Trying to find math inside everything else

Whole Class Test

I teach an SAT Math Prep this year, which has been an interesting challenge. We basically started off with lessons on all the different content in the exam, then had a long section on tactics (which can be framed as test-taking tactics but I noticed are often just tactics for solving problems in general, which was nice). But we reached the end of those, and the (in-school) SAT is a month away. The obvious thing to do is to just keep doing practice exams, but that can get a bit boring, for both me and the students. Plus, the class that meets Tues/Thurs hasn’t had very many graded assessments this marking period, so I needed to give them something.

I had decided that grading them on correctness in a practice SAT is not appropriate. I had told them this before, and they knew their grades on their assignments were more for things like how they applied the tactic we were learning. But last class they walked in and I gave them a Part 3 exam (the non-calculator part) and told them it would be graded – but there would be a plot twist. For right now, just take it individually, except this half of the room should start from the back and go forward. Oh, and you get 5 fewer minutes than normal.

While they were working, I went around on my whiteboards and put up the numbers 1 through 20 well spread out, and an ABCD for 1-15. (I wish I had taken pictures!) This started to get them suspicious. When time was up, I told them my grading scheme: it was out of 5 pts, and they lost a point for every question they got wrong. So if you got 15 right, that’s a 0. But! They had the remaining 20 minutes of class to work together and figure out what the right answers should be. And if anyone got less than 15, the whole class lost a point – forcing them all to work together. (With limits, of course – they won’t be penalized for that kid who went to the bathroom for 15 minutes during this, for example.)

A suggestion I made to them was to go around and make votes for their answer for each question. A clear consensus might mean that that is the right answer. However! Don’t be afraid to put your answer down even if everyone else’s is different. I’ve seen questions where only one person got it right. I told them they need to convince each other of what the right answer is.

Let me tell you, I heard so many great conversations as they and I went around the room. Because it’s the SAT, no one gets them all right, so everyone is being pushed to make a convincing argument that their answer is right. Students who weren’t sure got explanations from others. It was delightful!

About halfway, I noticed a clear consensus for about 15 of the 20 questions, but the middle 5 were really quite split. So I lead the class in sharing out their reasoning for some of those questions – never saying what the right answer was, but again letting them convince each other.

It was a nice collaborative effort – I highly recommend it.

Vietnamese Age and the SAT

Dwight Eisenhower was born on October 14, 1890, and died on March 28, 1969. What was his age, in years, at the time of his death?

(A) 77
(B) 78
(C) 79
(D) 80

When my boyfriend went to his grandmother’s funeral, he found himself confused about exactly how old she was. Was she 93 or 94? He heard different people say different things. Eventually he figured it out. In Vietnam (and apparently in other places in East Asia), when you are born, you are 1. The next year, you are 2. And this ticks over at the beginning of the solar year, not on your birthday. So I, born on December 22, would, 374 days after my birth, have been considered to be 3 years old using this reckoning. (It might be more accurate to say that I’m in my 3rd year – being alive during 1985, 1986, and 1987 at that point.)

Earlier this week, in my SAT Problem Solving class, we encountered the problem at the top of this post. The correct answer, according to the book, is (B) 78. But according to the Vietnamese reckoning, he’d be 80, and the answer would be (D).

Before my boyfriend went to that funeral, I wouldn’t have even looked at this question twice. I had never heard of another way of determining age. And I’m willing to bet the people who wrote this question haven’t, either.

It’s a small example of the way tests can be biased, and how having more diverse voices in the process could help avoid this kind of mistake.

TMC17 Speaker Proposals

We are starting to gear up for TMC17, which will be at Holy Innocents’ Episcopal School  in Atlanta, GA (map is here) from July 27-30, 2017. We are looking forward to a great event! Part of what makes TMC special is the wonderful presentations we have from math teachers who are facing the same challenges that we all are.

To get an idea of what the community is interested in hearing about and/or learning about we set up a Google Doc (http://bit.ly/TMC17-1). It’s a GDoc for people to list their interests and someone who might be good to present that topic. The form is still open for editing, so if you have an idea of what you’d like to see someone else present as you’re writing your own proposal, feel free to add it!

