tag:blogger.com,1999:blog-10282867919246598122017-07-11T11:32:06.847-07:00Anna's Action Research 2011-12What will I learn about collaborative professional development by getting together with math colleagues and doing math problems together?Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.comBlogger23125tag:blogger.com,1999:blog-1028286791924659812.post-82928804306699264162012-06-03T16:31:00.000-07:002012-06-04T16:44:26.879-07:00Implications for Future WorkAs 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 <a href="http://www.teachingmatters.org/" target="_blank">Teaching Matters</a>. 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.Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-59837350775082147712012-05-19T16:10:00.000-07:002012-06-04T16:31:24.584-07:00ConclusionsSome 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: <a href="http://apacura.blogspot.com/2012/03/how-much-is-your-time-worth.html" target="_blank">How much is your time worth?</a> and <a href="http://apacura.blogspot.com/2012/02/tiles-in-bag.html" target="_blank">Tiles in the Bag</a>. 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. <br /><br />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? Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-31137154727352294802012-04-29T15:34:00.000-07:002012-06-04T16:09:21.225-07:00FindingsBack 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.<br /><br /> To begin working on this goal, I asked myself the question <b>"What will I learn about collaborative professional development by getting together with math colleagues and doing math problems together?"</b> 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.<br /><br />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. <br /><br />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.Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-68195936701091933802012-04-15T16:50:00.000-07:002012-04-15T16:50:15.618-07:00<span style="font-family: Verdana, sans-serif;">Since it was Spring Break this week and I didn't formally meet with my colleagues, I wanted to share this article that I got in this week's <a href="https://www.smartbrief.com/nbpts/index.jsp" target="_blank">Accomplished Teacher by SmartBrief</a> email, <a href="http://www.chicagotribune.com/features/tribu/sns-rt-us-usa-education-mathbre83a182-20120411,0,2320002.story?page=1" target="_blank">Numbers Game: America's Struggle to Make Math Fun</a>. </span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><br /><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;">This article talks about <i>"America's cultural problem with math... and how a</i><span style="background-color: white; text-align: left;"><i style="color: #292727; line-height: 21px;"> 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." </i><span style="color: #292727;"><span style="line-height: 21px;">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.</span></span></span></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><span style="background-color: white; text-align: left;"><span style="color: #292727;"><span style="line-height: 21px;"><br /></span></span></span></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><span style="background-color: white; text-align: left;"><span style="color: #292727;"><span style="line-height: 21px;">To me, the most interesting quote from the article is "</span></span></span><span style="background-color: white; color: #292727; line-height: 21px;">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. </span><span style="background-color: white; color: #292727; line-height: 21px;">Every time he hears a parent tell a child, <i>"I've done fine without math," or "You don't really need to know that," he quietly but urgently interrupts. </i></span><span style="background-color: white;"><span style="color: #292727;"><span style="line-height: 21px;"><i>"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." </i> 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.</span></span></span></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><span style="background-color: white;"><span style="color: #292727;"><span style="line-height: 21px;"><br /></span></span></span></span></div><div style="text-align: left;"><span style="color: blue; font-family: Verdana, sans-serif;"><span style="background-color: white;"><span style="line-height: 21px;">What am I learning about collaboration?</span></span></span></div><div style="text-align: left;"><span style="font-family: Verdana, sans-serif;"><span style="background-color: white;"><span style="line-height: 21px;"><span style="color: blue;">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.</span></span></span></span></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-46626709305497867592012-03-27T19:29:00.003-07:002012-03-27T19:40:51.811-07:00How much is your time worth?<span style="font-family: Verdana, sans-serif;">For our math team warm up this week we spent the first 15 minutes of our meeting working on a <a href="http://www.figurethis.org/index.html" target="_blank">Figure This!</a> problem from the NCTM. The problem asks:</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><br /><span style="font-family: Verdana, sans-serif;"><i>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?</i></span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><br /><span style="font-family: Verdana, sans-serif;">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.