Last time we talked math in this space, I was trying to figure out a way to squeeze way too much content into the last five weeks of school, while still giving my students a chance to practice the skills and giving me a chance to assess their understanding, all while keeping a tiny sliver of their available brain cells focused on math stuff. Because it’s another fantastically gorgeous early May in The Region.
This week, I needed a performance assessment idea for Conic Sections. I also need to overlay final exam prep with new material in the finite time remaining before June 2.
And, I want to play with Desmos. Or rather, I want my students to play with Desmos.
Put all those ingredients in a blender, hit “Smoothie”, and you’ve got Piecewise Function Art!
See everything up there labeled “Conics Project”? This project plan of mine is not a new idea, obviously. I first came across it when Amy Gruen posted about her pencil/paper project back in the day. My co-teacher and I modified it for our Algebra II course that included several students with IEPs.
And then it sat in my back pocket for years until I changed schools and was assigned to Algebra II again this year.
So I used their work as a starting point, customized it for my students, made up a packet with some sample art, my expectations for the project and the points scale, annnnnd away we go….
I insisted they did the pencil/paper planning first. I want them to make some fun & cool pics, yeah, but first and foremost I want them to get good at moving between representations of functions, and to get some reps on writing and graphing conics. I gave them two days to roll it around and plan at home, maybe sketch a quick picture or two. Then I planned for a pencil/paper Work Day in class Thursday, with the expectation (slightly unrealistic, it turns out) that they walk into class the next day with a list of equations. Then input equations to Desmos on Friday, with the project submitted via Canvas by the end of class.
The initial reaction was… lukewarm: “Ugh”. “I’m taking the L.” “I can’t do this.”
Come on now. Don’t give up before you even try.
Most of them didn’t pick up a pencil before classtime Thursday, putting them in a hole to start. Fortunately I built in support, posting a Desmos Activity (via Stefan Fritz) to our page for them to play with, so they could see how to fine-tune an equation, and to restrict the domain. But the best progress was made in class on Thursday, when I convened some small groups, answered questions, walked through a couple of quick examples of drawing a graph and working backwards to its function rule, and also showing them how to translate a graph.
Next thing you know…
Guys, for real. In my least interested class, I had 26 kids engaged, helping each other out, graphing, writing, struggling through the rough spots, cheering for each other and squealing with delight at themselves.
If they aren’t at home right now high-fiving themselves, they should be.
Then Friday, the Big Finish:
OK, in reality, my students needed a lot of support to bring this project in for a landing. A lot of them made a pencil/paper design that was way too ambitious to finish even with two days to work in class. Many were asking questions Friday that they should have brought to me on Wednesday or Thursday. Most got down to business in class on Friday, because it was the due date. But almost no one was remotely close to being done.
There’s two ways to handle that: 1) “Too bad, so sad, I told you guys to get started on Tuesday and you didn’t so now you’re out of time and out of luck. F.”
Or: 2) “Look, I can see you guys are making progress. How many of you are happy with your picture as it is right now? Not many, right? But you’re making good progress and probably could turn in something really fantastic with a little more time? Cool. The due date in Canvas is today, but with a time of midnight. Go home, finish it up, turn it in before you go to bed and we’ll call it good.”
In his autobiography “My American Journey“, General Colin Powell stated often one of his life’s guiding principles: “Never step on another man’s enthusiasm”. Good advice from a great man. I’m in, all the way. Why crush my students’ spirit just when they are hitting their groove with Desmos and putting together the equations for a whole big mess of functions? Math is happening here, people. I’d rather ride that wave, let them finish and give me something they can be proud of.
So, midnight it is. And we all get better, together, at teaching and learning.
Piece by piece.
Real talk? If you ain’t counting, you lying. Yeah, I know. We’re not supposed to be counting.
But we are supposed to be planning. And adjusting when plans go sideways.
Which is how this happened at our Algebra II (Track 3) Late Start Wednesday Meeting:
1 day for the final exam, preceded by 5 days of review. That leaves 23 instructional days. For 21 sections across 4 chapters which will account for 32 final exam questions.
Yikes. Something’s got to give.
I’ve got a thought about how to fire up a spaceship on 12 amps. So do my math department colleagues.
But you know who else has a thought? My students. And they might be willing to go along with some changes if they have proposed those changes.
So I asked them.
Here’s what they told me:
Good Lord. Why don’t you just tell me to teach the class while standing on my head in a corner? Because that would be an easier change to make.
