PreCalc Curriculum

Unlike Geometry, last year was my first time teaching a full PreCalculus course.  I didn't go in with a plan and instead chatted with the AP Calculus teacher every time I was gearing up to do some long term planning.  Given all that, I'm pleased with how the course went last year.  And I'm excited to have the opportunity to rework things this year.  Like I did in Geometry, I dropped in the number of quizzes/tests I gave fourth quarter, though this time it can be at least partially attributed to the conics unit which I approached in a "let's study all the functions at once" direction, so I assessed them all at once (and gave them plenty of time to master them in any order they desired).  Next year I think I'll break that standard down into identify the conic section, sketch/describe the graph and write the equation.  We did all of those things but the distinction didn't make it into the grade book.

PreCalc 12-13

An explanation of the categories:

Investigations: tasks that students spend class time working on and sometimes finish for homework (this is an honors class so a couple were done entirely outside of class). Basically they're interesting problems or projects that I consider worthy of grading.

Standards: at the beginning of most classes I give a 3 question quiz on one recent standard. Every 2-4 standards there is a test. So each standard is assessed twice; old standards only cycle back in the way that shifting and stretching a graph works the same in trig as it does with polynomials, or exponentials, or logs, or any function. Students can retake quizzes and sections of a test throughout the quarter.

Vocabulary: I didn't use flappers with this (honors, juniors) class.  I introduced the note taking method in the fall and left it up to them.  However, the "word wall" fad seems to be a lasting one in my district, so I thought it would be worthwhile to make a vocab list for this course as well.  This one was off the top of my head so pretty please read through and let me know what terms I missed!


Goals:

• Talk explicitly about my thought process and the math practice standards.  This class is filled with students who have found math easy thus far, hopefully this class isn't easy, which means they need models of strategies in perseverance and problem solving.
• Actually use a grade record chart so they know what their strengths are and what to retake (we tried at least two, maybe three, but I never remembered to remind them to use it)
• Be better about checking that students went back to learn the material before retaking, this crew is eager to retake but they don't know how to study (see first bullet point) The problem here is - I don't want to collect their corrections or extra practice problems.  Although, I could have them staple the original test/quiz, the corrections/extra practice and the new assessment all together.  I only need to grade the new thing but then it's all together to discuss if they haven't mastered the new material.  (Sounds like a plan, good talk.) 
• Have fun!

Geometry Curriculum

I'm gearing up for my fourth year of teaching geometry! Having taught 11 sections over the past three years, you'd think I'd have this thing down. But that's the fun of teaching, I get to reimagine the course every year. Since I'm having a hard time getting excited about planning for this year, I'm continuing to analyze what I've done in the past. An awesome feature of doing (sorta) Standards Based Grading last year is that I can scan through my online gradebook and see exactly what topics I taught and in what order. Or at least, that's how it worked in most cases. It turned out I didn't really do quizzes or tests fourth quarter, no wonder one group was complaining so much about all the projects they had to do! Granted, we did most of the work in class so it shouldn't have been too overwhelming, but I hadn't realized how drastically I changed the class at the end of the year.

Geometry 12 13

An explanation of the categories:

Investigations: tasks that students spend class time working on and sometimes finish for homework (I will be teaching all Fundamentals of Geometry this year so homework is limited). Basically they're interesting problems or projects that I consider worthy of grading.

Standards: at the beginning of most classes I give a 3 question quiz on one recent standard. Every 2-4 standards there is a test. So each standard is assessed twice; old standards only cycle back in the way that you need to know properties of an isosceles triangle to determine something about right isosceles triangles. Students can retake quizzes and sections of a test throughout the quarter.

You can see all the topics at once!
And if you want to know what ASA means,
just flip up the cards in the way.

The "T" in the corner is for Top.
Helps kids figure out how to flip since
they write on the card before taping.

Vocabulary/Flappers: Each word/phrase is the title of an index card, definitions and examples (including diagrams!) fill the rest of the card, then it gets taped onto card stock so you can see the title of every card. This was the only formal note taking we did and it worked beautifully. An entire year's notes on a single (double sided) page - easy to refer to! Words in parentheses were discussed and used frequently, most appeared on a flapper but they were not the title of a flapper.

The plan that I wrote last summer is organized by unit, which is a more logical way to lay things out for any purpose other than analysis. I did a decent job of sticking with the plan and most of my standards line up though they're named differently. (I'm glad I did all of that work last summer and then forgot about the second document by mid-September! At least I used the first one all year, it took the most effort.)






Goals:

• Don't answer questions until flappers (or the appropriate reference sheet(s) in third quarter) are out on their desk.
• Be more focused about organizing binders (we did a great job with flappers, now I'd like to move on to keeping tests/quizzes and a chart of standards so they know what their strengths are and what to retake)
• Give some tests and quizzes in fourth quarter and don't collect every assignment (end of year slacking will happen, there's no reason to punish yourself by threatening them with grades)
• Make a comprehensive vocabulary list and talk to the English department about how we can support each other in vocabulary. (Did I miss any words?)
• Reformat the intro to triangles exploration so they learn "Angle-Side Relationship" at the very beginning (is there a better title for "longest side is opposite largest angle"?)
• Have fun!