</span><br /><span style="font-family: Verdana, sans-serif;"><br /></span><br /><span style="color: blue; font-family: Verdana, sans-serif;"><u>What am I learning about collaboration?</u></span><br /><span style="color: blue; font-family: Verdana, sans-serif;">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.</span>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-42117121164006555312012-03-21T19:10:00.001-07:002012-03-27T19:28:55.677-07:00Filling Glasses problem<span style="font-family: 'Trebuchet MS', sans-serif;">During our math team meeting this week, I shared with the group the <a href="http://mathforum.org/pd/process/glasses.html" target="_blank">Filling Glasses problem</a>. 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.</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">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.</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><u>What am I learning about collaboration?</u></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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. </span>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-63428124147953520232012-03-15T19:49:00.000-07:002012-03-15T19:49:35.058-07:00Six Keys to Successful Collaboration By Braden Welborn<span style="font-family: 'Trebuchet MS', sans-serif;">Got this <a href="http://www.edweek.org/tm/articles/2012/03/13/tln_collaboration.html?tkn=YSCF7UcqF0qS%2F7SBjVV55vquuDKBxFSD%2Fimj&cmp=clp-sb-teacher" target="_blank">article</a> 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."</span><div><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">What I am learning about collaboration?</span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">What a great way to empower teachers with that last statement!</span></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com1tag:blogger.com,1999:blog-1028286791924659812.post-5205460887692236322012-02-24T09:05:00.001-08:002012-02-24T09:15:51.837-08:00Why Great Teachers Are Also Learners<span style="font-family: 'Trebuchet MS', sans-serif;">This article was also in this week's email newsletter, and I thought it also connected very closely with my action research.</span><br /><div><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div><div><span style="font-family: 'Trebuchet MS', sans-serif;">In her article, "<a href="http://www.theatlantic.com/sponsored/impact-of-one/archive/2012/02/why-great-teachers-are-also-learners/253376/" target="_blank">Why Great Teachers Are Also Learners</a>," Vicki Davis (2012) talks about how educators can inspire students with their own curiosity. Davis states that "As a teacher<span style="background-color: white;"><span style="line-height: 19px;">, 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: </span></span></span></div><div><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="background-color: white;"><span style="line-height: 19px;"><br /></span></span></span></div><div><ul><li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;">"Talk about the new things you're learning, and let your enthusiasm show,"</span></span></li><li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;">"Show students that you are willing to investigate," and</span></span></li><li><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;">"Let students see you proudly sharing your learning."</span></span></li></ul><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;"><u>What am I learning about collaboration:</u></span></span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;">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! </span></span></div></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;"><br /></span></span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;">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. </span></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><span style="line-height: 19px;"><br /></span></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="background-color: #fff9ee; color: #222222; line-height: 21px; text-align: left;"><span style="line-height: 24px;">Davis, V. (2012, February). Why great teachers are also learners. The <i>Atlantic.</i> Retrieved February 21, 2012 from </span></span><a href="http://www.theatlantic.com/sponsored/impact-of-one/archive/2012/02/why-great-teachers-are-also-learners/253376/">http://www.theatlantic.com/sponsored/impact-of-one/archive/2012/02/why-great-teachers-are-also-learners/253376/</a></span><br /><br /></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com3tag:blogger.com,1999:blog-1028286791924659812.post-49369014234910169942012-02-23T19:43:00.006-08:002012-02-24T09:16:11.302-08:00Becoming a Teacher Leader<span style="font-family: 'Trebuchet MS', sans-serif;">Being off from work this week for Mid-Winter Recess, there was no math team meeting to blog about. However, in my <a href="https://www.smartbrief.com/nbpts/index.jsp" target="_blank">SmartBrief</a> weekly email newsletter, that I subscribe to, I did read two articles that I thought tied in nicely with my action research. </span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><div style="text-align: left;"><span style="font-family: 'Trebuchet MS', sans-serif;">In her article "<a href="http://www.edweek.org/tm/articles/2012/02/21/tln_ratzel_teacherleader.html?tkn=QUMFu2vyRe0z60QQwryTAOM0HcxYgpsR7Poh&cmp=clp-sb-teacher" target="_blank">5 Tell-Tale Signs You're Becoming a Teacher Leader</a>," Ratzel (2012)<span style="line-height: 1.3em;"> describes five signs "that may signal that you're on the road to becoming a teacher leader." Ratzel states that "</span><span style="line-height: 24px;">If you find yourself yearning to take an idea beyond your classroom, you're probably ready to become a leader. </span><span style="line-height: 24px;">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</span><span style="line-height: 1.3em;"><span style="line-height: 24px;">."