Today was the first day back for teachers. We came, we talked, we felt like we'd never really left. There are lots of new teachers, it's hard to believe that I was there just a year ago (and there weren't nearly so many of us last year!). But, you don't really care about the meetings or how I organized blocks this morning, what this post is actually about is the first days for students. I've done these activities in some combination or other for the past several years and I think they all set the tone I want in my classroom.

Start of year questionnaire: It's a fairly basic one with the focus being getting to know them a bit and having them set down some goals. While they're filling it out, I fill one out on the projector, the message being: I'll share with you if you'll share with me. The last question asks "Is there anything else you think I should know about you?" I tell them that I can only hear out of my left ear (so it's a much better idea to wave than call out to get my attention) but I get a really wide variety of responses, maybe I'll share some of my favorites next week.

Index card game: As students finish I distribute index cards and instruct them NOT to put their name on it, but to write down one thing from their questionnaire and one thing they did over the summer (both that they don't mind sharing). When everyone is done I collect and shuffle the cards, then redistribute and have them make some predictions on how many people they will need to ask to find out whose card they have. Then, I make every single one of them get up and out of their seat! It's a crazy thing to do on the first day, but the truth is we move around, talk to each other (teachers and students) and make a bit of noise all the time in my class. Finally, we compare numbers and do a bit of data analysis. If there's time I have them introduce whoever they have the card for, and they introduce whoever they have etc. Then we get to analyze the number and size of loops too.

Turtle: I have accumulated quite the variety of expanding sponge sea creatures along with packaging that makes various claims about how much it will expand. Each class will get one to measure, interpret the claims and then predict and track its growth. Splashing in water is fun, plus I get to see who knows how to use a ruler. You think I'm kidding but it's really an issue.

Syllabus: On to the second class, we read the syllabus together. Every year I try to be even more up front and clear about my expectations. The only rules I have are be safe and be respectful, so we get to work together to interpret them.

From there in Geometry we'll head into patterns and conjectures and in Learning Skills we'll start working on some logic problems (we have no idea what level these kids are, so I'm trying to assess their thinking skills without overwhelming anyone with mathematical notation).

## August 31, 2011

## August 24, 2011

### Technology for Teachers

In my Goals post I mentioned some technology that I would like my students to use, but the more frequent use of technology in my classroom is the programs/websites that I use. As I set up for the new year I thought I'd share some of my favorites.

Dropbox: I almost forgot to include dropbox since it's more a way of life for me than a tool I use. No, seriously, I'm 3 referrals away from maxing out my referral bonus. If you don't have it yet, make sure to get an invite from someone because it means extra space for both of you! Okay, so what is this life altering item? It's a folder. Really, that's all it is on the surface. Underneath though, it has hidden magic powers so that everything you put into the folder is automatically backed up online. Then, when you open that same folder on another computer the new version is already sitting there waiting for you, no jump drive required. But it's way better than google docs or similar sites, because it's a folder, on your computer. You can get to it when you're offline, you can work in your favorite program and you can save all different types of files in the same place. Plus there's the sharing and the web access and... oh just go watch the video. Point being, it's awesome if you use more than one computer (home and school anyone?) or want to collaborate on anything.

*Free, remember more space for free if you get an invite!

PlanbookEdu: I started out with a paper planbook, then used google docs, then a word doc in dropbox and last year a co-worker told me about PlanbookEdu. For the first time (I'm about to start my 5th year of teaching) I'm going to use the same method 2 years in a row! The website is very simple, which is exactly what I want. There are boxes in a weekly grid like a traditional paper book but you can customize the number and orientation, and they change size to fit the text. You can create a template, set things up to repeat, bump lessons when you have a snow day and much more. They are awesome about hearing feedback and accommodating requests, they're currently in process of adding tons of standards, and you can customize your own. When I emailed to ask how to copy only some of my classes from last year to this year they responded "just let us know what you need and we'll take care of it!" If you need to submit lesson plans there's a button to push and they're sent. You can also share your planbook with other teachers, which is a great way to see what your co-workers are working on when you don't have much time to meet.

*Free to use, $25 for Pro version which I happily pay

Engrade: At my first school we used PowerSchool. I loved that kids and parents could log in to see a complete progress report at any time. When I switched schools I wanted that same access, so I did a bit of googling and ended up with Engrade. Similar to PlanbookEdu, they're constantly adding new features (and respond quickly to emails) but the basic format remains simple. It works with weighted categories and all that good customizability. I'm not sure if we're going to be required to use iPass this year (that's what we use for report cards but last year they started giving 9th grade parents access) so I haven't started setting up Engrade yet.

