A central tenant I hold is that humans are inherently capable in mathematics. All of them. I don’t think we got to be the most stupendous badasses on the planet without knowing a bit about the basics of if-then and creative minds. My students are capable of great mathematical thinking, but years of numbers circled at the top of their papers have taught many of them to believe they are failures. By the time I get them as teenagers I am one more person to put down one more number outlining their inadequacies.
I hate being that person. I hate seeing that ‘yeah, whatever’ look as I tried to go over a test with a student and point out the things they did know. I also hated looking through tests and trying to understand the specific pieces that were missing from student understanding–a 65% meant about as much to me as it did to them in regards to useful information.
For the sake of my students and my self I needed to change the conversations happening in the classroom surrounding grades and what students could do. Their beliefs regarding their mathematical proficiency were so low, that I couldn’t have pried their mathematical self-efficacy off the floor with one of those spatulas the custodians use to get gum of the tables. In addition, my spatula was pretty weak to begin with because I didn’t have a good grasp on what students could really do skill-wise. Sure, sure, I had homework (mmm, copying) and class/individual discussions and some projects, but students don’t seem to regard those things as evidence that they are capable. They want numbers. They want a percent. They want to be able to come in, get some help, work hard, and see their effort improve their grade. Go-go-gadget SBG.
the what i did
Back in late 2008 I sat down with my state standards for Algebra 1 and made a spreadsheet with all of them in one column. I then started breaking down the standards and identifying the skills that a students would have to know and be able to do in order to achieve that standard. I’ll note that some standards cannot be broken down this way due to the amorphous nature of words like ‘synthesize’ and ‘discuss’, so I put them to the side as the types of things that class projects/discussions were invented for.
Some standards have only one skill attached while others have a small handfull. My favorite is the one about writing quadratic equations that breaks out into about five separate skills. The skills were then broken down into beginning level and advanced level. At this point, there were three columns: skill, levels, and state standards. The last column to get added was the chapter of the textbooks my district uses that the specific skill could be found in. Final step: sort by chapter. The document gave a chapter-by-chapter summary of all the things the state curriculum was expecting from Algebra 1 students. It also demonstrated quite clearly that the first two chapters were all 8th grade skills and that a number of sections could be ignored if time was pressing.
I was pretty psyched. Here was something tangible I could use to assess the basic skills my students needed to have in order to be successful. My admin liked it as well and green-lighted me trying out the new assessment system along with a colleague of mine in a total of 3 pilot classes. I’m not going to go into the grading specifics here as my entire assessment system is based on Dan Meyer will very little changes. I figured I would try something tested before getting my own ride and adding a roof rack and spoiler.
Does this list address thinking skills and habits of mind? No. But that’s not what I was trying to do. I think trying to get students into a mathematical frame of thinking when the merest hint of using a variable sends them into a downward spiral of despair is a bit silly. I needed to un-stick their mathematical self-efficacy from the floor and get them to trust my sincerity when I tell them “you can do this” before going onto the big stuff. Though that’s not to say it was all skill assessments all the time until they were bleeding roses with golden proportions. While implementing the new assessment system my teaching stayed relatively the same.
The conversations started to change (slowly). My spatula got stronger as the kids started to understand the system. That part took the longest. At the end of the year I still had kids looking at me like I was crazy when I showed them how that skill assessment they just retook improved their grade. Need to work on that whole ‘giving instructions in a way students remember’ bit.
In the 2009-2010 school year all 11 of my schools Algebra 1 classes were shifted over to the SBG system piloted the year before. I only had an algebra 1 support class last year so I was a bit out of the picture, but the main algebra 1 crew expanded on the original skill list, hauled kids in to skill retakes, and expressed happiness at how nice it was to look at the online grade book and be able to pinpoint exactly where a student dropped off the bandwagon and plan remediation accordingly. Parent conversations were also improved during phone calls and conferences. So nice to tell a students’ parent exactly why their beloved progeny is having trouble and what the student needed to do to improve their grade and that yes, so long as your progeny can demonstrate that they are back on the bandwagon and grokking these concepts their grade will improve.
But all of that stuff is secondary to the student reactions. The “wow, I can do this stuff!” moments. The joy and victory dances when they turn in a skill assessment for me to grade and I plunk in full credit to the gradebook and they watch their grade go up. It’s in those moments of weakness I sneak in with a “that was awesome! Now that you have that down, I’d like you to take a look at this skill, which is similar to the one you just pwned.” Lips were bitten and noses would scrunch after I would say such things, but then I would see something amazing. The student would take a breath, nod, and say “lay it on me!” After a while, they would come in without my poking them about it with a level of determination that I hadn’t seen in the past. A belief in their eyes that if they worked at it, they would master the skill. A belief in their own mathematical capability.
As I was mostly off the Algebra 1 train this past year, I turned towards the classes that I was teaching (precalculus and a precalculus alternative) and implemented the skill-based grading as my quiz structure. Just going through those classes and thinking about how to break down the topics skill-by-skill was a wonderful way to start the school year. There are no state standards for these classes, so I used the college readiness standards as a springboard supplemented with requests of ‘critical items’ by the AP calc and stats teachers at my school.
SBG with upper level kids was much different that with Algebra 1 students. They caught onto the system quicker and needed far less poking about skills. Their victory dances were also a bit nerdier. And while a lot of them didn’t need any help in the mathematical self-efficacy department, a surprising number did. It felt really good to haul in C/D students and give them focused help on exactly what they need. Example: “Hi <insert student name here>. I can see that you are having some problems with the exponential chapter. Your skill quiz score for translating between exponential and logarithmic form isn’t a perfect yet, so let’s start by going over that skill. Could you show me how you would approach this problem and talk me through your thoughts?”
my last thoughts (for now)
While I don’t feel like the system is perfect RE: scoring system, I love the power it gives students over their grade. I love how many more positive interactions I have with my students. I love being able to glance at a chart in my room of my different class’ skill percents and know that I’ll need to spend a bit more time on skill X or that skill Y had a fantastic percent right away so I need to make sure to look back at how I introduced that skill and do it again.
It’s not a panacea for all your ills, but I believe that by turning grade conversations toward the positive I am able to improve my classroom atmosphere from a defeatist mentality to one of determination and persistence. Students will tell me they can’t do a skill and I respond with “yet!” After a while, they believe in the ‘yet’. They believe in themselves. Because they are stupendous badasses, and I live for putting the glint of determination back into their eyes.