## Sunday, June 3, 2012

### Implications for Future Work

As this school year begins to come to an end, and I reflect on my action research, I am grateful that I have had this opportunity. I think that after coming together for the past eight months, the JBA math team is stronger, and I know that I for one have a deeper appreciation for the subject that I once hated. Because of our work together, my Principal has signed me and the 7th grade math teacher up for a three-day professional development on becoming a learning team leader through Teaching Matters. She picked us with the idea that she and I will facilitate PLCs with the Math and ELA departments at our school next year. We had our first training this past Thursday where we learned about team building, norms, and protocols (I was proud, being a Bank Street-er, I was already familiar with norms and protocols). I am not sure if this opportunity would have necessarily happened had I not done this action research this year, but I am very excited and looking forward to seeing where this training takes not only myself, but the JBA math team next year.

## Saturday, May 19, 2012

### Conclusions

Some of the struggles that I have encountered through doing this action research are balancing doing math together with my colleagues and sticking to our agenda. A teacher's time is limited and therefore very valuable and there were at least two occasions where our math team meetings went longer than we planned because we got so wrapped up in doing the math. The more times we met, I felt like we got better at pacing our meetings so that we did some math together, but did accomplish other things on our agenda as well. Another struggle I encountered was finding "good" math problems for the team to do. I didn't want to bring in problems that were necessarily too easy or too challenging to do, but I wanted to bring problems to the group that were thought-provoking or at the very least, we could bring into our own classrooms. In my opinion, examples of some of the interesting problems that we spent a good amount of time on were: How much is your time worth? and Tiles in the Bag. Not only do I remember doing these with the group, but I feel like I left with good problems that I was excited to do with my scholars afterward. Having already done the problems with the math team, I felt like I was better prepared to give this problem to my own scholars.

One of the highlights that I encountered through doing this action research this year is that I realized that if I want my scholars to enjoy thinking and doing math, I need to enjoy thinking and doing math, and what better way to do that than with my math colleagues. There were a few meetings were we brought in problems that we had encountered in our own lessons. One major thing I learned about collaborative professional development and getting together with math colleagues and doing math problems together is that the problems don't have to be these big, multi-step tasks, they can be simple. By doing math together with my colleagues, my own appreciation and understanding of mathematics grew, and when I think about it, shouldn't that be the ultimate goal of any professional development?

One of the highlights that I encountered through doing this action research this year is that I realized that if I want my scholars to enjoy thinking and doing math, I need to enjoy thinking and doing math, and what better way to do that than with my math colleagues. There were a few meetings were we brought in problems that we had encountered in our own lessons. One major thing I learned about collaborative professional development and getting together with math colleagues and doing math problems together is that the problems don't have to be these big, multi-step tasks, they can be simple. By doing math together with my colleagues, my own appreciation and understanding of mathematics grew, and when I think about it, shouldn't that be the ultimate goal of any professional development?

## Sunday, April 29, 2012

### Findings

Back in September, one of my own professional goals for this school year was to find a way to professionally collaborate more with my math colleagues. Being the 8th grade math teacher, I wanted to understand where my scholars were coming from in 6th and 7th grade math. Mathematical understanding is something that develops over time, and just like I wanted my 8th graders to be ready for high school math when they left me, I wanted my incoming 8th graders to be ready for 8th grade/ Integrated Algebra.

To begin working on this goal, I asked myself the question

Some meetings we started off doing problems and would spend 10-15 minutes on them, other times we would get so engrossed in the math, that our whole meeting would be simply doing the math, and talking about it. For me personally, it was a positive experience getting together with my fellow math colleagues and taking off our "teacher hat" and just be this group of people discussing and solving math problems together. I believe that my action research blogging journey shows that what I have learned most about collaborative professional development, so far, by getting together with math colleagues and doing math problems together is that you build a team by constructing community knowledge. One of my biggest fears back in October was that even though I was trying to bring the math team together, I wasn't trying to run the math department. As we continued to meet together every other week or so, I found that that became less of a concern and I think that doing math together was part of the reason for that. Doing and discussing the problems together made everyone equal on our math team.

I hope that as a team, we can sustain what we have been doing through the exhausting test-prep season. Even though we won't be able to meet as a whole group for a while because most of us will be out scoring state exams over the next few weeks, I am looking forward to collaborating with my colleagues to close out the year strong for our scholars and for ourselves as a team.

