tag:blogger.com,1999:blog-2177245624751813162018-03-06T17:46:39.892-05:00Points of ReflectionExploring changes in teaching and learning mathematics.Taranoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-217724562475181316.post-21250340718969192092012-10-02T21:16:00.000-04:002012-10-02T21:16:53.604-04:00Blogging is HardAs I look back at the first five weeks of the year this far, I am pleased with many things that are happening in my classes, frustrated by others, and disappointed in the number of posts I have made to my blog! Blogging is hard. The importance of reflection in the teaching profession is underrated, perhaps because it is so challenging to fit in to the daily schedule. Despite my lack of blog posts, I am fortunate to work in a school and department that is highly collaborative. While writing and reading blogs is a fantastic form of professional development, I am fortunate to work in a department that collaborates and reflects on our practice regularly.<br /><br />This year I teach Algebra I, Strategic Math, and AP Calculus. Since there are more sections of Algebra I than the other classes, this is the largest team I am on. There are three math teachers and one special educator teaching Algebra I this year (the special educator in a co-taught class). We are fortunate enough to have common planning time every other day, that we use diligently. During this time, we plan lessons, discuss student work, reflect on lessons that went well and brainstorm ways to improve lessons in the future. We have a lot of autonomy over our curriculum, so although it must be aligned to current standards and other math courses in the progression, we are able to speed up or slow down as our students need us to. <br /><br />One of the things we are finding challenging this year is the balance between teaching for depth and moving a a pace that will allow us to teach all of the concepts in our curriculum. Our first unit is on Expressions, Equations, and Inequalities, a unit that we think will mostly be taught in the middle school once our district is fully aligned to the Common Core Mathematics Standards. Throughout this unit, we are trying to place an emphasis on problem solving. We use many word problems from the Philips Exeter Academy texts, as well as those from the <a href="http://map.mathshell.org/materials/index.php">Mathematics Assessment Project</a> and<a href="http://illustrativemathematics.org/"> Illustrative Mathematics Project</a>. This is a rewarding as well as frustrating process because it seems that many of our students have not been asked to think about math as much as to memorize rules and procedures. Because of this, we are finding not only that our students struggle with the content, but also about applying and thinking about that content beyond the most basic rules. As a result, my CLG (our school's version of PLCs) is going to focus on problem solving. I look forward to doing more research on this topic so I can try new ways of teaching problem solving in my classes. Taranoreply@blogger.com0tag:blogger.com,1999:blog-217724562475181316.post-55822433948822410342012-09-06T21:54:00.001-04:002012-09-06T21:54:33.835-04:00Classroom OrganizationA lot of people at the First Six Weeks conference were interested in how we organize our classrooms. Good classroom organization is one of those things that I think can make a class run more smoothly, seemingly without trying. Some of the systems I like to put in place are shown here. Getting students used to these systems during the first six weeks can make them a seamless part of your class for the remainder of the year. Hopefully my early establishment of these systems will help thing go more smoothly for my sub and the students will still be using them when I get back from my maternity leave!<br /><br />Extra Handouts & Student Mailboxes:<br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-iB_vEYRkubA/UElMw6uTJpI/AAAAAAAAD2w/OcSyL8aXiLc/s1600/Classroom+Organization+005.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="http://2.bp.blogspot.com/-iB_vEYRkubA/UElMw6uTJpI/AAAAAAAAD2w/OcSyL8aXiLc/s200/Classroom+Organization+005.jpg" width="200" /></a><a href="http://1.bp.blogspot.com/-9i2aZJ0S1P0/UElM09-tf3I/AAAAAAAAD24/rmFeJY80l-g/s1600/Classroom+Organization+004.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="http://1.bp.blogspot.com/-9i2aZJ0S1P0/UElM09-tf3I/AAAAAAAAD24/rmFeJY80l-g/s200/Classroom+Organization+004.jpg" width="200" /></a> </div><div class="separator" style="clear: both; text-align: left;">Instead of passing back papers to students, each of my students has a mailbox in a hanging file. All of their papers get filed by my student aide, who makes copies, files, laminates, updates concept test charts, and does various other projects for me. Our school gives student aides half an elective credit for doing this job for teachers. Teachers get their nuts and bolts done for them, students learn valuable on-the-job skills, its a win-win. In addition, these crates also serve as a place for students to find extra copies of assignments. I do my best to put handouts in their mailbox when they're absent, but students can always go here when they miss or lose something. For the more electronically inclined, I keep files in a virtual filing cabinet on my <a href="https://sites.google.com/a/csdvt.org/sharkeymath/Home/algebra-i-2012-2013/unit-1-handouts">website</a>. (There are many other resources on my website as well, feel free to explore.)</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Popsicle Sticks:</div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-TUwRljpizb0/UElNH0HMaOI/AAAAAAAAD3c/Gkk03tc01eE/s1600/Classroom+Organization+006.