End of Year Reflections

For more years than I can remember (all of them?) I've had students fill out an end of year reflection after they finish their final exam. I don't read them in June though, or even in July. I save them, as precious motivation, for sometime in August when I decide that I want to start getting back into school mode but I'm not sure where to start, or if I even want to. This may not be true of all students, but mine are totally honest with me when I ask them to reflect. I don't get beautiful prose (it's the last days of school and they just took an exam) but I know that whatever my students share will be truth.

The prompts:

As I read, I took notes on some of the aspects. I included every Favorite, Hard and Interesting that students provided (I know the numbers don't add up, some students listed more than one per category and others skipped categories) and in the bottom right corner I wrote down phrases that made me happy or that I wanted to remember. The big letters are for the class sections, we run a block schedule and each period is associated with a letter. A and C are fundamentals of geometry (co-taught with a special education teacher), B is CP geometry, F and G are Honors PreCalc (F was a boisterous class while G was so, so quiet, do you notice any major differences in reflections? Nothing jumped out at me.)

End of Year Reflections

There was 100% growth mindset in geometry!! Seriously, every comment in the "This year I learned" section reflected the understanding that mastering the material takes work, and more work (of the correct types) results in more understanding. Sure, kids said they don't like math/algebra/geometry, but they all knew that they could achieve anything I asked of them in the course if they tried (and wrote that down!). This makes me so amazingly, unbelievably happy!!

You'd think after all the time we spend reminding students that it's important to challenge yourself, I wouldn't be surprised by this fact, but I still am:

The students who thought trigonometry was hard and the students who listed trigonometry as their favorite topic were the same students.

More than one student wrote "trig was my favorite because it was hard." The topics in the top right corner are the ones they found challenging, not the ones they hated. I'm sad that I expect students to have a negative association with difficulty but I'm thrilled to be proven wrong and I hope that next year I don't find this surprising.

There was some resistance to the investigative approach in PreCalc, but not a lot, and certainly not as much as you would have expected had you attended my first quarter parent conferences! A few students asked for structured notes or the formula first, although they all recognized their capability to do what I asked of them. Most were compromise requests such as: some structure before investigation so we don't flounder (though I laughed because in the same paragraph this student wrote how cool the folding conics activity was because the curves came as a total surprise!). The course will gain some clearer direction when I get to teach it again, but I won't be adding scaffolding because I know they don't need it. Generally speaking, changing the mindsets of PreCalc students who see themselves as 'successful' math students is more difficult than changing the mindsets of my geometry students who hadn't seen themselves as 'successful' math students. That doesn't mean I will change how I teach either course; it does mean that I will be more mindful in communicating my expectations to the PreCalc students next year.

There is some tendency to use the most recent projects/topics since those are fresh in students memories. That said, I still think it's safe to say that the Conics unit is a keeper. I was really proud of that unit (so proud I wrote three posts on it!) and its nice to see that the students had the same impression as I thought they did. Other than conics, the diversity of topics that students came up with is awesome. Each student is different and I'm happy to see that they all found something they enjoyed and something that pushed them outside their comfort zone. The more diversity there is in these lists the better I feel- I didn't butcher any one topic, students merely identified with some approaches more than others in a well balanced way.

Note: I think I've blogged about all of these units and activities by now, but if you are interested in hearing more about one and can't find the post, please drop a comment and I'll provide more information!

Twitter Math Camp Mind Dump

Last week I attended Twitter Math Camp (#TMC13) and it was amazing. I arrived in Philadelphia after 6 pm and so went directly to dinner with college friend even though I really wanted to stop by the hotel and say hi to everyone. It says a lot about the people there that I was wishing to be with my tweeps rather than a best friend from college I hadn't seen in over a year.

First thing Thursday morning, before we even made it to breakfast, Heather and I realized we took a class together at BU. We've been following each other on twitter for a while but it didn't connect until we saw each other in person. Weird. I met several people from the Boston area throughout the weekend that I had no idea lived so close. We need to have mini-TMC's (like regional NCTM conferences) throughout the year!

The geometry session was fun and productive. We spent a lot of time working on a skills list but it's not complete (it includes key vocab, SBG skills and CCSS standards). Help us finish and leave feedback?