One of my students heard her classmates making these suggestions about cutting back on notes and not taking “homework” home and said under her breath “Oh God, that’s stressing me out”. Guess what, my dear: it’s stressing me out too. Wayyyy too traditional a classroom for my tastes. And for my students’ needs.
Or is it?
If they are telling me what they need right now, and what has worked well for them in previous years with teachers in my building, it’s worth a listen. Using a solid, ancient negotiating tactic, I came to the table with a mental list of concessions I was willing to make. Then I can can lay it on the table at make-or-break time, like it’s something that it absolutely kills me to give up. I love giving my students a chance to engage deeply with math thru Estimation 180, Which One Doesn’t Belong, 101qs, and Would You Rather?, but right now I’ll make the trade for the time and hope that over the last 7 months we built a culture of curiosity and problem-solving in my class that carries over to “traditional” tasks.
Plus, it’s nice to have a little leverage as the temperatures (inside and outside the classroom) warm up. “Hey you guys, you told me if I did x, you would do y. Time to hold up your end of the bargain.”
Now, it’s time to go try to land a 747 on a two-lane road. In a crosswind.
Wish me luck.
When you drive an old car you get used to some rough sounds.
You also get very attuned to new, strange sounds. To the point where you almost don’t need an engine light to know when something’s not right.
So it is when you teach Algebra 1 frequent fliers, or in my current position, Track 3 Algebra II students with “Junioritis“. As my math coach in a previous district once told a room full of algebra teachers: “Your students have been going to school now for what, 11 or 12 years? Don’t fool yourself. They are not going to instantly start liking math all of a sudden just because you are their teacher this year.”
So we started a chapter on exponentials and logs last week. We kicked the whole thing off with a day of graphing exponential functions by making a table of values. How did it go, you ask?
“I didn’t get to the back page because the front page made me cry.”
How do we fix this? (Hint: The answer is not “Call the Car-X Man.”)
We go Back to Basics:
Opened up class with the odds of a perfect NCAA bracket, graphs included. Because, the first day of the tournament (mid-day games, yo) dominates my students’ attention like little else.
Then on to the bellringer – a Would You Rather on the evergreen task: would you rather have (insert giant sum of money) for a month’s work, or would you rather get one penny the first day, two pennies the second day, four cents on the third day, and so forth, with the daily pay rate doubling each day.
Several students lowered their shoulder and did the grunt work, either on calculator or on paper. And the answer became crystal clear. They actually “justified their answer with math”. Serious “light bulb” moments. (“Woah!……..”)
Then we walk through graphing an exponential with a fractional base, from the previous day’s assignment. Once I reminded (and showed) them that a negative exponent means write the reciprocal to the positive power, things fell into place. And hey, wait a minute. The shape of that graph looks very familiar. Like, we’ve seen it before. Maybe, today even…
They still freeze up any time they are asked to graph a function from an x-y table, but I think they left class that day having a little clearer view of the *concept* of an exponential function. For just one day, I’ll take it. Let’s just say I’m guardedly optimistic. We’ll do some review at the end of the week, and a partner quiz on the day before Spring Break.
Moral of the story: it’s my job to stay in tune with my students’ level of understanding, and back them up when it’s needed. Visuals, a chance to play with numbers, and a chance to manipulate graphs definitely helps.
Or I could sit in a corner and mutter H – E – Double – Hockey Sticks. Those are the options.
The Dreaded Algebra II. For many of the high-achieving students at my school, it’s a forgettable stepping stone on the path to AP Calc and beyond. For my students, it’s the last required math course before graduation, and a figurative peek into the very bowels of Hell.
We’ve finished up the first semester, which is really just a re-hash of Algebra I. Now the fun begins. Brand new material. Brand new material that my students see as having no connection to their actual lives whatsoever. Also, the math is hard. Especially if your foundational algebra skills are weak.
So, we’re struggling with motivation these days. Not quite open revolt, but we’re on the edge of a bad place.
We just finished up operations with rational expressions, and their level of understanding is sketchy at best.
I’m not sure a traditional quiz is what they need right now. Check that. I’m positive a traditional quiz is not what they need right now.
So, some type of performance assessment is more like it. In class, in groups, display understanding, take your time. So: Old standby? Or a new thing?
“Make a worksheet of problems organized in two columns. Column A and column B. The tricky part is the pair of problems in each row has to have the same answer. Obviously some topics are more suited to this than others. (Solving linear systems, easy. SOHCAHTOA, easy. Graphing inequalities, hard.)
