Standards-Based Grading

There’s lots of talk out there, and especially in New England, about standards-based education. Whatever you think about standards-based, or proficiency-based, or competency-based education (they are all the same to me – just using some different words), the bottom line is that we teachers are now supposed to be able to certify that, regardless of any other factors beyond our control, our students are able to _________. Fill in the blank with your skill or habit of choice. This is tricky business. The tricky part is

  • not to distill learning into a checklist of discrete items that have no connection to each other.
  • to maintain a cohesive, robust curriculum with a clear scope and sequence.
  • to develop cross-curricular, integrated courses that give students rich opportunities to build those skills.
  • to build an assessment system that students, teachers, and parents have a common understanding of.

My school has put a lot of energy into creating a standards-based assessment (and reporting) system. Since we are still a new school, there is nothing to change except our own perceptions. We started out using the old 1-2-3-4 system, but ran into trouble with different interpretations of what those numbers represented and how students were able to achieve, or not. Some teachers maintained that standards in a course were global and that there was little chance for a 9th grader to demonstrate at a level higher than a 2. Other teachers defined course standards as local, so that students could earn a 3 or even a 4 on the standards within that class. Clearly, this was a problem.

The other problem is that any time grades are represented using numbers, people want to operate with them, or break them down further (using 2.3, for example). But those numbers represent discrete categories of performance or understanding. A 2.3 doesn’t make any sense if it isn’t defined. So we had to create a brand new system.

Each reporting standard – those big things like Algebra & Functions – has indicators that are connected to each level on the big scale toward graduation benchmarks. These are defined in a rubric. For any given course, we identify what the “target” knowledge & skills are, what level of the rubric we are targeting. For example, in the Modeling in Math class, the target level is Entering.

During a course, we report if a student is “below target,” “on target,” or “above target” for an assessment on particular indicator of a reporting standard. This way a student can be “on target” – meaning that the student is making solid progress and is doing what is expected in the course – but still not be at the graduation benchmark for that standard. After all, Modeling in Math is the first course that our 9th graders take. It’s unlikely that they will meet the graduation benchmark after just this one twelve-week class.

Report cards and transcripts report the big picture status toward graduation. So that 9th grader who was “on target” during the class has made progress toward graduation, but still has work to do to meet that benchmark. And that work could happen in a series of courses or through some combination of courses and portfolio, giving the student control over her education.

 

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#LessonClose versions 1.1 & 1.2

WordPress tells me that I created this draft 3 months ago. I had every intention of updating along the journey of my Lesson Close adventure. Alas, that didn’t happen. Here’s what did happen …

I found it very difficult to decide, in the moment, which survey to send to students. So, I edited the survey to allow the students to choose what they wanted to tell me about the class – what they learned, how they learned it. I used the same survey structure as before, but this time students made a choice. I honestly thought that given a choice of what to reflect on, students would engage more. Wrong.

I asked them what happened: Too many choices, completing it electronically was too much of a hassle, there wasn’t enough time at the end of class to complete it.

Enter version 1.2: paper option, fewer choices, a few extra minutes. Still didn’t work. So I asked again: Still too many choices, still not enough time. One student said, “Even though the posting reminder came up with 5 minutes to go, our conversations about the math were so engaging that we didn’t want to stop to do a survey.” Another said, “The first question was fine, but I really didn’t want to take the time to write stuff for the second question.” This was the general sentiment.

When I reflected on this sequence of events with my colleagues at the Better Math Teaching Network, one teacher (who also has several years of teaching experience) said, “I feel like exit slips are just data for someone else who isn’t in my classroom. I know what my kids know and what they don’t know because I talk with them.” And I thought, she’s absolutely right. Here I was, trying to do something with exit polls – trying to get my students to reflect on the class, to be meta-cognitive about their learning. They were telling me through their actions and class engagement that they were learning just fine, thank you.

I have lots of formative assessment strategies, but this is the last time that I try to implement exit slips for the sake of implementing exit slips. I know what my kids know because I talk to them.

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Note from a graduate

Hey everyone! I just felt like I should email all of you to say hi, and to assure you that I haven’t forgotten Baxter, and to remind myself to stay in touch, and to tell you that [college] is great and almost everything is going really well! I’m actually kind of tearing up writing this, which surprised me since that’s not something that happens to me very often. I’ll try to remember to stop by the school if it’s in session while I’m visiting home!

Teaching is about building relationships with our students.

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Tidbits from the Week

I tried my #LessonClose a couple of times this week in my 3D geometry class. The first time I used the Collaboration poll and the second time I used a new Learning from Mistakes poll. Both polls were given while working on the question: “Which Platonic solids can tessellate space?” It was clear that cubes would work, but there was some disagreement about the tetrahedron.

Student comments about how they collaborated included:

  • I was part of the conversation when we were brainstorming answers
  • I participated but did not lead
  • I argued about shapes that would or wouldn’t work
  • Everyone’s voice was heard

Student comments about Learning from Mistakes included:

  • I assumed an angle stayed that same when rotated on the plane. This turned out to be false, and I had to later revise my answer.
  • I forgot Trig, and I may have messed up a little bit with the answer of #1
  • A few times, we started to follow a faulty train of logic, based on angle assumptions, that messed us up until we figured it out.
  • I wasn’t exactly wrong just wasn’t very sure. My group had made a prediction that was actually true.

I’m finding it difficult to decide on the specific poll to give. I might create a new poll that let’s the student select which aspect they would like to give me some information about. This is the heart of the PDSA cycle – learning quickly and making changes to improve.