</span></span></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-align: left;"><span style="line-height: 24px;"><br /></span></span></span><br /><u style="color: blue; line-height: 24px;"><span style="font-family: 'Trebuchet MS', sans-serif;">What have I been learning about collaboration?</span></u></div><div style="text-align: left;"><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="color: blue; text-align: left;"><span style="line-height: 24px;">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.</span></span></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="color: blue; text-align: left;"><span style="line-height: 24px;"><br /></span></span></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="text-align: left;"><span style="line-height: 24px;">Ratzel, M. (2012, February). 5 tell-tale signs you're becoming a teacher leader. <i>Education Week Teacher. </i>Retrieved February 21, 2012 from </span></span><a href="http://www.edweek.org/tm/articles/2012/02/21/tln_ratzel_teacherleader.html?tkn=SRSF9cPYYaJGCZsKm5T6fgpOV0c30h32egnv&cmp=clp-edweek">http://www.edweek.org/tm/articles/2012/02/21/tln_ratzel_teacherleader.html?tkn=SRSF9cPYYaJGCZsKm5T6fgpOV0c30h32egnv&cmp=clp-edweek</a></span><br /><br /></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com3tag:blogger.com,1999:blog-1028286791924659812.post-22314077755812806302012-02-12T13:36:00.002-08:002012-02-23T14:17:18.940-08:00Learning Conference Tasks<span style="font-family: 'Trebuchet MS', sans-serif;">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 <a href="http://www.saskschools.ca/~bestpractice/celebrate/index.html" target="_blank">website</a> has some general information on Learning Celebration Conferences, and in addition, <a href="http://capersresearch.blogspot.com/" target="_blank">Sandra</a> and I will be presenting about them this summer, so stay tuned =)</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">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. </span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">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. </span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><u>What I am learning about collaboration?</u></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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). </span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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.</span>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-60196875378648243732012-02-02T16:33:00.000-08:002012-02-23T13:34:22.361-08:00Tiles in the Bag<span style="font-family: 'Trebuchet MS', sans-serif;">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.</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">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."</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">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. </span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><u>What am I learning about collaboration?</u></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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!</span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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...</span>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com3tag:blogger.com,1999:blog-1028286791924659812.post-27535537463848134622012-01-26T19:06:00.000-08:002012-02-07T19:51:51.333-08:00The Digit Place game<span style="font-family: 'Trebuchet MS', sans-serif;">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. </span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">This elementary school teacher's classroom <a href="http://susan-carpenter.blogspot.com/2011/10/digit-place-game.html" target="_blank">blog</a> 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?" </span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><u>What am I learning about collaboration?</u></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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. </span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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?</span>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-48284365403431434992012-01-18T18:57:00.000-08:002012-01-18T19:04:25.437-08:00Accepting the fact that I do not know it all...<span style="font-family: 'Trebuchet MS', sans-serif;">I have been following a fellow teacher (and blogger) on <a href="http://www.thenerdyteacher.com/">http://www.thenerdyteacher.com/</a> 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 <a href="http://twitter.com/?ref=nf&utm_campaign=thenerdyteacher&utm_content=159431959678947328&utm_medium=fb&utm_source=fb#!/thenerdyteacher">"Collab for me was accepting the fact that I didn't know it all and I learn and grow with others. #edchat"</a> 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. </span><br /><div><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div><div><span style="font-family: 'Trebuchet MS', sans-serif;">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.