Pair up the kids. Decide who is A and who is B. Tell the kids to only do the problems in their column. When done, compare answers to each question number with their partner. And if they don’t get the same answer, work together to find the error. That last step is where the magic happens. I know how well I taught the topic by how busy I am while they are row gaming it up. (Sipping coffee: go, me. Running around like lettuce with its head cut off: self-recrimination time.)”
So, my twist: make it DIY. We tried this with Kahoot! this year, students creating their own questions and distractors, I gather them up, make the Kahoot! quiz, kids play, angel choirs sing, all is well.
Here’s the deal: My students need a day to catch their breath from the forced march of rational expressions. I’ll give it to them. They’re gonna make their own Row Games activity. I took one of the Row Games from a google folder Nowak graciously shared. The kids will work through that exercise on Monday. So now they know what a Row Game looks like. Tuesday I introduce the project, give them the design requirements, list of deliverables, and the rubric, and turn them loose. It’ll go in the gradebook as a quiz grade. Even better: The plan is to take the finished products and use them as a review day activity somewhere down the line. Each class will get an activity designed by students in a different class.
How’s it going to work out? I’ll let you know. But I’m betting the results (in terms of students’ understanding, and grades) will be better than on some barf-tastic quiz.
A hell of a lot better.
End of Semester 1: imminent. That must mean it’s time for five days of endless, mind-numbing review worksheets so we can all pretend I helped them prepare for a really hard test.
Then, the actual beginning of review. Snap back to reality…
We only got to like 5 practice items out of the 25 on the Jeopardy game board. That’s not enough. I had students grouped up so they could work together and lean on each other. I hoped that would help more students get more assistance than I could give alone.
“I can’t learn like this.”
“My group isn’t doing anything.”
“Can’t we just have a worksheet?”
(record scratch/freeze frame….)
Wait a minute. Aren’t all the MTBoS-inspired, student-centered lessons and activities supposed to be a magic wand that miraculously transforms unmotivated, under-prepared students into raging cauldrons of curiosity?
Ugh. Yeah. Fine. But it’s not working for the class.
Carly, for example — the student who respectfully pointed out “we shouldn’t be tested on this if we didn’t cover it in class” — called me over during test review last week.
She asked, “Mr. Vaudrey, when are we going to practice more… like… actual math? Like, I understand that all these things (she motions at the review problems printed on colorful “stations” around the room) are important, but like… are we gonna get more notes on, like, equations and stuff?”
Students like Carly are accustomed to math class working a certain way. When their usual method of success no longer works, they get nervous.
It’s not wrong to give students what they require to succeed in class; a variety of nutrients is necessary for a healthy diet. If they want notes, it’s okay to give them that for a meal sometimes.
So, a moment of decision: What’s more important – doing a cool/fun game, or providing an opportunity for students to review/relearn?
Call me greedy. Like St. Maximilian Kolbe, offered a choice of two crowns, I call “both”. To the MTBoS Search Engine we go.
And we come away with Four In A Row (hat tip to Sarah Carter/Fawn Nguyen). Long story short, I needed 25 practice problems (in this case, for solving systems). And as Fawn Nguyen points out: Kuta makes it easy. Pick the level of difficulty and type of system to solve, generate the problems, have Kuta make a separate answer sheet so the problems and answers can be printed back-to-back.
So what happened?
Oh BTW: to give the activity a long tail I posted the problem set on our Canvas page for students who wanted more practice on their own before the final.
They got what they wanted. I got what I wanted.
Learning has occurred. For students, and for teachers.
A piece of our teacher evaluation rubric is evidence of using data to drive remediation and instruction, not just on a one-time basis but as a habit, throughout the year. The suggested method is doing a quick analysis of quiz/test grades, then planning intentionally in class based on the results.
Here’s what the quiz over solving quadratics by factoring looked like:
I… feel shame.
It’s a Track 3 class, but that doesn’t mean I don’t have high expectations. But coupled with those high expectations has to be a plan to help students rise to meet them. I’m big into “you do, y’all do, we do“, and collaboration and 1-on-1 student sharing is baked in the cake just about every day. My long-time philosophy is: Accommodations For All. Quizzes are open-note, and we do a day of review before every quiz. I tell them exactly what is going to be on the quiz itself. There’s no “gotcha”. Everything but walk them by the hand, sit them down, and give them the answers.
And yeah, at some point it’s on them to prepare for class. Those 39 of the 55 F’s that scored less than 40%? I don’t know what to say.
But I do know what to think: “what else do I need to do for them to have success?”