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="http://4.bp.blogspot.com/-TUwRljpizb0/UElNH0HMaOI/AAAAAAAAD3c/Gkk03tc01eE/s200/Classroom+Organization+006.jpg" width="200" /></a><a href="http://3.bp.blogspot.com/-h9CdR5JxDmo/UElNNHCKuMI/AAAAAAAAD3k/kQe6TG73DF8/s1600/Classroom+Organization+007.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="150" src="http://3.bp.blogspot.com/-h9CdR5JxDmo/UElNNHCKuMI/AAAAAAAAD3k/kQe6TG73DF8/s200/Classroom+Organization+007.jpg" width="200" /></a></div><br /><div class="separator" style="clear: both; text-align: left;">I LOVE using popsicle sticks! Every student has a stick with his/her name on it in their class' jar. During class, I use these to randomly call on students. This ensures that all students know they are "on call" at all times and it makes me call on all students, not just the ones with their hands raised or those not paying attention. There are certainly times when volunteers or specific students should be called upon, but in general, the use of the popsicle sticks allows me to quickly call on many students to ensure everyone is part of the class discussion. When making new seating charts they also come in handy for showing students their new seats. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Calculator Sign-Out:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-j4JbjaT_MHI/UElM_toyIXI/AAAAAAAAD3I/0MxlPF3ZnxY/s1600/Classroom+Organization+002.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="http://1.bp.blogspot.com/-j4JbjaT_MHI/UElM_toyIXI/AAAAAAAAD3I/0MxlPF3ZnxY/s200/Classroom+Organization+002.jpg" width="150" /></a></div><div class="separator" style="clear: both; text-align: left;">Maybe calculator sign-outs seem trivial to you, but as the keeper of my department funds, I see how much we spend replacing "lost" calculators each year! These things grow legs and walk right out of your room if you're not careful! This is a new system for me this year. After 6 days of school, so far so good. I have large white-out numbers on each calculator that correspond the laminated numbers on the board. The permanent numbers and colored electrical tape make writing and erasing student names easy without getting rid of the sign-out set-up. </div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Homework, Agenda, and WALT:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-G_1UZ17tVIg/UElNDuCXF9I/AAAAAAAAD3Q/WpWtLQt3S84/s1600/Classroom+Organization+003.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="http://1.bp.blogspot.com/-G_1UZ17tVIg/UElNDuCXF9I/AAAAAAAAD3Q/WpWtLQt3S84/s320/Classroom+Organization+003.jpg" width="240" /></a></div><div class="separator" style="clear: both; text-align: left;">If you haven't discovered colored electrical tape yet, I truly recommend it! I use it to create the HW sections on my board. Although this information is also given to students on note packets, verbally, and online, this is a clear visual at the front of the room that allows students to easily see their assignment for the night. The HW Questions box is a way for students to anonymously let me know which HW problems they struggled with from the night before. I try to keep mysteries to a minimum in my class, so every day I advertise our agenda as well as the WALT (We Are Learning Today). If a student feels lost during class they can be reminded what we've done, what we're going to do, and what the main learning for the day is just by looking up at the board.</div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Student Supplies:</div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-ks_--3eytcU/UElM7vt-bzI/AAAAAAAAD3A/BEeB-p0YhvU/s1600/Classroom+Organization+001.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="150" src="http://4.bp.blogspot.com/-ks_--3eytcU/UElM7vt-bzI/AAAAAAAAD3A/BEeB-p0YhvU/s200/Classroom+Organization+001.jpg" width="200" /></a></div><div class="separator" style="clear: both; text-align: left;">Although I still keep my pencils under lock and key (but lend them out whenever a student needs one), I set up a student work station this year so students can easily find pencil sharpeners, lined, graph, and plain paper, as well as the three hole-punch in one easy to spot location. </div><br /><div class="separator" style="clear: both; text-align: center;"></div><br /> I think these strategies keep transitions and procedures in my classroom running smoothly so I can focus my time and energy on instruction and student learning instead of papers and calculators. Maybe there's something here you haven't seen before, maybe not. Regardless, this will remind me what I need to set up next week to ensure a smooth first six weeks! <br /><div class="separator" style="clear: both; text-align: center;"></div><br /><div class="separator" style="clear: both; text-align: center;"></div><br />Taranoreply@blogger.com0tag:blogger.com,1999:blog-217724562475181316.post-80935248574923298742012-08-30T21:11:00.000-04:002012-08-30T21:11:08.876-04:00The First DaysWe just completed our second day of school today, which means I have now had each of my classes once (we're on an A/B day rotation). I am happy to say that the <a href="http://changeinconcavity.blogspot.com/2012/08/welcome-to-blogging.html">Algebra I Questionnaire and Gatorade Problem</a> were both successes and served the purposes I had hoped. In both of my Algebra I classes, students were excited to share their answers on the Questionnaire and we definitely began to establish a strong classroom community as we laughed at responses and saw how different people interpreted the various questions. <br /><br />The two questions I found most productive to share were #1, What is the largest number you can write in the space below, and #7, In as many steps as possible explain how to make a bowl of cereal. Question one really allowed students to see how they could interpret questions differently from