</span></div><div><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><b><u>What am I learning about collaboration?</u></b></span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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 <b>with</b> 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.</span></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com3tag:blogger.com,1999:blog-1028286791924659812.post-55497821178500957062012-01-12T17:04:00.000-08:002012-01-18T19:04:44.207-08:00Not giving them the answer<span style="font-family: 'Trebuchet MS', sans-serif;">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." </span><br /><div><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;"><b><u>What am I learning about collaboration?</u></b></span></div><div><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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. </span></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com3tag:blogger.com,1999:blog-1028286791924659812.post-12527472480154287052012-01-08T17:05:00.000-08:002012-01-18T19:05:43.978-08:00Proving the Pythagorean Theorem<span style="font-family: 'Trebuchet MS', sans-serif;">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!</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">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.</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">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.</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">After we had explored and talked for almost an hour, I suggested to Molly that we look at the Connected Math: Looking for Pythagoras (<a href="http://math.buffalostate.edu/~it/projects/Walczyk.pdf">http://math.buffalostate.edu/~it/projects/Walczyk.pdf</a>) book for some other possible ideas to teach her students, as well as the NLVM Pythagorean Puzzles (<a href="http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html">http://nlvm.usu.edu/en/nav/frames_asid_164_g_3_t_3.html?open=instructions&from=category_g_3_t_3.html</a>)</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">(To be continued...)</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><b><span style="font-family: 'Trebuchet MS', sans-serif;"><span style="color: blue;"><u>What am I learning about collaboration? </u> </span> </span></b><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">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. </span>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-64166583897893865452011-12-07T20:19:00.000-08:002012-01-18T19:03:23.083-08:00The Game of Poison<span style="font-family: 'Trebuchet MS', sans-serif;">Today during our Math Team meeting, I taught my colleagues how to play the game of <a href="http://letsplaymath.net/2007/07/19/math-club-nim/">Poison</a>. I had recently taught the members of the Math Club how to play and thought it would be fun...</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="font-family: 'Trebuchet MS', sans-serif;">(To be continued...)</span><br /><span style="font-family: 'Trebuchet MS', sans-serif;"><br /></span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">What am I learning about collaboration?</span><br /><span style="color: blue; font-family: 'Trebuchet MS', sans-serif;">Sometimes something as simple as a Nim game can be a great way to get students and adults to start talking about math. Who knew?</span>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com1tag:blogger.com,1999:blog-1028286791924659812.post-71818778445694776902011-11-30T21:11:00.000-08:002012-01-08T16:18:53.827-08:00Making time for MathThe math team met again this evening. Like last time, I set up an agenda on Google Docs and encouraged the other math teachers to add on to it. This time, however, I set aside the first half of the meeting to do some math together. I asked everyone to bring their laptops, so that I could introduce them to the Peg Puzzle <span style="font-family: 'Century Gothic', sans-serif; font-size: x-small;"><span style="line-height: 14px;">(</span></span> <a href="http://nlvm.usu.edu/en/nav/frames_asid_182_g_3_t_1.html?from=category_g_3_t_1.html">http://nlvm.usu.edu/en/nav/frames_asid_182_g_3_t_1.html?from=category_g_3_t_1.html</a>) When we started, I directed everyone to NLVM website and asked them to play around for a bit, and then suggested that we come back together and share what we learned....<div><br /></div><div>(To be continued...)</div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-40312551609955514482011-11-14T19:25:00.000-08:002011-11-14T16:26:13.927-08:00Setting up Meeting #2I sent out an email earlier this afternoon, asking our JBA math team when the next availble date to meet that works for everyone is. Because of PDs and Thanksgiving, I suggested Monday, November 21st or Wednesday the 30th, but opened it up to the group. Within an hour, the AP, ICT teacher, and 6th grade teacher got back to me! This was encouraging!<br /><br />It looks like we may have a Faculty meeting on Monday the 21st, so I asked the AP if we could possibly have that time to meet and I am waiting to hear back from her. If not, it looks like Wednesday the 30th will be our 2nd meeting. I have already revised the agenda on Google Docs slightly to reflect this.<br /><br /><b>What am I learning about collaboration?</b><br />The feeling that I get from my colleagues is that they do want to meet and want to collaborate, but that isn't always easy. We all take our job and responsibilities very seriously and teaching comes first. I completely agree, and hope that future meetings can tie into what we are teaching. Again, I want these meetings to be practical and as useful for my colleagues and I as possible.Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-55449302003224029512011-11-09T16:17:00.000-08:002011-11-14T16:17:56.241-08:00A Minor SetbackUnfortunately, at the last minute, the math team meeting that we were supposed to have today, didn't happen. The 6th grade teacher had a personal reason, the ICT teacher had an after school club, and the AP was called into a meeting. The 7th grade teacher and I debated whether or not to meet "officially" and thought it would be best to reschedule for a date when the whole team could meet.<br /><div><br /></div><div>I was a little disappointed, but I understand that things do come up and that it's important to be flexible. So far I haven't gotten the vibe from my colleagues that they don't want to be these meetings to happen, so I will be optimistic that this is just a minor temporary setback.</div><div><br /></div><div>In the meantime, I created the agenda so that when we do meet, our meetings would have a focus. Nobody else has added to the agenda specifically, but the 6th grade teacher did add a document to our Google Collection.</div><div><br /></div><div>The good news is that the 6th grade teacher, ICT teacher, and AP said that they were glad that they didn't miss anything, which makes me feel like they want to be a part of these meetings also. I just don't want our group to slowly happen less frequently as the school year goes by.</div><div><br /></div><div><b>What am I learning about collaboration?</b></div><div>It's not easy to get, even a well-meaning group of people, together. I am a little disappointed, but am still looking at this as only a minor set back. It has been a crazy week at JBA with grades being due, Benchmark Assessments, and the schedule changing for the new marking period. I will be sure to send out an email asking for the next best available dates for people so that we can get our math team back on focus.</div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-34059085837437848552011-11-02T19:51:00.000-07:002011-11-14T16:07:22.990-08:00Our First MeetingSo we just had our first math team meeting. Originally we planned to meet for an hour, but ended up meeting for an hour and a half after school, in my classroom. The 6th grade math teacher, assistant principal, and I (and briefly our ICT teacher) were the only ones in attendance. The 7th grade teacher was unable to make it, and at the last minute the ICT teacher was unable to either. The three us us decided to meet either way and take notes on our Google Doc so that we could share it with the others.<br /><br />Our agenda consisted of:<br /><br /><ul><li>Discussing Math Portfolios (the principal had asked the AP to talk to us about this)</li><li>Teaching strategies that should be used across all grades so they are ready for Algebra I</li><li>What are our department goals?</li><li>Where are we now? Where do we want to be?</li><li>Looking at our data?</li><li>How often do we want to meet? </li></ul><div>Together the three of us went though each of these points and discussed our responses. We had the agenda up on the Smart Board and as we collaborated, we added to the document. For each of the points, we discussed next steps. This was important to me because (1) we had an "official" working document from our meeting, and (2) our next steps were practical things that we would bring or do during our next meeting. (I can attach our "final" agenda in another post.) </div><div><br /></div><div>We decided that Wednesdays overall seemed to work best for everyone, and meeting every other week would be a good start for us. Due to upcoming PDs, we decided to meet the following Wednesday, November 9th.</div><div><br /></div><div><b>What am I learning about collaboration?</b></div><div>It feel really good to actually get the chance to meet. I think our agenda also helped to keep us focused, so that we didn't get off topic. We had specific goals to accomplish and we were able to speak about all of them. For our next meeting, in addition to addressing our next steps, I want to actually do some math with my colleagues. Using the "Teaching Math in the Middle School" article about Teaching Circles, I have decided to use the Frog and Toad problem. I even found a website that we can all go do.</div><div><br /></div><div>I am a little worried that we might be trying to do too much during our meetings. Personally I would rather do less deeply, than try to cover too much, however I want everyone to feel like they are contributing to these meetings, and it's not just me. I think the Google Doc agendas that everyone can add too will help with that.</div><div><br /></div><div>Looking forward to our meeting next week!</div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com2tag:blogger.com,1999:blog-1028286791924659812.post-69713636020301588092011-10-30T18:49:00.000-07:002011-11-14T15:50:20.048-08:00Preparing for Our First Math Team MeetingI am very happy to announce that the JBA Math Team will be having their first meeting on Wednesday, November 2nd. Unfortunately it doesn't look like everyone one will be able to attend, but my fellow colleagues have shown a real interest in meeting an a regular basis to make the Math Department as coherent as possible.<br /><br />So how did this all happen?