*Free

LaTeX: When sorting through a large pile of papers last week I came upon some handwritten tests. I forgot we didn't have computers my first couple months of teaching (we'd just moved into a new school). I use Microsoft Word for most things, but when I taught Algebra 2 I realized how much easier it is to type in TeX (a math programming language, there's a bit of a learning curve if you've never used it but the internet is awesome and can tell you how to do anything you'd ever want and more!). It also works much better for image placement in geometry, so now I use it for all of my tests and some other assignments. I made the mistake of announcing that I had typeset the common midterms I was giving (the versions I got were a mess!) and then got assigned the duty of fixing the others. At least it will make them easier to re-write this year. Downside: you can only share documents in .pdf so they aren't editable to non-TeX-users (meaning any re-writes will be done on my computer). At least if I'm useful I'll get to keep my job?

*Free, I use MacTeX, not sure what's the best distribution for PC

Powerpoint: I know, you all use it all the time. But, in addition to making things nice and big so that even the kid in the back who forgot his glasses can see the assignment, it has really nice image manipulation. It's a quick and easy way to draw a diagram and then export it as a .jpg to use in your worksheet.

*It's already on your computer (unless you're cheap like me and only have Keynote, same deal though)

Lunarpages/iWeb: I have a course webpage: (mylastname)math.com (feel free to check it out if you know my last name, I just don't really want kids googling the course page to end up here, not that anything bad is here, but, ya know, it's mine for now at least). I pay $0 for the domain, I paid $0 to get the domain. That's right, a free domain of your choosing and all you have to do is mail in some school letterhead! Any public school teacher, administrator, PTA head etc. can get a website to use for pretty much whatever you like. Once I got the domain I thought back to the html class I took in high school, and then clicked on iWeb, no html required! I have a page for each course that I update daily with homework and extra copies of assignments, plus a calendar (from google calendar) and some silly math comics. Not a lot of students use it, but it's so easy to maintain that it's worth it.

*Free domains for teachers (sorry, public schools only), either you already have iWeb or you have to find some PC equivalent

What are your favorite programs and websites to make teaching just a bit easier (or at least more organized)?

If you want more information on any of these let me know. I love them all and would be happy to expand and expound.

Dropbox: I almost forgot to include dropbox since it's more a way of life for me than a tool I use. No, seriously, I'm 3 referrals away from maxing out my referral bonus. If you don't have it yet, make sure to get an invite from someone because it means extra space for both of you! Okay, so what is this life altering item? It's a folder. Really, that's all it is on the surface. Underneath though, it has hidden magic powers so that everything you put into the folder is automatically backed up online. Then, when you open that same folder on another computer the new version is already sitting there waiting for you, no jump drive required. But it's way better than google docs or similar sites, because it's a folder, on your computer. You can get to it when you're offline, you can work in your favorite program and you can save all different types of files in the same place. Plus there's the sharing and the web access and... oh just go watch the video. Point being, it's awesome if you use more than one computer (home and school anyone?) or want to collaborate on anything.

*Free, remember more space for free if you get an invite!

PlanbookEdu: I started out with a paper planbook, then used google docs, then a word doc in dropbox and last year a co-worker told me about PlanbookEdu. For the first time (I'm about to start my 5th year of teaching) I'm going to use the same method 2 years in a row! The website is very simple, which is exactly what I want. There are boxes in a weekly grid like a traditional paper book but you can customize the number and orientation, and they change size to fit the text. You can create a template, set things up to repeat, bump lessons when you have a snow day and much more. They are awesome about hearing feedback and accommodating requests, they're currently in process of adding tons of standards, and you can customize your own. When I emailed to ask how to copy only some of my classes from last year to this year they responded "just let us know what you need and we'll take care of it!" If you need to submit lesson plans there's a button to push and they're sent. You can also share your planbook with other teachers, which is a great way to see what your co-workers are working on when you don't have much time to meet.

*Free to use, $25 for Pro version which I happily pay

Engrade: At my first school we used PowerSchool. I loved that kids and parents could log in to see a complete progress report at any time. When I switched schools I wanted that same access, so I did a bit of googling and ended up with Engrade. Similar to PlanbookEdu, they're constantly adding new features (and respond quickly to emails) but the basic format remains simple. It works with weighted categories and all that good customizability. I'm not sure if we're going to be required to use iPass this year (that's what we use for report cards but last year they started giving 9th grade parents access) so I haven't started setting up Engrade yet.