To begin working on this goal, I asked myself the question

**"What will I learn about collaborative professional development by getting together with math colleagues and doing math problems together?"**and started this blog to document my action research journey. Beginning in October 2011, the JBA began meeting regularly after school, and in addition to talking about work and lesson plans, we began doing math together. Oftentimes I would be the one bringing math problems or tasks that I found to the group, but there were a few occasions where the other math teachers would bring in a math problem for the group to do.Some meetings we started off doing problems and would spend 10-15 minutes on them, other times we would get so engrossed in the math, that our whole meeting would be simply doing the math, and talking about it. For me personally, it was a positive experience getting together with my fellow math colleagues and taking off our "teacher hat" and just be this group of people discussing and solving math problems together. I believe that my action research blogging journey shows that what I have learned most about collaborative professional development, so far, by getting together with math colleagues and doing math problems together is that you build a team by constructing community knowledge. One of my biggest fears back in October was that even though I was trying to bring the math team together, I wasn't trying to run the math department. As we continued to meet together every other week or so, I found that that became less of a concern and I think that doing math together was part of the reason for that. Doing and discussing the problems together made everyone equal on our math team.

I hope that as a team, we can sustain what we have been doing through the exhausting test-prep season. Even though we won't be able to meet as a whole group for a while because most of us will be out scoring state exams over the next few weeks, I am looking forward to collaborating with my colleagues to close out the year strong for our scholars and for ourselves as a team.

## Sunday, April 15, 2012

This article talks about

*"America's cultural problem with math... and how a**brave group of educators and entrepreneurs think they can change that. With games and competitions, museums and traveling road shows - and a strategic sprinkling of celebrities - they aim to make math engaging, exciting and even fun."*This is something that I struggle with on a daily basis. Growing up, I was a "good math student" but I struggled with it constantly. I could study and pass tests, but it wasn't until I started teaching with math really started coming together for me. I have been in the middle of many lessons with my 7th and 8th graders, and all of a sudden, something clicked and the math made sense to me.... more than 10 years after I first learned the material. Back then, knowing why things worked it math didn't matter to me. I was able to memorize formulas and procedures, but it was only recently did I start "doing math." Math wasn't fun then, but I was still able to be successful with it later on.To me, the most interesting quote from the article is "While he applauds the tournaments and treasure hunts and most especially the math museum, veteran math teacher J. Michael Shaughnessy says it will take more than good PR to boost math's appeal. It will take a cultural revolution. Every time he hears a parent tell a child,

*"I've done fine without math," or "You don't really need to know that," he quietly but urgently interrupts.**"That gives kids permission not to try hard at a subject that's really challenging for everyone," said Shaughnessy, the president of the National Council of Teachers of Mathematics. "It's doing national damage."*My catchphrase this year in my Integrated Algebra classroom is "Trust yourself" because ultimately that is what I want my students to do. It's not my math, or some ancient person's math, it's just math. And yes its confusing sometimes. But it's OK to struggle. And part of what makes that struggle so worth it, is trusting yourself and trusting the math.What am I learning about collaboration?

I love reading articles like this and I think it's important for teachers to be able to read and share information that is important to them and their teaching whether it's through a weekly email newsletter, blog, or PLC. We can't do it alone.

## Tuesday, March 27, 2012

### How much is your time worth?

For our math team warm up this week we spent the first 15 minutes of our meeting working on a Figure This! problem from the NCTM. The problem asks:

We spend the first 5 minutes or so working individually (it was interesting that all of us automatically went to work on our own first, rather than just start talking about it) and then came back together and shared out our thoughts. We all agreed that we would prefer the second option because we would end up with more money after seven days, but any days less than seven, we would prefer the $20 per day. I asked everyone in the group to share out how they approached the problem and it was interesting to see and hear how people organized their information.

I am curious to see what other Figure This! problems are out there because I think that these would be awesome to do with my 8th graders. This problem in particular is an interesting problem to think about because it deals with money and bring up the idea that you'd only want to choose the second option if you were working for seven or more days. I think this problem would lend itself great to discussions on how we represent data as tables, equations, and graphs. It was awesome to see my colleagues approach this problem the same way I hope my students would approach it.

