Category: algebra

Choose Your Own Adventure

Wednesday broke a lot of people in our building.

Last Tuesday my school board voted to close three elementary schools at the end of the year. It was the worst-kept secret in the Region as the closings had been long-rumored, generating a series of demonstrations by teachers and community members.

At the same meeting the board voted to approve layoffs for 173 employees with support staff, paraprofessionals, and custodial staff taking the brunt of the cuts.

Wednesday about half the teachers in the district woke up with a mysterious illness, causing the district to close for the day.

That afternoon the mayor held a virtual town hall and stated, “I don’t think they’re done cutting. If we don’t fix the funding problem, next year it may be Morton High School.” (46:40 mark of the video).

Morton High School. My school. Well. That’s a lot to process for one day. I have no desire to change schools again, but a year or two from now I may not have a choice.

Most of us just want to put this year out of its misery. Teachers are done with PD, kids want to get to the last week of May and get out of here.

It’s a delicate balancing act, reading the room.

In my district tests and quizzes account for 70% of the overall grade so the last thing I need is to offer my kids an assessment that will bomb their grade. But wait Mr. Dull, isn’t it your kids’ job to prepare for quizzes? I mean, if it’s that big a factor in their grade, shouldn’t they take it more seriously?

Yes, but. It’s also my job to determine the most appropriate way to assess my kids, to select a way for my kids to demonstrate their learning. In the first week of May in Algebra II, wrapping up the rationals unit, that looks like an activity. Choose your own adventure, it says here.

Enter DIY Row Games.

Row Games were a darling in the heyday of the #MTBoS. Students pair up and work a page of problems in two columns, one column for each student. Catch is, the answers for each pair of problems is the same. So the exercise is student-centered and self-checking. There’s a couple of folders of pre-made row games out there.

I grabbed one up (multi-step equations) to use as a bellringer, then set the hook: “Man, the answers to both problems were the same. All the way down? Hunh, that’s a weird coincidence. How’d the teacher that made this page do that?”

So we bounced some ideas around and eventually settled on working the problem backwards, starting with the answer and using inverse operations to work back to the original problem.

Then I introduced the assignment. (Doc here, template here). Students work in pairs to create a page of row games, one each of simplify, multiply, divide, add, and subtract rationals. They turn in a page of problems, a worked-out answer key, and the work they did to go backwards from the “answer” to the original problem.

They were tentative at first, then started to dig in. I made my way around the room to check for stuck students and demonstrate the process for a problem from the bellringer.

The big payoff came late. Students were working diligently on Day Two of the activity and making good progress but starting to sense they wouldn’t finish. The question developed independently from two sides of the room: “Can we keep working on this tomorrow?”

Wait. You guys want to do more math? On a Friday?

I don’t know….. well, maybe. OK. Fine. Due date is tomorrow.

And yes, I totally planned that in advance.

Because I’ve been doing this for a while and you learn to anticipate these things. So instead of all of us being frustrated with a traditional pencil/paper quiz over a really tough topic, bad grades and hurt feelings all over the place, I got kids so invested in an activity they want to keep working on it for a third day.

That’s a good Thursday in Room 130 right there.

Oh, and they’ll see Row Games again. I plan to take one or two of the student-made sets and use them as part of my semester review package coming up a few weeks from now. Because authentic audiences are awesome.

The coalition of state representatives from my Region put together a press release this week blaming the state GOP leadership for my district’s financial woes. (Indiana is super-majority Republican in the Statehouse so one party has great influence on education policy). You can make a case for their position on property tax caps and referendums and vouchers, just like you can question the decision-making at the local level. I spent all of last school year as a Teach Plus Policy Fellow studying the school funding model in Indiana. There’s aspects that need fixing.

But what I do know is that both of those things, state-and local-level policy-making, are outside of my control. I can advocate, but I don’t get to make laws. What I do get to do is make decisions about how I organize my classroom and plan my instruction to suit my students’ needs.

Choose Your Own Adventure. And I’m going to keep doing just that until they take my keys and lanyard away.

Keepin’ It Real

all: To keeping it 100.
Source

We had our last-ever New Tech Network training this week. The project-based learning model which arrived with great fanfare concurrent with our district’s consolidation from four high schools to two will continue in practice, but our contract with NTN is up and is a luxury in our district’s current financial state.

We spent part of the day with our school coach doing learning walks through our classrooms, looking for evidence for the Thinking indicator on our evaluation rubric. One of the descriptors is that students apply what they have learned to “real-world” situations.

Back in the 2010’s those would have been fightin’ words amongst my online math connects. Like, what even is “real-world”? Especially if the problems don’t match up with our kids’ actual, real-life, real world.

While state standards, evaluation tools, and every textbook ever call for applications of the math, in reality that means students often wrestle with problems that have been rendered unrecognizable by the contortions required to bend them into a word problem.

Our Wednesday Early-Release PD was a session from the New Tech Annual Conference last summer on Problem-based learning, what the NTN people call PrBL. (If you know three-act math, you have a good mental image). Long story short, we created a math fight over the proper way to evaluate exponential expressions, including negative exponents.

The assembled math, science, and special ed teachers were good sports despite well, (gestures broadly) everything. They played the role of freshmen algebra students to a T. It took a nudge to get them to describe their thinking, not just to speak out loud the math they’d put down on poster paper. But they got the spirit right. Student-centered learning, with a competitive twist.

