatically. Even the kids who ultimately failed due to attendance issues saw a big bump in their ability to solve multi-step equations and factor quadratics.

Some earlier posts that expand on these issues: Teaching Algebra I and Teaching Algebra, or Banging Your Head with a Whiteboard


Teaching Humanities, History of Elizabethan Theater, (III)

Days 1 and 2, and 3 and 4.

Day 4 part I: Recreating History
Students use their notes and documents from Day 3 to sketch the details of an Elizabethan era theater. Fishbowl discussion: what did they sketch for seats? What about curtains? What did “backstage” look like? How do historians “fill in the blanks” when they don’t have primary evidence to point them in the right direction?

After the discussion, students took a virtual tour of the Globe theater. How would someone go about establishing the source material and accuracy of this tour?

No deliverable here. I just wanted the kids to grasp the choices involved in recreating history, whether it be for a book, a movie, or simply an image. I thought something familiar and specific would give them a better idea of how many thousands of decisions are involved in filling in those blanks. And while I can offer no tangible proof that this worked, I can say that every student had that “aha” moment, when they realized how much they didn’t know, and how every decision in a recreation can further affect our general understanding of history. The discussions were active and everyone was engaged; we had some great exchanges. One of my delightful ditzes suddenly realized she couldn’t assume that there would be bathroom stalls.

“But….the plays could be hours. What would they do? Go back outside? What if they were way up front?”

“Maybe they had pots,” offered a classmate.

I broke in with a brief history of the chamberpots.

Another student’s eyes widened. “Hey, maybe that’s where the phrase comes from–they didn’t have a”

“pot to pee in!” the class choruses.

“What about the actors, though? They had to have at least one bathroom. They didn’t even need girls’ bathrooms, right?”

One of my top historians pointed out, “But look, they didn’t even have running water back then. Did they even have toilets?”

“When did they get toilets?”

I gave them the story of Thomas Crapper and ended the segment during the ensuing hilarity.

Underneath all the fun, they really did get an inkling of the challenges involved in understanding the past. And, of course, some potty jokes.

Day 4 part II: Sonnets
Lecture on the sonnet, including its history and the two major styles (Petrarchan and Shakespearean). Students listen to five sonnets written from Shakespearean to modern times, and write responses to each. They identify the link between one of the sonnets and a modern song.

I am not a cut-and-dried planner. I’d always known that this unit would have a sonnets lesson. I’d vaguely thought of them reading the poems, which seemed unsatisfactory but I figured something would occur to me. The “something” waited until 30 minutes before class time, when I suddenly realized how much the sound of the sonnets would add to the experience, and so spent a frenetic half hour hunting down them all (mostly on youtube).

After all that, though, it went beautifully.

Day 5 and 6: Shakespeare in Love

They got all the jokes. They didn’t giggle at the sex scenes. They were engrossed by the story. They enjoyed the movie, understood the movie, and were completely aware that enjoyment and understanding came from their new content knowledge. I could tell.

So if I have a disappointment, it’s only that I would have preferred they’d be blown away by the movie. I am a film propagandist who shows movies that students would never think of watching and are nonetheless enthralled. I’m very good at this, so when I could tell that they just enjoyed the movie, it felt like a letdown.

In retrospect, though, Shakespeare in Love isn’t really a propaganda film; I’d never deliberately try to sell it to early teens. In this case, it was curriculum. And from that perspective, it worked beautifully.

Note: My kids had all been approved for R-Rated films for health class. I doubt most teachers could get away with showing SiL to freshmen otherwise.

Day 7: Content Knowledge and Art
Students write an essay on this prompt: “To what extent did content knowledge help you appreciate Shakespeare in Love?”

In fact, I had seen the answer in their faces as they watched the movie, but I wanted them to think about it.

SilFinal


Teaching Humanities, History of Elizabethan Theater (II)

See Days 1 and 2, if you’re interested.

Day 3 Part I: Elizabethan Theater Who’s Who
Students, grouped roughly by ability and content knowledge, were given different readings about key figures in the era. After reading, taking notes, and discussing, they created posters about their subject(s). The lesson ended with a “gallery walk” in which the students take notes about the key figures who weren’t part of their reading.

Yes, posters. Given my druthers, I’d have given them all four readings and 25 minutes to peruse, followed by a class discussion. But there you go. Well over half of all students I’ve worked with love making posters, and I always commiserate with the ones who don’t.

This lesson uses a form of “jigsawing”; as I’ve mentioned before, while most trendy math teaching techniques are hooey, I’ve become fond of more than a few used in history and English. Jigsawing is a terrific way to provide content by ability group. In this case, it allowed me to make sure that the students focused in on the content area most appropriate to their abilities.

