## Better feedback through structure?

When assessing, I do my absolute best to provide detailed remarks and comments on student papers. The problem I run into is doing this for every student. If it’s an exam I’m marking, I’ll usually pick and choose the length and depth of my feedback depending on the particular student and the work they displayed on the exam. This is fine because different students need varying feedback, but, looking back, I find that I shortchange some students.

If I chose to be meticulous with the work of every student, I’d spend an overwhelming amount of time assessing. So I don’t. The result is that some kids get feedback that is robust and thorough while others receive relatively minimal feedback. In addition, how I indicate a specific error may vary slightly from one exam to the next, which I think could be more unified. I also want to have a systematic approach that keeps feedback consistent amongst different students. This way when kids are analyzing and assessing work, there is uniformity amongst us all on how specific errors are indicated.

What I’ve thought about doing next year is using a set of abbreviations or symbols that would indicate certain errors. For lack of a better term, let’s call them “indicators.” I would use these indicators on exams and other assessments to highlight mistakes.

For example, if a student didn’t know they needed to factor on a given problem, I could indicate this by writing “FCT” next to the error, instead of writing an explanation or setting up the factoring for them. On the same problem, if another student attempted to factor, but committed a computational error in the process, I could write “FCT” with a circle around it. The subtlety of the circle would differentiate between the two errors.

Another simple example could be when a student commits a computational error involving addition, subtraction, multiplication, or division on any problem. Near the error I could indicate this by drawing a star, say. When a student sees a star, they will know to look for a computational error involving an operation to find their mistake.

Those are three pretty sad examples, but I can’t clarify others at the moment.

My goal would be for students to easily identify an error on an assessment by calling up the indicator. The indicators would be commonplace throughout the class and we’d build on them over time. I would create a key for all the indicators, post it in my classroom, and give them a copy. I could even include them in my lessons for reinforcement.

Since there are an endless combination of errors that can be made on any given problem, I couldn’t have an indicator for every possible error – only common ones or those that are conceptual in nature. These would form a “database” of errors that would be used throughout the year. For those errors that don’t align with one of the indicators, I could combine the indicators with regular comments to clarify the mistake(s).

By using these indicators, it could allow me to quickly and easily provide precise, detailed, and consistent feedback to every student.

Based on the type of error, these indicators would also help students distinguish between SBG scores. For example, if a student gets a FCT indicator they may earn a score of 2 (a conceptual error), but if they get a FCT with a circle, they could earn a 3 (a computational error).

All these are just ideas at this point. There’s still a lot of work I need to do to actually implement a systematic approach to feedback. I don’t know if it’s feasible or even useful compared to my traditional feedback. But I do see the need to improve the qualitative nature and efficiency of the feedback given in my class – either by me or my students.

bp

P.S. Another way to implement feedback in a non-traditional way would be to use different color highlighters to represent the different types of errors. I remember John Scammell mentioning something about this during his formative assessment talk at TMC14.

## Observe. Think. Share. Connect.

One day during a class exam a couple months back I paused to look around at my students. They paid me no mind. They were working diligently, finding their way through the problems, struggling, succeeding, you know, the usual.  During exams, I’m usually keeping an eye out to make sure the kids don’t feel the need to take a peek at their neighbor’s work. But this time was different.

I thought about who they are. I thought about who they’ll become in ten years. Will they be engineers? Marketers? Electricians? Marines? Teachers? Fathers? Mothers? I thought  about their interests and hobbies: beat-boxing, track and field, repairing computers, TV, basketball, music. I thought about how they’ve grown and how they’ve struggled in my class. I thought about their personalities and insecurities. I thought about their families. It goes on and on.

In that moment, I felt deeply connected to them in a weird sort of way and wanted to share this with them. As a teacher, I’ve always cherished being able to share the human experience with my kids. Beyond teaching, beyond learning, beyond report cards, beyond learning objectives, beyond school. That’s how I’ve always tried to relate to my students.

So with all this racing through my mind, what did I do?

I wrote to them.

Besides, I couldn’t just blurt out all of these thoughts in the middle of the exam. Plus, even if I did, this would initiate a conversation – which I didn’t really want. Not only did they need to focus on their exam, but I wanted to share my thoughts in a one-sided manner. I wanted to express how I felt and not have them feel the need to respond.

I looked around and began writing short notes to an array of students. I placed the notes face-down on their desks while they worked. I wrote down things concerning their effort, how much they’ve grown, how I appreciate them, why I believe they’re awesome, and where I think they’ll be in the years to come, among other things.

Some students read the notes immediately while others waited until the end of the period. (Some didn’t even realize I put it on their desk.) Afterward, I didn’t get much reaction from those students I wrote, nor was I expecting it. One student passively said “thanks” while others simply smiled as they walked out.