My co-presenter did an outstanding job of pointing out that this wasn’t a “real-world” problem as traditionally understood but it hooked them in in a way no worksheet or MathXL assignment can.

Algebra II taxes a teacher’s ability to make “real-world” connections like maybe no other high school math course. I once described the second semester of Algebra II as “weird” to an administrator, which didn’t win me any points with him but I think at least accurately described a super-theoretical, super-abstract semester of math that relies in large part on a group of kids with terminal junioritis recalling and using their algebraic manipulation skills from long ago.

So we do a lot of projects second semester. This year (in a nod to NTN’s project-based model) I led off the probability and statistics unit with a March Madness investigation and Bracket Challenge. That hooked them in and has served as an anchor as we work our way through the unit. Plus it gives me something other than gambling as a real-world application.

Today, once we had finished notes and guided practice on probability of multiple events, I switched gears again. I had hinted that TV game shows all revolve around math, and several kids copped to watching The Price Is Right at grandma’s house as kids.

So I shared a piece of video with them.

We paused often as we went along. “How many of those baseballs have digits on them? How many strikes? OK, what’s the probability she draws a ball with a digit on it? Five out of eight? Awesome.”

I let Drew Carey fill in the contestant on the rules, and then a quick aside: “OK, so there’s five digits in the price of the car. How many ways can she put 5 digits in order? Five factorial, yeah. So somebody do the math. What is that? 120 ways? Wow.”

Every time she pulled a baseball out of the bag we re-calculated the probabilties of a digit and a strike.

“OK, so if she gets a number and puts it in the right position, then how many ways are there to arrange the other four digits? Just 24? Let’s go.”

We agonized as she struggled to put the digits in order to nail down the price of an Alfa Romeo. (A what now? When we were kids that would have been a pretty nice Chevy, but welcome to 2024). Everybody had a pretty good sense the first digit wasn’t a two but after that? Anybody’s guess. Including the contestant, who wasn’t able to place a single digit before striking out. “This game is impossible! How does anybody ever win?”

It was five quick minutes, but five good minutes. Some rapid-fire, non-Google-able practice on a couple of the topics we’d covered this week.

And it made the math real. Which is all I want with 38 school days left and spring fever here and teacher cuts and school closures looming. When teaching’s all I got left, I’m gonna use every tool I got.

Adventures In PBL – SCH Enrollment Investigation

Complied from publicly available IDOE Enrollment data

Last month I gave my students access to almost two decades’ worth of enrollment data for our district and asked them to model it mathematically. And then to analyze the data and think deeply about the challenges facing our district, which has around 40% the enrollment it did 60 years ago.

They did some quality work, and when asked to summarize their learning in a slide deck, they produced some solid documents.

(Planning doc, student doc.)

Their conclusions were based on their research, both into the enrollment trend and also reading contemporary news stories, and from classroom discussions as well as their own experience. In addition, many of the business and government teachers in my building have been showing segments of the school board meetings in class as a learning opportunity, so my students are up-to-date on issues as well as the opinions of various groups regarding a way forward.

But what turbocharged this project experience was a visit from Trustee Carlotta Blake-King, who was generous enough with her time to join us as a community partner the day after a board meeting, and shared the benefits of her life and board experience with my students.

I primed the pump by asking as part of our bellringer: “If you could ask an expert one question you still have after studying the enrollment data, what would it be??”

I displayed the questions for Trustee Blake-King and that’s all the start she needed. She had my kids enthralled, and maybe never moreso than when she introduced them to the concept of the school-to-prison pipeline.

She told them that when government organizations are scouting locations for prisons, they seek out areas where third grade reading test scores are poor. (More on that claim here.)

My students instantly understood how data is used outside of the classroom, including in ways that are to their detriment, and how valuable the ability to use math to frame the world around them could be. It was like cracking a secret code.

The next highlight came after a student question – “What would we need to do to reverse the declining enrollment trend?”

The trustee’s response: “We don’t promote ourselves. Driving around the city or on the Borman you see billboards for other districts and for charter schools – why aren’t there billbards for Hammond schools? Why don’t we tell people about the great things happening here?” She went on to explain that she had a long career as a real estage agent and the number one concern parents of children had when thinking about buying in a particular neighborhood or town was the perceived quality of the schools.

So we talked about the success stories – from the Hammond Arts and Performance Academy and its graduates to four-time world champion robotics Team 71 to our accomplished Mock Trial and dance teams to service projects sponsored by National Honor Society, Black Student Union, Bible Club, and other student groups.

This piece hit home with me as I’m a fellow on the Teach Plus National Policy Advisory Board this year tasked with advocating for education issues and shaping policy at the federal level. During coaching sessions for our virtual meetings with congressional staffers we are reminded to tell the stories of our schools, the bad and the good. It’s good advice.

Rather than asking them to make recommendations to the board on the way forward (kind of an unfair ask given the number of variables involved in the decision and the relative lack of information my kids had, even after the research) instead I asked them to develop three pros and cons of the district’s proposed action plan, specifically closing two elementary schools and laying off a quarter of the teaching staff.

I synthesized this experience while reading a couple of news articles this morning. The Chicago Tribune editorial board examined the Chicago Teachers Union president ask for a pay increase in light of the city’s ongoing financial troubles. Increased property taxes have a tendency to incentivize families to move out of the city to lower-tax environment suburbs.