<br /><br />Well, around the middle of October I sent out an email to the 6th and 7th grade math teachers, our ICT teacher, both assistant principals, and the principal, asking if they would be willing to meet as a department. The overall response I got (not from everyone) was positive, so I followed up asking everyone what days specifically worked best. We realized that there was no real time during the day that we were all free to meet, so we decided that it would have to be after school. Since we would be meeting after school, I emailed the principal and asked if we could get paid for any collaboration that we did, and she agreed.<br /><br />Deciding on a date that worked for everyone wasn't easy, even with a department as small as ours, between after school clubs, grad school, and other commitments. Eventually we decided on Wednesday, November 2nd, and everyone except the 7th grade math teacher would be able to attend. Since it was our first meeting, we felt that we could fill her in.<br /><br />In order to prepare for our meeting this week, I set up a Google Collection as a place to keep our team meeting agendas and any other resources we might out together. I chose Google Collection because this year the Faculty and scholars all have their own Google email addresses, and I felt that this would be a good place to centralize our materials. In our collection, I set up a Google Document with a tentative agenda, and encouraged, via email, the math team to add to it. I emphasized that I wanted our meetings to be as useful for us as possible. So far, one teacher as added to it.<br /><br /><b>What am I learning about collaboration?</b><br />I am excited to be setting up our math team meetings. I feel like I am being productive, and it feels good to have the support of my colleagues. As of right now, I don't plan on doing any math in our first meeting, but I do plan to do some math with my colleagues in future meetings. I am happy to see this finally happening! My assistant principal even commented that she is looking forward to seeing someone else besides her run the meeting, and that she happy she can focus on math once again (she was teaching Social Studies in the beginning of the year briefly).Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com1tag:blogger.com,1999:blog-1028286791924659812.post-62655525371950480372011-10-16T18:13:00.000-07:002011-10-19T15:30:36.567-07:00Literature Review<div class="MsoNormal" style="line-height: 200%; margin-left: .5in; tab-stops: 123.0pt; text-indent: -.5in;"><br /><div class="MsoListParagraph" style="line-height: 200%; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Fernandes, A, Keohler, J, & Reiter, H. (2011). Mathematics teachers circle around problem solving. <i>Mathematics Teaching in the Middle School. 17(2)</i>, 109-115.<b><u><o:p></o:p></u></b></span></div></div><div class="MsoNormal" style="line-height: 200%;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">The National Council of Teachers of Mathematics Standards “recommend that students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort and should be encouraged to reflect on their thinking” (NCTM, 2000, p. 52) My action research last year focused on my own instruction of problem solving. Some of the challenges that I encountered came from my limited experience teaching problem solving in a constructivist way. Fernandez, Keohler, & Reiter (2011) state that “making problem solving a central part of teaching may be challenging to teachers who have limited experiences in learning and teaching mathematics in this way” (p. 109). From my experiences the last two summers at Bank Street, I believe that by collaborating with other math teachers at my school, I can bring richer problem solving experiences into my own classroom. <o:p></o:p></span></div><div class="MsoNormal" style="line-height: 200%; text-indent: .5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">In their article, they examine the key features of Math Teachers’ Circles, which “were developed with the aim of establishing a “culture of problem solving” among middle school mathematics teachers” (p. 109). The authors use a vignette of a Math Teachers’ Circle as they attempt to work on the Frogs and Toad problem, to describe how teachers coming together to do math can be an enriching and inspiring experience. “By making problem solving the central focus of the Circles, the teachers are provided with opportunities to engage in nonroutine problems and get firsthand experience of the challenge and thrill of finding a solution (Fernandez, Keohler, & Reiter, 2011, p 114). I hope to use their article as a framework for my own collaboration with math teachers at JBA. <o:p></o:p></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: .5in; tab-stops: 123.0pt; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: .5in; tab-stops: 123.0pt; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Hiebert, J., et al. (1997). <i>Making sense: Teaching and learning mathematics with understanding.</i> New Hampshire: Heinmann<i>.