#UnsexyMath Days 3/4: Bias and Sampling

A recent instagram post lead to four people (both IRL colleagues and #mtbos members) complimenting and asking for more info. I had a conversation or two with Kate Nowak and others about the need to share more “unsexy math” – the regular-but-still-pretty-effective things we do more often in our classroom than the super awesome projects or really pretty foldables. So here goes my first one.

To start of our new geography/statistics course, our students are creating a survey inspired by some aspect of human-environment interactions (if you didn’t know this (like me), this is apparently a HUGE part of what is learned in HS World Geography). After administering the survey, they’ll create propaganda and administer it, then re-administer their survey to compare the results.

The entire idea behind project-based learning though is that most of what we do in the classroom should be tied to the projects our students are currently working on. So to hook our students, we decided to try to survey them on the cuteness and strength of hippos, show them a video of Fiona the hippo, and re-administer the survey. It worked! For some, at least. There were a handful in each class that changed their rankings after the video. So then I told them about the project and the majority got really excited. “You mean we’re going to try to brainwash our peers? Sweet!” I think they might get disappointed when we have to turn down some of their propaganda ideas for legal and ethical reasons later this month but it’ll still be good. Another lesson to learn.

Anyway, after the project intro, we talked about bias. I asked students what they thought bias was, then I projected four questions with varying levels of bias on the screen:

  • Do you think bike helmets should be mandatory for all bike riders?
  • Do you prefer the natural beauty of hardwood floors in your home?
  • Do you eat at least the recommended number of servings of fruits and vegetables to ensure a healthy and long life?
  • Do you want your kids to receive a faulty education by having their school day shortened?

After reading them to themselves, they offered up thoughts on which ones were more biased than others, what made them biased, what the questions were trying to imply or what responses they were leading you to, and how to eliminate bias as much as possible from them.

Then we did some vocab matching. You can see the list of terms they are learning about here. These students mostly know each other from their PBL courses last year, but in the first few days we’ve spent time doing a lot of collaborating on Geography (and Biology and English) course work, low-floor/high-ceiling math warm-ups, talking points, etc. I was still shocked by how much conversation was happening within most groups. The goal was to see what they could match based on the context clues – could they figure out “nonresponse bias” and “size bias”, for example, just based on knowing what “nonresponse” and “size” were? (For the record: 18/20 groups could. The fewest amount of correct matches was 3, greatest was 8.)

After they checked and copied down the correct vocab terms and definitions, I projected four examples and explained them a little more. Students identified at least one correct type of bias for each example. I was happy.

To end class we started talking about sampling methods. I had each class come up with a question we could ask students (“How often are you late to school?”, “Do you like the school’s food?”, “What’s your favorite food?”, and “What’s your favorite color?” were the suggestions) and we created Frayer models for each sampling method with our “example” going along with the question the class wanted to ask and how we could use that method at school. I thought this would be important as they are actually going to be surveying students (or other things at the school… I’m really hoping one group does something on amount of trash/recycling or use of our refillable water bottle stations!), so hopefully when they’re doing their survey design they can choose an appropriate method.

We didn’t get through all of the survey methods in 3/4 classes, so we’ll finish that slideshow up Monday/Tuesday along with some/all of the questions on the student work document linked above.

This wasn’t anything monumentally new. They wrote or typed a lot of notes while I talked up front and projected info on the screen. But there was a lot of peer-to-peer and whole-class conversation and for that, this unsexy lesson was a win.

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First Day Plans

I still have more than three weeks before school begins but I spent hours each day this week working on plans for the upcoming school year. Nothing is set in stone yet, and all of these plans are totally dependent upon the assumption that I’m teaching certain subjects in certain rooms with certain people, so things will probably change… BUT here is the plan:

Man vs. Earth – 85 students for 3 hours every other day

  • Students will be randomly assigned to tables in groups of 3-4. We’re planning on doing visibly random grouping but changing every 2 weeks because we’ll be seeing students every other day. They’ve got fun names and logos which I’ll share once they’re nicely printed.
  • We’ll be starting the year’s warm-ups with the “Week of Inspirational Math”. We probably won’t do all of the activities associated with each day but will definitely do at least one every day for the first three weeks. Anyway, Day 1 is Four Fours. We have a decent amount of whiteboard up front (trying to figure out more VNPS in this new space) so I plan on having each group of students share a few of their solutions and especially having conversation about solutions that were found using different methods.
  • At this point we’ll be about ready to split the class into two groups, so we’ll briefly have a conversation about our program rules. The students will be a part of creating more norms, suggesting ways to celebrate success, and have a conversation on punishment vs. consequences in the next few days.
  • SPLIT:
    • I’ll be completing two team-building activities with the students. The first will be a small-group one about Cooperative Logic. Haven’t decided which of those activities we’re doing yet though so if you have suggestions please share. After that we’ll do a team-building activity as a larger group called Meaningful Adjacencies. I am super excited for the possibilities that can come from this activity.
    • My co-teacher will be working through map basics at this time with the other have of the class.
  • SWITCH AND REPEAT
  • Return to the whole class setting and complete a conflict management style assessment. The plan is to have students take the assessment and determine their preferred conflict management style based on the assessment results, then somehow discuss pros/cons of their style with other students that got the same one before having a whole class discussion about it. As I’m typing this I’m thinking talking points would be a good idea but that means I’d have to either replace one of the team building activities with an intro to talking points or move conflict management to a later date so we’ll see.
  • Finish up with name tents.