*Would you rather work seven days at $20 per day or be paid $2 for the first day and have your salary double everyday for a week?*We spend the first 5 minutes or so working individually (it was interesting that all of us automatically went to work on our own first, rather than just start talking about it) and then came back together and shared out our thoughts. We all agreed that we would prefer the second option because we would end up with more money after seven days, but any days less than seven, we would prefer the $20 per day. I asked everyone in the group to share out how they approached the problem and it was interesting to see and hear how people organized their information.

__What am I learning about collaboration?__I am curious to see what other Figure This! problems are out there because I think that these would be awesome to do with my 8th graders. This problem in particular is an interesting problem to think about because it deals with money and bring up the idea that you'd only want to choose the second option if you were working for seven or more days. I think this problem would lend itself great to discussions on how we represent data as tables, equations, and graphs. It was awesome to see my colleagues approach this problem the same way I hope my students would approach it.

## Wednesday, March 21, 2012

### Filling Glasses problem

During our math team meeting this week, I shared with the group the Filling Glasses problem. We were not allowed to write anything, just talk with our partner on matching glasses to four unusually shaped glasses with the graphs that best describe the height of the water in the glass over time. We spent about 10 minutes talking with a partner and then the pairs shared out with the whole group and we discussed whether we agreed or not, and justified our responses.

I really enjoyed this problem for a few reasons: (1) although it was annoying at first, not being about to write anything really made me think about how I communicated my thoughts to my partner, (2) its not a "typical" kind of problem, yet totally real-life based, (3) I felt like I got a lot from listening to my colleagues comments. My co-teacher liked this problem so much that he and I decided to use it as a warm-up for our CTT class one day to see how that would go.

The math problems that we have been doing have been a great way to "even the playing field" during our team meetings because they make all of us responsible for sharing. Although I have gotten better at it, there have been many lessons with my scholars, where the bell rings in the middle of the scholars working, and the lesson really has no final share-out. Being mindful of these problems have really emphasized to me the importance of bringing a lesson (or a problem) back together at the end and the share out main ideas.

I really enjoyed this problem for a few reasons: (1) although it was annoying at first, not being about to write anything really made me think about how I communicated my thoughts to my partner, (2) its not a "typical" kind of problem, yet totally real-life based, (3) I felt like I got a lot from listening to my colleagues comments. My co-teacher liked this problem so much that he and I decided to use it as a warm-up for our CTT class one day to see how that would go.

__What am I learning about collaboration?__The math problems that we have been doing have been a great way to "even the playing field" during our team meetings because they make all of us responsible for sharing. Although I have gotten better at it, there have been many lessons with my scholars, where the bell rings in the middle of the scholars working, and the lesson really has no final share-out. Being mindful of these problems have really emphasized to me the importance of bringing a lesson (or a problem) back together at the end and the share out main ideas.

## Thursday, March 15, 2012

### Six Keys to Successful Collaboration By Braden Welborn

Got this article in an email today and thought it brought up some interesting points on teacher collaboration. The two points that resonated with me the most were clarity of purpose and individual commitment. I feel with our math team meetings after school, I am lucky that the 6th and 7th grade math teachers are just as invested in working together to improve student achievement and our practice. I think the article sums it up best at the end when it says "There's no magic formula for successful collaboration. But this dialogue demonstrates that teacher's know a great deal about what works - and what doesn't work."

What I am learning about collaboration?

What a great way to empower teachers with that last statement!

## Friday, February 24, 2012

### Why Great Teachers Are Also Learners

This article was also in this week's email newsletter, and I thought it also connected very closely with my action research.

In her article, "Why Great Teachers Are Also Learners," Vicki Davis (2012) talks about how educators can inspire students with their own curiosity. Davis states that "As a teacher, the most important asset I can teach my students is a love of learning. In my 10 years teaching high school, I have found that making a deliberate and transparent effort to continue my own learning allows me to inspire my students to follow my footsteps." She describes nice best practices that have served her well throughout her career. The three that resonated the most with me were:

- "Talk about the new things you're learning, and let your enthusiasm show,"
- "Show students that you are willing to investigate," and
- "Let students see you proudly sharing your learning."

__What am I learning about collaboration:__

My love of math has grown exponentially since I became a math teacher. (Seriously, I was not a fan of math when I was in school.) But I think since starting the Math Leadership program at Bank Street, and doing math with my colleagues this year in our team meetings, my love of math has grown even more. I used to be afraid to try and solve problems more than one way. Now, I get excited when a student does. I used to only focus on getting the right answer, because I thought that that was all that mattered. Now, I love hearing a student explain their whole process... it's beautiful!