Did some soul-searching after pondering the results of that quiz. We had a quick turnaround to solving quadratics by completing the square, and using the quadratic formula. I needed to make some changes, pronto.
Upon further review – my students’ needs:
A sure-fire way for students to get a chance to solve three (or four or five) quadratics in one class period. Enough to go from a 1 to a 5 or 6 on the confidence meter. Build some muscle memory. By the time I was ready for the review, Thanksgiving had come and gone. But, hey, I know enough to stick a good thing in my back pocket for future reference.
As for the second and third items on my wish list: an old standby. Give them a list of problems from which to choose. In my mind’s eye, here’s what I saw: give ’em 8 quadratics, solve two by factoring, two by taking square roots, two by the formula, two by completing the square.
But, is that still too much? Covers all the skills, but man, that’s a long quiz. What to do, what to do?
Ask the MTBoS:
The response: Tighten it up.
So perfect. Done and done.
It is Indiana, after all, so “Turkeys In The Oven” became the basketball-themed “They Got Game.”
I’m not above bribery when it comes to methods of getting students to participate in a review. And if they think “extra credit to the winning team” is their idea, all the better.
No lie, you guys, they were begging me for another problem to work out. Asking each other for help when they got stuck. Calling me over to show off work.
Last period, one group was practically high-fiving each other: “We be ballin’!”
So we totaled up points, announced a winner, gave a pep talk, checked for understanding. They assured me they all felt much more prepared for a quiz than they did an hour ago. And for those who wanted or needed more practice, I posted a review module on our Canvas page with all 10 problems and worked-out solutions.
I think we got this. Looking forward to tomorrow.
One Shining Moment, baby. Because we be ballin’.
A live look-in to my class as I try to teach solving absolute value equations:
Any resemblance between Axel Foley and my students is purely coincidental. But there are days when this is what it feels like to be me.
The hook to solving absolute value equations is: there are two cases. Two numbers (say 5 and -5) both have the same absolute value , because they are both the same distance from zero on a number line. So students need to consider both cases when solving the equation. Which means writing and solving Two Equations. To solve One Problem. Ugh.
And I might as well be talking to the wall.
Here’s the smart way to do it, courtesy the great Kate Nowak. I’ll try it that way again sometime.
But for one day, just for One Shining Moment, they were writing and solving two equations. Making sure their table partners did too.
What’s the secret? Grudgeball.
Who knew? All it took was a little cutthroat competition to get a handle on this skill.
Anything gets old if you do it too often. Kahoot!, Speed Dating, all of it. My students even grumbled about 3-Act Math last week. (I think I bought myself a reprieve when they nailed the “girl scout cookies in the trunk” edition.) So: My Never-ending Quest for new review ideas. (As an aside: it’s OK if they are other people’s ideas. That’s what the #MTBoS is for).
PPT file here: alg-ii-3-4-4-4-6-grudgeball-review
Shorter version, if you didn’t click the link: Teams of students work on a math problem. Each team starts with 10 Xs on the scoreboard. Each team that works out the problem correctly can erase two Xs from the total of the other teams. And thus alliances are formed and strategies are planned:
“Take out the smart people.”
As one of my little cherubs remarked after class (with a wry smile on her face): “There’s so much love in this classroom, I swear.”
Of course the best strategy is only as good as your three-point game. I mean, you all are from Indiana, right?
Teams can earn the right to erase 4 or 5 Xs by making a basket from about 10-15 feet out. Paper ball in a wastebasket, or nerf ball into a nerf hoop, as classroom equipment dictates. My 2nd hour class? Clang. Brick. Oooooo…
My 5th period are ballers tho.
And the 7th period? Savages. By far the most cutthroat. By. Far. They turn on each other like soap opera villans.
The Indiana-based teacher and author Matt Miller (Ditch That Textbook) wrote about how infusing principles of video gaming into his classroom changed the way his students looked at (and engaged with) something as basic as a unit review.
They call it “Gamification”. Based on what I saw in my classroom for 50 minutes in each of three sections of Algebra II, I call it Fun and Learning.
Seriously, one of the girls pictured above asked me if we could keep playing Grudgeball even after we finished the quiz today. Who does that?
Engaged students, that’s who does that.
My go-to catchphrase leading up to a quiz, or any moment where I’m checking for understanding, is: “Show me something incredible, will ya?”
What they showed me this week…. man. “Incredible” is an understatement.
So: Quiz Review.
