~Objective:
Lesson: I started right away in groups at the boards. We quickly reviewed the structure of slope-intercept form. I then gave the groups a line in standard form and asked them to turn it into slope-intercept form. When they were done, they were supposed use Desmos to check their equation versus the original equation. (I like to use Desmos as an "answer key" whenever I can to connect the algebra with the graph in a natural way). The first equation was 2x+4y = 8 This first one took a while. Many groups had various strategies and I roamed around and visited with them about their ideas. I chose to consolidate right after this problem because there were a few different strategies and I wanted to discuss the pros and cons of each one. There were also some mistakes that we needed to address as a class. (We found that the most efficient strategy was to move 2x and then divide everything by 4). I had the groups then do a 2-3 more problems:
I next wanted to get the students working more individually while I was around to help. I decided to add a little movement and fun with a snowball fight. (I think I got the original idea from Sarah Carter). I put a large set of equations of lines in standard form on the board and gave each student a piece of paper. They chose one equation and wrote it down. Then they crumpled the paper into a ball, I set a timer for 20 seconds, and they threw the snowballs around until the time ran out. Then they each found a snowball and worked out the problem on it so that it was in slope-intercept form. Again, I had them check their work on Desmos. I would have liked to do another snowball fight, but this brought us to the end of the class period. I used Delta Math for Check Your Understanding problems.
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I have made some big changes this year! I am finally applying all 14 of the Building Thinking Classroom principles and loving it. I did as many as I could before from my research on websites, blogs, podcasts, and interviews. But there were a few principles that I just couldn't grasp until I finally got to read the book. (If you are interested in using BTC, I highly recommend you get the book: BTC). I decided Thanksgiving was a great time to reflect and write about what changes I am making this year and how it is going. I am specifically writing about check understanding, build autonomy, and formative assessment. Most of these are based off the work I did this summer in preparation for the changes. I went through each chapter and decided what I wanted to assess for basic, intermediate and advanced (My grading is 3, 4, 5 since they will be translated into letter grades like the rest of my school). I created a table for each chapter and included it in the meaningful notes packet I make for students at the beginning of the year. You can see an example from Algebra below. 1. Check understanding. I have given homework for a grade my entire career. I have never graded it based on being correct, but instead on completion and showing of work. Doing it this way cut down on how much time I spent on grading since I didn't have to grade each problem for correctness, but I still found myself often wishing the students would go away so that I could get my work done. I needed to grade it all and get it into the gradebook. I hated that part of teaching. I felt like only part of my job was educating students, but the majority of it was correcting and recording work. This year I am no longer grading homework. I still assign problems, but I do not ask them to turn it in. I rarely give problems from the book, but I really like using Delta Math (deltamath.com) for problems. The students get immediate feedback and can see the solution if they get it wrong. I have seen my students put more value into doing their problems correct rather than just getting the problems done with this program. Because I am not correcting/grading their work, the points system doesn't matter, so the students can do as many or as few problems as they would like. Which is another bonus of DM, they can do lots of problems if they would like, where a textbook has a limited number of problems to work on. Reflection: As expected, fewer students are doing the problems than I would like. But, as we do little formative assessments each day, students find out where they are in their own understanding and I see them go back to the DM to practice. They are learning the new system and finding out that they need the practice in some places and not in others. Ultimately, if they are successful in the formative assessments, it doesn't matter to me if they do the DM. (BTW: I just realized have not worried about Photomath once this year!) I created a table for the students to reference which DM assignments align to the topics they will be assessed on (see below). I also include this in the meaningful notes booklet. I have found this table to be useful when helping a student figure out what they can do to get ready for more assessment problems to help improve their grade. 2. Build Autonomy: Managing flow! How do I get my students to help themselves instead of waiting for me to get to them? I was the teacher that would tell my students to steal a problem from another board if they finish and are waiting for me. But then I would leave a group and see two groups just sitting there! Finally, after reading the chapter, I have figured it out. Instead of giving the next problem to the waiting groups, I point at the board that already has the next problem and tell them to take it. (I was enabling them when I would give it to them). Now, my students have started helping themselves instead of waiting for me. Thank Goodness! (This is also true if a group is stuck. I will often tell them to go peek at a certain board to get an idea instead of giving them any help) Another thing I am working on this year is what I do BEFORE groups need help. I used to wait idly and just watch the groups work. Now, I walk to each group, point at a specific item on the board and ask them to tell me about it or to convince me it is right. I am finding the lesson goes much more smoothly than before, I am keeping more involved in their learning, and I am having much richer observations of each and every student. 