Basically, since becoming a math teacher five years ago, my appreciation of math has grown. But I don't think an appreciation is enough. I can appreciate good art, or a good piece of music, but when you create that piece of art or music, that brings your appreciation to a whole new level. My new thinking? I don't just appreciate math. I do math. And every single day, I strive to inspire my 8th graders to do the same.

Davis, V. (2012, February). Why great teachers are also learners. The

Davis, V. (2012, February). Why great teachers are also learners. The

*Atlantic.*Retrieved February 21, 2012 from http://www.theatlantic.com/sponsored/impact-of-one/archive/2012/02/why-great-teachers-are-also-learners/253376/## Thursday, February 23, 2012

### Becoming a Teacher Leader

Being off from work this week for Mid-Winter Recess, there was no math team meeting to blog about. However, in my SmartBrief weekly email newsletter, that I subscribe to, I did read two articles that I thought tied in nicely with my action research.

In her article "5 Tell-Tale Signs You're Becoming a Teacher Leader," Ratzel (2012) describes five signs "that may signal that you're on the road to becoming a teacher leader." Ratzel states that "If you find yourself yearning to take an idea beyond your classroom, you're probably ready to become a leader. The first step might be as small as sharing a lesson plan with a colleague down the hall... Perhaps you will blog about how your students are using iPads to work on letter recognition, submit an article to your favorite professional journal, or share your knowledge in topic-focused Twitter chats. Or maybe your next step will be to help "unpack Common Core standards" for your department, or to offer to lead a workshop on bullying."

__What have I been learning about collaboration?__My whole action research experience this year has been about what I am learning about collaborative professional development. And since I started coming together regularly with my math colleagues at JBA this year, I have learned quite a lot. We have shared lesson plans, discussed issues that are important to us and our teaching, and because of this action research, we have been doing math together. On top of all that, I have been blogging about my whole experience on here, and reading about other fellow math leaders experiences this year on their blogs, and it's been great. I honestly feel that we have become more than just a group of teachers, we have become a group of learners, and like Ratzel (2012) describes, I am finding myself "writing, advising, listening, collaborating, networking, seeking knowledge, and reflecting." So collaborative professional development doesn't have to be this BIG thing that happens right away - it can start small. It can start in a classroom, after school, once a week, with 3 or 4 math teachers coming together, simply, to do some math together.

Ratzel, M. (2012, February). 5 tell-tale signs you're becoming a teacher leader.

Ratzel, M. (2012, February). 5 tell-tale signs you're becoming a teacher leader.

*Education Week Teacher.*Retrieved February 21, 2012 from http://www.edweek.org/tm/articles/2012/02/21/tln_ratzel_teacherleader.html?tkn=SRSF9cPYYaJGCZsKm5T6fgpOV0c30h32egnv&cmp=clp-edweek## Sunday, February 12, 2012

### Learning Conference Tasks

Last year, the 6th graders at JBA had End-of-the-Year Learning Celebration Conferences, where scholars presented some of the things they have learned to their parents. Being a 7th/ 8th grade teacher, I didn't participate, but I heard good things about it. This website has some general information on Learning Celebration Conferences, and in addition, Sandra and I will be presenting about them this summer, so stay tuned =)

This year, as a staff, we decided that instead of 2nd marking period Scholar-Led Conferences, the whole school would participate in Learning Celebration Conferences (LCC). To prepare, we had been working in small grade teams to come up with a menu of tasks for scholars to pick from, and during this week's math team meeting, we decided to try out each others tasks to get a feel for what our scholars would be doing. Although we were in separate grade teams, the 7th grade teacher and I had previously worked together coming up with our LCC menus, so today we actually did each others math tasks.

We decided that it would be best to work through the 7th grade tasks first, and then the 8th grade tasks. The tasks are meant to do done without teacher input, but we wanted to be able to ask each other questions as we worked through them. Some of the 7th grade tasks that I worked on included solving equations and proving the Pythagorean Theorem. Some of the 8th grade tasks that the 7th grade teacher worked on included solving equations with variables on both sides, and a coming up with a geometric transformation dance routine. We spent about the whole hour of our meeting time working through the tasks, asking questions, and modifying the tasks when necessary.