This conference is by teachers, for teachers. That means we need you to present. Yes, you! In the past everyone who submitted on time was accepted, however, this year we cannot guarantee that everyone who submits a proposal will be accepted. We do know that we need 10-12 morning sessions (these sessions are held 3 consecutive mornings for 2 hours each morning) and 12 sessions at each afternoon slot (12 half hour sessions that will be on Thursday, July 27 and 48 one hour sessions that will be either Thursday, July 27, Friday, July 28, or Saturday, July 29). That means we are looking for somewhere around 70 sessions for TMC17.

What can you share that you do in your classroom that others can learn from? Presentations can be anything from a strategy you use to how you organize your entire curriculum. Anything someone has ever asked you about is something worth sharing. And that thing that no one has asked about but you wish they would? That’s worth sharing too. Once you’ve decided on a topic, come up with a title and description and submit the form. The description you submit now is the one that will go into the program, so make sure it is clear and enticing. Please make sure that people can tell the difference between your session and one that may be similar. For example, is your session an Intro to Desmos session or one for power users? This helps us build a better schedule and helps you pick the sessions that will be most helpful to you!

If you have an idea for something short (between 5 and 15 minutes) to share, plan on doing a My Favorite. Those will be submitted at a later date.

The deadline for submitting your TMC Speaker Proposal is January 16, 2017 at 11:59 pm Eastern time. This is a firm deadline since we will reserve spots for all presenters before we begin to open registration on February 1st.

Team TMC17 – Lisa Henry, Lead Organizer, Mary Bourassa, Tina Cardone, James Cleveland, Daniel Forrester, Megan Hayes-Golding, Cortni Muir, Jami Packer, Sam Shah, and Glenn Waddell

Name That Solution

I was reviewing solving equations for my SAT Math class. It’s a tricky thing to do because “equations” includes linear, systems, quadratic, and exponential equations. A lot of different skills to go over in a short amount of time.

After working through the requisite problems, I wanted a little more practice, so I came up with a game that they could play, based on the Bid-a-Note sections of the old “Name That Tune” game shows. I called it Name That Solution. Gameplay goes like this:

• Start over with a simple equation, like “x = 2.”
• Each turn, a team can change the equation in one way to make it more complex. (For example, make it “x + 3 = 2” or “5x = 2”.) Only one operation and one term can be added at most per turn. The team finished by saying “I can name the solution of that equation.”
• On a team’s turn, they may challenge the other team to, in fact, actually solve it. (“Go ahead! Prove it!”) If the challenged team can, in fact, solve the equation, they earn a point. If not, the challenging team gets a point.
• First team to 5 points wins.

They played on whiteboards so they can change the equations quickly. The students quickly learned to not overextend themselves when making the equations harder, lest they find themselves challenged. So it leads to a nice exercise of constantly mentally making sure you know the steps to solve something before you take your turn, getting a lot of practice.

At the end of one of the classes, I did a big class-wide version, half the class versus the other half. But they wound up being very conservative, with neither team challenging the other and only take moves they knew they could solve. Which I guess was the point.

That final round.

Day in the Life: October 5th, 2016

This is part of the Day in the Life Project.

5 1/2 AM – alarm goes off

5 11/12 – I actually get out of bed and start getting ready. I always get home late from trivia on Tuesdays, so Wednesday mornings are the toughest. On top of that is this being the first day of the school week thanks to Rosh Hashanah, and it was a struggle.

6 11/20 – Out the door. Even though I got my bike fixed yesterday, I’m not taking it today because I’m carrying my laptop, all my student work, and the five packs of markers I bought online. I head to the subway.

7 1/20 – That took much longer than it should have. If I had gotten on the first local train, it would have beaten the express I waited for. But the express did wind up beating the second and third local that passed through, so I guess it was right to wait.

Because I’m teaching Mathalicious’s Sweet Tooth in Calculus today, I spent the subway right reviewing the assignment and lesson guide. (Since I taught it last year, it was more of a review than a deep dive.) While I read it, I decided that I needed to add some supplemental questions to more explicitly tie it to what we’ve been doing with area functions and Riemann sums. So that’s on the agenda.

I got off the train, loaded up a podcast (Within the Wires), and started walking to school.

7 7/12 – I arrive at school (after also stopping to get breakfast). As soon as I get in a guidance counselor pops in and asks me to find a room in the school for the attendance meeting they’re having today. I run up to my classroom and grab my SAT book to prep for my problem solving class, then settle into my office to get some things done.