So, in our view, this eventually will lead CPS and CTU to the inevitable discussion about how to reshape a school district that now is serving far fewer students than it has in decades. There’s an influx of migrant children whose likely addition to CPS needs to be appropriately accounted for. But the elephant in the room for CPS is dozens of schools that are serving 30% or fewer of the students they were built to instruct.

Under state law, CPS can’t close any schools until next January. But after that there’s no legal impediment. The savings from making some tough decisions could well yield more resources for the schools, and the teachers, that truly need the investment. Indeed, there are parts of the city where schools are over capacity.

Closures, of course, are anathema to CTU and to Johnson. Emanuel’s 50 school closures following the 2012 strike are referenced repeatedly in debates around CPS and its future today. But school closures aren’t unusual outside of Chicago. In the suburbs for decades, districts wisely have consolidated schools in response to reduced school-age populations.

https://www.chicagotribune.com/2024/03/10/editorial-stacy-davis-gates-chicago-teachers-union/

Hammond’s much larger urban schools neighbor is facing the same fiscal cliff and may have to make similarly difficult decisions.

Then an article from Jerry Davich hit the Times of Northwest Indiana (formerly the Hammond Times, which is a long story but part of the larger and long-term flight to the suburbs that has Hammond and other urban school districts hemorraging students and dollars).

Davich spoke with business and civic leaders to get a sense of how the Region can redefine and reinvent itself in the years and decades to come. A shift away from traditional manufacturing to a tech-oriented base is at the top of the list for the mayor of Hammond:

Hammond Mayor Thomas McDermott Jr. is convinced that Northwest Indiana — and his city in particular — will see major advances in technology and investment in the near future.

“Technology advances that will draw large amounts of capital to Hammond’s downtown area,” he said.

https://www.nwitimes.com/opinion/columnists/jerry-davich/jerry-davich-whats-the-next-big-thing-in-northwest-indiana-region-visionaries-look-into-the/article_f15bebb6-c924-11ee-af4b-eb5b7981e3a3.html#tracking-source=home-top-story

A Region product who is now owner of a company funding some of that tech development downtown caught my attention:

“The theme for the Next Big Thing is the integration of Northwest Indiana into the Chicago tech hub experience and the whole technology ecosystem that exists in Chicago,” said Tom Dakich, a principal owner at YAB Development Partners.

“Mayor McDermott is brilliant in that he recognized that the downtown concept on the double-tracking is the easiest way for somebody to live in Indiana and work in downtown Chicago. He’s building a downtown living learning area in Hammond and I’m going to put technology people there,” Dakich said.

“When kids graduate from Big Ten universities, more of them go to Chicago than any other city in the country. That is for all Big Ten schools, not just Indiana, Illinois, Northwestern, etc. We have to get some of those people to come over to Northwest Indiana. The only way to do it is by technology jobs.”

https://www.nwitimes.com/opinion/columnists/jerry-davich/jerry-davich-whats-the-next-big-thing-in-northwest-indiana-region-visionaries-look-into-the/article_f15bebb6-c924-11ee-af4b-eb5b7981e3a3.html#tracking-source=home-top-story

Dakich is right, of course, in his assertion that Chicago is the number-one destination for B1G graduates. But Mrs. Dull wisely noted that although kids from Michigan or Iowa may be lured here by a low cost of living, easy access to Chicago via the South Shore Line, and lakefront amenities, eventually they will start families, have kids, and start to think about quality of schools.

“If he thinks they’re going to draw people to Hammond long-term, they’re gonna have to get the schools right.”

(This is why you always marry smarter and prettier, guys. You’ll never regret it.)

I was pleased with the arc and the outcome of my first full-on project-based learning experience. Part of my intent was to introduce my students to exponential and logarithmic functions before we studied them. Part of my plan was to give my students an opportunity to see how math shapes the world they live in right now. As a wise person once stated, we can’t pretend that “the real world” for our students is some far-off abstraction.

They learned about how schools are funded and how school boards make decisions. They had the opportunity to discuss their learning and get expert input on the issue from Trustee Blake-King.

And the optimistic teacher in me, the one who gets irrationally happy on Cap & Gown photo day when our seniors are walking the hallways in their graduation regalia and taking enthusiastic group selfies, that teacher holds out hope that when my students get their hands on the big problems facing our world that they will be the ones to hammer out a solution.

Otherwise what is problem-based learning even for?

Lemons. And Project-based Lemonade

Source

Being a teacher in my district in 2024 is a daily mental struggle. A protracted contract battle, threats of school closures, an upcoming reduction in teacher force, all things contributing to a morale problem the size of a volcanic crater. It’s hard to see a moment on the horizon where things turn around and get better.

Declining enrollment is the root of the problem. Fewer kids means less state money. And eventually it means you have too many employees and too many buildings.

So being a math guy and a pessimistic optimist, of course I decided to give my students access to the enrollment numbers over the last 20 years and start doing some math with it. Project-based learning and all, right?

Introducing the SCH Enrollment Investigation. (here’s my planning doc including the basic format ChatGPT spit out when I asked it to write the project for me).

