I’ve been incorporating more art into math this year. This project continues this theme. I had the students draw a pre-image, and then accurately translate it, reflect it, and rotate it into images. They could do these transformations in any order; they just need to document all the transformation rules and label the vertices correctly. Here’s some student work:
It’s that time of year again…when parents and administration tour the school and my room to see interesting, creative, and, hopefully, relevant projects completed by my students. I try to pick a project that by its nature will be unique for each student. This way it will make the room more fun to explore, and the students can learn from each other’s work.
This year in my Algebra 1 class we are currently doing geometry : constructions, transformations, and congruency. This is because the students are going into an integrated common core curriculum in high school and I am preparing them to skip freshman Integrated 1. Anyway, for their open house project, I gave each student a unique design (given design) that they had to reproduce using constructions (only a compass and straightedge). I got the idea and designs from this pdf after searching the web for such projects (thanks Mr. Baroody). On a poster they needed to 1) write out the steps they used to construct it, 2) show the finished construction with the construction marks, and 3) create a clean finished copy without marks. They also were required to do this again with their own design. Here’s my one page set of Construction Project for the students. The students loved doing this project; they worked on it inside (2 days) and outside of class (a lot). Some used this online construction tool to help them figure out the construction method; this tool is super handy once you get the hang of it.
Here’s some of my students’ work (for this first one a particularly artistic student put a paintbrush in her compass to construct the eye):
Back in 2008 I attended the ETS conference on Assessment for Learning, and Ken O’Connor’s breakout on grading had a lasting effect on me.
Regarding retakes, he gave the compelling argument regarding parachute packing. Do you want to use the parachute from the packer who was doing excellent packing work but recently got sloppy with the packing, or the packer who started off badly, but has been doing perfect packing in recent weeks? I would go with the latter. What matters is that the student eventually learns how to master the topic, and not all students learn at the same rate. Here’s my retake philosophy this year:
- Only one retake allowed (from my experience if a student doesn’t study and get help before first retake, they don’t do it for subsequent ones either)
- Students must retake assessment week following original (implemented this because students were waiting too long)
- Retake score overrides original score (good or bad; this encourages studying)
- In the gradebook, in the comment field for that student’s test grade, I document that the student retook the quiz, and I state the original and retake score.
I think it was Ken O’Connor who also introduced me to the no-zero grading policy. Why are grades A-B-C-D all separated by 10% point while we give the F a 50% band? If a student falls into this F abyss, they may never get out even after they have worked hard their grades begin to get better We all know how averages can be skewed. For more information on this, read Douglas Reeves’ article, Case Against Zero. Here’s my no-zero philosophy this year:
- Apply no-zero philosophy on assessments
- If students get a 25% on a test, I put 25% on the test that I hand back to the student; however, I enter 50.25 into the gradebook. This lets me retain the actual grade info while still giving them a 50% F.
Both of these policies, retakes and no-zeros on assessments give students a second chance to succeed. They are also great discussion points when talking with parents on how their child can improve in my class. There is never a time when a student should lose hope.
Students seem to always have trouble grasping that x=2 is a vertical line, and that y=2 is a horizontal line. I understand their issue with this; x is the horizontal axis yet x=2 is a vertical line. Boy, that’s confusing! In class we talk about how it’s counter-intuitive, and we repeat the “x=2 is vertical because it cuts through the x axis at 2″. To help the students understand this more, and to get in more domain and range practice, I had them write their initials in Desmos. A good structured yet open-ended activity where students could go simple with basic block letters or get creative with more curves (parabolas), etc.
I teach a 7th grade intervention class, and have been for several years. In addition to working to fill gaps in fundamental skills, I try to increase the students’ interest in math and to build their perseverance in problem solving.
To help fill the skill gap I use:
- White Board Practice: About twice a week, the students use small white boards to work out problems I put on the the front board. I only put two problems on the board at a time; walk around to check their work; go over the two problems with their input; then I put two similar problems on the board if the majority did the first set incorrectly, or I take it up a notch or switch to a different skill. I find that this practice with immediate feedback is one of the effective tools for skill improvement. Update: An English teacher at my school regularly uses gaming strategies to invigorate practice via worksheets. Check out her post to learn how to gamify your worksheets: Worksheets=Complete and Utter Engagement.