<o:p></o:p></i></span></div><div class="MsoNormal" style="line-height: 200%;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">In this book, Hiebert emphasizes the importance of teaching and learning mathematics with understanding. He uses one definition of understanding that “says that we understand something if we see how it is related or connected to other things we know” (Brownell 1935; Heibert and Carpenter 1992). Heibert (1997) states that “To help think about how people make connections in mathematics and how they make connections that are useful, it is helpful to consider two processes that play an important role in the making of connections: reflection and communication” (p. 5). I believe that getting together with math colleagues and doing math problems together will give teachers an opportunity to reflect and communicate on the math. <o:p></o:p></span></div><div class="MsoNormal" style="line-height: 200%;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Little, J. W. (1993).<i> Teachers’ professional development in a climate of education reform, Educational Evaluation and Policy Analysis. </i> 15, 129 – 151.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 200%;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">“Collaboration is increasingly identified as a key aspect in teachers’ professional growth. Education reformers have recommended placing more attention on collegial relations of teachers for the purpose of professional growth” (Little, 1992, as cited in Syn-Jong, 2006, p. 178). This article describes how teacher collaboration is an essential part of their professional development practice and school reform. What I hope to learn from this experience of getting together with math colleagues and doing math problems together, I am curious about what I will learn about collaborative professional development. <o:p></o:p></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">National Council of Teachers of Mathematics (NCTM). 2000. <i>Principles and Standards for School Mathematics</i>. Reston, VA: NCTM<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 200%;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">According to the Professional Standards for Teaching Mathematics (National Council of Teachers of Mathematics, 1991), an essential factor in teachers’ professional development is the degree to which they “reflect on learning and teaching individually and with colleagues” (p. 168). Unfortunately JBA does not have weekly or even monthly departmental math team meeting, therefore there was very limited collaboration between the teachers. According to Professional Standards for Teaching Mathematics (NCTM 1991, p. 128), teachers need opportunities to experience mathematics instruction that will “enable all learners to experience mathematics as a dynamic engagement in solving problems. These experiences should be designed deliberately to help teachers rethink their conceptions of what mathematics is, what a mathematics class is like, and how mathematics is learned.” I believe that in order to be a stronger department, we need a space for the math teachers to come together to learn more about big math ideas and reflect on how their own mathematical understandings influence their practice. I am interested in how doing math problems together will influence my own thoughts of collaboration and professional development. <b><o:p></o:p></b></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div><div class="MsoNormal" style="line-height: 200%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Smith, M. S. (2001). <i>Practice-based professional development for teachers of mathematics</i>. Reston, VA: NCTM<o:p></o:p></span></div><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 115%;">Smith (2001) states that “Professional development must provide teachers with the opportunity to improve their understanding of mathematics content and to reflect critically on their learning experiences” (p. 42). Math teachers need the opportunity to not just reflect on what they want their students to know, but what they themselves know about math. “Teachers must begin by making sense of mathematics. In considering how students solved the problems, teachers must engage with the mathematical ideas that are at the heart of the tasks (Smith 2001, p. 43) I believe that by doing math problems together with my colleagues, I will get a better understanding of the mathematical ideas that are at the heart of the tasks that I give my students and will result in </span><span class="Apple-style-span" style="line-height: 32px;">a deeper mathematical understanding.</span></span><br /><div class="MsoNormal" style="line-height: 200%;"><span style="font-family: Georgia, serif;"><b><o:p></o:p></b></span></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com1tag:blogger.com,1999:blog-1028286791924659812.post-16773937386719598282011-10-10T14:02:00.000-07:002011-10-10T14:02:31.015-07:00Research Document 2011<div class="MsoListParagraphCxSpFirst" style="line-height: 150%; margin-left: .25in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b>1.<span style="font: normal normal normal 7pt/normal 'Times New Roman';"> </span></b><!--[endif]--><b><span> </span>The Question<o:p></o:p></b></span></div><div class="MsoListParagraphCxSpMiddle" style="line-height: 150%; margin-left: 0in; mso-add-space: auto;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">What will I learn about collaborative professional development by getting together with math colleagues and doing math problems together? <o:p></o:p></span></div><div class="MsoListParagraphCxSpMiddle" style="line-height: 150%;"><br /></div><div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-left: .25in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span>2.<span style="font: 7.0pt "Times New Roman";"> </span></span></b><!