So my weakest kids got the Shakespeare reading, because I wanted them to get a solid grasp on who he was, what he’d written, and some important quotes. If that was all they got from the exercise, that was a good get. Next group of kids up, I figured would be able to get the key ideas about Shakespeare from the poster, so I had them focus on the other Elizabethan playwrights. That way, they’d get some solid new information on Marlowe, Kidd, and Webster, whilst still picking up the key facts about Shakespeare. Again, if that was all they got, terrific.

Next group up, I knew, would be interested in learning about the new playwrights and would pick up the content from the poster–so they got the actors. The strongest group got Henslowe and Tilney, and the responsibility of figuring out what it was they did.

I know I’ve said this before, but I really wish I’d had an android back then, since the posters were stunningly good—not just in terms of artistic value, but in terms of how the students incorporated the readings into their posters.

In the gallery walk, each group took turns explaining their subject to the others, so they could take notes. I quizzed everyone it later, but I can’t find that document. They all knew enough to laugh at John Webster as the young boy with a violence fetish, and several were sad knowing that Marlowe must die, so the content definitely filtered in.

Day 3, Part II: Theater and its Impact on the Economy
Students reviewed pages of Philip Henslowe’s diary. What evidence did this primary document provide to support the claim that Henslowe was a producer who worked with some of the key playwrights of the day?

Using diary entries, write an essay supporting or contradicting this assertion: “The rise of the theatrical industry probably had a positive impact on London’s economy.”

I’m not sure if the pages in the attachment the pages I actually used. I spent several hours looking for three or four pages that would give them a wealth of evidence for both parts.

This was definitely an activity I designed primarily for the stronger students, and their essays showed they appreciated the challenge. However, all the students were interested. Much chortling when they discovered how much time Henslowe spent with his lawyers and on “copywrighte”.

Day 4: History In Motion
Reading and lecture on the constantly changing nature of “history”. Not only does it keep on building up, but we keep discovering more about our past. Students learn of the Swan drawing, by Johanes de Witt, which wasn’t discovered until 300 years later. Then, 30 years ago, a routine building excavation led to the discovery of Philip Henslowe’s Rose Theatre–and then the Globe was quickly located as well. But is there a cost to these discoveries? Students discuss the impact of living in a historical site.

This is the third really cool “primary” document (well, a copy of one) that I found for this unit, and I spent much of my own time researching it because it’s exactly the sort of tidbit I find fascinating.

What we know of the London theatres of Shakespeare’s age is, to a disproportionately large extent, due to the records such as diary entries left by tourists….Two of these tourists are Johannes de Witt and Aernout van Buchell, friends from the city of Utrecht, the Netherlands….To them we owe the best piece of visual evidence of what an Elizabethan theatre looked like on the inside: the sketch of the Swan theatre on Bankside, along with a brief Latin text describing the London theatre scene….First of all, it is unclear precisely what each of the two friends contributed. We do know that de Witt travelled to London, probably at some time between 1596 and 1598, and visited some theatres there, including the Swan; at some later point, he apparently gave (or sent) his sketch and written ‘Observations’ to his friend van Buchell, who copied the drawing as well as the text–or part of it. It is van Buchell’s notebook that now survives in the Utrecht University Library……There is no evidence that de Witt’s information had an immediate impact on his own culture. Sure enough, van Buchell made a copy of (some of) the information, but he never published it. Not that he was merely a collector of information for his own amusement; the documents he gathered, the facts and impressions he noted down, were made available to fellow scholars on demand for future generations. But for practical purposes, van Buchell’s main function as a go-between lies in transmitting de Witt’s sketch and observations to posterity. For some 300 years, the notebook gathered dust in libraries, until it was discovered by the German scholar Karl Theodore Gaedertz in 1888.

(Source: Renaissance go-betweens:
cultural exchange in early modern Europe
(page 79-81)

So. For centuries, we had no actual image of an Elizabethan theater. Then, for a few generations, the de Witt drawing was all we had, until The Rose was discovered, and once they had that location pinpointed, finding the Globe was pretty easy (hell, my kids found them using a 400 year old map). The past just won’t have the decency to sit still.

And yet, what of the developers? Lucky them! Their business plans had to be postponed; they had to incur additional expense to protect the Rose “until a future date”. Their building had to be suspended over the excavation. and what, exactly, will that do to the retail value of their property? Good, if the rich movie stars propose to buy it out. Bad, if the efforts never get far enough to the purchase level but stay at the annoyance level.

I told the kids about a hospital in my area moving from its old space to an empty lot that held the last orchard in an area that once was devoted to farming. I mean, couldn’t they have moved it anywhere? This orchard had somehow lasted that long, couldn’t we preserve it as the last little piece of heritage in the area?

On the other hand, the hospital can’t move there, it moves to another town, and bye bye jobs and property taxes. Discuss the degree to which we should interfere with business development in order to protect our past.

The essays were great. Heartless guttersnipes all. “Hey, it’s only trees!” “They lasted for 400 years without the theaters. What’s the big deal?”