I’ve got a Desmos activty examining school district enrollment I’ve been doing with my kids forever (so long that when I first rolled it out it was a pencil/paper activity). I show them a coordinate plane with five (linear-ish) data points. I ask them to create a line of best fit and write equations for the line, then use that model to predict future enrollment. Hook is, I give them five years of data that were the tail end of decades of linear growth, that leveled off a year or so later when the global financial crisis hit. Takeaway: The model is good until it isn’t. Sometimes the model is bad to start, sometimes the world changes. (Foreshadowing alert!)

In that Desmos activity I asked them to model the enrollment of a district (Clark County, NV, home to the Las Vegas schools) that was experiencing rapid growth. Now I want them to think about whether we could use a similar tactic to model enrollment in a district in decline. Pointed them to a couple of recent newspaper articles on the issues in the district and aked them to write some facts.

Then I set up a table in a spreadsheet for them and linked them to the IDOE’s giant mega sheet of enrollment by district since 2006. OK kids, go grab the figures you need for our district, complete the table and insert a scatter plot and trendline.

My motivation for this project is to get a look at exponential and logarithmic functions before we study them in the upcoming unit. So I encouraged the kids to try out different functions for their trend line and see which one modeled the twenty or so data points best.

At 30,000 feet (the Google Sheet chart) the four types of functions don’t look all that different, so Tuesday when we get back together I’m going to give them a quick look at a Desmos graph of the 20 or so data points, and the trend lines for exponential, logarithmic, and polynomial functions.

One of these things is definitely not like the others. Those last four data points are the post-pandemic, post-consolidation years. There are a couple of other contributing factors, but what I’m hoping my students will see is the model is broken, and then I’m hoping that will get them asking questions.

I also linked them to a demographic study our district commissioned after two elementary closings but before we consolidated from four high schools to two. I’m asking them to compare the real-life numbers to the projections of a paid professional.

My hope is this underlines that such reports are built around a specific set of assumptions, and sometimes the world changes. That doesn’t mean the researcher didn’t know what he was doing, or that the numbers were bad.

The culminating event of the project is a student presentation sharing their findings and including their recommendations for the district.

As part of their work I asked them to think about why they thought the enrollment was shrinking in our district. They gave it some serious thought:

Others mentioned increasing housing costs in our city and families seeking new districts due to school closures or seeking in-person school during the shutdown.

They are on this, folks.

I suspected they would connect with this activity because it is 100% real to them right now, and that connection has played out. The last thing I want (or need) to put a bow on the project is a community partner, someone who could come to the classroom and answer questions from students (why close that school? what if we kept more kids/families from leaving the district? is there a way to keep more teachers and still cut costs? why doesn’t the state provide more funding? can the city do anything?)

Real data is messy. Which is why I love it. Giving kids a chance to math with real numbers that really matter to them is absolute gold. Can’t wait to see their presentations this week.

Just Chillin’

I’ve known for a while that the day was coming when I’d be too old to battle a raging snowstorm on my drive in to work. I am a safe driver (if somewhat of a leadfoot) and have decades of experience driving in bad weather, including 15 years of commuting to work 185 days a year on the notorious Borman Expressway (the portion of I-80/94 in Lake County).

Until that day arrives I know that in winter I need to be prepared ahead of time for an e-learning day that may be called on short notice. Sometimes that is an assignment from our online math tool provided by our textbook publisher, other times a digital activity that may not necessarily involve computation.

Back in the embryonic days of e-learning in my area I created a Desmos activity for just that purpose, and it came in handy earlier this week when a snow day and a day off for bitterly cold temperatures bookended Martin Luther King weekend.

Rather than virtually teaching a topic I’d have to re-teach the folllowing day in person, on Tuesday I reached for Just Chillin’, a Desmos activity where my students investigate how temperature and wind speed affect the wind chill figure reported by forecasters.

The activity includes mathematical modeling, interpreting graphs, and using a model to make predictions, all kind of evergreen topics in algebra and beyond. After I set the scene with a couple of beach photos (one summer/one winter), students read an article outlining how Antarctic scientists tested their hypothesis that an increase in wind speed increased the rate of heat transfer.

Next I show them three points on a coordinate plane representing wind chill at three different air temperatures with a wind speed of 15 mph and ask them to determine the type of function suggested by the points:

The next screens ask them what temperature would combine with a 15 mph wind to create a minus-30 wind chill, or a minus-25 wind chill.

This is a skill I spiral back to often in activities, because it is a really good life skill in addition to being a state standard and a staple of testing. Also because it is an area where my students have historically struggled.

Then, a twist:

That point isn’t on the graph, which only contained temperature and wind chill data with a 15 mph wind. They have to take into account the relationship they saw from now five points on the graph, and determine how to estimate the conditions with a stronger wind. (Translate? Something else?)

That was a tougher challenge. They were pretty much guessing at this point. Although honestly, closer to correct than their responses to the questions where they were using a graph or equation.

I showed them the actual formula for wind chill, which involves two variables and is more complex that I needed the first part of this activity to be. So, kids, which variable (temperature or wind speed) has a greater effect on the wind chill, just from looking at the equation?

We haven’t quite reached rational exponents yet (next week) so I knew that 0.16 power was going to be about as clear as mud. So let’s look at the data a different way:

I was hoping they would zero in on rate of change given just the one row and column. The change in wind chill at 35 mph is pretty consistent per 5 degree change in temperature while the change slows rapidly as wind speed increases in the 5 degree column. Almost no one picked up on that. It may have been a factor of remote learning, it may be that they transposed the temperature and wind speed axis, but I didn’t get the traction I thought I would from this question.