3. Formative Assessment: I have been trying to figure out standards based grading for years. I have tried a few different things, but none of them felt quite right or worked the way I wanted. I am using the assessment and grading from BTC and I love it! Quizzes. I don't give quizzes any more. I have to admit, when Peter says that you will find you give too many quizzes already, that wasn't true for me. In the first two units this year, I found that we got to the end of the unit and I have very few data collections. I am finding my way though. I try to give one or two problems every day at the beginning of the hour and we call is an "understanding check" instead of a quiz. I also like to use "My favorite no" for these. I make sure the students put their name on them so I can record the data, but it lends itself well to having a purpose in our lesson instead of just a quick check. Quiz reflection: I learned through this process that many students see a quiz as potential punishment. If they aren't ready for the quiz then any problems they do incorrectly lose them points that they can never get back. It is taking me a long time to get them to understand that there are no points taken away for a wrong solution; there will always be more opportunities to show me they can do it. An x at the beginning followed by check marks means they learned, which is the goal. Not all of my students have grasped this yet, but we keep working on it. End of unit test. I hate writing tests. It really is the worst part of my job. Since I am changing how I assess, I have to rewrite all my tests. I am not enjoying it, but it isn't as bad as writing a test from scratch. I use my table (see above) as a guide and make two problems for each cell of the table. I am not completely sure this is what I should do, but it makes sure that a student can possibly get two check marks if they haven't gotten any yet. I do like separating the test into all the basic problems first, followed by all the intermediate problems, and finishing with all the advanced problems like Peter suggests. I find it gives students a reference to where each problem fits in the table. The second worst thing about teaching, after writing a test, is grading a test. However, this has improved with BTC grading. Now I just give it a check mark, x, or S. I don't have to debate how many points to give! Transferring their marks onto their progress tracking sheet is time consuming, but it is easy enough to do that I haven't minded it yet. Test reflection: I was worried the grading would be "inflated" (is that the right word)? At the beginning, students would finish a test and say they failed as they turned it in. But then they would end up with a 20 out of 22. They felt like they failed because they couldn't answer four of the problems in the advanced section. In the past, if they didn't answer four problems, they would have lost a lot of points. But with this, they only lost two points, getting 4 out of 5 on two of the topics. However, when I look over the final grades each time, the letter grade seems very appropriate for each student. So I don't think grades are inflated, they seem to be more appropriate than before. (Side note: this is my 19th year of teaching. Quarter 1 was my very first quarter in my career that I did not have a student fail my class. FIRST TIME EVER! Reflecting on why, I think there were just some students before that found homework to be too big of a workload and could not/would not do it all. I also think that there are so many valuable things we do with all 14 principles that they are just learning better too). Below are a couple examples of the progress tracking sheets for a unit. I put them on a google doc and update it as we go. Students and their parents have access to this sheet at any time. I still have one question about grading. If a student has x's all the way across a row, I will give them a 0 out of 5. But, what if they have a couple check marks sprinkled throughout the row, just not two in a row? Do you give them a 1 or a 2, or do you still give a 0? Improving grades after the test. This has also changed my teaching life. I used to have students stay after school to get help on their homework. Their focus was on getting the assignments done, not necessarily learning the math. I hated it! I do not have the patience for homework help. But now, when a student needs/wants to improve their grade, they stay after with me. We look at their progress tracking sheet and their test to see what they need to learn. The time we spend going over problems is in an attempt to learn, not complete problems. I usually send them on their way with problems to practice. Then we find another time for them to do "assessment" problems to add to their data. Since they only need to do a couple, they can usually get this done during a part of class, at the end of lunch, or during their resource hour. It feels so much more worthwhile now. The students are more focused and aren't coming to me with the stress of a mountain of homework and a checklist to complete. I have also found this useful for a particular student that has extreme test anxiety. We now have scheduled him to come to my room during my prep (his study hall) every Wednesday. We use the time to do some old or new problems and then I can add to his data with my observations instead of just formal assessment problems. It has been a huge help in making sure his grade reflects what he knows. Below is an example of his data after a few Wednesday's of going over a previous chapter. Final Reflection:
After writing all this and rereading it, I realize that there were more things about teaching that I hated than I thought! I really love my job, so I am a bit surprised. But it has also made me realize why I have been leaving the school building earlier than usual and with less weight on my shoulders the last couple weeks. The things that I disliked the most about teaching have changed drastically. I still don't like writing tests, but I don't hate it. Grading them is no big deal. The paperwork of homework and grading is pretty much nonexistent. The time I spend with students is actually teaching rather than assisting with a checklist. I finally feel like the majority of my day is spent educating. I was in love with BTC before because my class changed for my students. They were engaged and THINKING. I have fallen in love with it all over again this year because my class changed for me. I am more engaged, less overworked with tedious tasks, and enjoying how I assess the learning of my students. Objectives:
Lesson: I start this lesson at the boards right away. I tell the groups they will be doing the opposite from the lesson before this. I want them to tell me what the two bubbles are that would multiply to give me the quadratic. Their answer should be the two bubbles written out as factors (multiplied). The thin slicing for this is structured that I give them some "clues" but gradually take them away. The series of problems I go through are below. (Please forgive my crude notes, I haven't taken the time to make them more professional). This pretty much takes up most of the class. I consolidate with the class and often give them class time to work on check their understanding problems. I want to make sure they take the time to work on it individually right away.
Objectives:
Lesson: I like to start this lesson with a series of notice/wonders or stand and talks. BTC Note: I wonder sometimes if I am giving too much front-loading with the notice/wonders. But they work so well in general that I haven't experimented with the lesson without them. Boards: I get the students into groups and we work through the series of problems pictured below: I like to have an extra challenge ready if a group finished early or before the rest. I often use open middle problems for this reason (and they work really well on VNPS in groups). I love them for everyone, but I especially love them for the students that could use some extra challenging. Below is a good one for this lesson. Finish with a consolidation and meaningful notes. I also give some Delta Math problems for check your understanding practice.
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AuthorI teach mathematics for grades 7-12. Teaching mathematics is my passion. Archives
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