8 – Official start of school day

8 7/15 – I’ve written up the supplemental sheet for Sweet Tooth, adjusted my lesson plan, and decided what we were doing in SAT Problem Solving. I also had to print a schedule for a student who didn’t have one at the request of a different guidance counselor. Now to get some printing and copying done.

8 4/5 – That was surprisingly painless, considering it’s the equivalent of Monday morning. Maybe it’s because I went at the end of 1st period instead of the beginning of 2nd, when there’s a line. Now the morning announcements are going on, which make me very grateful I don’t teach 2nd period (and, thankfully, it is in my power to make sure I never do).

9 23/60 – I stapled all my feedback slips to the assignments I graded over the weekend and looked into some of the IEP Compliance issues that need to be corrected soon, as well as a few other miscellaneous programming tasks I had to do. Now I’m just last minute prepping myself for class.

12 1/2 – Well, that was a mess. SAT was fine, but Calculus – I tried to do too much. Sweet Tooth was a really great lesson last year, but it was much later in the year after the students had had more time to grapple with the ideas. But because of the holidays and the fact that I may have jury duty next week, I was feeling pressed for time, and so I tried to squeeze the lesson that should have been a follow-up to Sweet Tooth into the same period. And now I’ll need to take another period (or at least another half) working through those ideas anyway. During 4th period my AP came in for a formative observation (not rated), and I’ll be meeting with her tomorrow for feedback. Not the best first lesson to see.

I’m also having a hard time adjusting to not being in my classroom all the time. I spend most of my day in my office and carry all my stuff to the classroom when it’s time. So I feel like I’m spending so much class time doing things like setting up my computer, putting all the papers in the right spot, etc. Most days the SMART board markers don’t work, which was always something I could check before class started but now I can’t, and if they don’t work, I just have to roll with it. It’s a little stressful.

After class ended I went out to Trader Joe’s to grab some lunch, which I am eating now – though my lunch period ends in 5 minutes.

13 2/5 – I’ve spent all of 7th period trying to figure out exactly what needs to be changed and what doesn’t for compliance purposes. Usually the students are getting all the services they need, but the documentation doesn’t match up, so it’s a lot of getting all those ducks in a row. And the systems for doing it are, of course, not all neatly aligned and in one place.

14 4/15 – Just had to do some schedule changes with one of the guidance counselors and chatted with the AP of Special Education about next steps for the compliance process. Then I futzed around on the Internet for a bit because I’m running low on brain capacity. I was intending on staying late today to do work, but I’m not sure I have it in me, thanks to my lack of sleep last night.

14 1/3 – Official end of the school day.

14 4/5 – I made copies of the assignment that I’m going to do either tomorrow or Friday – I’m not sure yet. I had originally planned it for today, and thus made it yesterday, but decided yesterday to move in back in favor of Sweet Tooth. Based on how today went, I’m not sure I want to move forward to it – but I might also want to, as it might let me clarify some things in a new way rather than sitting on the same ideas in the same way.

Either way, I’m heading home now.

17 – Made it home. I took the long way around, playing Pokemon Go and getting a lot more walking in, and stopping for a snack at the taco cart. (I had wanted to go to the Chinese bakery, but ran across the taco cart first.) Now I’m checking up on e-mails that I got in the past 2 hours, and then I’ll probably watch some TV.

19 1/2 – Or wind up falling asleep. I guess I really needed that nap.

20 1/2 – I made a smoothie for dinner and now am working on my Interim Assessment – sorta like midterms that my school gives but we need to submit several weeks ahead of time. It’s a weird thing to me and I still don’t understand how/why it’s different from a normal test – especially for a course that is not taught by more than one teacher, such as my Calculus classes.

21 1/2 – I’m giving up the ghost on this one – I’ll work on it more in the morning. Luckily I’ll have time then since I’m already planned and copied for tomorrow. Now it’s time for maybe a little Ace Attorney 6, then bed.