*Free

LaTeX: When sorting through a large pile of papers last week I came upon some handwritten tests. I forgot we didn't have computers my first couple months of teaching (we'd just moved into a new school). I use Microsoft Word for most things, but when I taught Algebra 2 I realized how much easier it is to type in TeX (a math programming language, there's a bit of a learning curve if you've never used it but the internet is awesome and can tell you how to do anything you'd ever want and more!). It also works much better for image placement in geometry, so now I use it for all of my tests and some other assignments. I made the mistake of announcing that I had typeset the common midterms I was giving (the versions I got were a mess!) and then got assigned the duty of fixing the others. At least it will make them easier to re-write this year. Downside: you can only share documents in .pdf so they aren't editable to non-TeX-users (meaning any re-writes will be done on my computer). At least if I'm useful I'll get to keep my job?

*Free, I use MacTeX, not sure what's the best distribution for PC

Powerpoint: I know, you all use it all the time. But, in addition to making things nice and big so that even the kid in the back who forgot his glasses can see the assignment, it has really nice image manipulation. It's a quick and easy way to draw a diagram and then export it as a .jpg to use in your worksheet.

*It's already on your computer (unless you're cheap like me and only have Keynote, same deal though)

Lunarpages/iWeb: I have a course webpage: (mylastname)math.com (feel free to check it out if you know my last name, I just don't really want kids googling the course page to end up here, not that anything bad is here, but, ya know, it's mine for now at least). I pay $0 for the domain, I paid $0 to get the domain. That's right, a free domain of your choosing and all you have to do is mail in some school letterhead! Any public school teacher, administrator, PTA head etc. can get a website to use for pretty much whatever you like. Once I got the domain I thought back to the html class I took in high school, and then clicked on iWeb, no html required! I have a page for each course that I update daily with homework and extra copies of assignments, plus a calendar (from google calendar) and some silly math comics. Not a lot of students use it, but it's so easy to maintain that it's worth it.

*Free domains for teachers (sorry, public schools only), either you already have iWeb or you have to find some PC equivalent

What are your favorite programs and websites to make teaching just a bit easier (or at least more organized)?

If you want more information on any of these let me know. I love them all and would be happy to expand and expound.

## August 22, 2011

### Goals (Post PCMI)

I found some time to go back through my notes from PCMI and write up my goals today. Over the 3 weeks of the program I took notes from the sessions and also wrote down ideas from conversations in Notebook (a program for Mac from Circus Ponies, it's awesome and they didn't ask me to say so). As I went I highlighted any ideas that I wanted to specifically apply in the upcoming school year. One of the awesome features of Notebook is that it compiles all of the highlighted text onto a single page, so by the end of the program my goals list was pretty much already complete. I took some time to decide what was doable and came up with the following:

Assessment:

- Look up standards based grading (SBG)

- Comments only on projects

I've done this sporadically, but now I have a system! Last year one of my students told me that "even high schoolers like stickers." I didn't get stickers, but instead found a star shaped stamp and a gold inkpad. From that point forward every A was accompanied with a gold star (which that same student loved doing, I sorted and she stamped). This summer I found a "take your time" stamp, so papers that need revision will get one of those (not sure if that will be everything below an A or just below a C). I still record grades in my gradebook in case students don't resubmit and because it makes the averages much more accurate.

- Make classwork grade more transparent

Students get a daily classwork grade based on preparation/effort/focus but it's something I've just quietly marked on my clipboard in the past. Sometimes I make a show of walking around to check progress, but usually that grade is a mystery to kids. I tell them what's involved, and we read the school rubrics (new push) that they're based on at the beginning of each semester, but they quickly forget. I'd like to use participation quizzes and also have kids self-assess on the rubrics so they get a better sense of what's needed to get full credit. (I use classwork grades because I rarely collect any work done in class, it gets checked off as I circulate.)

Technology

Technology

- Use geometers sketchpad

We have geometer's sketchpad in all of our classrooms and in the computer labs, but it's not used much. After using it this summer I definitely have a better sense of when it would be useful. We do a lot of compass and straight edge constructions, so I might use it to show how the construction works after they've each tried an example. This way everyone gets to see all of the varieties, not just hear about them from classmates. Some ideas (like trigonometry) require more precision than we were able to get using paper and pencil, those will be worth reserving the computer lab for. I will also look into projects to do and use the idea of lab reports. This idea actually came from a professor whose son took Geometry last year, we got to talking over breakfast and he shared this great idea. I'd love to get the report format from the science department and modify it slightly to fit our needs.