So we closed with a couple questions putting the students in charge of “school”:

I appreciate that they are upfront and real with their responses. The last slide is the entire wind chill chart I excerpted earlier, with the “dangerous” level wind chills highlighted in a darker shade of blue. Those are the readings below minus-25, which not coincidentally is the traditional cutoff in many districts for calling off school.

That led to a quality conversation, which kind of rescued the day for me. In my experience, “what would you do if you were in charge?” is a winning question in a high school classroom. Probably something there about student voice and agency, if I had to guess.

All told, I was pleased with how the day went. My students stayed engaged on a Google Meet with me for pretty much an hour, which as my veterans of the remote teaching game know, is saying something. We did some math, I learned about their strengths and weaknesses with some foundational algebra skills, and the topic was obviously timely.

This class came to me at the semester from a teacher who left our building, so I also got to slowly introduce them to Desmos activities, problem-based learning, and “how we do math” in Room 130. Which is also a plus. Pretty positive e-learning day as I see it.

As an epilogue to the first graf way up there: parts of northwest Indiana got slammed with lake effect snow overnight. The band set up over communities a little bit to my east and they got literally two feet of snow today. Some roads won’t re-open for 24-36 hours according to reports I saw. I was right on the edge of the plume so right around the time I was starting the shower this morning and system snow moved out, the lake effect flakes started falling. And one by one, my local districts started calling for e-learning today. The roads were terrible. Meanwhile, my district was well outside the band and got about an inch of snow, if that.

Decision time.

A quick look at Google Maps and INDOT’s live web cams, and a swing around my socials told me the road conditions were lousy for most of my commute. What to do? My class was well set up for a sub if needed. I was in touch with a couple of my math colleagues who also drive in from a distance and we could see this was going to be a challenging drive, if not outright dangerous.

So I made the call.

Not gonna lie, the district’s attempt to cap sick days over a career factored into the decision. A sick day is basically Halloween candy under the proposed contract, like a timeout near the end of a half in football. Can’t take it with you. Might as well use it. Especially when weighing a sick day against a possible injury and car repair from an accident on snowy, slick expressways.

Easiest call I’ve made in a while. No regrets.

Uncharted Waters

Source

Announced Evaluation Season is wrapping up in my building. I sat with my principal for our pre-conference the week after Thanksgiving, and I was upfront with him that I was in uncharted waters – I knew what I had planned but I had no idea what he would see the next day.

We are in Year Three of a conversion to a project-based learning school, and though I have plenty of experience with problem-based learning through Three-Act Math, I hadn’t taken the plunge on a full-on project until this year. In fact I was scheduled to be observed during Day Three of the project. No not a “traditional” class session by any stretch.

I’ve got a stack of second-semester projects from a previous go-round with Algebra II but I was searching earlier this year for something I could roll out earlier. I stumbled across a timely topic that peaked my interest and I hoped would make sense to my students as well: a debate project from Next Gen Personal Finance titled “Should Municipal Bonds Fund Stadiums?“

The Chicago Bears are pondering a move to the suburbs and presumably would be seeking some level of public support for a new stadium on the former Arlington Park property, although there is a late push for a stadium site in the city. And the state of Nevada recently approved $380 million in funding for a new stadium on the Las Vegas Strip for the former Oakland A’s. The ballpark is facing stiff opposition from teachers’ unions who say the state can’t afford to give away millions to an out-of-state billionaire while the schools in Nevada go underfunded.

So there’s plenty of current coverage of the stadium public-funding issue to go along with multiple links in the source document, which I edited a bit for our class purposes.

I opened the intro day with a quick piece of video:

We talked a little bit about what kind of things cities pay for with tax dollars (student replies included public safety like police and fire; parks and recreation, health care, and education). Then they dug into a few of the links provided in the document to get a basic understanding of the issue. They took notes on articles that opposed using public funds for pro sports stadiums.

By Day Three, my observation day, they were ready to generate supports for the argument in favor of public funding. It’s a tougher ask. There are fewer articles out there in favor. But I had hinted at the Bears and A’s stadium discussions, so they were not fumbling around completely in the dark.

I had an ace up my sleeve. With my principal sitting in the back of the room, I asked them to come up with reasons they would be opposed to our district’s new “no cell phone” policy. They were a bit reluctant to speak out with an administrator in the room but eventually opened up.

  • “We concentrate better when we can listen to music during math”.
  • “It’s how we communicate with family and friends”.
  • “Some of us have health or productivity apps on our phones.”

Not bad. Then I asked them for reasons folks might be in favor of a ban. Three students replied in unison “distraction”!

I explained that they just recreated a simple version of the debate that took place amongst our board of school trustees last spring before the ban was implemented, and that was the process that adults often used to work through contentious issues.

I had tipped my administrator that rather than assessing a content standard, this project was based on a standard of mathematical practice, SMP 3 (“construct viable arguments and critique the reasoning of others”) and he just saw me hook my kids in with a relevant example in real time.

And they were hooked. Over the next few days of the project they dug deeper for additional supports on both sides. They split into two teams of five students each to organize and rank their top five supports, and also to anticipate their opponents points, and to decide how to counter those supports. I selected two students to act as judges.

Come debate day, they were ready to go.