Trying out each others tasks was really helpful for me this week because I had no previous experience with LCC, and the 6th and 7th grade math teachers had. It was interesting, because several times, the way we approached a task, was different then how the teacher initially designed the task. For example, the one teacher (as a scholar) set up a proportion to solve a sales discount/tax problem, while I had designed it as a straight multiplication problem. It really reminded me that just because I am comfortable solving a problem one way, doesn't necessarily mean that that is how my scholars will approach it, and that good tasks have multiple entry points (which is something that came up during my action research last year).

I think it was not only really helpful, but really important for us to go through each others math tasks during our team meeting. Collaborating with the other math teachers helped me revise my own LCC menu and gave me a better idea of how my 8th graders will be approaching the tasks. And although I am still nervous about the conferences, I definitely feel more confident and I am fairly confident that that wouldn't have happened if I had come up with the menu and tasks on my own.

This year, as a staff, we decided that instead of 2nd marking period Scholar-Led Conferences, the whole school would participate in Learning Celebration Conferences (LCC). To prepare, we had been working in small grade teams to come up with a menu of tasks for scholars to pick from, and during this week's math team meeting, we decided to try out each others tasks to get a feel for what our scholars would be doing. Although we were in separate grade teams, the 7th grade teacher and I had previously worked together coming up with our LCC menus, so today we actually did each others math tasks.

We decided that it would be best to work through the 7th grade tasks first, and then the 8th grade tasks. The tasks are meant to do done without teacher input, but we wanted to be able to ask each other questions as we worked through them. Some of the 7th grade tasks that I worked on included solving equations and proving the Pythagorean Theorem. Some of the 8th grade tasks that the 7th grade teacher worked on included solving equations with variables on both sides, and a coming up with a geometric transformation dance routine. We spent about the whole hour of our meeting time working through the tasks, asking questions, and modifying the tasks when necessary.

__What I am learning about collaboration?__Trying out each others tasks was really helpful for me this week because I had no previous experience with LCC, and the 6th and 7th grade math teachers had. It was interesting, because several times, the way we approached a task, was different then how the teacher initially designed the task. For example, the one teacher (as a scholar) set up a proportion to solve a sales discount/tax problem, while I had designed it as a straight multiplication problem. It really reminded me that just because I am comfortable solving a problem one way, doesn't necessarily mean that that is how my scholars will approach it, and that good tasks have multiple entry points (which is something that came up during my action research last year).

I think it was not only really helpful, but really important for us to go through each others math tasks during our team meeting. Collaborating with the other math teachers helped me revise my own LCC menu and gave me a better idea of how my 8th graders will be approaching the tasks. And although I am still nervous about the conferences, I definitely feel more confident and I am fairly confident that that wouldn't have happened if I had come up with the menu and tasks on my own.

## Thursday, February 2, 2012

### Tiles in the Bag

Earlier in the week, the 7th grade teacher told me that the next unit that she was covering with her classes was Probability and Statistics, which is a huge part of the 7th grade curriculum and makes up 30% of the State Exam. Since I had taught 7th grade in the past, she asked me for any thoughts or suggestions. I shared with her some of my past unit plans and offered my thoughts on teaching certain topics, and decided to share the Tiles in the Bag activity from Marilyn Burns during this week's math team meeting.

Burns actually has two versions of this activity, and for our team meeting, I choose Version2. For this activity, I filled three brown paper bags with red and blue tiles. One bag had 25 red & 5 blue. One bag had 20 red & 10 blue. And the last bag had 10 red & 20 blue. I told my fellow math teachers this information and had it written on the Smart Board. We chose a bag at random (I didn't even know) and then we went around, and each person drew a tile from it, noted its color (red or blue), and then replaced it. One of the teachers kept a record of the colors on a sheet of paper. We all took turns participating till we had 25 random samples with replacement. After we had done that, we computed the percentages of red tiles for: the first five samples, the first 15 samples, the first 20 samples, and finally all 25 samples. We briefly talked about the importance of being comfortable working with percentages and the misconceptions that scholars sometimes have with percents. As a group, some of the things we noted were: "Not understanding that percent represents a whole," "Converting between fractions, decimals, and percents," and "Percents less than 1 and greater than 100."