The Breaking Out of Ourselves session generated some awesome ideas. Check out the projects and sign up for one! The only way this community functions is if people pitch in; you can't do everything, but you can always do something. More projects are appearing all the time. (example via k8nowak: Don't get mad, get organized. http://t.co/lMfInNibJx #standupandbecounted)

My favorite portion of the My Favorites sessions was @sophgermain's activity where we spent five minutes listening (without speaking) and then five minutes talking (without feedback). Listening wasn't too much of a challenge for me, but that's largely because I didn't have anything else to do at that moment. When I'm teaching, the temptation is to listen while continuing to hand out papers. I know that my students never have 5 minutes of air time during class; after school I can move a bit slower and do stop to listen, but even then there are frequently other students vying for my attention as well. On the other hand, talking for 5 minutes was challenging and revealing. I rarely take the time to talk all the way through something, I cut myself off far more than I do other people. Instead of talking about how I feel about the start of school, I'd rather be doing something to get ready for it. This was the other message of the activity: teaching is rough, teachers need people to listen to them too. Food for thought (or maybe it should be food for discussion!).

Organization Panel (it's rough to look at a presentation without people talking, tweet @crstn85, @samjshah, @borschtwithanna and @fawnpnguyen for more information!)

Friday night was FUN! First there was origami and good conversation at dinner. Then singing and dancing which I rarely get to do. The personalized nature of a piano bar (a new experience for me) made it feel like our party which was awesome. In fact it was so much our own party that they played the TMC12 song. 

Saturday Morning: Origami Installation. Coming together to create something? Way cool. 

Plus it made an awesome backdrop for the Explore MTBoS crew photo!

Saturday evening: Great conversations on the way to dinner (complete with a "you MUST send me that link"), amazing, deep, thoughtful conversations at dinner and still more awesome conversations on the way home from dinner. On the bus ride home Sunday @mpershan proposed a session next year called "Take a Walk." I'd take this idea a step further and propose that we spend the entirety of TMC14 walking and eating. Maybe there could be some drinking too. Food and wine tour in California anyone? I can say for sure that I had the most fun, built the strongest foundations of relationships and participated in the deepest conversations while walking and eating. Certainly part of that is the lunch meetings I crashed where people were planning great projects. But it's also the personal nature of the conversations. I've heard a lot of discussion about introversion, which I'm particularly keyed in to since I finished Quiet: The Power of Introverts the week before TMC. I'm lucky enough to not be a shy or anxiety prone introvert which means that when I'm sitting on the side of a conversation I'm not wishing I could speak up or worried that other people are judging me for not talking, I'm just content to listen. While walking, though, it's natural to pair off and that's where introverts are at their prime- one other person and a conversation that they care about (and if you're at TMC it's guaranteed you'll have a math ed topic you're both passionate about). So who's in? All we need is a location that will have a restaurant week style deal set up for us so we can walk and talk our way through town.

In conclusion, this post has no big message. Check out the links, they're all great. Talk to the people, they're way cool. If you couldn't make it to TMC this year I'm sorry for making you read yet another "TMC was amazing!" post. If I missed something you thought was important, which I definitely did, it's partly because I didn't even open up my folder of notes since this post has taken too long to publish already. If you don't feel like you're a part of this spectacular community yet, please consider joining us in October to Explore the Math Twitter Blogosphere. I certainly haven't regretted a moment of my engagement with this community.

Nix the Tricks: An Update

I have a slew of posts I need to get written, but I got some motivation to prioritize this post via a tweet:

The tweet he was referring to:

I've written about this document before but, as is wont to happen, school got in the way and it fell off people's radar.  

In the beginning, there was a calculus teacher complaining about students' lack of a definition of slope.  Then there was a conversation among my department members on tricks we hate seeing kids show up to our classes with.  I expanded the conversation to members of my online math community.  We brainstormed and debated what constituted a trick and which were the worst offenders.  I organized.  More people joined in on the conversation and shared better methods to emphasize understanding over memorization.  I organized some more.  Contributions started to slow down.  Ashli created an awesome table of contents with links.  The end result was 17 pages.  I had grand dreams of a beautifully formatted resource that we could share with teachers everywhere.  A few people shared my dream.  We discussed formatting and organization and themes.  Then the end of the school year craze happened, and suddenly it was August!

Before we got distracted by life, we decided on this format as the most flexible:

At this point I would like to create a document that is accessible in a variety of formats (eBook, PDF, printable), searchable (grade band, CCSS) and easy to read.  

I need help on several fronts:

• Rewriting each trick in the format above
• Tagging
• Illustrating (butterfly method anyone?)
• Writing an introduction that allows someone to send the text to a colleague without offending them (without an introduction it says: Your method is wrong. Full stop.)
• Formatting- I'm good in google docs but have no idea how eBooks work
• The things that haven't even occurred to me because I have no idea what I'm getting into

I know you are busy, but if you think this project is important could you help with just one part?  Together we can make this happen.  Imagine how awesome it would be if students could use precise mathematical terms to describe all of the math they've learned.

Sign up to help out: 

Update August 7, 2013:
We're gaining momentum! This post and project are being featured in The Math Forum Newsletter.