Earlier this week, Dan Meyer wrote this post about explanations and mathematical zombies using z-scores as an example. In the comments I shared an activity that I’ve used, one that I posted about last year. It so happened, that it was time for that activity again this week. In both classes, students were able to develop the reasoning behind the formula through discussion. One student even described what we were doing as a transformation to the standard normal distribution. Never once did we write a formula.


Once again my Flex Friday work connects me with students who are new to Baxter Academy. This year we are teaching them skills through workshops. This Friday’s morning workshop employed design thinking: asking and answering “How Might We … ” (HMW) questions. (For more about this approach check out The Teachers Guild or the d.school at Stanford.) Once you have a bunch of HMW questions, you attempt to answer each one in as many ways as you can think of. My colleague called this “thinking around the question” and illustrated it with the question, “What’s half of thirteen (or 13)?” And here’s what we came up with.

img_20160916_120055631

 

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Lesson Closure & Exit Polls – Images

I’ve received a couple of requests for some larger images from the last post on Lesson Closure. Here’s my attempt at providing them.

First, the process map.

exit poll process map

A few exit poll examples.

I have a few other exit polls, but you get the idea. One question to rate the day and one question to elaborate a little bit.

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Lesson Closure & Exit Polls

At the end of June I wrote about Continuous Improvement and promised that I would share updates throughout the upcoming school year. Well, here’s update #1, thanks to a great post by @druinok about Closure and Exit Slips.

Just like the post says, I, too, have always struggled with wrapping up lessons before the bell rings. Okay, we don’t have bells, but there comes a time when the students have to move on to another class. Too often, it seems like we are all so involved that the time just creeps up on us and off we go. That means that I have to rely on my gut instincts to plan for the next day. After so many years of teaching, it seems to work, at least from my perspective, but am I really serving my students in the best possible way that I can?

As a member of the Better Math Teaching Network, I had to come up with a plan – something in my practice that I can tweak, test, and adjust with ease. So, I decided to focus on class closure. Since I don’t have an actual process for this, I had to think intentionally about what I might be able to do. I created this process map:

exit poll process map

I focused on the final 10 minutes of class. Who knows if this is appropriate or not. That will be one of the adjustments that I will have to make, I’m sure. But, I have created a set of Google forms that are designed to solicit some focused feedback that I’ve designated as “process” or “content” oriented. Here is a sampling of “process” Exit Polls I’ve created:

And for “content”:

 

What I like about the Google Form is that I anticipate it will be easy for students to access (most have smart phones, all have laptops) and I can post a link on the Google Classroom.

I am hopeful that this process, this structure, will push me to gather deliberate and intentional data from my students so that I am able to plan better each day. Time will tell.

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Continuous Improvement

How do teachers improve their practice? This is a question I have been asking for my entire career (over 25 years). During the past year, I was involved with a group of high school teachers, coaches, administrators, and researchers working on how to scientifically study how to improve. In our case, the focus was on improving student engagement, specifically in Algebra 1. Since this is seen as such a gateway into high school mathematics, if we cannot help students to engage, we are narrowing their future opportunities. So we tried this new (to me) approach called a PDSA (Plan, Do, Study, Act). You set a goal, decide how you will measure your progress toward the goal, make some predictions, collect the data and analyze it, then revise. These are meant to happen in short cycles, 1 to 2 weeks.

What did we do?

My small group focused on student communication. Students often seem reluctant to share their thinking, so we devised a protocol called “Structured Math Talk” during which students were given a task to work on individually for a few minutes and then turn and talk with a partner. The partner talk was by turn and timed. One partner talked and the other listened and then they switched. This is our first PDSA form. It turned out to be quite challenging to gather this data. We were teaching under different circumstances: some of us had 55 minute classes that met every day, some had 80 minute classes that met every other day, and others had 90 minute classes that met every day. Trying to figure out the right amount of time that constituted that 1 to 2 week cycle was a challenge. (Plus, I often forgot to have students complete the exit slips.) But, it was clear that our students were compliant. We asked them to talk about math and they did. We were concerned, however, that they were only talking to each other because of the structure we imposed. Would they continue to share their thinking with each other even when we weren’t watching? This was our revision for PDSA cycle 2.

Our data was showing so much success that we questioned our entire process. Are we asking the right questions on the exit slip? Do our students understand the questions on the exit slip?  Are we using the right kinds of tasks? Are we asking our students to engage in meaningful mathematics? So, we paused. We went to the ATMNE 2015 Fall Conference together. We read. We learned. We regrouped and refocused on the idea of productive struggle. That would feed the conversations, get our students to persevere, and push us to make sure that we were providing meaningful mathematical tasks.

What did I learn from this experience?

  • It’s difficult to document the small adjustments that teachers make every day, all the time. It’s difficult to be scientific about those small changes that happen in the moment. It’s important to develop a mindset of doing this, however, because that is how we can help each other improve.
  • I’m not sure we were asking the right questions. Not the right question to study, not the right questions of our students, and not the right questions to help us learn.
  • My students are generally willing to engage in whatever task I throw at them. It was never a problem for me to get them to talk to each other or to try something that they had never done before.
  • This process is an adaptation of Edward Deming‘s process cycle. My brother has done this work for 30+ years and is an expert in Lean management techniques.

What’s next?

The small group has expanded and we’re now known as the Better Math Teaching Network. Our first meeting is in July, a 4-day institute where I hope to share my new learning with others and learn better techniques for meaningful data collection. The trick, I think, will be to ask the right questions.

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