Reflection

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?Well, the decisions I made planning Sweet Tooth are documented above. My good decision today was probably in eating right, haha.
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?I’m looking forward to settling into a routine. It’s started to come about – programming is starting to peter off (for now), but we have a lot of holidays disrupting the flow.
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.I went to a trivia night with some of my coworkers (they brought me in as a ringer). I got to know some of them better – one of my APs tried to purposely make two of us friends because we have a lot of interests in common.
4. Teachers are always working on improving, and often have specific goals for things to work on throughout a year. What have you been doing to work toward your goal? How do you feel you are doing?My Friday Letters, of course, have been helpful, but I’ve also tried to be more actively there. Some students invited me to see their volleyball game and I actually went, which was nice.
5. What else happened this month that you would like to share?I caught a lot of Pokémon? September is always a work-heavy month, so not a lot outside of it.

Day in the Life: First Day

The day I signed up for in the DITL project was the 5th, but this month that was Labor Day. So I figured I’d write up both.

Monday, September 5th (Labor Day)

I woke up at 930. Not exactly a getting-ready-for-the-school-year time, but not, like, noon, so it’s fine. I roll up and get started on some chores – laundry and dishes. While the laundry goes I work on the blog post I wrote about teaching Integration first. Thinking through the post helped me solidify how I wanted to start the year in Calculus, so that was productive.

Laundry, however, took much longer than it should’ve because one person decided to split a single washer load into all three dryers and hog them for an hour. That gave me some time to start working on captioning the photos from my August trip. All the chores were done and we were ready to go around 1215. We grabbed some lunch and headed to the apartment of a friend of my boyfriend. There we played some video games (including the hilarious Ultimate Chicken Horse, a game where you lay traps that everyone has to race past and over to get to the finish, and the creepy Push Me Pull You). Then we played some board games (Coup Rebellion, Tokaido, and Alhambra). Around 730 we went for dinner at a nearby Japanese restaurant. Then the BF and I went home to get some rest for the big day tomorrow.

Tuesday, September 6th (First Day Teachers Report)

I had my alarm set for 7, but I woke up at 630 because I couldn’t sleep anymore. Anxious? Trepidation? Excitement? Who knows.

After getting frustrated with Facebook a bit because of the aforementioned subtitling, I got ready and caught a ride with my BF so I could get there by 8. There were bagels and fruit and tons of people excited to see each other. It made me miss my old LAD coworkers, as we’re all scattered to the winds after fleeing our previous school. I settled into a table in the library and found two more teachers new to the school. Of course, I’ve been here for 15 days over the summer working as the programmer, so I know some people fairly well, but there’s still so many new faces. And this school is over twice as big as my old one! So it’s a little overwhelming.

Around 830 my principal (who is also new to the school) does an introduction and talks a little bit about the instructional focus for the year. Then she introduced some key people like the APs, as well as the new teacher (there are 7 of us out of the 71 teachers on staff). After that the programming team and the guidance counselors were dismissed while the rest of the staff stayed for other procedures, announcements, and PD.

My coworker Luke, who was the programmer last year and has been working with me on it all summer, and I went down to our office and started to work on the final touches of the schedule  (as when I had left on Friday evening all the students had schedules).

Or so we thought.

I was working on mapping course codes (tying one class to another) and Luke was replying to some emails. But then we got more emails. And more. We had to send out a list of students without full programs to the guidance office so they could tell us what classes to give them. We had a teacher who didn’t have a schedule (because she is retiring in a month) in need of one. We had sudden changes in who was teaching certain classes that needed to be accommodated.

Around 1015, the meeting upstairs was on break, and so we started to get a lot of teachers popping into the programming office to make their requests in person. Often they were the results of typos, or information we didn’t know before (such as, say, Chemistry needing to be in a certain room for labs), or new students arriving that had to change classes around.

Around 11 I went and delivered the newest, most up to date teacher schedules I had to the meeting, as they were going to do a run-through of a school day to make sure no one was teaching the wrong amount or in two places at once (or two classes in the same place at once). Of course, lots of confusion and issues arose from that. I sent out a staff email to collect all of those issues and began hammering them out.

At 12 the school’s food services provided food for all the staff and faculty members in the cafeteria. Luke and I headed down and got some – it was pretty good for school food (though I felt the same way last year, too). I sat at a table with some people I hadn’t met yet and we chatted a little bit. But by 1230 it was back to programming.

By this time I finally got back to work on those mappings I had barely started in the morning. I finished those around 2 and did some final checks on the student schedules, but found out that a lot of changes made that day have caused overcrowding issues that we’d have to resolve. On top of that, the AP of Special Education came in to request the schedules of all of her students, so she could check they had the right services. I got those printed out and waited for her changes, as those would have a big effect.

