Author: brian

I’ve contracted a SEVERE throat infection. I cannot speak at all.

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I recently wore this sign on my neck during class. I placed it around my neck and went about the business of being the teacher in the classroom.

At first there was high levels of concern. There were comments like “Are you ok?” or  “Stay away from me, I don’t want it.”

And then one student remembered to having seen my speaking just fine earlier in the day. There were snickers, laughs, and smiles all around. They were picking up what I was putting down.

I silently gestured them through a slide that explained that although I couldn’t verbally communicate, this didn’t mean that they couldn’t learn. There was a handout. They have brains. They had each other. No excuses. The focus was recursive sequences.

I don’t think this idea would work well with any class, but it was an awesome experience with those I tried it with.

There were natural leaders who volunteered to demo examples on the board for the class. Some kickstarted conversations about what they noticed and wondered. There were others who made their way across the room to seek help or give it to other groups. And yet others did their thing on their own or with a partner.

Throughout all of this, I said nothing and did very little. For the entire period I peered over shoulders, pointed out (literally) interesting steps in student work, and wrote on the board the time remaining before the exit slip was to be administered. I reminded them (with a slide) that they needed to ensure everyone in the class could be successful on the exit slip, as it was the measure of their success as a team. (They ended up being 90% proficient.)

I closed by reiterating with them the fact they need me far less than they think they do. I’m no gatekeeper of knowledge.

 

bp

Developing rational exponents through geometric sequences

Soon I’ll be teaching rational exponents in algebra 2. I’ve never found an intuitive way of teaching it…until now. Thanks Bowen.

The approach leverages geometric sequences. I’d love to regurgitate it, but this tweet from Bowen is my source and sums it up:

The unit prior focused on sequences with a heavy emphasis on geometric sequences, so this is the perfect bridge to developing this idea that most students find confusing. It all comes back to repeated multiplication, as it should.

In the past, I’ve usually had students enter various expressions (e.g. 100^(1/2)) into their calculators to stumble upon the relationship between rational exponents and radicals:

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But this painfully ignores the mathematics behind exponentiation and instead lures them into believing that these two concepts are magically connected through a few keystrokes on their calculator. It treats rational exponents as an isolated concept and unrelated to repeated multiplication.

After discovering my new strategy for teaching rational exponents, I found this video from Vi Hart on logarithms. The similarities run deep.

 

Now I can’t wait to teach logarithms.

 

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On the purpose of exams

Teachers: think of a recent class exam you administered. What purpose did it serve?

In many educational circles, class exams are thought of as assessments that teachers use to measure student learning. It’s an opportunity for the student to demonstrate their abilities. In other cases, exams simply serve as a grade – nothing more, nothing less. Often times, exams mimic standardized exams and help prepare students for what lay ahead at the end of the school year.

A recent comment by a colleague has me wondering what an exam tells me about my students’ mathematical abilities that I shouldn’t already know.

In other words, if I’m throughly assessing my students on a daily basis and attune to their learning, isn’t a class exam merely a formalized way of collecting this data? For the assessment-conscious teacher, isn’t an exam just more needless paperwork?

I beginning to think so. But this doesn’t mean that they are worthless.

Exams are great tools to support retention amongst students. In a low-stakes environment, they challenge students to individually recall information in context that can lead to high levels of reflection. When used in a group setting, like a two-stage exam, these assessments serve as a springboard for collaboration, meaningful conversation, and deep learning.

 

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Day in the Life: October 24, 2016 (Post #4)

I’ve decided to chronicle this school year through my blog. It’s part of Tina Cardone’s Day in the Life book project. This is the fourth post in the series.

5:30am | I wake up. I rode the Tour de Bronx yesterday, so I’m somewhat sore. To add to the that, on my way back home from the ride I had a pretty nice spill over my handlebars avoiding a young boy in a crosswalk. It could have been worse, especially for the boy. Thankfully, I just have some minor dings.

I have breakfast, read a bit, and I’m out the door.

6:55am |  About halfway to school I hear a dreadful sound….pisssssss. A flat tire. I don’t have a pump or any tubes with me so I hail an Uber back home to drop off my bike. Unfortunately, I still haven’t replaced the front wheel on my other bike that got damaged by a careless driver, so I’m forced to take public transportation. Rushed and flustered, I arrive at school at 7:55am. I spend the few minutes I have before first period prepping the lesson on introducing inverse functions.

8:12am | First period. The lesson on inverse functions is mediocre at best. I adapt Bob Lochel’s approach, but the kids struggle to make the connection between the coordinate pairs of inverse functions. The class is composed of seniors who aren’t particularly in love with math, so my struggles with them are compounded. I still haven’t figured this class out. This is their second year in algebra 2 (by design), so some of them immediately begin using the procedure for finding the inverse of a function (interchange x and y and solve for y).

9:00am | On top of a crazy, upside-down morning, I have a coverage 2nd period for a teacher that is absent today. It’s a good group of kids, but it eats up one of my preps which I definitely need on a day like today to catch up. I recognize many students from the class and realize that I actually know students now.

