End of Year Reflections: Geometry Favorite vs. Hard

Continuing analysis of student's reflections... (see first post for a full description)

Geometry CP students' Favorite Topics:

Ch 1

Ch 5

Ch 10

Ch 12

Triangles

Triangles

quads

quads

quads

Solving Triangles

Similar triangles

Ratio/proportion

Proportion

Area

Area

Area/Volume

Trig (interesting)

Pythagorean thm

Pythagorean thm

Translation

Polygons

Polygons

SAS etc. Theorems

Geometry CP students' Hard Topics:

Nothing

Nothing (if I paid attention)

I don't know

I don't remember

A lot

Everything

Everything

Everything

Everything

Everything

Everything

Triangles

Finding lengths and angles

Ratios/proportions

Trig

Trig

Trig

Trig

Trig

Trig

Trig

Trig

Trig

Trig

Trig

Trig

Trig

Proofs

Proofs

Proofs

Circles

Area formulas

What's the most striking thing? The million Trigs!

That pattern isn't surprising to me at all. I haven't figured out yet what I will do next year (suggestions??), but Trigonometry was the only section where I had students asking "When will I ever need to know this?" We studied plenty of topics that were difficult (at best) for students to see the applications of, but they never stopped to ask that question because they were interested, involved, curious and they understood enough to be able to work toward the problem. In trig, that didn't happen. I saw confusion, frustration and kids giving up. It may have started when the first investigation we did gave data that was too far off to see real patterns (perhaps technology would be better than measuring by hand for this?) or perhaps when we started synthesizing too many ideas at once. When 'solving a right triangle' (finding all the side and angle measures given a few) we applied angle sum rule, pythagorean theorem, trig ratios and a lot of algebraic manipulation. Next year I'd like to do more problems throughout the year that synthesize topics so hopefully that won't be so overwhelming. Last, but certainly not least, trig was the first topic we did after MCAS (the state exam, required for graduation) and students feel like they should be done when they've finished that test (even though it happens mid-May and we didn't finish until June 29 this year). Overall, trigonometry got a bad deal last year. I'll try to do it more justice in the future.

Proofs are another challenge, and I believe that a lot of that is related to how they are presented. Student in my classes are accustomed to "defending their answers" and usually can do so well. However, when it comes to writing a proof they get caught up in format, and formal language. Precision is key and I certainly want my students to be able to write concise and carefully worded explanations, but I wish that they were more willing to just write something to start with. Does anyone have a method of draft proofs or easy entry formats?

Otherwise, I appreciate the overlap of favorite topics and hard topics. Different students had different preferences, and geometry has plenty of variety so most students get to experience a balance of topics they enjoy and others that they struggle with.

Take aways:

Do multi-step, synthesizing problems (before Trig)

Make proofs more 'low threshold'

End of Year Reflections: In Geometry I learned...

For the past few years, I've had students write reflections on the course and their year after they complete the final exam. The prompt is as follows:

• This year I learned…
• About myself
• About mathematics
• About studying/school/how I learn
• In this class…
• My favorite chapter
• The most interesting activity
• The hardest thing to learn

At the end of the year I'm spent, so I put these away until a day I'm ready to reflect. Today was that day. I'm getting geared up to prep for the arrival of students, take what I learned at PCMI and put it all together into a great new year. I pulled out the pile of reflections and they sparked fond memories of: my students, how much they grew over the year, and how willing they were to give meaningful feedback even after taking their final exam.

I compiled their responses for analysis of the year past, but also to remind myself on those tough days that even though it isn't obvious, they are learning and the ideas are sinking in. I'll divide this analysis into lots of posts so they don't get too long!

In Geometry College Prep I learned...

• I'm actually kind of good at math
• I'm good at geometry
• I'm not very good at geometry
• I'm not good at geometry, I'm a number person
• You can be very good at algebra but really suck at geometry or it can happen the other way around
• I am horrible at geometry, but if I just push extra hard I can do it
• I'm better at math than I thought
• I'm worse at math than I thought

• If you miss one class you can be lost forever!
• I need an explanation for everything
• I learn well from examples/book

• To work hard
• Studying is hard for math
• Studying really helps you become successful
• I don't do well in math unless I study
• If I study, I will do well
• Study sheets and flashcards help
• Doing the same problem over helps me understand

• You have to work to understand math
• I liked the experience
• I hated having to redo everything but it made me more conscious I should study hard before the first time
• I can figure out a lot of problems myself
• I am capable of doing all the work, I just have to focus
• I do my work well if I am alone
• I work better: not under pressure, by myself, when mad

• I learned who the real me really is
• I learned too much to put on paper
• I can achieve anything I want if I put my mind into it
• If I try I can do anything
• I never knew that we could learn so much about math in one year

It may have been the phrasing of the question, but I love that no one said 'I can't do math' or 'geometry is too hard' or 'I don't care about it.' And nearly every kid who said that they struggled then went on to say they should have worked harder, studied more or focused better. The fact that people learn by effort, not genetics or intrinsic understanding was a recurring topic this summer. I'm glad to see that most students internalized that message last year.