- Playing Zonk: Zonk is a fun, group-work game that I discovered my first year teaching, eight years ago. You can use it to review any topic. Basically it requires a pocket chart where you place 25 cards; each card has a picture on one side (mine has a bulldog, the mascot from my previous school) and on the other side are points or the word “ZONK”. I put a problem on the board, and the groups work together to solve it. The groups try to get consensus on the correct answer, helping each other were needed. If group 1 gets the answer correct, they get to pull a card after we have reviewed the problem. If not, I go to team 2, and so on. The part the kids especially love is picking the card. If they get a ZONK, their turn is over and they didn’t earn any points. If they get a number card, they can keep those points, or risk them by picking another card; however, if they pull a ZONK, they lose all the points they just earned (points they earned from earlier rounds are unaffected). The students never seem to grow tired of playing this game, and some serious review and student-to-student tutoring goes on during the game.
- www.buzzmath.com and www.SumDog.com: I use buzzmath for grade-level practice of topics and sumdog for general practice of basic operations.
- Almost everyday we start the class off by playing the daily online SET puzzle. The first time the students play it, it takes about 20 minutes to solve, but after a few weeks we solve it under 3 minutes. We record all our times on the board. Our current record is 1 minute, 33 seconds. How do we play it as a class? I tell them that each column is labeled A through D, and each row is labeled 1 through 3. Students communicate their set using ordered pairs like (B, 3), (D, 2), (A, 1). I think this game has taught them that working together can be more efficient than working alone, and from a math standpoint, there’s a lot of analysis, proving, and comparing/contrasting that goes into creating each set.
- Tower of Hanoi: Another puzzle that pushes the students to improve and persevere. I eventually connect the game to math as we work out how to come up with a solid method for achieving the least number of moves, and predicting what the least number of moves is required per puzzle.
Last week I introduced my students to Desmos. After doing a short lesson to show off the power and “what-if” capabilities of desmos, I pretty much let them loose on creating equation-driven art. My main objective here was for students to get a deeper understanding of linear equations, and specifically more experience with restricting the domain and/or range of a linear equation. So I showed the students how to restrict the domain and range, and my only requirement of the art is that they include at least one instance of a restricted domain/range. Very soon the kids wanted to know how to create and manipulate parabolas, circles, sine waves, etc. The students absolutely loved this activity; I was hearing comments like “Desmos is the best app I ever”, and “oh, now I see how that works”. I gave them two class periods to work on their art, and told them they can complete it at home and save it to the google folder they have shared with me. Here’s some of the artwork I received back. This first one, the Hunger Games’ Mockingjay uses 40 equations and the student worked on it for over 3 hours.
To see Mockingjay in all its glory in Desmos: https://www.desmos.com/calculator/ihxor3kijv
To see butterfly in Desmos: https://www.desmos.com/calculator/zwmkq6gxx5
To see Birds by the Sea in Desmos: https://www.desmos.com/calculator/poq9oyptce
To see star in circles in Desmos: https://www.desmos.com/calculator/tweud3vjdw
I’ve been doing a lot of professional development lately in preparation for common core. Everything from monthly meetings at the district office to a week with Silicon Valley Math Initiative this past summer. Also I am taking a Stanford MOOC called: Constructive Classroom Conversations, where I am waking up to the fact that my students need to learn how to talk to each other, and this class is providing me tools to teach them and ways to measure success (I’ll do a post on this later).
A common thread to all these PD sessions is for students to articulate their thinking and to listen to other students’ thinking in order to expand their own. I’ve incorporated Number Talks into the start of my classes (especially on Mondays since I’m not checking homework on Mondays). My students and I like these because most feel comfortable participating because there’s no one right answer, and there’s lots of aha moments.
Number Talks is when you pose a math problem, math dilemma, or other math visual to the students, and they are challenged to think about a strategy for solving the problem mentally or to form an analysis on the problem. Next you have them share their thought-process with the class, often after they have shared it with their partner. Also you get feedback on students’ progress by having them do a thumbs-up close to their chest (way better than raising their hand since students aren’t pressured).
These are the topics/sources I’ve been using for my Number Talks:
- Home brewed prblems relevant to my students: 19(21) , √1089
- Graphing Stories
- Visual Patterns
- San Diego Unified Routine Banks
- Mental Math for Junior High
If Number Talks are new to you, I highly recommend learning about them and introducing them into your classroom. There’s lots of resources about them on the internet, and even youtube videos.