Many of my students leaned into the opportunity cost of stadium funding, coming at the expense of education and other needs. It’s kind of a touchy subject in our district right now. They did a fantastic job researching and building arguments, and were able to insert their supports at appropriate moments in the debate. The following day was set aside for reflection, and they all felt that they were well-prepared for the debate and that they helped their team’s side with their efforts.

They also prepared to present their findings to the community at our New Tech Winter Showcase this week.

This debate project was a new experience for my kids, and for me. I’m not new to risk-taking in the classroom, but I think we all get a little twinge of nerves on observation day. I haven’t seen the outcome of my evaluation yet, but I feel like we both exceeded expectations this week.

And I’m already planning our next project. Gonna talk school enrollment trends and school funding. They’ll crush it like a belt-high fastball.

Plane As Paste

It started (as most things did in the naughts/early teens) with an xkcd comic. (The actual title is NSFW).

Source. Used under CC BY-NC 2.5 DEED

Then the internet’s most brilliant math-teacher-minds got ahold of it and Pomegraphit was born.

There was definitely a minute where coordinate plane things were all the rage amongst my online PLN.

Spend enough time with algebra teachers and the conversation turns deficit model: “They can’t even plot a point?” Which might be followed by “But with Desmos they don’t have to.” Maybe that makes this type of exercise even more valuable than it was when it originally rolled out. Here’s Dan Meyer when he wrote about the process of developing the Pomegraphit activity:

A gridded plane is the formal sibling of the gridless plane. The gridded plane allows for more power and precision, but a student’s earliest experience plotting two dimensions simultaneously shouldn’t involve precision or even numerical measurement. That can come later. Students should first ask themselves what it means when a point moves up, down, left, right, and, especially, diagonally.

https://blog.mrmeyer.com/2017/pomegraphit-how-desmos-designs-activities/

Then: I somehow stumbled upon Lucas Kwan Peterson, the food writer for the LA Times. I think this might have been the tweet that sent me on the quest:

His shtick is ranking categories of things on a coordinate plane – spicy snacks, Halloween candy, fast-food french fries, Girl Scout cookies. And I saw an opening:

What does it mean to be further right on the x-axis in this image? Higher up on the y-axis? And now it was plain as paste. Or, plane as paste, pardon the pun.

And in the days of teaching Algebra II from my dining room table, the Spicy Snack Desmos activity was a hit with my remote learning kids.

But since then, I’ve wondered: could we do more with it? Could my kids create their own Peterson-style coordinate plane ranking, of a subject of their own choosing? Then I switched to geometry and the question kind of went on the back burner. Until this year when Algebra II was back on the menu and I needed a next-to-last-day-of-the-quarter activity.

Got it. Went and dug up the 1.0 version of this activity I made for an e-day a couple of years ago. Made some edits and refined the questioning (one of my ongoing areas of emphasis for myself, especially post-pandemic).

And I rolled out The Coordinate Plane Power Rankings activity. I wanted students to come up with their own characteristics for the x- and y-axis labels, and to be able to insert photos and text of their items, so Google Slides was the right home for this activity.

I showed them Peterson’s Spicy Snacks graphic and asked the FH Doritos vs. FH Cheetos question, got some positive feedback on their understanding of positioning, and challenged them to create their own Coordinate Plane Rankings, using a topic of their own interest:

They jumped in and as I made my way from table group to table group I was able to peek over shoulders, encourage, ask clarifying questions, and just in general enjoy watching my kids create.

We had about an even split between kids who identified two strong and somewhat unique characteristics for the rankings, and those who just kind of stated the same idea twice. But they had strong feelings when they wrote their justifications for the rankings and I knew I had a good hook. We can always go back in and tweak the math understanding part after the fact, right? Even in a 45-minute class.

I had one more question to ask, as an extension. We looked at Peterson’s Fast Food French Fries graphic and write-ups, noted the shape of the grouping of points and:

We ran out of time to give this one the attention that it deserved. The categories were “texture” and “taste” and I was hoping they’d see how closely related the two descriptors were – like, it’s really hard to have a good-tasting fry with bad texture. That’s either a chip, or mashed potatoes. A location deep in the second or fourth quadrant doesn’t really make sense here.

But a couple of the kids who focused on music got the basics. Did you rank a song that had great lyrics but you didn’t like the beat? And the world is full of bangers that one day you look up and say “Wait, what did they just sing? Uhhhhh…. yikes”. In some categories that’s possible in a way that the fries relationship isn’t.

Also: everything he said about Del Taco is gospel truth:

Last time I had them I was sitting in the front seat of my car in a grocery store parking lot just off the 95 in Vegas and I’m not sure but I thought I faintly heard angel choirs singing.

One last thing: we’re in our third year of a conversion to a project-based learning school so we’re always seeking out community partners and/or an authentic audience, and even tho I haven’t made a #teach180 post in years I still love bragging on my kids on social. So I shared some of the day’s work and tagged Peterson in the tweet.

And this happened:

I agree. And thanks.

One other teaching/coaching-related thought: our evaluation rubric language has changed in the last couple of years, leaning heavily towards student-centered/student-focused classrooms as our exemplar. I definitely saw my kids taking control of their learning during this activity, creating a document that relied on understanding of concepts and then interpreting the graphs they made (evergreen algebra state standard). And we used a real-world example of the type of work I was asking them to do so they had an idea of what the final product could look like.