Going back to the activity, we had to decide which bag, of the three possibilities, we think we used, and which bag would we have chosen if our decision was based on five samples? Ten? Fifteen? How many samples do we think we needed? We each took turns sharing what we thought and then explaining why. After we had shared and talked with each other for about 15 minutes, we opened up the bag and actually counted the tiles.

What I noted, as everyone was sharing out their predictions and reasoning, was how into the conversation I got. I try to write myself notes during our team meetings, of things to remember to write about on here, but I found myself really listening to my fellow colleagues, and focusing on the math that is going on. And although, it is challenging because I do want to keep these entries authentic, I think the fact that I am getting draw into the conversation says a lot. I wasn't aware of it, but my focus wasn't "What am I learning about collaboration by doing this activity with my colleagues?" but "How can I use what I know about probability and statistics to come up with an viable argument to share?" I was thinking about the math!

Although I was very pleased with this experience and the other teachers thought that this was an awesome activity, it did make me wonder about what better ways I could possibly record data during our meetings? That way, I could really focus all of my attention on the math we are doing, and less on gathering data for my action research. Plus, with video clips I would have another record of authentic data, in addition this this blog, for my research purposes. This may be something to look into...

Burns actually has two versions of this activity, and for our team meeting, I choose Version2. For this activity, I filled three brown paper bags with red and blue tiles. One bag had 25 red & 5 blue. One bag had 20 red & 10 blue. And the last bag had 10 red & 20 blue. I told my fellow math teachers this information and had it written on the Smart Board. We chose a bag at random (I didn't even know) and then we went around, and each person drew a tile from it, noted its color (red or blue), and then replaced it. One of the teachers kept a record of the colors on a sheet of paper. We all took turns participating till we had 25 random samples with replacement. After we had done that, we computed the percentages of red tiles for: the first five samples, the first 15 samples, the first 20 samples, and finally all 25 samples. We briefly talked about the importance of being comfortable working with percentages and the misconceptions that scholars sometimes have with percents. As a group, some of the things we noted were: "Not understanding that percent represents a whole," "Converting between fractions, decimals, and percents," and "Percents less than 1 and greater than 100."

Going back to the activity, we had to decide which bag, of the three possibilities, we think we used, and which bag would we have chosen if our decision was based on five samples? Ten? Fifteen? How many samples do we think we needed? We each took turns sharing what we thought and then explaining why. After we had shared and talked with each other for about 15 minutes, we opened up the bag and actually counted the tiles.

__What am I learning about collaboration?__What I noted, as everyone was sharing out their predictions and reasoning, was how into the conversation I got. I try to write myself notes during our team meetings, of things to remember to write about on here, but I found myself really listening to my fellow colleagues, and focusing on the math that is going on. And although, it is challenging because I do want to keep these entries authentic, I think the fact that I am getting draw into the conversation says a lot. I wasn't aware of it, but my focus wasn't "What am I learning about collaboration by doing this activity with my colleagues?" but "How can I use what I know about probability and statistics to come up with an viable argument to share?" I was thinking about the math!

Although I was very pleased with this experience and the other teachers thought that this was an awesome activity, it did make me wonder about what better ways I could possibly record data during our meetings? That way, I could really focus all of my attention on the math we are doing, and less on gathering data for my action research. Plus, with video clips I would have another record of authentic data, in addition this this blog, for my research purposes. This may be something to look into...

## Thursday, January 26, 2012

### The Digit Place game

For this week's math team meeting, I decided to start us off by teaching my colleagues how to play the Digit Place game. I had learned about this game during a PD I had gone to in December and thought it would be a simple and fun way to get us started. The 6th grade teacher was familer with the game, but the 7th grade teacher, and our ICT teacher were not.

This elementary school teacher's classroom blog has the instructions on how to play. After I explained the directions, we got a white board, marker and paper towel, paired up and started playing. We ended up playing for about 15 minutes or so, and then had a discussion on how we could potentially use this game in our classroom and questions we could ask to encourage our scholar's thinking. As we were sharing, I wrote down the questions that were coming up with on the board. Some of the questions we came up with to ask our scholars were: "What do you know so far?" "Are there any digits that you are certain are in the number? What information helped you?" "Have you eliminated any digits?" "What would be your next guess any why?" and "How could it help you to guess a number that included digits you had already eliminated?"