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Teaching Humanities, History of Elizabethan Theater (I)

Writing up the Twelfth Night unit reminded me how much fun I’d had and how thoroughly the students had learned the material. I need no reminding with my Elizabethan history unit, which is still the single finest two-week period I’ve ever had as a teacher.

Learning Objective: Students can discuss the milestones of the transition from mysteries to plays, and provide the rationale for the development of physical theaters. They can identify the tensions involved when archaelogical remains don’t have the courtesy to become inactive, but just keep inconsiderately piling on history unto the present. They can identify the key Elizabethan playwrights and theater personnel. They know how many lines are in a sonnet.

Secondary Objective: They would understand every in-joke in Shakespeare in Love, which they’d watch at the end of the unit.

Day 1: Lecture on the development history of Western European theater, which disappeared entirely after the fall of the Roman Empire for over five hundred years, until it returned again in the form of “mysteries”, the performance of Biblical scenes, and slowly developed into the morality plays of the late Middle Ages. During the Renaissance era, the morality plays developed slowly into plays written more purely for entertainment, and thus were born both the acting profession and the theater (which allowed the actors to collect money from their audience). The lecture covered the development of the first theater (started by James Burbage, as we all know from SiL) through to the great razing of the theaters in the mid-1600s.

I can’t find my lecture notes, but the gist can be derived from the handout:
It must be said: I give a great lecture, and am particularly good, I think, at making the kids see developments as interesting when they’d never before given them a thought. Movies are a huge part of their lives, and before movies there were plays. But how did plays start? I often test attention by popping in questions during the talk, and the kids were all right there with me.

“So you had these acting troupes traveling from town to town, acting out these morality plays to big audiences, whereas before, the churches themselves put on the mysteries. How would that change things, Meg?”

“Well, the church is religious, and the actors aren’t.”

“Okay, and how would that matter? Renee, your hand is up.”

“The church probably had priests who acted!”

“Okay, and what does that mean? Think about the difference between a priest and and actor. Isaac?”

“The actors would need money, right? The Church had money already.”

Ian said, “Yes, they’d have to get money. How do you get money if it’s just a big crowd?”

“You pass the hat,” said Dom, “like they do in the movies.”

“You can’t pass the hat if you’ve got hundreds of people in the audience,” said Kayla.

“And what if no one wants to pay? How would they make money?” asked Sheena.

“Wow. You all are taking my lecture away from me. You’re right about the differences, the money, and passing the hat works well as a voluntary payment for small groups, but if actors were going to make a business of it, it’d be really convenient to have, oh, I don’t know, maybe a building? To let people in after they’ve paid? Otherwise known as….”

“Theaters!” they chorused.

The handouts, as well as their work over the next week, confirmed that this stuck with them.

Day 2: Using Primary Documents
Students had to map out the theaters of London during the Elizabethan era, using the “Agas Map” (Civitas Londinium). They had a handout with descriptions of theater locations, and they had to use the big map as well as the map on their handout to place all the theaters. When they finished, they checked their work against the placement based on current historical knowledge.

I printed out the Agas Map of London in 32 full page sections, which I then glued together. And trust me, crafts ain’t my thang, usually. But it was worth it, if only for the great visual. It’s a gorgeous map.

These were the clues:

Here’s the map they used to check their work:

Doing it again, I’d have magnifying glasses to read the Agas map more clearly. Still, it was a successful day. The students, working in pairs, found all the theaters and enjoyed the scavenger hunt aspect.

To be continued….


Test Pattern

The polynomial quiz results were fantastic. Over half the class got a perfect score; no one outright failed–that is, all of the students did at least one of the four problems correctly.

Which brings up something that I’ve been bothered by for a while: around a dozen of my algebra II students are nailing the quizzes and failing the tests, or close to it.

All of the students showing this pattern are hard workers. Some have shown strong math skills; a few of them struggle but patiently work things out. I know they are discouraged by their low test scores, and I’ve been encouraging, but puzzled.

Certainly, I expect some fall-off between quizzes and tests. My quizzes are directly on point with no surprises. I give problems exactly like the ones we’ve been working in class. My tests slant off sideways and crisscross (my geometry students constantly whine about this). Some of the strugglers might get flummoxed when the problems don’t appear in exactly the same form, sure. But others of these students are well beyond that. They work the toughest problems of the day with minimal guidance; when they have questions, they are logical and structured.

I don’t know what’s going on, but since all the students in question did excellent work on the last quiz, I decided it was time to step up to the problem. Rather than try to set up time with them individually, I just made an announcement in class when I returned the quiz.

“If you are a student who is looking down at an A on this quiz, but got a C or worse on the last test, I want you to know that I’ve noticed this pattern–great on quizzes, near-disaster on tests. So here’s the deal: I will be adjusting your grade on the next progress report. It’s now clear to me that something about the test is causing you problems, not the math itself.”