--[endif]--><b>The Statement of Purpose<o:p></o:p></b></span></div><div class="MsoNormal" style="line-height: 150%; text-indent: .5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">In my previous school, part of my teaching schedule included a weekly meeting with the whole math department.<span> </span>Either the math coach or the assistant principal led the meetings, and during my first years of teaching, these meeting were especially valuable because they gave me the chance to collaborate with and learn from my colleagues in a formal setting.<span> </span>This past year was my first year at my current school, Jonas Bronck Academy, and we didn’t have weekly math team meetings.<span> </span>As a result, one of my biggest challenges this year was finding time to collaborate with the other math teachers at JBA.<span> </span>“Collaboration is increasingly identified as a key aspect in teachers’ professional growth.<span> </span>Education reformers have recommended placing more attention on collegial relations of teachers for the purpose of professional growth” (Little, 1992, as cited in Syn-Jong, 2006, p. 178).<span> </span><span style="color: black;">Through this research, I want to create a math learning group at JBA that will engage in constructivist mathematical problem solving.<span> </span>I hope that by getting together with other math colleagues at my </span>school and doing math together, I<span style="color: black;"> can get a deeper understanding of what it means to participate in professional development and we can improve our math department at JBA.</span><o:p></o:p></span></div><div class="MsoListParagraphCxSpFirst" style="line-height: 150%; margin-left: .25in; mso-add-space: auto;"><br /></div><div class="MsoListParagraphCxSpLast" style="line-height: 150%; margin-left: .25in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span>3.<span style="font: 7.0pt "Times New Roman";"> </span></span></b><!--[endif]--><b>Methodology<o:p></o:p></b></span></div><div class="MsoNormal" style="line-height: 150%;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">I will take notes during our meetings to keep track of our discussions.<span> </span>I will also keep a reflective ongoing blog on my own observations on what I am learning about collaborative professional development with my math colleagues.<span> </span>I will also ask for feedback from my colleagues participating in the group, on their thoughts on collaboration before, during, and after participating in our learning group.<span> </span>In the analysis, I will look for concrete examples of any shifts in my thoughts on collaborative professional development.<b><o:p></o:p></b></span></div><div class="MsoListParagraph" style="line-height: 150%; margin-left: .25in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span>4.<span style="font: 7.0pt "Times New Roman";"> </span></span></b><!--[endif]--><b>Resources<o:p></o:p></b></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Boalar, J., & Humphreys. (2005).<span> </span><i>Connecting mathematical ideas: Middle school video cases to support teaching and learning.</i><span> </span>Portsmouth, NH: Heinemann.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Fernandes, A, Keohler, J, & Reiter, H. (2011). Mathematics teachers circle around problem solving.<span> </span><i>Mathematics Teaching in the Middle School. 17(2)</i>, 109-115.<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Hiebert, J., et al. (1997). <i>Making sense: Teaching and learning mathematics with understanding.</i><span> </span>New Hampshire: Heinmann<i>.<o:p></o:p></i></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Little, J. W. (1993).<i> Teachers’ professional development in a climate of education reform,<o:p></o:p></i></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: .5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><i>Educational Evaluation and Policy Analysis. </i><span> </span>15, 129 – 151.<i><o:p></o:p></i></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">National Council of Teachers of Mathematics (NCTM). 2000.<span> </span><i>Principles and Standards for School Mathematics</i>.<span> </span>Reston, VA: NCTM<o:p></o:p></span></div><div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.5in;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">Smith, M. S. (2001). <i>Practice-based professional development for teachers of mathematics</i>.<span> </span>Reston, VA: NCTM<o:p></o:p></span></div><div class="MsoListParagraph" style="line-height: 150%; margin-left: .25in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]--><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;"><b><span>5.<span style="font: 7.0pt "Times New Roman";"> </span></span></b><!--[endif]--><b>Sharing my Research<o:p></o:p></b></span></div><div class="MsoNormal" style="line-height: 150%; tab-stops: 154.5pt;"><span class="Apple-style-span" style="font-family: Arial, Helvetica, sans-serif;">I intend to share my research by documenting my observations on a Google Blog. I will post my thoughts and what I am learning about collaborative professional development after each math learning group meeting. I will also comment on if and how participating in this group is influencing my practice and my growth as a professional and leader. By sharing my research on a blog on the internet, I hope to also share collaborate with other teachers outside JBA.</span><span class="Apple-style-span" style="font-family: Georgia, serif;"><o:p></o:p></span></div>Annahttp://www.blogger.com/profile/13166477975985486716noreply@blogger.com1