One of the reasons that I chose the Digit Place game was because I wanted to keep it simple. I anticipated that we would play the game for a few minutes, talk about it briefly, and then go on with the rest of our meeting, but that was not the case. After playing each other, the discussion that we had was awesome. What started out as a simple game, became a discussion on transforming the tasks that we ask our scholars to do to encourage our scholars to use thinking, reasoning, and problem solving skills. I was amazed at the enthusiasm that something so simple as a game on digit place, could lead to.

I think one of the reasons that this worked well was because it was something that the teachers could potentially share with their classes. One of my complaints of past PDs has been the lack of practically. There might be some good ideas, but I always liked the PDs where I left with something I could bring back to my students and try tomorrow. A teacher's time is valuable, and nothing makes me more frustrated than feeling like I just wasted time at a useless PD, so I think one way to make collaboration more meaningful is by keeping things practical. Who knew that something as simple as the Digit Place game could be so productive?

This elementary school teacher's classroom blog has the instructions on how to play. After I explained the directions, we got a white board, marker and paper towel, paired up and started playing. We ended up playing for about 15 minutes or so, and then had a discussion on how we could potentially use this game in our classroom and questions we could ask to encourage our scholar's thinking. As we were sharing, I wrote down the questions that were coming up with on the board. Some of the questions we came up with to ask our scholars were: "What do you know so far?" "Are there any digits that you are certain are in the number? What information helped you?" "Have you eliminated any digits?" "What would be your next guess any why?" and "How could it help you to guess a number that included digits you had already eliminated?"

__What am I learning about collaboration?__One of the reasons that I chose the Digit Place game was because I wanted to keep it simple. I anticipated that we would play the game for a few minutes, talk about it briefly, and then go on with the rest of our meeting, but that was not the case. After playing each other, the discussion that we had was awesome. What started out as a simple game, became a discussion on transforming the tasks that we ask our scholars to do to encourage our scholars to use thinking, reasoning, and problem solving skills. I was amazed at the enthusiasm that something so simple as a game on digit place, could lead to.

I think one of the reasons that this worked well was because it was something that the teachers could potentially share with their classes. One of my complaints of past PDs has been the lack of practically. There might be some good ideas, but I always liked the PDs where I left with something I could bring back to my students and try tomorrow. A teacher's time is valuable, and nothing makes me more frustrated than feeling like I just wasted time at a useless PD, so I think one way to make collaboration more meaningful is by keeping things practical. Who knew that something as simple as the Digit Place game could be so productive?

## Wednesday, January 18, 2012

### Accepting the fact that I do not know it all...

I have been following a fellow teacher (and blogger) on http://www.thenerdyteacher.com/ since the beginning of this school year. He often blogs about technology and how he uses it in his ELA classroom, and he usually posts some interesting stuff. Yesterday he posted something on Twitter that caught my attention. He said "Collab for me was accepting the fact that I didn't know it all and I learn and grow with others. #edchat" Being that my action research and this blog is all about what I am learning about collaboration, while using math problems with colleages as a focus, that tweet really got me thinking about why I chose collaboration as the focus of my second action research topic.

Teaching isn't easy. Or at least teaching has't always been easy for me. Don't get me wrong, I have seen growth in myself as a professional since I started, but I take it very personal when I am not successful. I knew that I enjoyed teaching, but going into my fifth year teaching middle school math, I was feeling the strain that comes from feeling like I have to do it all on my own. I still believe that it is ultimately up to me whether I am successful or not, but I am learning (and slowly accepting) that I cannot do it alone.

__What am I learning about collaboration?__Collaboration doesn't have to be this formal "thing" that you do, but it should be focused around what you are trying to do. If I want to be a better math teacher, I need to surround myself with those who I believe to be great math teachers. And it's not enough to mealy surround myself with them... I need to talk to them, question them, and ultimately learn

**with**them. I don't think any good teacher can do it alone... and it has taken me almost five years to realize and begin to accept that.## Thursday, January 12, 2012

### Not giving them the answer

The 7th grade math teacher and I co-coach our school's math club after school. Today, as we were doing math problems together with our scholars, as a group, she paid me one of the nicest complements I have ever received. She said "You are so good at not giving them the answer and asking them questions so that they can get to the answer on their own."