10:00am | Finally back in my room for a period to sit and work. I tweak my intro to inverse functions from first period for period 4 and prep my lessons for periods 5 and 8. I send out a couple of emails, one of which is a letter of reference for student at my previous school.

10:40am | My period 4 students walk in. I do my best to give high-fives on entry. It really does have a positive impact on the start of class. They’re also investigating what it means for two functions to be inverses of one another. The lesson goes slightly better than with 1st period, but the students still have trouble discovering the relationship between the domain and range of inverse functions. I am forced to walk them through the tail end of the lesson.

On a semi-unrelated note, I also realize at the end of the period that the homework questions this year haven’t been fully aligned with the lesson. This explains a lot.

11:27am | Period 5. This group is one day ahead of my other class, so today we’re focused on the algorithm to find the inverse of a function (interchange x and y and solve for y). Things go smoothly. The students spend over half of the period in groups working collaboratively. The energy in the room is great, the conversation is engaging, and the time flies…and as all this is happening, I realize that this sort of what I hoped for group work this year. But this is one of the few times (like 3) that it’s actually happened. Before today, if students are working in groups, it’s usually for a couple of minutes and then we come back together as a whole group. I must structure more time where students are working without me.

12:15pm | This is “lunch,” whatever that means. I spend most of the time prepping for my periods 7 and 8, meeting with a co-teacher, and making copies. The day is a blur. I take a couple bites of a sandwich just before the bell rings.

1:03pm | Period 7 is retaking a checkpoint (i.e. exam) from last week. The period is low-key. I spend some time at the beginning and end of the period connecting with one of the more challenging students. I sit next to her and chat. She’s an awesome young lady with loads of energy…and she’s growing on me. After this period, I can sense the day getting better.

1:53pm | I welcome my lone group of freshman to period 9 algebra. A great group. We’re studying linear equations. Due to a lack of common planning, my co-teacher and I haven’t really ironed out the details of the lesson…and it shows. The goal was to have students identify the series of operations performed on the variable and then use this to discover the series of inverse operations that would need to be performed to “reverse” those operations. Let’s just say a second day is needed.

2:40pm | Faculty meeting. We meet as an entire faculty and then break off into co-planning teams. My co-teacher also teaches with two other members of the math team, so it’s all over the place. We talk moving some ninth graders around and also some structures for tracking understanding. A colleague mentions how he has one or two “focus” questions for his daily homework check. He takes note of which students get it and don’t by means of his formative assessment and uses this info for intervention purposes. I love this and make a note to start doing it in some form. I manage to spend some time structuring the parallel teaching that we hope to begin implementing later in the week. We hope it turns into somewhat of the norm.

4:00pm | Grades for the marking period are due this week, so continue the process of finalizing those for around 30 minutes. I targeted some kids a few weeks ago as in danger of failing and I’m please that many of them are not going to fail due to some tutoring that I did with them.

4:30pm | I get word that there’s a girls volleyball game, so I head down the gym to end this stressful day on a high note. It doesn’t disappoint. I don’t any of the girls on the team, but I love attending school sporting events. I have great conversation with a few students (one of which is mine) selling goodies at the game as well as the drama teacher who also attended. She’s also in her first year at the school.

5:15pm | I’m too lazy to catch a bus, so I hail another Uber back home. My bike has spoiled me.

I’m still backed up from the day, so I spend about a half-hour on some planning when I arrive home. I do everything I can to stay away from work on weekday evenings, but today was one of those rare occasions where it was absolutely necessary. I’m exhausted and get to bed around 9:30.

1.Teachers make a lot of decisions throughout the day. Sometimes we make so many it feels overwhelming. When you think about today, what is a decision/teacher move you made that you are proud of? What is one you are worried wasn’t ideal?

My hope was to have students more or less stumble upon the relationship between inverse functions. The planning was there. What ended up happening in large part was me forcing this discovery by telling students what they should have found out themselves. Their learning didn’t come naturally. Should I have left them to struggle? How could I have made the activity better align to my goal?

2. Every person’s life is full of highs and lows. Share with us some of what that is like for a teacher. What are you looking forward to? What has been a challenge for you lately?

My days this year have been so long…and grueling. I don’t think I’ve had days this taxing since my first year of teaching. Seriously. I find myself constantly planning to keep my head above water and my classroom routines are essentially nonexistent.

My students are AWESOME and they are very capable of amazing things. But right now, in many ways, I’m holding them back.

3. We are reminded constantly of how relational teaching is. As teachers we work to build relationships with our coworkers and students. Describe a relational moment you had with someone recently.

The after school interactions at the volleyball game were truly a breath of fresh air. For some reason, I feel I’ll always remember these moments that I spent with the students. They were laid back, natural, and just what I needed.

4. Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What is a goal you have for the year?

Goals? Today marked the close of the first marking period and work towards my goals has been fairly minimal thus far. Most of my energy so far this year has been dedicated to establishing standards-based grading with students who are accustomed to traditional means of assessment. This has been exhausting. But this has help me improve my SBG structure to better reflect student learning…I think. More on this later.

5. What else happened this month that you would like to share?

It’s almost November. Wow.