“BUT. You must schedule time to come in after our next test and work quietly, either at lunch or after school, so I can watch you and see what’s going on when you take tests. I’ve invited everyone to do that after every test, but for you guys, it’s mandatory if you want a grade adjustment. You can’t keep going through life tanking important tests when it’s clear you know more.”

In all three classes, I scanned the room as I said this, and every one of those dozen students looked up in hope and relief.

Which makes me a bit sad. It’s not like they haven’t had this option all along. Why don’t they take advantage of it? Why wait until I mandate it?

But it also reminds me that no matter how many times I think I’ve made it clear that my door is open, help is here, even on tests—I haven’t said it enough.


Discovery Doesn’t Work

I had trouble in ed school because (well, at least in my view of it) I openly disdained the primary tenets of progressive education. I am pro-tracking, anti-constructivist, and pro-testing, all of which put me at odds with progressives. Here is the irony: I mention often that I am a squishy teacher (squishy=touchy feely). I am not just squishy for a math teacher, I’m the squishiest damn math teacher from my cohort at the elite, relatively progressive ed school that made my life very difficult. My supervisor, who knew me first as a student in a curriculum class, was genuinely shocked to learn that I didn’t talk at my kids in lecture form for 45 minutes or more, given my oft-expressed disagreement with discovery. Even my lectures are more classroom back and forth than me yammering for minutes on end. (In fact, my teaching style did much to save me at ed school, but that’s a different story.)

Here is what I mean by squishy: My kids sit in groups, not rows. When I set them to practicing, which is usually 20-35 minutes of class, they are allowed to work independently, in pairs, or as a group of four. I often use manipulatives to demonstrate important math facts. My explanations are, god help me, “accessible”. I don’t just identify the opposite, adjacent, and hypotenuse and then lay out the ratios. No, I’ve been mentioning opposite, adjacent and hypotenuse for weeks, whenever I talked about special rights. I introduce trig by drawing a line with a rise of 4, a run of 3, and demonstrate how every right triangle made in which one leg is 3 and the other 4 (that is, have a “slope” of .75) must have the same angle forming it. I spend a great deal of time trying to think of a way to help kids file away knowledge under images, concepts, pictures, anything that will help them access the right method for the problem or subject at hand. (For more info, see How I Teach and The Virtues of Last Minute Planning.)

However, I am not in any sense a constructivist as progressive educators use it. I use discovery as illustration, not learning method. I don’t let kids puzzle over a situation and see if they can “construct” meaning. I explain, give specific instructions, and by god, my classroom is teacher centered. I am the sage on stage, baby. And that’s why I got in trouble in ed school, despite my highly accessible, extremely concept-oriented teaching style; I routinely argued against constructivist philosophy, and emphasized the importance of telling kids what to do.

Anyway. I was incredibly excited to read an article that openly states the obvious: Putting Students on the Path to Learning: The Case for Guided Instruction. This article is just so dead on right. To pick one of many great excerpts–click to enlarge, but why can’t I copy text from pdf files any more?:

Yes. Low ability kids like discovery; it is less work for them, yet they feel they are doing something important—but in fact, they aren’t learning very much. High ability kids tend to be “for chrissake, give me the algorithm”, when they would be better off puzzling through the math for themselves.

The article talks about the importance of worked-out examples. I read the article this morning and had a worked out example on the board the same day—step by step factoring of a quadratic. Here’s the weird thing: the kids who need the help with factoring had to be prompted to use the example, but the kids who got factoring were clamoring for worked examples in the area they had trouble with.

This would be a great thing for notebooks. But how do you get the kids who need help to keep the notebooks?

Great article, that changed my teaching immediately. How often does that happen?


Teaching Polynomials

When I met with my new supervisor in ed school (the second one), I told her that I didn’t feel like I was introducing topics well. She was extremely supportive, and it became one of our favorite discussion points. How do you introduce a math topic? And in my two plus years of teaching, I think I’ve become good at it–particularly in first year algebra, which I’ve taught more than any other. When I taught CPM Geometry, I hated everything about it except the way it introduced tangents (as a slope). I often spend several days mulling a good intro, and have been known to toss in a few days of review just to get my story right.

The story is usually a problem the kids can understand—and understand that they don’t have the tools to solve it. Or sometimes it’s a parallel. Either way, I try to give them an image, a reference, a bucket. Maybe it will help them trigger memories, because retention is a huge issue in teaching math.

It’s weird, the quick descriptors that teachers use. When I say I’m “teaching polynomials” in Algebra II, any math teacher knows I’m teaching everything but quadratics in their binomial/trinomial form, since quadratics is its own unit. Teaching polynomials means the kids are learning polynomial multiplication, polynomial division, synthetic division, maybe some binomial expansion, certainly some brute force factoring In general, the polynomials unit in Algebra II doesn’t have any obvious purpose other than to prepare the kids for pre-calculus. It’s just “let’s learn how to manipulate polynomials to no immediate purpose”. And that makes the intro tough.

