We’ve changed our in-school professional learning model from late-start Wednesdays to a quarterly Half-Day PD this year. The first afternoon session of the year took place a couple of weeks ago, with a triple focus:
The Canvas LMS as curriculum map and parent portal
Formative assessments driving instruction
Increased Depth of Knowledge, with an emphasis on integrating DOK 3 tasks.
Our department chair related her frustration about the fruits of a planning session with two of our teachers, putting together an in-depth activity as they try to amp up DOK: “We spent 3 hours making one problem!” These are three really good teachers, people.
You guys. Desmos. Desmos Desmos Desmos Desmos Desmos Desmos Desmos.
I totally appreciate the effort, but, damn, let’s not kill ourselves trying to reinvent the wheel when there are approximately 3 billion awesome activities at teacher.desmos.com. I told my colleagues, “I don’t know how many of you guys are using Desmos activities, but it’s a machine for cranking out DOK 3 opportunities in your classroom.”
Plus: Classroom Chef & Ditch That Homework. We ordered a set of both books for everyone in the department and passed them out at our department meeting today. Except for me. I already ownbothbooks. I offered to read along with anybody who wants to do a mini-book club.
Who’s with me?
Trying not to be “that guy” but where we’re headed with being detracked, & being 1:1… it’s the elephant in the room. We’ve got a ton of work to do. The other emphasis going forward is making sure our graduates are ready for the workforce or to handle entry-level college math. Our lower-track kids this year… aren’t. Sorry. We need to give our kids a chance to think deeply about math, to reason, to notice and wonder. We know the lower-track students have been sliding along, getting by with minimum effort and no real understanding of the math. That’s not a knock on their previous teachers. It’s what they’ve told us and what we’ve seen with our own eyes. Our guidance counselors have told us horror stories of kids trudging into the office complaining how hard Algebra II is this year.
Thing is, we owe them the chance to do this. If you don’t believe me, believe someone way smarter than me:
Anyone that still thinks that Algebra 2 shouldn't be offered in high school hasn't spent time with a college kid struggling in college algebra, while being absolutely aware that what they learned in High School mattered greatly, as they learn even more.
We’ve got the tools. We’re not the first math department to stare down this challenge. In a conversation with my former department chair, now an administrator, I said “we’re trying to change the culture of the classroom on the fly here. We can’t wait until our kids are “ready”. We need to move forward with what we know is the best way to teach, and be confident that our students will rise to the challenge.”
The battle lines are drawn in Alg 2. The price of poker has gone up.
Beginning this year, our district has mandated that we weight tests and quizzes as 75% of the overall grade. For track 3 kids, who historically struggle on unit tests, this is a huge deal. They are feeling a little pummeled, watching their grades nose-dive with every assessment. Doing what they’ve always done is not getting them what they’ve always got. Their grade is now performance-based. Mastery is the goal. And the ones that are used to skating by, copying worksheets and guessing on multiple-choice tests are panicking at having to actually do math and support their answer.
“I have no clue, I study the very same way for years and now is the only time that my method hasn’t worked. The 75% is crushing my GPA because “I didn’t show work.” So I have no clue, I don’t have all the free time in the world.”
—One of my students, responding to a survey question on how they could change their study habits to obtain better outcomes on quizzes
That’s like saying, “no fair grading me down on my essay because my spelling and grammar is poor and I didn’t support my argument”. We’ve spent a lifetime letting our low-level students slide, turning our heads, giving them freebie points for busy work and extra credit for tissue boxes (guilty!) and we’re crippling them.
But no creature fights back like a hurt bear.
That goes for kids and grown ups.
My ego is stinging a little bit too. Fight or flight is a powerful impulse. We stopped mid-unit to review when an informal formative assessment showed they were struggling. I started usingJulie Reulbach’sOne-Sheets for unit review. Then I ran the data spread on their Unit 2 quiz and the average score in both classes is about a 45%. Over stuff they learned when they were freshmen. I want to get on my soapbox and have that Come To Jesus meeting with them. But I know from experience that preaching at them won’t change things, except maybe to make it worse.