After class, I felt whole. I conveyed my thoughts and feelings to my students in a way that was personal and direct. And writing allowed me to express everything in a way that I could never do by speaking to them either as a class or individually. I felt connected.

I didn’t get a note to every student that day, but during subsequent exams I have made sure to reach out to other students. Has it become a “thing”? I think so.

Writing these short notes has been analogous to Friday Letters. It’s all about connection. Connecting not for the sole purpose of bettering their grade or getting them to work harder, although those things can result from writing my students. Instead, it’s about sharing the human experience and connecting with someone else that just so happens to be my student.

bp

## Another one added to the toolbox

Just a quick post on a strategy I recently used so I don’t forget to use it again in the future.

We were working on law of sines (LOS) in trig. We spent one day deriving the law of sines and one day solving basic triangles. At this point, about 30% of the class was ready to move on to complex LOS applications (the next lesson) while the rest of the class needed more practice solving triangles using LOS. Without planning it all the way through, here’s what I decided to do.

The next day I placed students that were ready for the application questions together in two small groups. Let’s call this the “advanced” students. I provided them with instructions, materials, and let them go explore the problems in their groups. I provided minimal scaffolding. For the most part they were able to work their way through the first few problems, which was what I hoped for.

As for the students that needed reinforcement and more practice, I placed them together in a few groups and provided heavy scaffolding and detailed attention to their needs. I’ll call these the “developing” students. I floated, sat and worked with them individually, and clarified any misconceptions that came up. By the end of the period, I was pretty confident that almost all of them could solve a triangle using LOS.

The following day, I brought the groups back together by using the advanced students to teach the developing students the complex LOS problems that they had already solved. I placed 1-2 advanced members with 2-4 developing members, depending on their levels. I found it to be a pretty good proportion. Of course, I was around to help and answer questions, but the kids ran the show and worked independently of me. The advanced students reinforced their understanding of the problems while the developing students shared a private tutor. And because the developing group got to practice more of the basic stuff the day before, they were much more fluid with the new material. It worked so well that I had them continue this peer tutoring for a second day.

What I loved about this stretch of days was that it promoted independent thinking and allowed me to reach the kids that needed it most. It also incorporated peer tutoring and kickstarted some great discussion amongst the kids. To top it off, it all required minimal prep. It was a win across the board.

Although we were studying the law of sines, I don’t see why I couldn’t use this strategy somewhat regularly with other topics. It could work well with anything that starts off fairly straightforward and gets complex, but still is obtainable without much scaffolding. Even if it does require a bit more guidance, I could provide more detailed scaffolding to the advanced group to help get them off the ground. And, of course, the advanced students could change based on the concept so one would get too comfortable.

Another collaboration strategy added to the toolbox.

Boy, do I need them.

bp

## Two-Stage Exam

My kids have been struggling this spring and their exam scores have been pretty sad. Its been one of those years. To help matters, I began adjusting my pace, but I also wanted to implement some sort of structure for collaborative learning. Idea: group exams.

Sadly, I’ve never really used group exams. To be honest, the collaboration aspect of my lessons is usually pretty lackluster as a whole. I may have used group exams once or twice before, but it wasn’t significant enough for me to remember the experience. So, I had no idea on how I was going to structure it now. Brian Vancil mentioned that I try a two-stage exam.

It was amazing.

During a two-stage exam, you first have students take an exam independently, like they normally would (this is stage one). Immediately after you collect it, you get them in groups and give them the same exact exam  (this is stage two). They collaborate and submit one document with everyone’s name on it. Their final grade: 80% stage one and 20% stage two. These percentages can certainly be adjusted.

Student discussion during stage two was rich and completely focused on the mathematics. The kids were consumed with sharing their ideas, strategies, and misconceptions. Even my more introverted students were voluntarily sharing their thoughts in the groups. As I was walking around observing, part of me felt like I was dreaming. It was that good.

Their scores didn’t disappoint, either. I’ve given these exams a few times over the course of this spring and, overall, the results have been better than my traditional exams. But their scores are the least of my concerns. And two-stage exams do way more than merely inform me about how well my students understand something.

Students actually LEARN from these exams.

They’re driven by the students, reduce anxiety, and afford the kids a great opportunity to communicate their thoughts in a meaningful way. I’ve polled my kids after each of the exams and their attitudes towards the experience were overwhelmingly positive. The kids loved the immediate feedback and the ability to learn what they did wrong (and right). They were teaching and learning from each other in ways I’ve never seen. There were so many “ah-ha!” moments during stage two that they were hard to count. The groups were reflecting about what they did and didn’t do and unifying these thoughts to really learn from each other.

My kids are looking forward to the next exam. I’ve never heard that before.

bp

P.S. There’s also some introductory research on two stage exams conducted by Carl E. Wieman, Georg W. Rieger, and Cynthia E. Heiner. A good read!

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