- Use Snap

I discovered Snap/BYOB (3rd or 4th generation Logo) in the spring and was able to use it for my project at PCMI. My Merrill textbook is so old that it still has Logo activities in it, so I want to adapt those for Snap. I'll also implement the lesson I wrote this summer on similarity.

- Google docs

We used Google Docs a lot this summer, and I do love all things Google. I'm not sure how often I'll be able to get into the computer lab, so they may not be as useful as I'd like. They were great for recording and compiling ideas during group work, maybe I'll be able to share a laptop cart with another teacher? I am also asking on the first day how many students have internet access where they do homework, perhaps I'll be able to assign something in the form of a Google form occasionally. They integrate into my course webpage so nicely it would be a shame not to use them!

Other Quick Ideas:

- Be silent! - to get students to use each other as instructional resources (last year I participated in the Day of Silence and it was great to see how well kids worked together once they got past the frustration of being largely on their own)
- Ask "how did you know that you were done?" or "how confident are you with your answer?"
- Present a "good bad answer" to promote discussion (authentic student work)
- Use "I observe ______ and I wonder _______" slips after investigations
- Journal: instead of math learned, "how did you meet the objective(s)?"

Take Aways:

(the whole post...)

Quiz regularly

Comments only on projects

Make classwork grade more transparent

Use GSP, Snap, Google Docs

## August 17, 2011

### End of Year Reflections: Algebra II

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

I'm not sure I want to share this publicly. To be honest, I didn't include some quotes because they were too depressing. This class was by far my most frustrating. A lot of that was me: it was my first year in a new school and I didn't understand what was covered in Algebra I, I'd never taught Algebra II before, I got irritated when students didn't remember how to do things that they really, really should know how to do by junior year. Some of it was the kids: most didn't start coming for extra help until the last quarter, they didn't work as a cohesive class, they didn't have high expectations of themselves. Plenty of the blame can go elsewhere: some went to 3 weeks of summer school over a year ago and that meant they 'got Algebra I', many weren't ready for Algebra I so they didn't retain as much, lots didn't want to take more math beyond Algebra II and society says that's fine, society also says math is hard and it's okay to say you're bad at it. I learned a lot from this class, but I learned it all the hard way. It helped that the other Algebra II teacher shared my frustrations, but I wish that we'd had time to work together. Instead, after each chapter or two we made plans for adjustments next time we teach it, which neither of us will be able to enact this year since I'm not teaching Algebra II and she's taking a year off. However, this post isn't about all that, it's about what the kids wrote in their reflections.

That was the last of the End of Year Reflections (until next year!). Maybe by now I have some more posts written, but this daily posting thing will definitely be a rarity, so I hope you didn't get used to it ;).

I'm not sure I want to share this publicly. To be honest, I didn't include some quotes because they were too depressing. This class was by far my most frustrating. A lot of that was me: it was my first year in a new school and I didn't understand what was covered in Algebra I, I'd never taught Algebra II before, I got irritated when students didn't remember how to do things that they really, really should know how to do by junior year. Some of it was the kids: most didn't start coming for extra help until the last quarter, they didn't work as a cohesive class, they didn't have high expectations of themselves. Plenty of the blame can go elsewhere: some went to 3 weeks of summer school over a year ago and that meant they 'got Algebra I', many weren't ready for Algebra I so they didn't retain as much, lots didn't want to take more math beyond Algebra II and society says that's fine, society also says math is hard and it's okay to say you're bad at it. I learned a lot from this class, but I learned it all the hard way. It helped that the other Algebra II teacher shared my frustrations, but I wish that we'd had time to work together. Instead, after each chapter or two we made plans for adjustments next time we teach it, which neither of us will be able to enact this year since I'm not teaching Algebra II and she's taking a year off. However, this post isn't about all that, it's about what the kids wrote in their reflections.

Most investigations in this class were of the "graph a lot of equations to find out what the different coefficients and constants do" variety. Shockingly, those didn't make it onto the list of favorite activities. We also acted out some of those when we studied parabolas (turning the squares on the floor into a giant coordinate grid), that activity didn't make it onto the list either. Other investigations included lots of numerical examples, followed by a generalization. Still not on the list! So, which ones did make the list? Just two:

The rolling markers lab, and the interest rates activity.