Teaching them is the only thing that’s gonna work. Took extra care Monday to model “showing work.” Gave them an example of what “meeting expectations” looks like in a job setting (teachers get evaluated too). Offered them a study skill guide from an AVID school. I’ve set up a remediation plan after school, enrolled interested students in it, and emailed all my parents to let them know it’s an option for their child. The students who commit to getting help from me and working to master the skills can re-take a mini-assessment. If they show mastery, I’ll change their quiz grade. I’ve asked my colleagues for advice. I’ve dug pretty deep into my bag of tricks.
Now my job is to listen, and then to do.
Today we used another of my long-time go-tos, the “Solving Systems Three Ways Miniposter Project“. Students divide a poster page into three sections, and solve the same system by graphing, substitution, and by elimination. Of course, since it’s the same system, they should get the same answer all three times, so it is kind of self-checking. But I allow them to work in groups, use their notes, ask me questions, making sure that I support those who need a little one-on-one time. Then they complete some reflection questions about the methods.
Then I’m going to let them replace three exercises on the upcoming quiz with the three worked-out problems on the poster. They don’t know that yet. But on a unit that is universally, historically a disaster, it’s just my way of meeting them halfway.
I figure that’s only fair. Their struggle is my struggle.
My online PLN is blogging about Favorite Lessons this week. I have a handful of topics I really enjoy to teach, such as quadratics. I think this has to do with the subject matter being a challenge for my algebra students, and that there are so many ways to inject life into the subject. I also really like some of the class activities I’ve tried out, but those belong to someone else and have been written about by way better teachers than me. (This fantastic teacher‘s treatment of the In-N-Out 100×100, for instance. I’ve taught that one at two different schools, as well as to teachers at a conference session on building a PLN. It’s always a hit!)
So I want to write about a lesson that is my baby. Rewind to about 2010. The WCYDWT bug got me. Inspired by Dan Meyer, I was always looking for things in the world around me I could use as a hook for math. We had moved back to the Region from Las Vegas a few years earlier. The Clark County School District is the fifth-largest in the nation, with over 300,000 students, and had been growing rapidly for years. When we lived there, 5000 people were moving into the Valley every month. The district was opening roughly a dozen new schools a year. Then: the crash. I was curious what effect the Great Recession would have on enrollment trends, and dug up a little data. I compiled a worksheet, printed it back-to-back with a grid, and the CCSD Enrollment activity was born.
It lived on paper and pencil for a few years. Then along came Desmos, smoothing over the struggle of a paper graph. Then Desmos Activity Builder. And…
They think. They write equations. They analyze data and make predictions. They examine each other’s work. and they think some more.
(They also do some inappropriate teenager things, but what the hell). That’s a day, right there. In anybody’s class. We just spent a department meeting talking about needing to embed SMPs in our lessons and amp upDOK. It was all I could do to keep from leaping out of my seat and going “You guys! I got something I need to show you RIGHT NOW!”
Plus, just the fact that I’m on version 4.0 of this activity makes me feel like I’ve grown as a teacher, giving my students a chance to notice and wonder, appropriately using technology to amplify the learning target, and improving the questions and the way they are asked.
I think my students enjoy it almost as much as I do. Almost.
This is my small contribution to a larger community of teachers who write, tweet, and share and call themselves the Math-Twitter-Blog-O-Sphere (#MTBoS). In an effort motivated at Twitter Math Camp this summer and boosted by JulieReulbach, teachers are sharing around a single topic each week. Look for the collection every Sunday under the #SundayFunday or #MTBoS hashtags, or at I Speak Math. And don’t be bashful: there’s a google form there so you can jump in too.
Rampant stress. Like the kind you can feel welling up in your chest.
That was me Friday afternoon, 63 hours before students walk through my new classroom doors to begin the school year.
As background: we’re in the midst of a three-year, $140 millionrenovation project at my school. It’s being done in phases, so teachers have been shuffling from room to room as the construction project advances. “Flexibility” is practically our school motto.
My principal is a good guy with a really strong team. I don’t imagine it’s easy overseeing a huge 4-star school that aspires to be a top-10 school in the state each year. Doing that while in the midst of remaking the physical plant sounds like trying to defuse a bomb while someone repeatedly pokes me in the kidneys. There’s a million moving parts complicating the already complex process of opening school. “Building the airplane while flying it”, as the saying goes.