One comment that makes me really thrilled is:

I hated having to redo everything but it made me more conscious 

I should study hard before the first time

I worried that allowing students to correct their work would make them blow off studying the first time and just settle for whatever grade they could get with corrections. But, if going back over their assignments and having to re-work problems makes them wish they'd studied the first time around then I'm looking forward to continuing that option.

I shared these with a few friends before posting, and the one that jumps out at others is:

I work better: not under pressure, by myself, when mad

I won't pretend to understand exactly what this student meant. I can say that she was quite the talker, so the 'by myself' part makes sense. I wonder if the 'when mad' comment relates to the idea of 'struggle' that we all try to find a way to discuss. In the summer camp I taught at we talked about writing problems that would make students 'frustrated' or 'challenged.' We don't want angry kids, but the point is, that if a problem is too easy no one learns.  We need to give assignments that make students think and that they have to work to understand. I have no idea if that's what this student was trying to say, but it's interesting to think that students are having these same thoughts and are aware that they learn and grow through challenges.

Tina starts blogging again...

This summer I attended PCMI and had my eyes opened on a lot of levels.  One of those levels was the existence of this awesome community of math teachers online.  I mean, I knew that any group you could even think of has a presence on the internet (I even managed to find a new family for my degu in a matter of days this spring thanks to google), but it never occurred to me that so many rich conversations were happening both on twitter and on an overwhelming number of blogs.

So, I decided to join in with the fun on twitter, which led me to all of the blogs on my sidebar (I have a feeling I will be sad I've subscribed to so many once the posting picks up during the school year!).  Then the other day I was reading my students' end of year reflections and realized that I could share how adorable and insightful my kids are if I restarted this blog.  (If you look back into the archives you'll find this was once an environmentalist's blog, I'm still living that life, but don't really feel the need to write about it.  Using this blog rather than starting a new one seemed easiest, especially since its address is the same as my twitter handle- can you tell I've been using the same username since the internet was invented? Okay fine, since I was introduced to the internet.)

So, I'll start off with an analysis of end of year reflections, it's good for me to do and gives you some sense of how things were in my class last year.  Before we start that I suppose there are a few things you should know about me:

• I will be starting my 5th year of teaching this fall.
• I taught for 3 years in one school, then last year switched (and it was a really good move)
• I worked within a 90 minute alternating day schedule last year, the previous 3 years were 47 min daily classes (although I taught some double periods so 90 minutes wasn't new to me).
• I end every class with journaling (math learned, another question about key ideas) so the idea of writing in math for an end of year reflection was nothing new for my kids
• I've taught everything from pre-algebra to AP calc. I miss my calc kids but geometry is way fun
• I've done PCMI, PROMYS at BU and undergrad with licensure at MHC (omg abbreviations!)

This blog is really all for me to get my ideas sorted, but hopefully you can get something out of it too.  I'm going to try to end posts with 'take aways' so that I can go back and remember what I want to do when the going gets tough, feel free to jump to the end and then go back and really read if the take aways appeal to you!

Math Blog?

I'm playing with the idea of turning this into a math teacher blog (because I really need one more thing to do during the school year!) but I'm not sure if it's too open to spam. Hence the test post...

If I'm still in your google reader from ages ago, hi! I'm still doing everything I used to write about, and I actually talk about environmentalism regularly on my craft blog (TintedGreenCrafts.wordpress.com) which is on summer hiatus. You're also welcome to continue to follow along and learn something about teaching and math!

Pantry Challenge

So, apparently I haven't blogged for a while. Twitter is easier, life was crazy (3 grad classes and teaching full time last semester) and I didn't have a lot to say that wasn't being said. Tonight I watched Julie & Julia (I know, I'm way behind the times, I also signed up for the netflix free trial today, haven't decided yet if I'll keep it, it might make me catch up with the world of movies) and simultaneously realized that I'm moving in 1.5 months. In an effort to pack less, I am going to attempt to eat meals inspired by my pantry daily until I move.

There are two reasons my pantry is full- first, I tend to eat in phases. I'll be really excited about rice dishes for a long time, then get sidetracked by stir fry, and then move on to couscous. Of course I buy everything in the big bag/box because I'm so excited about it, or trying to reduce packaging, or the "harina precocida" only comes in a huge bag. The second reason is that I often know only one or two recipes to make with that particular noodle/flour/rice. Especially in cases where I wasn't particularly excited about the results of the first attempt to use something, it lingers, getting pushed further and further back on that endlessly deep shelf, until I have more bags of flour than I care to admit (or am brave enough to open!).