Those are good days in the classroom. Fun days. Fun with a purpose. I’ve got a few more things in the tank that will keep moving me in the direction we want to be as a staff and as a building, and hopefully keep my kids curious about math.

And if this post made you hungry, go check out Peterson’s take (inspired by the success of The Bear) on why it’s hard to get real Italian Beef outside of Chicago. And don’t skip on the gravy or the giardiniera.

Planning, And Planning Ahead

“Parabola Bean”

I toggled back to Algebra II this year after a couple of years of geometry, and we also switched from Google Classroom to the Schoology LMS so my planning has taken a slightly different form. I’m still working off our district-made curriculum map and using a digital calendar/planner as well as planning out quarters on paper, but I’ve been tweaking my lessons to fit an in-person audience since last time I taught Alg II we were still remote for three-quarters of the year, then hybrid.

In the midst of my planning, and sharing resources with the math team, I realized I needed something better to use as an assessment for quadratic functions and after rooting around a little bit ended up on the Parabola Selfie Project ($) from Algebra and Beyond.

I planned out three days in class for the work and one day for the gallery walk/parabola swap where they verify a classmate’s math. But that timeline counted on my students finding a parabola in the wild outside of school over the weekend and taking a couple of photos so they could start work right away on Monday morning.

OK, so what happens on Day One if no one comes back with a photo?

Writing in his Substack last week, Dan Meyer pointed out that one of the most important skiils a teacher needs is knowledge of student misconceptions, or common errors. This is not exactly that, but related. I’m not sure I would have had the foresight to do this as a first or second year teacher, but in the days leading up to the launch of this activity, I definitely scouted the building to see if I could find anything that could stand in for a parabola in a pinch. Then if we needed to, we could take part of that first day and make a field trip of the second floor and snap photos.

Planning ahead paid off. Big time. Virtually all of my students needed a parabola photo to get started.

Everyone got a parabola (-ish) photo they could pull into Desmos. Most were able to wrap that up in the 15 or so minutes we had left in class after our “field trip”. From there over the next couple of days they identified characteristics of their parabola including the equation of the axis of symmetry, coordinates of the vertex, named a point and its reflection, the zeros and y-intercepts. Then they wrote the equation of the quadratic in vertex form and enetered that to their Desmos graph to confirm it matched their shape. They also converted to standard form.

I’ve mentioned often in this space that we’re still dealing with the long tail of pandemic-era schooling. I plan everything knowing that my students are going to come to me with gaping holes in their foundational math knowledge. I spent much of the three class days we spent on the activity sitting at our table groups and providing support on things like binomial multiplication.

Which is good. One-on-one time is hard to come by in a 45-minute class.

We ran out of time to make poster displays so I collected their pencil/paper work and made a quick Google Doc where they could paste in the Desmos link, a screen shot of their graph, and their original photo and selfie. They submitted this doc to me through Schoology.

They did some pretty solid work. There was actual math in there. And I’m not above bribery so I made it a quiz grade.

But it was not a spur-of-the-moment decision to make this activity a quiz grade. Every topic we covered was included on the project. I planned from the outset to use this activity as my assessment for the first half of the quadratics unit.

We’ve spent a considerable portion of our PD time this year on NIET rubric, which is our evaluation tool. We want to help our teachers see how their actions in the classroom correlate to scores on the rubric. As part of our early-release time a couple weeks ago our PD focused on the areas where we as a school scored lowest last year: questioning, grouping, and problem-solving. Part of our purpose was to help our teachers see how they could increase their own scores, part of our purpose was to help them see the evaluation tool is meant to support teaching/learning and student achievement, and part of the purpose was to show that many of the descriptors are inter-related. How does intentional questioning relate to teacher content knowledge and assessment? Intentionality felt like the common thread.

I shared a couple of things out by email to the math and science departments a few days after the PD. Not only the Meyer Substack, but also some documents on the Backwards Assessment Model (BAM) from the Southern Nevada Regional Professional Development Program back in my Vegas Days, and an excellent article on the topic from Jennifer Gonzalez. Like, it’s the top search result in Google for “backwards assessment model”. That good. Gonzalez walks her readers through the process of matching assessment items to the standards before the teaching even begins. Super-powerful stuff.

It’s been one of my areas of emphasis for myself in a year when I’m kinda-sorta planning a new prep from the ground up. It helps me walk my talk. And, in a year when the state of Indiana is rolling out a streamlined version of the standards for each course, it will help us implement the new standards with fidelity.

As an added bonus, backwards planning also helps develop project-based activities as we continue in year three of a shift to a project-based learning school. In the SNRPDP materials, teachers see how they can plan a unit assessment together, determining what type of items will be used to assess what standards. Now trade out “project planning” for assessment planning and let’s go.

In a year when teachers in my district have seen their plan time cut in half and their department and PLC time cut to zero (at least during contracted hours) due to a schedule change, this might feel like an impossible ask. Like, “backwards planning? with what time?” But it also feels like the teaching equivalent of “measure twice, cut once”. A little bit of care and up-front planning avoids a lot of duplicate work and keeps us en route to the goal.

The T-Shirt Shop

Source

Plenty of things have changed about my day-to-day with my shift to instructional coach in my building, but one constant is my attitude about creating and sharing materials. I’ve been sharing everything I make with my geometry colleagues the last two years, and I’ve continued to push resources out to my fellow algebra II teachers this year.