After a day of meetings, I arranged the desks and chairs into pods for a couple hours on Thursday. Good way to burn off nervous energy. These desks belong in the room of the teacher who was using that space last spring while her hallway was rebuilt. I knew intuitively the furniture was probably headed back to her room, but I held out hope her new classroom might be getting a furniture makeover.
So with freshman orientation and the activities fair eating up my morning, I shot a quick email to my office staff hoping for guidance and asking (gently, since everybody’s got a to-do list a mile long on the day before school opens) who I should see about getting some desks delivered.
Then I went to work. It was the best way I could think of to stave off the vision of my kids sitting on the floor for class Monday. I’m a first-day veteran. I know what my job is: to be ready to teach on Day One. They’ll tell me what to teach, who to teach, and where to teach, and I’ll take it from there. Friday’s Motto: I’ll do what’s in my hands and trust that others will do what’s in their hands. It’s all good.
(Sounds a little bit like this post from Sarah Carter, whose One Word Goal for the year is “grace”.)
And by the time I left the building at 5:00, the custodial staff was rounding up student desks from all corners of the building and delivering them to my room. Just like I knew would happen.
Broke: Here’s the Syllabus
Woke: Here’s how we do things around here
Bespoke: Let’s do math and collaborate!
I’m loud. mostly because my students are loud. And after 10 weeks of summer, I’ve found I typically lose my voice by the end of day one. Because I talk too much. “Hey kids, I’m not gonna read the syllabus to you because I know you can read”…. then I read them the syllabus.
Students will reflect using a Google Form and submit a snap of their work solving the system (after we discuss and defend arguments) through Canvas.
I’m hoping to welcome a group of students who may not have had great math experiences in the past to my classroom. And have some fun.
In the last week before school I read Ditch That Homework by Alice Keeler and Matt Miller. This activity integrates several of their suggestions. I think it’s a good first step to making my classroom more student-centered and student-friendly.
We’ll introduce course expectations to students on Tuesday and to their parents on Wednesday at Open House. I’m hoping my kids will do some of the PR work for me after Monday’s activity. Either way, by then most of the stress of Back To School will have dissipated.
It’s Year 15 for me. And Year One for me and my students.
When I was in high school, my buds and I had goals. We wanted to steal enough material from the chem lab to build a still, like Hawkeye Pierce on M*A*S*H.
Pretty unrealistic, I know. In those pre-Google days, I’m not sure we even knew exactly what parts we would actually need. But we thought we had a decent shot at emulating Jeff Spicoli and ordering a pizza into class.
That never happened, either. Despite our inability to pull off the wackiness of Hollywood high school kids, senior year was pretty awesome, from a social standpoint at least. I had no idea what I really wanted to do after high school.
I was good at math and science, and finally settled in on pre-dentistry. That lasted, like, a semester. Teaching was not even on my radar screen. Safe to say I took an L on my career goals as stated at age 17.
But in the grown-up world, it’s important to keep in mind goals need to be specific, measurable, and achievable. Day-to-day, year-to-year improvement at teaching is all of those things.
It’s early August. The school year is here. Or soon will be. Happy New Year, BTW.
It’s my 15th year of teaching, my second at my current school. I’ve done this enough times that the basics of the first week are pretty much scripted. And I’m new enough at my school to know I should still be asking plenty of questions.
On the positive, my courses are already set up in Canvas, and since I was a travelling teacher last year (and probably again, at least to start this year), I don’t have a whole lot of “classroom stuff” to set up. I can put about 96% of my efforts into curriculum planning & lesson design.
And thanks to a blogging challenge from my online PLN, a chance to sit down and plan intentionally for the year. To set some goals.
The two major initiatives in my building this year are a move to a 1:1 environment, and de-tracking our math classes. Big changes. Huge. Like, you can’t just roll up to the door on Day One and wing it.
For 1:1 I’m gonna lean on my PLN. I see Desmos Activities being a much bigger part of my classroom when I don’t have to wrestle a computer cart across the building to use this awesome tool. MyMathlab is the other piece of the puzzle for outside of class, self-paced, self-grading practice.
For de-tracking I look to my lean on my department team. They’ve taught Track 2 and Track 3 (where I was last year). They have intimate knowledge of how the two classes might mix, and how we can anticipate our students’ needs. Got a big planning meeting set for next week, but I imagine I’ll be in touch with the ladies on my team on a regular basis throughout the year. I’ve taught mixed-ability classes at a previous school and I’ve got some practices in mind that have seemed to benefit all students. Time to brush up on flexible seating and on-call groups, especially for formative assessment & quick feedback purposes.
