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.
- 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.
Student solving SET by himself, learning it takes a lot longer compared to when we solve it as a class.
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:
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.
This was a hoot! A couple of weeks my algebra students and I were going over graphing relationships. I had a story about Bob driving a car to demonstrate a speed .vs. time continuous graph. Later we used the example of a squirrel gathering acorns to demonstrate a discrete graph. The students started mashing the stories together to create a story and graph of Bob chasing the squirrel….it didn’t end well.
Anyway, scary graphing stories were born. So today for Halloween, I created this Scary Graphing Stories worksheet. After the students created the stories, we shared out. Here’s a small sampling of student work:
What makes my classroom uniquely mine? Well, my students would probably say my occasional rapping and our many choral response ditties.
But when I think about what I do that I am most proud of, I think about the questions I pose to them and how I listen to their ideas… (btw, these are all a work in progress):
– Really listening to student ideas and learning from them! I try to follow their train of thought, and I try to be open to allowing them to adjust my thinking. This reminds me of something interesting that happened a couple of weeks ago. I gave the students a MARS performance task where they had to create an equation for a situation. The graph of the situation was a horizontal line (constant > 0) that at a given point increased linearly. The rubric expected the students to create an equation for the linearly increasing piece only. So when one of my students said he had created an equation for the entire graph, I listened although I was, inside, skeptical, that it would work. As a class we tested his equation, and amazingly it works. The equation included an expression in absolute value, and it was really brilliant. I am so glad I listened.
– Asking open-ended questions for the students to think about. When they respond to a question, I try to ask clarifying follow-up questions. It’s exhausting sometimes, but worth it.
– Lately I’ve been trying to get the class to answer each others questions more. I’m trying to follow the advice: A teacher should never answer a student question that another student in the class can answer.
– Each week, as part of their homework for the week, my students write about a reflection topic that I give them. These are topics where they either synthesize information we’ve gone over recently or think more critically or creatively about a topic. Some examples are:
- What’s the difference between 0/x and x/0? Is there a way to prove why they evaluate to differently?
- Create a math story for the equation 3(x+2) + 5 = 23 . What is x in your story? Solve equation. Does the solution make sense for your story?
- Summarize the conditions for when you would get a compound inequality, a single inequality, no solution , or all real numbers as the solution for an absolute value inequalities.
I love these. I think it gives students a chance to use the math vocabulary in their own words, to organize their thoughts, and to respond creatively in order to make more sense of a topic. A little time consuming to grade, but many of these response put a smile on my face. Math teachers don’t get to see original written work like this enough.