one another. Students had numbers followed by lots of zeros, as many 9s as could fit in the box, physically large numbers that filled the space, and the infinity symbol. Question seven allowed students to see the importance of detail when sharing their work with one another. We also had great conversations about being respectful of classmates' work, organizing and writing work clearly, and the fact that we can learn from seeing others' and recognizing our own mistakes. <br /><br />Doing the Gatorade Problem with the aid of a document camera this year definitely beat not having one like last year. After sharing their "safe" answers from the Questionnaire, many students wanted to volunteer their work for the Gatorade Problem. It was great to share student work in this fashion; students shared correct answers, incorrect answers, answers in price per ounce, ounce per price, comparing the same number of ounces, and different numbers of big bottles and 6-packs. I didn't get to finish part two in my second class, but I think by the end of class all students had a basic grasp (which is hopefully a review), of finding a rate. In addition to the math, students recognized the importance of labeling units and organizing their work in a way that their classmates can follow.<br /><br /><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/--n9JgT3VfKw/UEANbDFCFII/AAAAAAAAD2U/udIH3-PDaJE/s1600/elmo" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="179" src="http://4.bp.blogspot.com/--n9JgT3VfKw/UEANbDFCFII/AAAAAAAAD2U/udIH3-PDaJE/s200/elmo" width="200" /></a></div><a href="http://2.bp.blogspot.com/-5CeESYsX6h4/UEANeCVhFgI/AAAAAAAAD2c/e8kFu_SJMo0/s1600/doccam" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="http://2.bp.blogspot.com/-5CeESYsX6h4/UEANeCVhFgI/AAAAAAAAD2c/e8kFu_SJMo0/s200/doccam" width="170" /></a><br /><br /><br />Already, I feel as though I have established a better community of learners who are willing to share and discuss their work than I have in the past. I look forward to many more discussions and analysis of student work by students in my classes this year. Taranoreply@blogger.com0tag:blogger.com,1999:blog-217724562475181316.post-39871872493389089232012-08-21T22:07:00.001-04:002012-08-21T22:07:36.330-04:00Welcome to BloggingTwo weeks ago, I was fortunate enough to be part of a great team that presented a workshop called "The First Six Weeks" through the <a href="http://www.vthec.org/">VT Higher Education Collaboration</a>. The workshop focused on how teachers can use what we know about the brain, mind, and learning to re-design the first six weeks of their school year. As the high school math teacher on the team, I presented a ninety-minute segment on how to incorporate brain-based strategies to establish a strong classroom community from day one.<br /><br />After completing the workshop, the director of the TASS program (part of VTHEC) recommended I keep a journal for the first six weeks of school to share with workshop participants. Being an avid "lurker" on the Math Blogosphere, I decided to <a href="http://mathtwitterblogosphere.weebly.com/">give blogging a shot myself</a>. First and foremost, this will be a space in which I can reflect on my teaching and my students learning. Perhaps it can also be a resource for those who attended "The First Six Weeks", provide insight for next year's presentation, and who knows, maybe I'll get on the Math Blogosphere radar at some point and other math teachers can extend my quest for exploring changes in teaching and learning mathematics. <br /><br />Here's my plan for day one in Algebra I, as outlined at the workshop: <br /><br />The very first thing I will do in my Algebra class on day one is an Algebra I Questionnaire based on CalcDave's <a href="http://longtailsofinterest.blogspot.com/2010/08/calculus-questionnaire.html">Calculus Questionnaire</a>.<br /><br /><embed allowfullscreen="true" allowscriptaccess="always" height="400" src="https://www.box.com/embed/o8gl0ldm14ustd8.swf" type="application/x-shockwave-flash" width="466" wmode="opaque"></embed><br /><br />After having the students complete the questionnaire on their own, I will have students display their answers using a document camera. We will discuss similarities and differences between their responses and talk about how students interpreted the questions differently. Through the survey and the sharing of work, we will all begin to get to know each other, I will begin to see some of students' previous math knowledge, and I will get a sense of their mindsets about themselves as mathematicians.<br /><br />Next, we will dive in to a <a href="http://blog.mrmeyer.com/">Dan Meyer</a> problem on rates. Through this problem, students will get a review on how to work with rates in a way that is accessible to all. As a class, we will generate a question about the image, students will make predictions about the outcome, and then show work to prove their predictions correct or incorrect.<br /><br /><embed allowfullscreen="true" allowscriptaccess="always" height="400" src="https://www.box.com/embed/rjfbs0z8l50gham.swf" type="application/x-shockwave-flash" width="466" wmode="opaque"></embed><br /><br />My overall goal on the first day of school is to begin to establish a community of mathematicians. I rarely lecture for more than twenty minutes, so why should I spend our first class together talking at them about rules and regulations?<br /><br />I have two fifth mod Algebra I classes this year (that's ninth graders at the end of every day), which should be quite the challenge despite my previous eight years of practice. Hopefully day one goes as well in reality as it's going in my head right now. Stay tuned for reflections on the actual first day of Algebra I.<br /><br />Taranoreply@blogger.com0