For day-to-day lesson design, I’m still wrestling with two pieces. I need to make a call on bellringers & homework.
For the last two years, following the lead of one of my onlineteacher connects, I’ve used a rotating series of tasks for bellringers. I know that giving my students an opportunity to begin each class with an opportunity to think deeply and critically, with a low barrier for entry, is beneficial. They don’t always see things the same as I do, tho. Several students, used to “sit & get”, wanted to spend less time on estimating or justifying, and more time on practice and note-taking. In a 50-minute class, they may have a point. Part of that is classroom management, and transitioning from task to task. That’s on me. If I dump the MTBoS-inspired bellringers, I am going to use a 3-2-1 or summary exit ticket. One way or another, I’m determined to have brain cells rubbing together in my class.
My big leap this year may be homework. We’re talking like Lance Armstrong/Deadman’s Hole-level leap here. It’s a little scary. But more and more I’m wondering if homework is doing what I need it to do for my students. Alice Keeler and Matt Miller have written a book (Ditch That Homework) that outlines the case. I’ve got it on order. For me, the big issue is: Can I give students the opportunity for practice, and the quality feedback they need, and notes, and everything else, in a 50 minute class? I bet the time we use “going over” yesterday’s homework can be re-purposed. And I’m already on board with “You Do – Y’All Do – We Do“.
My mental conflict is: how to balance discovery with practice. Part of that is me accepting alternate ways of students showing their learning. Ain’t but one way to find out. And the case for making the move is pretty solid:
From an Xs and Os standpoint, a couple of student support goals that I did haphazardly last year: Videos. Worked-out answer key. Posted to Canvas. Every. Damn. Day. If homework is going to go away, these are two critical pieces for my students, especially those that need additional help. I’m just going to have to carve out the time to make this happen.
So that’s it. Goals for the 2017-2018 school year. Last year I was getting my feet wet in a new building. My most trusted advisor, knowing my preference for out-of-the-box tactics and knowing the culture in my new building reminded me to “keep your head down” in year one. I’ve gone to school on myself and my students. In Year Two, it’s time to Rise Up.
Apple doesn’t fall far from the tree, obviously. She’s self-taught on a lot of web tools, mostly because her dad gives her the freedom to find and use the tools that help her learn, and express her learning.
That graphic from the Speak Up survey up there? The one that shows what tools kids want in their dream classroom versus what adults think is needed for kids to learn? Brooke and her dad don’t just give that lip service. They live it. On fire, man.
So: What if we could blow the whole thing up and start over? What would that look like?
We can’t rebuild institutional school, but we can change what we do and how we do it within the existing framework. That’s how I’m approaching the coming school year.
My school is going 1:1. We have a unique opportunity to rebuild how we “do school”, what lesson design looks like, how students interact with us, with each other, and with the math.
Close your eyes. What do you see and hear when I say “punk rock band”?
I don’t imagine too many teachers or administrators will be mistaken for punk rockers. But like Dewey Finn’s kids in School of Rock, we can steal a little bit of the ethos. I’m currently reading Route19 Revisitedby Marcus Gray. It’s the 500-page backstory of how the Clash made their seminal double-albumLondon Calling.
They lived punk. They looked punk. But the sound drew on a variety of influences, including early R&B, blues, rockabilly, reggae, pop, and jazz. And while the stereotypical punk rock song is raw and unsophisticated (“volume, velocity, and aggression”, as Gray puts it), the Clash took its time to craft its masterpiece.
As Gray writes: “The original version of the lyric came first. But the final version of the lyric came last.” The educational equivalent is: “It’s OK to teach 20 years. Just don’t teach the same year 20 times.”
So: Now’s the shot. A chance to take a little bit of this, and a little bit of that, and build something awesome. This tool and that one, and remake my Algebra II classes. My kids are gonna walk in every single day with a laptop. That device can either be a paperweight, a distraction, or an awesome tool for learning. My option.