It might even be more imperative this time around. Our district shifted from an A/B block schedule to a traditional seven-period schedule this year, meaning everyone’s plan time has been cut in half and they’re seeing twice the amount of student work per day. Creating problem-based activities is probably pretty far down the list of priorities. Sound like they could use a partner in that effort.

Source

Someone to set the table.

Julie Reulbach’s linear inequalities discovery lesson has been floating around in my head for a while. Meanwhile, our Algebra II team is beginning the year with Unit 3 (Linear Systems). We recognize the need to support our students with review in graphing and solving equations if we’re gonna jump right in to systems first thing. And we are in Year 3 of an ongoing conversion to a project-based learning school.

Taking all those points into account, my solution was to build a problem-based activity (think Three-Act Math) around Reulbach’s work. Thus “The T-Shirt Shop” was born. (Documents here, here, and here).

The scenario was students reseraching costs for t-shirts and hoodies to be sold as a fundraiser for a student group. In our set-up, a community organzation in Hammond had donated $2000 to cover the costs. My kids dove right in, brainstorming “knows” and “need to knows” and posting them, so that the group could share the collected knowledge. Then it was off to Google “t-shirt printers” and spend some imaginary money.

It was about this time that one of my students (returning to me from geometry last year) asked, “Hey Mr. Dull, this is cool and all, but when are we gonna do real math?”

My two big takeaways:

  • Real Data, chosen well and used well, hooks students in like no textbook or worksheet problem can
  • Real Data is messy, and sometimes that serves as a hurdle to doing the math we’re focusing on in class

Once they had prices in hand, their job was to determine combinations of t-shirts and hoodies that would cost exactly $2000, combinations that would be less than $2000, and combinations that they could not afford because the cost was more than $2000. They recorded these on paper and then entered them to a Desmos graph I had set up in advance and shared to them through Schoology.

And here’s where things kind of went off the rails. The “real math” they were asking for a minute ago? I had to provide plenty of support when it came to writing an equation of their “exactly $2000” line. Which cost us time, and kind of took away some of the power of the reveal when I changed the equals sign to “less than or equals”. And they had trouble articulating the significance of the dots in the shaded region.

Once I helped them see what they were seeing I asked them a series of reflection questions to close out the day, so they could put in words what it meant that the dots were above the line or below the line, and set the table for next time when we’d use this process on paper to solve systems of linear inequalities.

Part of the New Tech model is grading using a rubric of some of the NTN Learning Outcomes. I selected Knowledge and Thinking, and Collaboration. I was looking specifically for them to use multiple representations of the data (table, graph, equation), to understand and express the significance of the points in the shaded region or outside the shaded region, and that they participated in the brainstorming and research.

I’ll count the two days as a partial success as we introduced the problem-based learning model we’ll use throughout the year, and used one of our go-to sites in Desmos to meet the state standard of graphing with technology. I’ll keep building in supports for the “actual math”.

And now that I’ve taken a test drive I’ll keep my eyes out for one of my Algebra II colleagues who might want to roll it out in their class. With my full support, of course.

On The Flip

Michigan sunset ahead of an advancing storm

Snuck away for a long weekend to get my head straight before Back To School. Those 9:00 EDT sunsets in late July they got in Michigan are pretty sweet. But the world turns and things change.

That’s life on the eastern edge of the Central Time Zone. But wait, there’s more.

Abby Weppler, meteorologist at WSBT in South Bend (an hour east of me but roughly the same latitude), shared this the other day:

More than an hour less daylight by the end of the month in Northern Indiana. Things change rapidly aound here this time of year.

My teacher work days are the end of next week and students return on August 14. And for the first time since the remote learning year, I’ll be teaching Algebra II. In 20 years in the classroom I’ve never taught the same course for more than about 4 years in a row. I’ve flipped back and forth between Algebra I, Geometry, Algebra II, credit recovery in various forms, Project Lead The Way. I don’t mind the shuffle. Honestly, it keeps me fresh.

What it does mean is I’ll have to update my materials since the last Algebra II class I taught was designed for remote learning. I’ve got the course built in Google Classroom but it only exists digitally. I don’t have paper materials of any kind, those all went away with my last change of district. I’ve got a line on putting fillable notes and practice sets and review/quiz problems in place, and I’ll also need to update my lesson notes slides in Quizizz. Which (coincidentally enough) I attended a webinar this morning to get a certification in Quizizz. It’s good to go back and be reminded of some of the features in that platform.

It also will dovetail nicely with our continuing transition to Project Based Learning. I have a stack of slides-based activities I used as assessments the last time I taught in-person Algebra II and it also gives me the opening to re-introduce Desmos Art. Which led to a fruitful conversation with some of my Twitter teacher friends last week. (Yeah it’s still Twitter in my world just like it’s still the Sears Tower. Sue me.)

There’s ongoing cleaning and repair going on in my building as the summer winds down so that’s going to limit our ability to get into school and work on things early. Any prep will have to happen from home. We’ve got two work days in the building so classroom stuff can happen then. In the meantime I’ve reached out to my colleagues in the department to plan together and share project or activity ideas. I can feel the onset of the new school year in the pit of my stomach but just like always, it’s a good nervous. The nervous that comes with a desire to do your job well.

Let’s go.