The rolling markers lab was pretty cool. We set up 'ramps' of different heights (folders propped on books), rolled markers down and measured the distance traveled. It was a nice review of scatter plots, best fit lines and the different equations used to describe lines. We had some fun building crazy ramps and trying to find markers which would roll in a straight line. It was from the first quarter and they remembered it at the end so clearly it made an impression. I'll probably try this activity with my Learning Skills class this year (math for students with disabilities who can't access the traditional high school curriculum yet).

The interest rates project was bad. A couple other teachers wrote an outline while I was in a geometry meeting. I missed the discussion, I didn't make it precise before distributing it, and none of us were really thinking about exactly how low interest rates have fallen! Students went to the bank (or internet) to get rates on savings accounts and CD's. Pairs were given a certain amount of money to invest and then compare the outcomes of different scenarios. The scenarios were too vague and the final products reflected that. The idea was cool, the kids appreciated the value of it, but it was poorly executed on my part.

The specific topics they enjoyed or found challenging weren't particularly noteworthy, as in the other classes some students listed a topic as a favorite, while others listed it as hard. The one surprise came from a student who listed the same topic (factoring) as both hard and his favorite. That kid gets brownie points in my book.

After reading this you may be surprised to hear that the kids learned anything. They did, the class wasn't awful every day, but my lasting impression was of a group of rather uninspired kids. I didn't get them excited about math. When I asked them what they needed, all they could offer was a change of scenery might help. They did get more work done when we hung out in the library, but it was a very unsatisfying class in my mind. Still, they learned, and they can tell you about it in their own words:

- If I try my hardest I could get a good grade
- My intelligence is not enough, I need to work and study hard too
- I found out that I can do it
- I learn best by doing the work by myself
- I need to study more and make practice problems
- Study best with flashcards
- Staying after can help you make up a lot of points and help you understand
- When I really want something I can achieve it
- I learn best by doing projects
- I can learn to solve any problem with practice
- There are at least 2 ways to do anything in math

That was the last of the End of Year Reflections (until next year!). Maybe by now I have some more posts written, but this daily posting thing will definitely be a rarity, so I hope you didn't get used to it ;).

Take aways:

Thank goodness you're not teaching Algebra II again!! (jk, but not really)

Do rolling markers in Learning Skills

Emphasize importance of making up work early and often.

## August 16, 2011

### End of Year Reflections: Fundamentals of Geometry

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

In addition to two college prep geometry courses, I also taught two fundamentals of geometry courses. Our levels are fundamentals (SPED and struggling students), college prep (aka CP, the 'regular' class) and honors. The fundamentals courses were co-taught and I got to use an amazing book: Merrill, from the 80's with only blue and black ink, filled with discoveries students should do before theorems were presented. I used many of the ideas in this book in my CP class, and I followed the ordering of each book in most cases so the two levels were taught in a slightly different order. Another thing to consider when planning for this year.

In addition to two college prep geometry courses, I also taught two fundamentals of geometry courses. Our levels are fundamentals (SPED and struggling students), college prep (aka CP, the 'regular' class) and honors. The fundamentals courses were co-taught and I got to use an amazing book: Merrill, from the 80's with only blue and black ink, filled with discoveries students should do before theorems were presented. I used many of the ideas in this book in my CP class, and I followed the ordering of each book in most cases so the two levels were taught in a slightly different order. Another thing to consider when planning for this year.

Most of the responses in the class that I had do the end of year reflection (I'm kicking myself now for forgetting in the other class) were similar to the ones in CP. The investigations were the same across the courses, but there are a few things to note.

Students in this class mentioned struggles with: algebra, formulas, measuring and square roots. Oftentimes placement is based on Algebra 1 scores, so those topics are more likely to be an issue in the fundamentals classes. Next year I might want to do some more explicit review of Algebra.

There was also one student who listed "working with others" as the hardest thing to learn to do. We discuss classroom norms a few times during the year, and I try to start the year with an activity emphasizing the importance of team work, but it's good to be reminded that it's still a struggle for many students. In truth, it's still a struggle for me! Some people I immediately click with and we're ready to share and learn together, but with others I find myself shutting down. I would like to have a better way of assessing how students are working together. The participation quiz (Sam wrote about it here) that I saw at PCMI might be a good way to do this, and I'd also like to see students discussing with each other.

In one class I gave students a daily checklist based off of our school's Habits of Mind rubric. It included points for being on time and prepared, working with others, asking questions and participating. Of course, this is the same class that I neglected to give the end of year reflection to. Maybe I can modify it from a daily list to a every 5 classes list and collect it when I collect journals... One of the best features turned out to be the "Is there anything else you'd like to share?" section where students vented frustrations, owned up to misbehavior and were generally their honest and insightful selves.