Around 3 I noticed a big problem with the schedules of about 30 9th graders, so I had to really work on how to solve that problem, considering everything was so tight and locked up for most of the school’s schedule by now. During that time we were getting changes from the AP of SPED, throwing even more disorder into the process and I watched those “Students Partially Schedules” counter tick up higher and higher. Around 430 the AP who’s been in charge of programming came in and we ordered some sushi as a snack. By 530 we finally finished those SPED changes, and now had to make everything work again.

By 715 we were starting to hit a roadblock. 1120 students were fully scheduled, but 12 remained and we were just running out of spaces in the classes they needed. Luke and I took a short dinner break to Trader Joe’s, and I informed my trivia team that I would not be making it to trivia tonight.

Armed with a burrito and an egg salad, we set back into figuring out these final few students. We also worked on closing gaps that students may have had in there schedules. We tried a lot of different changes and were unsuccessful with many of them, but finally, at 945, every student was scheduled! We did some saving and tidying up and left the school at 10.

I walked to the subway (the bus is faster/shorter but I’d been sitting all day and needed the walk) and got home around 1115. Notice how I didn’t do anything with setting up my classroom or planning my courses! Luckily we have one more day before students arrive – I hope I can get some work in them.

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?

There were some choices I made about the PE schedule that made most of the PE department angry. Part of it is because what I thought they wanted was not what they actually wanted. It should be mostly a solvable problem, though. I hope.

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?

Since I’m starting at a new school, I’m looking forward to a fresh start in a new environment. And in a new building, like, literally new, built 7 years ago. My old school was built 150 years ago and felt like it. The challenge has come with not feeling like I’m prepared to teach because I’ve spent so much time with programming.

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.

Working with my coworker and AP over the summer I’ve been initiated into many of the in-jokes of the office and of the school, which has helped me feel more belonging for the school.

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?

My major goal is to be more kind – and to have students see that. I’ve always care about my students and how they are doing, but I’m not always sure they pick up on that.

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

Well, I traveled in August, which was nice. The 40 hours of plane rides and 10 hours of train rides were the only times I did prep work!

Integration First

Last year I went to a PD at Math for America that was about approaching calculus from a geometric point of view. The presenter mentioned during it that, historically, the idea of the integral was developed first, followed by the derivative, and then the limit. Yet in many calculus courses, they are taught in the exact reverse order. I decided that, should I teach calc again in the fall, I’d do integration first.

Well, school is rapidly approaching, and so I’ve been thinking about it again. I did so searching and found this intense forum discussion (oh, old Internet), which pointed me in the direction of the Apostol’s Calculus 1 textbook, which starts off with integrals. The post also had a bunch of arguments about why I shouldn’t do it. One of the notable arguments was that in order to fully teach integration (including u-substitution and integration by parts), you need differentiation. But I actually view that as a benefit, not a downside, because it forces a more spiraled approach. I can start with integrals, then go to differentiation, and then tie them together.

In general, I feel like area is a much more approachable subject than slope. My years of teaching Algebra I to 9th graders certainly seems to support that claim. But I also think it’s easier to understand the linearity of integration than the linearity of slope. “If you add together two functions, the area under the new function is the sum of the areas under the old functions” seems much more evidently true than “If you add together two functions, the slope of the tangent line for each point of the new function is equal to the sum of the slopes of the tangent lines at the same points on the old functions.”

Of course, Jonathan has already worked to restructure his calculus course, and I plan on taking a number of cues from his more spiraled sequence – but still with integrals first.

Here’s what I’m thinking:

Q1 (Intro to Integrals) – (Sam’s Abstract Functions, Area Under Stepwise Functions/Definite Integrals, Properties of Integrals, Riemann Sums, Area Under a Curve, Power Rule for Integrals, Trig Integrals, some applications)

Q2 (Intro to Derivatives) – (Average vs Instantaneous RoC, Tangent/Secant Lines, Power Rule, Trig Derivatives, some applications)

Q3 (Fundamental Theorem) – FTC, Chain Rule/u-substitution, Product Rule/Quotient Rule/Integration by Parts, Curve Sketching/Shape of a Graph)

Q4 (More Applications) – Related Rates, Optimization, Volume, etc

How does that sound?