Over half my students will not go on to pre-calc next year. Some will be taking Algebra II again, either with or without Trig. Others will be going into remedial college classes. So even leaving aside the intro, how do I help the kids make sense of this? I don’t care if they can expound on function notation or binomial expansion, but I do want to be sure they know the difference between multiplying two trinomials vs. two binomials, and when to factor. And for god’s sakes, I want them to know that they can’t “cancel out” the x2 term when presented with a rational expression.

I started the unit by explaining the preparatory nature of some of this—that they won’t really see how it’s used until pre-calc, that they just need to recognize these equations and know what to do. Multiplication, they’ve been doing for a while. Factoring, too. But then there’s division proper, which most of them won’t use again. I thought about not covering it, until I realized that I could use the lessons as a way to get them to think about division and factoring.

And so, the introduction:

I don’t present this all at once. I start with the first fraction, then ask what could we do. Someone will reliably say “reduce it”, and so we’ll reduce it. I then introduce the term “relatively prime”.

So then, I say, we do the same thing with variables and fractions, and we go through this step by step:

This isn’t the actual whiteboard example; I just wrote it up and took a picture. But it’s the idea.

And it worked. It gave the kids a great point of reference and most of them were able to divide a simple polynomial on a quiz a few days later.

I’m trying to build on that now. Thus far, I’ve taught them two forms of division and factoring. Ideally, they should be able to identify when to factor, when to divide and when, please, synthetic substitution is a good idea. So I went through the pros and cons of each:

  1. Factoring: the default. Pros: It’s fun to cancel out the common terms. In a test situation, you can pretty much assume that the terms will factor. Cons: Only works with first and second degree polynomials. After that, it’s brute force. Limited: if you can’t factor, you can’t. Nothing to tweak.
  2. Division: you don’t have to use it much, unless asked. Pros: It’s the easiest to relate to–works just like number division (most know this already. Most). It’s extremely flexible, works in every situation. Cons: you don’t have to use it much.
  3. Synthetic division: you never really have to use it. Pros: Incredibly useful for evaluating terms, which is what we’ve been using it for. Quickest method to find factors in higher order polynomials. Cons: It’s the most difficult to learn. Unless you use it often, it’s easy to forget. You have to know what it means in order to find it meaningful.

So they all copied it down. Did they get it? I gave them a quiz—a pop quiz, no less.

And with one exception, they did pretty well.

Question 2. It got to them. First, they saw the division sign. So they divide, right? No! Don’t they remember? “Division is…..” I prompt. “Oh, yeah, you flip it!” They flipped it. But then they multiplied, which made sense because they were being tested on that too, right?

Argggghhhh.

Still, it was a good quiz. Once I reminded them, they worked it correctly. Few misconceptions. I’ll need another week to beat in the triggers to tell them what to do when. But it’s working.

I think.


Teaching Humanities, Twelfth Night

Twelfth Night lesson plan and discussion.

This was a 100 minute block period daily, which was pretty cool. Rather than do history one day and English the next, we switched off between history and English. Block is pretty brutal for math, but it’s great for history and English. I have most of the assignment images at the bottom of this post.

As I mentioned in an earlier post, I went off the reservation for the last month of the school year. The original lesson plan called for an entire month of Twelfth Night, spent not reading and understanding it, but exploring issues of identity and gender and how the play helped the students see these issues in their own lives. Yeah, not my thing. I started out with good intentions, but by Day 3, I knew I’d done as much as I could. So I cut the time on Twelfth Night in half and then did a two week unit on Elizabethan theater. When I mention the “original lesson plan”, I’m referring to the plan I followed before jumping off.

Primary learning objective: Shakespeare becomes much more understandable when it’s seen and heard. Yes, the words can be simplified, but a great deal of the beauty and power is lost. Students who struggle with understanding Shakespeare can help themselves gain a better understanding of the material by hunting out a movie, talking it over with friends, and yes, reading synopses or translations. But they should also realize that the whole reason we still read Shakespeare has much to do with the beauty and strength of the words, and to make every effort to increase their understanding of those words.

Secondary learning objectives: Students will learn one of Elizabethan acting traditions (e.g., why was Viola dressing like a boy?). They will also form a greater awareness of the challenges and opportunities that emerge as the written word is translated to the stage.

Notes: Remember that a third of the class had reading skills at about the sixth grade level. Actually understanding Twelfth Night text was well beyond their abilities. The top kids, who read at college level (four of them) would find the assignments I was going to give intellectually interesting, even if we weren’t actually analyzing the literature–which they all would read. The mid level kids (half the class) probably would have benefitted from more close reading of the literature. However, as any English teacher can tell you, kids don’t usually do the reading at home, which means you have to schedule a lot of school time for it—and that would leave my low ability kids lost and bored and goofing around, all for the possibility that my mid-level ability kids might gain something from reading more Shakespeare. It was a tradeoff. Eh. Which is not to say the kids weren’t assigned the reading, and that my top level and probably half of my mid-level kids did. It’s just that I didn’t push the reading, as you’ll see.