Geometry

  • Same warm-up as Man vs. Earth
  • Cooperative Logic activity
  • Meaningful Adjacencies activity
  • I’d like to do “Angles Around a Point” from Henri Picciotto’s Geometry Labs next but I need to know if I have access to pattern blocks. If I don’t have pattern blocks we’ll have lots of arguments surrounding things like “Is a hotdog a sandwich?” I know there are other Geometry teachers in MTBoS planning on doing this and I hope there’s a way we can share student reasoning!
  • Finish up with name tents again.

Hopefully all of this will work as planned but we all know nothing ever does!

2017 – 2018 #Goals

I know that you’re not supposed to take on too many things, so I just have three goals for this year. Just three.

  1. Be better at using effective, evaluative feedback. It’s the chapter I’m reading from Never Work Harder Than Your Students by Robyn Jackson. It was the chapter I needed to focus on based on my self-assessment and I know that it’s important and that I’m not great at it. I haven’t made an action plan yet (haven’t finished the chapter yet) but once I do I’ll blog it out. If you have suggestions for how to give effective feedback please let me know!
  2. Actually have discussions about the daily warm-ups. I think this will be easier to do if I have them all created ahead of time, so here is the PowerPoint with the year’s warm-ups. They follow a pattern but it’s not the same one each day of the week – I have two classes that will be every other day all year and two other classes that will be every day for a semester, so I felt like this would be the best way for me to be prepared. I can also have slips of paper printed for each type of warm-up and leave them in the classroom for students to use whenever they pop back up (or they’ll respond on Canvas).
  3. I’ve seen this blogged before but I don’t remember by who (I think it’s been multiple people). I want to be more conscious about how I help students, so when students are seated in groups and I see a hand raised for a question, I will go to the table to help but ask someone else at that table what the question is. Ideally this will create some forced collaboration (and/or some forced research either in their notes or online) that will eventually get them used to asking others for help. It seems to work well for other teachers so I hope I can get myself to stick to it!

There are a lot of other things I’m probably going to try but won’t beat myself up over if they don’t pan out or if I stop because it’s too much work. I’m teaching ProbStats and building another cross-curricular PBL course as a teach it this year (hopefully more will be done up front but we’ll see…) so I know there’s still a lot of content I have to re-learn and figure out how to best teach!

Online stats resources

Compiling this so I can get rid of the piece of paper where these are written down but also to hopefully help teachers and students looking for places to find/analyze/visualize data!

#teach180: This year’s first classroom

It’s been too long and I didn’t do much worthy of a #teach180 tweet today so I’m doing a #teach180 blog post instead. Going to try to blog at least once a week during this school year, we’ll see how it goes. Be forewarned that there are a lot of pictures in this post!

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I’m traveling between three classrooms and two offices this year. It’s a pain. Thankfully the classrooms, my students, and my co-teachers are generally awesome and so far it’s been worth it. The first classroom is really long! When you walk in, you’re in a small entryway. On one side of this entryway is a supply table which has calculators and anything students leave behind. Don’t freak out too much, the keys are mine.

 

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Right past the supply table is the weekly schedule board and the teacher space. I didn’t take a picture of the board, but it’s broken down by day and each day has two parts to it:

  • broad topic (this week’s is probability)
  • daily question we’re working toward being able to answer (“what happens when events depend on each other?”, “what happens when probability changes based on given information?”, “how many different outcomes are possible for this experiment?”, etc.)

 

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On the far left of the board I also have the weekly homework assignment posted. On the far right of the board I have my weekly paper holder. Our copiers are unreliable, so I try to only make copies once or twice a week for all of my classes. I also don’t take work home during the week and rarely on the weekends, so this helps me keep organized.

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Currently students are in sets of two or three facing the front of the room. The teacher I’m sharing the room with and I have developed four seating patterns that we think we’ll be using regularly throughout the year:

  • black, which is individual seats (for standard assessment days)
  • green, which is the sets of two or three that they’re currently in (for notes or partner work)
  • green, which is two teams facing each other with students in pairs (for debates and games)
  • red, which is groups of four to five (for small group work)

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In the front of the classroom there’s a cabinet in the corner, which is where we have supplies that students can always use. Right now it’s pretty empty and only contains scrap paper, scissors, pencils, colored pencils, and highlighters. There’s also my “student of the week” trophy and two dinosaurs that I occasionally give to students who need them.

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Immediately to the right of that cabinet is our school rules bulletin board, which currently has the schedules, tardy policy, and electronic device policy. My classroom-sharing teacher is planning on changing the tree scene with each season.