“My top takeaway from the day: the different sessions I attended (and facilitated), the tools I got hands-on with, all existed as part of a framework. In reflecting at the end of the day, I realized I had curated my own little Lesson Design seminar. Whether using Docs & Forms for formative assessment, or creating a hyperdoc for a unit review, or creating an activity in Activity Builder, this was all about identifying a learning objective, and then laying out a path for students to follow, and letting them do the work. And the learning. I’m seeing that Google Classroom, Activity Builder, and hyperdocs can be a powerful combination for my classes.”
I’ve been building my toolkit for years. Tweaking and adjusting. Borrowing from Vaudrey and Nowak and Nowak some more and Carter and Meyer (of course).
At South Shore e-Learn Katie Bradford shared some cool tools for use of video in lesson design. I see this as an opportunity to go 2:1, pairing students up to annotate a quick video on the skill of the day.
The wildcard is MyMathLab. Several of our teachers who have on-demand access to carts have been using this Pearson tool on the daily to create practice exercises and assessments. It’s actually an expectation within the district. I picture it as a way to create extensions and additional practice as a way to differentiate for students. Gonna need some tutorial there though.
So that’s a lot of tools to sort through. It’s gotta be done though. The shift to 1:1 can be done well, or done poorly. It’s too great an opportunity to fumble away.
It can’t be just, OK, kiddies, open your computer, here’s the lesson, pencil/paper just like its always been. The laptops will be an afterthought. Forgotten. Left in lockers.
Or worse, I use them as a $300 worksheet.
And it will be an opportunity gone by the wayside. Instead, I’ve got an chance to build on what’s come before, give it my own personal touch through several rounds of revision, and who knows, maybe turn out a masterpiece.
“Sometimes it’s necessary to march a long way for glory….”
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.
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:
Skip the Friday Self-Assessment
Shorten up the notes
Do the practice assignment (“homework”) in class
Quick-hitter quizzes over a couple of day’s worth of skills
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.
A three-day Easter weekend (Dyngus Day included) is coming up. And of course, before we leave out, we’re due for a quiz. Because I can’t very well send my students away for three days and expect them to come back sharp for assessment, right? Let’s set them up for success, not failure.
Gotta mix things up, well, because even the good stuff gets stale after awhile.
I had promised my Little Cherubs™ a game for review on the day before the quiz. Really, really. Pinky-swear.
Yeah, and then life intruded. I spent every minute from 3:30 after my monthly Mentor-Mentee meeting until after (a very late) dinner taking care of Dad Job Description Issues, including my oldest son’s first car accident, my youngest’s middle school talent show, and whipping up a yummy, healthy (not really), budget-friendly meal. So I’m gonna start working on the materials for a game review at 10:30 at night and, yeah, no.
So I could just give my students a big old Kuta review packet, do some examples, say we reviewed, and then go home and feel shame and remorse for not coming up with something cool. And something with actual educational value. Or:
Provide some structure, teach some study skills applicable across the curriculum, and get some review done, all in a 50 minute class.
Easy as 1, 2, 3.
So yeah, I gave them that big old packet. But: instead of “OK kiddies, start working on these problems, I’ll be around to help” (barf), It’s: “Don’t start yet. Look at the section headings, glance at the problem, and rate yourself on that skill. Use this scale”:
1 = I got this. I am confident I can do this problem correctly every time.
2= I need some support. I can probably do this type of problem, but I’ll have to look at my notes, go online for help, or ask a classmate or teacher if I’m on the right track.
3 = I got no clue. I don’t even know where to start. Help me!
Now I set a 5 minute timer and have them try to do as many of the 1’s as they can. (Prove to yourself that you got this).
Now reset the timer to 5:00, and have them start on the 2’s. Maybe they find out some of the 2’s are actually 1’s. Or 3’s. But they get in some reps, and get some practice at locating help.
Now: Everybody has done probably 5-8 problems, they’re feeling pretty good. And we’ve only used, max, 15 minutes of classtime.
Now we kick it up a notch: “Everybody stand up. Look at your 3’s. Go find somebody in the classroom who has that type of problem marked as a 1 or 2. Sit together and work out a problem together. Go make a friend.”
We self-assess, we practice, we identify areas that need a little brush-up, and areas that need major attention before the quiz. We get out of our seats, we peer tutor. And we create an understanding that the quiz preparation will continue outside of class.
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.