Day 1-2: Watched the movie, a very good rendition. The kids had to create a “social network” of the characters.

This came from the original plan, it did help the kids focus on characters as well as plot. I then modified the assignment a bit to be less squishy, and off they went. I am not a teacher who goes to the art well much, and whenever I do I am reminded how much the kids love it. They were incredibly creative. I didn’t have an android back then, or I would have grabbed pictures of their work.

Day 3: Gallery walk through the networks and a reading of a Edith Nesbit’s short story of the play and then a fishbowl discussion of three questions. The questions were assigned by student ability (not obviously so). Students are graded in fishbowl on their participation and the strength of their discussion. While the discussion topics varied in complexity, students focused on the tradeoffs made in telling the same basic story in text, live action, or film.

It was the Nesbit story, in fact, that gave me my jumping off point and my new lesson objective. The only students who actually discussed the story were the lower ability students; the top students had to start wrestling with staging and technique.

It’s funny: I have little truck with math “techniques” (pair and share, blah blah blah). I am a big fan, however, of fishbowls and jigsaws in English and history. I suspect it’s because fishbowls and jigsaws work, whereas math techniques just make everyone feel better about trying something. No evidence to support this theory, though.

I thought the questions I came up with for this fishbowl were pretty strong; the kids liked them, too.

Day 4: Read the first act of Twelfth Night aloud. Discussed how much more difficult it would have been to understand if they hadn’t seen the movie first–or was there anyone who found it easier to read than watch? (there wasn’t) Reference back to the free write, short story, and staging.

Assignment: read Act II, scenes 1-3. In class, we looked at them to be sure everyone had a reference point from the movie. I told them yes, I knew of No Fear Shakespeare, and NOT TO USE IT RIGHT NOW. It was okay if they didn’t get everything; we’d discuss it tomorrow, and we would be talking about how to use NFS.

I did a longer stint with SSR today, because reading aloud can be deadly. The first day, the kids just took turns reading it aloud with no acting it out. I am reasonably sure that most of the kids did not use NFS to translate, given that I’d told them I wanted them to puzzle about it without that help and that I wasn’t criticizing NFS.

Day 5: Assigned SSR for 30 minutes–read the rest of Act II, looking for parts you remember from movie. Then we acted out most of Act III–not just reading aloud, but with emphasis and minimal staging. If a student muffed a delivery, I’d make him or her do it again. (Note: I had them skip through a lot of the boring parts.)

Weekend Assignment: Read Acts IV and V of Twelfth Night. Yes, No Fear Shakespeare was allowed, but as much as possible they are to look at both to gain a better sense of what those words mean. Extra credit: spot one scene that was definitely not in the movie. (four kids found some scenes that hadn’t been in the movie.)

As we read through Sebastian and Antonio’s scenes, one student asks “So, am I the only picking up on the whole gay thing? What were they doing on that ship, anyway?” “I think Antonio only helped Sebastian because he was hot for him” said another and the class quickly devolved into three minutes of ribald speculation until I reluctantly restored order.

Day 6: Freewrite: I gave them one scene in two columns, one of the original text, the other “translated” by NFS. It is my opinion, said the freewrite assignment, that NFS loses a great deal in translation. Do you agree or disagree? Be specific and discuss the use of descriptive language, particularly metaphors and similes.

They agreed in all cases (safe choice) but every student, from the strongest to weakest readers, gave thoughtful responses about what was lost in translation, along with some decent specific examples. I was pleased. By the way, I don’t have any documents from the past four days, because it was all done by my winging it through Days 4-6 while I planned out the next assignments, which start now.

Rest of Day 6 and Day 7: Gibberish assignment. No, not the game or the language, but literally words that couldn’t be understood. Students formed groups and chose from a list of scenes that I’d chosen. They had to stage the scene—props and costumes allowed—but they were only allowed to use nonsense language of their choice. They had to focus on making the staging as clear as possible to someone who wasn’t familiar with the play. They had close to two hours of class time to work on their staging, as well as during advisory and of course, after school.

I had no idea how this would work. I just didn’t want them spending time creating scenes that wouldn’t be very good to start with, and this promised to be funny

Day 8: Performance of the Gibberish Staging

This is undoubtedly the funniest 100 minutes of class time I have ever designed.

  • Two boys enacted Olivia’s proposal to Viola saying “glockle blockel stoppel” over and over again, with Olivia looking mooningly into Viola’s eyes and Viola–who was much, much larger than Olivia—desperately trying to escape.
  • Three girls acted out Malvolio’s yellow stocking scene in three languages: Tagalog (Malvolio), Japanese (Olivia) and Chinese (Maria).
  • Four students acted out Sir Andrew’s letter writing scene with Sir Andrew (a girl) doing knee bends, fencing stabs, and muscle preening while Sir Toby reads the letter aloud, giving reassurances to Sir Andrew as to its ferocious law-abidingness, which exchanging snide looks with Maria–and then the duel itself with Viola played by one of the tallest boys in the class, wincing in terror–all done to the sounds of Dubdubdubbiddybub.