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On the far end of the classroom are two boards for student use. One has the 2016 Challenge thanks to Sarah Carter at mathequalslove, and the other has Sudoku thanks to Christie Bradshaw at Radical4Math. Students can use these during our study hall time or if they finish something early in class.

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Finally, in one set of cabinets in the corner my students have personal boxes. This is where students can keep personal supplies, papers they don’t want to lose, etc. from day to day and it’s also where I put work when students are absent and where I pass back 98% of papers to. All of the cabinets are built into the wall and a lot of my stuff is in electronic form so this was a good way for me to utilize that space!

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So that’s my current AFDA classroom. I’m in there for first block every day from now until the end of January, when my schedule changes and I’ll be moving again for the spring… sigh. Bonus pictures below of decorations on our math department office windows. A handful of quotes I’ve collected over the past few years that are school-appropriate and potentially teenage-worthy as well as a collection of photos from Sara Van Der Werf’s Math Wall of Shame.

 

Tracking Student Achievement #MTBoSBlaugust

I blogged previously about how next year our math department has decided to move toward a department-wide grade replacement policy (see #MTBoS30 Day 9: Grade Replacement vs. Standards Based Grading) and I’ve been working on figuring out how I can still include students in the process. I enjoyed using Dan Meyer’s concept checklist over the last two years. Sometimes it was a hassle, but for the students that actually kept track of theirs they enjoyed knowing what their strengths and weaknesses were (and getting those stickers!)

Last spring semester I taught a new class called Algebra, Functions, and Data Analysis – this is a class that is not tested by the state but still has standards. I mostly used stuff from the other teacher who was teaching AFDA at the same time as me and only glanced through the standards before teaching the course… good job, past me. But, we live and learn. There were some days that seemed too easy and repetitive and others that seemed totally over my students’ heads, and the same was true about the quizzes and projects they completed as assessment. I didn’t really enjoy that, but I felt a little overwhelmed without a planning period so I kept pushing through. Well I’ve finally sat down and looked at the standards and boy did we do some interesting things. We taught multiple things that definitely are not required! Some of which I’ll be keeping, and some of which will probably get tossed.

ANYWHO, I digress… After reviewing our curriculum map and the state standards, and a little inspiration from someone on Twitter (I forget who) I made up slightly new Achievement Trackers. My plan is to have students keep these at the front of their assessment section of their binders so they’re easy to find.

Things I Like:

  • students being cognizant of what grades they’re earning (and hopefully why!)
  • helps me better plan lessons and assessments
  • the students have less to keep track of compared to the old concept checklist

Things I’m Not Sure I Like:

  • some of the wording isn’t necessarily the most student friendly/some boxes have a lot of text
  • it will take up two pieces of paper front/back
  • the homework section at the beginning of each unit

Let me know what you think and if you have any suggestions!

Experiential Learning #MTBoSBlaugust

hated history class growing up. HATED. I’m pretty sure this probably broke my dad’s heart on more than one occasion; a long-time English teacher who had struggles in math and science, I know that my dad had (has!) a passion for history. By the time I got to high school it was pretty much the only subject he could help me out with, and I needed it a lot. But all I remember is learning about the explorers, the American Revolution, the Civil War, and more over and over and over again. Why, by the time I got to my junior year of high school, did I still need to be spending time in class learning about The Boston Tea Party??? To me it was so incredibly pointless. I spent a lot of time agonizing over readings from my textbook and complaining about all of the people and events in there.

Fast forward to now, and I still don’t like history class. But I do enjoy learning about history. I love living in “America’s Historic Triangle” and getting to touch and see and do things like the Native Americans, early settlers, and soldiers in the American Revolution did. Two years ago I spent part of spring break at Independence Hall in Philly and walking the Freedom Trail in Boston, and last year I did historic walking tours and visited plantations in both Charleston and Savannah. Sunday morning I did an audio tour of Alcatraz. All of those experiences were awesome.

Being able to interact with history through artifacts and storytellers is what makes me enjoy learning about it still to this day. Is it possible to bring some of these things in the school environment? Yes. Is it possible to do the same in a math classroom? I’m not sure.

There have been a lot of amazing #MTBoS teachers doing awesome things involving the history of math; I’ve seen mathematicians of the day, research papers, poster projects, and more. And there are even more teachers doing amazing work within the classroom to help make math accessible to students. But again, how much are those practices helping students connect with and experience the math? I’m not sure. I’m not sure what the best way is for students to experience math. I’m not even really sure what that means. It probably means something different for everyone and there are almost assuredly different ways to do it.

But this is one of my goals for the year: to have my students experience math in a way they haven’t before. I know that this will happen in the Physics by Design class I’m co-teaching (which I’m super excited about and will blog about later this month) so really the focus will be on Algebra, Functions, and Data Analysis. Last year we did exclusively alternative assessments for each unit’s summative assessment but I was unhappy with them as a whole. So here we go. Year 3. Time to pull out those old assessments and get to work.

P.S. I also learned a lot about water this summer through my awesome time in Sarasota with DukeTIP, way more than I ever thought I’d be interested in learning. I can boil it down to: nature is pretty awesomely resilient, but we’re working pretty hard to ruin that.