I promise my students at the start of each year that I will never drop a quiz on them without scheduling a review day. Now, if they happen to be absent on that review day, that’s on them, not me, but still. I’m not here to play “gotcha”, right?
I also learned way early in my career that me standing at the board and working out problems while they watch me like I’m a trained seal is the worst kind of review.
Seriously, “Sit and Get” didn’t work the first time. Why should I think anything has changed because there’s a quiz tomorrow? So for a while now I’ve been on a quest for quality review activities. (Looking at you, Speed Dating.)
But the reality is, anything can get stale if you let it. Even really good, student centered activities. It helps to have a deep bench. Mix it up. Keep ’em on their toes.
Between the MTBoS and the Classroom Chef/Ditch That Textbook crew I
stalk follow online, there are virtually limitless ideas out there. Beautiful thing is, creativity breeds creativity. Reading about my fellow teachers taking chances and putting themselves out there inspires me.
So come time to do linear review with my Algebra II classes, I planned a double-barreled approach: A Desmos Activty based on my Clark County School District enrollment trend project (trend line, writing equations, making predictions), and (inspired by Rafe Esquith, who wrote in his book “Teach Like Your Hair’s On Fire” that as test prep he’d have his students predict the common mistakes that generated the distractors on the California state tests), a Make Your Own Kahoot.
I assigned the Desmos Activity as a do-at-home, which was probably a mistake. Other teachers I follow have had great success using AB this way, but the mistake I made was not priming the pump with an in-class Activity. Not too many of my students logged on to try it out after-hours.
Live and learn. I did do a little crowdsourcing for the slides, and got some good feedback.
That’s a good first step.
Still, I took some time the next day to debrief and walk through (OK, more of a 10k-pace run) through the activity screens, pointing out how the students that attempted the activity had the chance to apply what they had learned about slope to a (semi-) interesting problem.
Next up: a chance to dig in to the common mistakes that derail my students. Time for “Make your Own Kahoot!”
It was a two-day review of linear equations for an Algebra II class, which sounds excessive. But I think it was worth it. Day one, I challenged them in pairs to write their own Kahoot!-style multiple-choice question. With good distractors. No ridiculous, obviously wrong answers, but instead answers generated by common student mistakes, just like the testing companies do.
Then I collected the questions and answers and went home and made the Kahoot quiz.
Next day, we played their quiz.
Good folks have their issues with Kahoot.
Which is fine. I wouldn’t do it every day, or every week, for that matter. But damn, do the kids love it. You should have been in the class where one kid picked “harambae” as his screen name. (Get it? Haram-BAE”). Rich.
Doc here: diy-kahoot-ch-2-review-directions.
Are my Track 3 kids learning Algebra? They’re trying, which is what I ask. Are we having fun?
Oh, hell yeah.
We have liftoff on School Year 2016-2017.
Actually we’ve back long enough to make a couple of orbits and pick up a few rocks. But damn, some days it feels like going 17,000 miles an hour.
I share a classroom with our tech department chair. Brilliant dude. Has the relationships built – to the point where some of my students (who know Mr. E from last year) asked him if I was a student teacher. (Which earned me a nickname: “The Young Teacher”. I’ll take that.)
So I have a Home Base for two classes, but I travel for the rest. For real.
Six classes, four classrooms, two floors, never the same room for back-to-back classes. Me and my cart, ready to roll. Marathon training in slow motion. But it’s cool. I’ve got a routine in place already. The rest is standard issue Starting At A New School:
Learning my way. Learning new people and procedures and expectations and the most efficient way to get into the teachers’ parking lot. Trying to learn Canvas and MyMathLab on the fly. Late Start Wednesday.
But on the positive, I didn’t have to decorate a room this year. My two work days before students arrived were 100% given over to getting ready to teach. When we move downstairs into the new STEM Wing at Christmas Break, I won’t have much to move. And a bunch of us from the math department get together for lunch every day. Some days the conversation cleans up enough to earn a PG-13 rating.
I don’t feel very much like The New Guy. So far this year is: Just me, doing my thing. The thing I learned from the vast awesomeness that is Math Twitter. For example: It’s Year Two of the Themed Bellringers, and apparently that’s making an impression.
I’m getting good feedback from my students, which is no small thing. They are comfortable enough that one of them asked me if I’d ever seen Breaking Bad… because he thinks I look like Walter White. Don’t worry, I’m not planning on opening up a side gig anytime soon.
I don’t sit down and I’m working my ass off and mid-week training runs are a rumor and I took a half-hour nap after school on a Tuesday. In other words, school is back in session.