And those are just the three I remember specifically; they were all hysterical and in the main, very well staged. I dunno, maybe you had to be there. The students had a blast and wrote their own reviews.

HW: Final Essay–you have a friend who is complaining about how hard it is to read Shakespeare. Write a full-page letter (can be informal, but no text-speak) and give some advice with specific examples.

The results here were pretty much what you’d expect. Nothing spectacular, but they all got the idea.

Day 9 or Day 10—I can’t remember if I’m missing a day or if we had to do some assembly. In any event, the last day of the unit was the final. Students had to identify key plot points and quotes.

While I didn’t track specific results, all the students got a C or higher, and only 3 students got a C. I had spent the year emphasizing the importance of remembering content, not letting it just go in one ear and out the other, and it had really paid off. My favorite airhead got a B-, to her shock, and took a bow to the class.

Documents below.

It’s funny; I have many fond memories of the Elizabethan history unit, but not until I wrote this up did I realize that the Twelfth Night unit had also been quite successful. Learning objective definitely achieved by all students. I’m quite sure they increased their content knowledge and all of them, regardless of reading ability, have a decent memory of the main plot points of the play. All that and gender identity discussions, too!

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Teaching Humanities, Part I

I got lucky my first year out and was able to teach math and humanities.

Were I ever to get a full-time job teaching either English or history, I would feel guilty for abandoning math and taking the easy way out. That’s how much easier it is to teach either subject. Do not picture me as short-timer, stuck teaching math as some sort of dead-end, droning on praying for the day that I get to teach my true passion. No. I find teaching math, constantly struggling to find a way to make abstract concepts understandable to uninterested students with no inherent ability, to be one of the most fascinating tasks invented. I’m hooked. But teaching English or history is a hell of a lot easier, and my lord, is it fun.

I taught 9th grade humanities at an extremely progressive school. (You’re wondering why on earth they hired me. They were desperate and got rid of me as soon as they decently could.) I planned out the curriculum with two other teachers for most of the year. As a rule, I did tests, grammar, and history (I was the only certified history teacher of the three of us, had considerable experience with standardized tests and–also as a result of my test experience–a lot of background in teaching grammar). They did literature and most of the actual planning (weeks spent on each section and so on). It was all collaborative and lots of fun–I learned a lot about planning out a book, and they gave me great feedback on how to simplify a history lesson for freshmen, while I taught them how to keep the rigor in even if the vocabulary is simplified.

We did the history of India, history of the Philippines, a brief history of Russia from the freeing of the serfs to the Russian Revolution, and the Age of Enlightenment, Age of Discovery, and revolutions industrial and agricultural. The kids read Nectar in a Sieve, a book on post-colonial India, a choice of three books on the Philippines (can’t remember their names), Animal Farm, and Twelfth Night. They also did some sort of project on natural disasters, which interested me not at all except I learned a good deal about geography, and some sort of personal narrative.

There was a great deal of indoctrination in the course material from years past, but I convinced the other teachers to dump a lot of it (without ever mentioning my opinion of the indoctrination) and the rest of it I just cut from my lesson.

The kids’ reading abilities ranged from 6th grade to college level, as did their writing. We were supposed to do “sustained silent reading/writing” each day for 20 minutes (it was a block class of 100 minutes) and it was supposed to be based on student choice, but I realized that most of them were just sitting around doing nothing. So I instituted my own hand-made SRA program of three levels. I just went to the bookstore, picked out some enrichment materials at various levels (and yes, bought them with my own money), and made copies for the kids. The kids read nifty little passages on all sorts of subjects, answered questions, did crossword puzzles with new vocabulary, and had little tests at the end of each unit that I checked on.

The kids gained tremendously in content knowledge at all levels. My favorite example: when we were talking about Russian history and Trotsky, I mentioned in passing that Stalin hunted down Trotsky even after he fled to Mexico, where he lived for a while with two famous artists, Diego Rivera and Frieda Kahlo.

One of my weakest readers perked up. “Is that how you say her name?”

I laughed. “I think so, but I’m not sure. I’ll go look it up later. You know about Frida Kahlo?”

“She was in the reading packets. She was famous for painting herself, or something.”

“Self-portraits?”

“Yeah, that was it. She wasn’t happy with the Diego guy, right?”

“Oh, is that the one that had a car accident?” pipes up another weak reader.

Another boy pops in. “She crashed into something.”

A strong reader (who therefore had not read about Frida) was interested. “When was this?”

“Yeah, this was like….it was after 1900. I think it was a lot after 1900, but not like 1950 or anything.”