__What am I learning about collaboration?__I am actually beginning to believe that the difference between being a good math teacher and a great math teacher is more than just meeting frequently to talk about "teacher things." That stuff is necessary and important, don't get me wrong. But I am starting to really think that doing math with others is an important and necessary part of being a professional in math education.

## Sunday, January 8, 2012

### Proving the Pythagorean Theorem

Even though, the math team didn't officially meet this week, but the 7th grade teacher, Molly, and I spent some time proving the Pythagorean Theorem. She mentioned that she wanted her 7th graders to be able to come up with the Pythagorean Theorem on their own and asked if we could work on some ideas together. I of course said yes!

She started off by asking me how I had taught it in the past, and I admitted that I had never really given my students the chance to explore the Pythagorean Theorem. Looking at past lessons, I always told my students what the theorem was, and then we talked about it, but they had never discovered it on their own. I did mention how one year, I had my students work in pairs on a mini-lab that explored the areas of squares and how they relate to the Pythagorean theorem. Molly shared her idea that she wanted to use colored squares and have her students outline a right triangle and then compare the areas of the squares. I shared that during my mini-lab, I had students create a 3x3, 4x4, and 5x5 square on graph paper and then (1) find the area of each square, (2) how are the squares of the sides related to the areas of the squares, (3) find the sum of the areas of the two smaller squares. How does the sum compare to the area of the larger square, and finally (4) use grid paper to cut out three squares with sides 5, 12, and 13 units. Form a right triangle with these squares. Compare the sum of the areas of the two smaller squares with the area of the larger square.

As we talked, we got out some colored squares and graph paper, and began playing around with the Theorem. We created different sized right triangles and manipulating the squares to see show how the area of the square of the legs would always equal the area of the square of the hypotenuse. We started off approaching the Pythagorean Theorem as teachers, but very quickly found ourselves talking about the math behind the famous theorem.

After we had explored and talked for almost an hour, I suggested to Molly that we look at the Connected Math: Looking for Pythagoras (http://math.buffalostate.edu/~it/projects/Walczyk.pdf) book for some other possible ideas to teach her students, as well as the NLVM Pythagorean Puzzles (http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html)

(To be continued...)

After working with Molly this week I learned that collaborative professional development doesn't have to be something formal... it can happen between two teachers to want to explore something together. I also learned that it helps to stop approaching things "as a teacher" sometimes, and to to just play around with the math and see what happens. It was great getting the chance to work with Molly one on one this week and I am inspired to keep this action research going.

She started off by asking me how I had taught it in the past, and I admitted that I had never really given my students the chance to explore the Pythagorean Theorem. Looking at past lessons, I always told my students what the theorem was, and then we talked about it, but they had never discovered it on their own. I did mention how one year, I had my students work in pairs on a mini-lab that explored the areas of squares and how they relate to the Pythagorean theorem. Molly shared her idea that she wanted to use colored squares and have her students outline a right triangle and then compare the areas of the squares. I shared that during my mini-lab, I had students create a 3x3, 4x4, and 5x5 square on graph paper and then (1) find the area of each square, (2) how are the squares of the sides related to the areas of the squares, (3) find the sum of the areas of the two smaller squares. How does the sum compare to the area of the larger square, and finally (4) use grid paper to cut out three squares with sides 5, 12, and 13 units. Form a right triangle with these squares. Compare the sum of the areas of the two smaller squares with the area of the larger square.

As we talked, we got out some colored squares and graph paper, and began playing around with the Theorem. We created different sized right triangles and manipulating the squares to see show how the area of the square of the legs would always equal the area of the square of the hypotenuse. We started off approaching the Pythagorean Theorem as teachers, but very quickly found ourselves talking about the math behind the famous theorem.

After we had explored and talked for almost an hour, I suggested to Molly that we look at the Connected Math: Looking for Pythagoras (http://math.buffalostate.edu/~it/projects/Walczyk.pdf) book for some other possible ideas to teach her students, as well as the NLVM Pythagorean Puzzles (http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html)

(To be continued...)

__What am I learning about collaboration?__After working with Molly this week I learned that collaborative professional development doesn't have to be something formal... it can happen between two teachers to want to explore something together. I also learned that it helps to stop approaching things "as a teacher" sometimes, and to to just play around with the math and see what happens. It was great getting the chance to work with Molly one on one this week and I am inspired to keep this action research going.

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