And, just because they're corny yet sincere, here's the quotes from the "What I learned about myself" section

- If I push myself I can accomplish many things
- I can do better work when I put my mind to it
- I can achieve anything if I work hard for it
- I can do things, all I need is a push
- If I pay attention, I can learn more
- I'm too smart for geometry
- Homework is important
- Geometry is easier than algebra
- I am a lot better with geometry than algebra
- I am good at math
- I do well when I study
- Studying is really important
- If I try, I can get good grades
- I need to be organized

Take aways:

More Algebra practice in Fundamentals

Compare the order of the levels to see if there are compelling reasons to switch either

Ways for teacher and students to report group dynamics? (rubric?)

## August 15, 2011

### End of Year Reflections: Geometry Investigations

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

Even as early as student teaching I quickly realized that working from the book day in and day out was

**. For me even more so than for the students. When life is running smoothly I do what I call investigations weekly. Block scheduling messed up my weekly routine, so last year they happened sometimes, but not at regular intervals. In geometry it's easy to do a quick investigation of "everyone draw a triangle, measure the angles, tell me a hypothesis." But those aren't the activities that kids remembered at the end of the year; they remembered the applications, the field trips to the parking lot and the ones that involved coloring. Honestly, those are my favorites as well. I get to interact with students in a different way when we're identifying trees (how do MA residents not know what a white birch looks like??) or rolling circles down the 100 foot track.**

*boring*
Here's what the Geometry CP students named as their favorite activities:

Expanding turtle

Measuring height with mirrors

Measuring height with shadows

Pi day (4)

Sierpinski's triangle

Comic dilation (7)

Tree activity (7)

Tesselations

BINGO

Diameter (pi day or tree?)

Outdoor activities

I'm impressed someone remembered the expanding turtle, since we did that on the very first day of school! I presented them with a turtle, they measured whatever they wanted, predicted growth based on the package's claims and stuck it into a bucket of water. Over the following weeks students would occasionally remember the turtle was growing and poke, measure and smell it (smells like cheerios for some strange reasons). It's a nice way to get them thinking the first day, but no big deal if a kid switches in 2nd day and didn't get to see the turtle before it entered the water. Co-teachers and friends have started picking up expanding animals for me so I now have a whole crew of creatures to experiment with.

The pi day tradition started in my last school, and I've carried it with me. We gather as many circular objects as we can (wheels, jars, balls, baskets...) then students measure diameter and circumference to calculate pi. For increased accuracy on circumference (and a lot more fun!) we count the number of times it can roll down a 100 foot track. Anyone who accurately calculates pi, gets a slice of pie. I even got the grocery store to donate $25 worth of pies and the principal found funds to cover the rest!

I was happiest with the 'tree activity.' It was nearing the end of the year and I was feeling fine about where we were in the curriculum. It was hot in my classroom (no windows!) so I was looking for something to get us outside. We were studying circles and I happened upon a chart relating the circumference of a tree to its age. Each type of tree in the chart had a growth factor, so all we had to do was identify some trees and measure their circumference. In my first vision of this project we would all go out with those tree ID guides that work like choose your adventure books (if it has needles jump to page 45), but I didn't know how to find those in time. So, I gave them the identifying features of 4 common trees (dogwood, white birch, red oak and red maple) to go out and find. But, to prove to me they had the correct tree they had to draw or describe why

**both**the leaves and bark fit the description.
I anticipated that this would be a fun, but simple activity. Oh was I wrong! Kids started by running up to any plant, plucking a leaf and presenting it to me to identify. Dear children: don't harm the tree, read the description, look at the picture, think for yourselves! They got better, but even the ones following all my advice were missing something I assumed all would have- a basic idea of what these trees looked like. One group was looking at a tree- its leaves had jagged edges like a birch and the bark was light, but it wasn't until I pointed at the tree 5 feet away for comparison that they realized a white birch is really white! It still boggles my mind that kids can live in a city filled with parks and not know the first thing about the trees that fill them. I can't blame video games or TV, those existed when I was a kid too. Is no one interested in nature? I'm ashamed of how few plants I can identify, maybe this is something that we'll all work on together next year. In fact, this just may be one of the early activities on proof that I need.

Take aways:

Prove you correctly identified tree to intro proofs.

Take aways:

Prove you correctly identified tree to intro proofs.

## August 14, 2011

### 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'

## August 13, 2011

### 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.

## August 12, 2011

### 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 started this blog.

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:

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 started this blog.

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!

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