“I think her car crash was in the 1920s, but don’t quote me,” sez I. (It was.) “That was very useful information, and thanks for the interesting details. Back to Trotsky and the axe.”

Content knowledge, baby.

Anyway, the segment on Twelfth Night we were expected to do was designed by a student teacher, and it was all about identity and examining their own navel—exactly the kind of nonsense I don’t like to do. By now, I knew I wouldn’t be back next year and this was the last segment of the year, so I went off the reservation. I did two weeks on Twelfth Night and two weeks on Elizabethan theater, and every minute of it was joyous fun. For the kids sometimes, too.

This post is getting long, so I’ll put the lesson plans and a story about in subsequent posts.


Meanwhile, back in Geometry….

As much as possible, I want the students to know a few unifying ideas about triangles. That’s why I dumped medians, orthocenters, and a lot of the relatively obscure triangle facts—not because they aren’t useful, but because most of my students will never use them again and I want them to have plenty of time working with the geometry they’ll need forever. My top students get practice thinking through challenging problems but I don’t throw a lot of random facts into this mix.

This has a lot to do with my own preferences. I like to remember the big things and look up the little, and I don’t personally see much value in making students jump through hoops to remember obscure math facts. (History is a different matter.) I do want them to remember the important math facts (Pythagorean theorem, special right ratios, area formulas, and so on), so when I say, underscored five times, remember this, my students won’t treat it as one of a random flood. That doesn’t mean they’ll all remember it, alas. A distressing number of my students still look at me perplexedly when I ask them the formula for the area of a triangle. It is to weep. But that’s all the more reason to keep the memorizing to a minimum.

I taught special right triangles as a ratio, rather than a pattern. This worked very well for most students, and it also provided for continuity when we moved into similarity. Same process, but now the ratio isn’t fixed. (And this should make the move to trigonometry, which is also based on ratios, part of the same continuity).

I gave them a test after special rights and then a test after similarity. I tested much of the same material in both. (After break, I’m going to give them a test on other things from first semester, to see how their retention is.) Here are the tests and the correct percentages for each.


I just noticed that I forgot to fix the typo in question 14 before I made this image. The kids were given corrections before they started the test. (My tests often have minor typos, as I create them from scratch each time. My kids know this and are encouraged to check with me if they think they find something wrong. They are usually incorrect—that is, there was no typo—but I’m confident that no one is sitting silently perplexed for the wrong reasons.)

Overall comments:

  • Questions 1 and 2: see what I mean about area? I was actually pleased with those numbers. They are still forgetting to take half.
  • Questions 3 and 4: very good understanding of perimeter and algebra (I don’t think my diagonals are accurate on that pentagon).
  • Question 5: A straightforward test of Triangle Inequality, something I’ve emphasized. It’s frequently on the SAT and ACT and besides, it’s a useful limit to remember. And they did!
  • Question 6 and 7: The students had to know that triangles had 180 degrees AND that a “not acute” triangle must have one angle of 90 degrees or higher. Another 20% knew that triangles had 180 degrees, but didn’t catch the second criteria.
  • Questions 8, 9, 10–straightforward special right questions.
  • Questions 11 and 12 are a case of unintended consequence. I thought 11 would be the easy one, as we’d just reviewed congruent triangles and I’d reminded them (again) of the SSA (see the bad word? Yeah. Not a congruence shortcut). Most chose the SAS answer—the correct answers were all top students. While question 12 didn’t have great results, more students hroughout the ability spectrum answered it correctly.
  • Questions 13-15—more special right questions. (see note above about the glitch on 14).

The last five were probably too difficult; I wanted to see how my top students would do. I ended up dropping the last five and grading students on the first 20.

Average curved score: 68% (51% uncurved)

This was a much more solid performance, I thought. I’d increased the difficulty, and the average was just a little higher (70% curved, 54% uncurved).

In both tests, the students had a terrible time dealing with radicals and the Pythagorean Theorem, which is what led to a review. But they showed increased mastery of special rights, and their understanding of similar triangles was better than I’d been hoping for.

These percentages are the actual answers given. I went through the D and F tests and reviewed questions 15, 17, and 20. In all three cases, I’d put a spin on the question. So if a D or F student saw that the angle was 60 degrees but didn’t realize I was asking about the unmarked part, did the proportion correctly in question 17 but forgot to convert to feet, or solved for x and then forgot to plug it in, I gave them credit for that work.

Any geometry teacher knows that I’m going veeeeeery slowly. I have two major topics to cover before state tests—trig and circles—and two minor ones, volume/solids and regular polygons. At the same time, I’m definitely not giving my students an easy time. I’m working them hard and I think they’re doing challenging math. In fact, that’s the most consistent beef my students have about me—they think my tests are “weird”. But they also appreciate my curving, and they also, I think, accept my assurances that this is what actual standardized tests look like, so they may as well man up.