So, tomorrow I will take stock of everything that is in my pantry and head to the cookbooks/internet to learn exactly what I can eat to use up all of the assorted items that have accumulated. I'm starting with dry goods, though I have also built up quite the stockpile of sauces, vinegars, spices, etc. but those seem easier to move so they will get tackled later (or more likely used as I add flavor to everything on the other shelves of the pantry).

I will try to post recipes and progress here, if only because it will keep me focused. Feel free to share any ideas or suggestions!

Hello World, I live sustainably!

Kellie, from Greenhab is hosting this month's APLS carnival, and she asks this:

So, I'm wondering when, where, how, and how much you proselytize living green? When do you just let it go? When is it not worth it to start something? Or do you always speak up? How loud? Are you a tell-it-like-it-is person? Or do you try to take a gentle approach? And, although I use "proselytize" in the loosest way, does living a sustainable lifestyle feel almost like a religion to you?


I find that I run the gamut from silent to all points bulletins regarding my environmentalism. It depends on the situation, the people I'm with, the issue at hand and the mood I'm in. Sometimes I have the energy to get into a deep discussion, and think it would be profitable; at other times I just mind my own business and wish to myself that things were different.

The vast majority of the time I am quietly announcing my viewpoint by doing little things such as carrying reusable bags, using my reusable water bottle or sticking to a vegetarian diet. I don't usually think of these things as announcing anything, until someone else comments. As I was exiting the farm store a few weeks a go a couple walked past me in the parking lot, saw my bags, and said to each other "oh yea! we have bags in the car, let's go get them." I was secretly thrilled that they were inspired by my action to their own action, of course it was small, but it was still exciting. A similar thing happened when someone at a conference was explaining the excessive waste of plastic water bottles and used me (with my metal bottle) as an example. He was the one making the bigger impact, by actually speaking out, but I was proud to provide an easy reference point.

Sometimes the quiet announcements lead to conversations and education opportunities. I bring a vegetarian lunch to school each day, and one day another teacher asked why I had decided to become vegetarian. I took the opportunity to discuss the sustainability issues with meat production. Then, just a few weeks later she informed me that she'd decided to become a vegetarian, and to drag her whole family along with her. She asked a few more questions and I was able to be a further resource for how to transition meat out of her diet. And all I did was eat lunch in the presence of others.

People I know better (students and friends) are exposed to a slightly louder rumble of my eco-friendly behaviors. My classroom has paper and bottle recycling bins, and I vocally correct any student who uses the wrong bin. I usually don't have to do all the educating though, peers are great enforcers and yell at kids for "killing the trees!" if they ignore my reminders.

For those friends who pass the cut and make it into my apartment, things are much more obvious and I am more vocal. If you ask to use the bathroom you get told how to flush the toilet with grey water (but you have to ask to find out what the little pieces of cloth by the toilet are for). It's obvious that everything is on power strips, and that lighting is limited to just the area we are occupying. I don't hesitate to remind people to turn off the kitchen light as they leave the room or squirm at the idea of turning on the TV if we're otherwise occupied.

Some things, though, are just so exciting I have to shout it to the world. Getting my new (to me) keyboard was like that. I went on craigslist and found an amazing deal for a 72 key (that's huge in the keyboard world) instrument with amazing sound in excellent condition. It was so wonderful and I was so thrilled with this huge success of buying used that Twitter, my parents and my friends heard all about it. I still tell everyone who walks into the room how cheap I got it and how great the reviews are and just ramble on and on about it forever! Buying less is best, but buying used and getting something that you really love, just amazing.

So, while my blog banner says I "live life lightly and announcing it brightly" there are clearly many shades of brightness that occur on a day to day basis. And I think this is good; for me, and for those who have to spend time with me.

Does Size Matter? APLS Carnival

This month I hosted the APLS blog carnival and had a great round of contribution regarding all matters of size.

For Robbie becoming a mom was what got her serious about her environmental efforts, so the increase in family size played a big role in how she thought about being green.

Lisa and I thought about how having just a few people in our households affects things like meal planning. We also compared ourselves to the green moms who seem to dominate the blogosphere.

For others, family size was not the deciding factor, rather something else trumped it. For Steph family size is less important than time and energy available to dedicate to green efforts. And Kellie said, "I find the bigger contention lies not in how many people are in our family, but what those family members are willing to do."

Linda looked into product size, and discovered that the way to reduce packaging was by buying more.

Finally, a couple people looked at how the size of their house affected their ability to be environmentally friendly. At one end of the spectrum is Heather who finds that since her house is smaller than she might like it is hard to store food and have equipment for different green projects. At the other end is Abbie who feels some eco-guilt for having built such a large house for just the two of them (soon to be three!), but I have no doubt she will make good use of the space for a lifetime.

Thanks to everyone who contributed! It was great to read all the viewpoints of the APLS members who come to the sustainability movement from varying perspectives. Look for the next carnival at the APLS blog, Kellie will be announcing her fall themed topic soon.