Formative Feedback

I've been thinking a lot about feedback lately. It started with this tweet:

@MrAbend I would be really curious as to what the Math learning/cognitive science research says about error types. Does @mpershan know?

— Anna Blinstein (@Borschtwithanna) April 15, 2017

@mpershan was kind enough to respond with an email and sent me down a rabbit hole of articles and blog posts about the usefulness of feedback. Since Michael was the inspiration for this journey, it's only fitting that I try to imitate his style of writing out loud to try to organize my thoughts on this topic (sorry, Michael - reading this back after I've finished the blog post has shown me that you are inimitable. Also, I should probably avoid writing blog posts at 11 pm in the future).

The central question we discussed was: what is the purpose of feedback? Clearly, it is only useful if it changes a person's thinking. Does pointing out a mistake do this? Does categorizing the mistake do this? Does indicating a student's level of understanding of a topic ala Standards-Based-Grading do this? Do questions do this better than statements? Do students need to reflect on the feedback or do another problem related to the feedback received or implement it in some other way in order to get more benefit from it? Written vs. oral? Immediate vs. delayed?

Feedback while kids are working in class:

This is the type of feedback I think I know how to do the best. When kids are working on a task, either on their own or with someone else, I am usually able to ask questions, point out features of their work, or connect them with other students' thinking so they can make progress, identify and correct errors, and clarify their own ideas. The one blind spot that I think I still have in this area is when a student thinks about a problem in a way that is really, really different from methods I understand or have seen and thought about before. This doesn't happen very often, but when it does, I'm really stumped. I can help them verify that their answer is incorrect. I can ignore their method and show them a way to think about the problem correctly or point them to another student in the class with a different approach. But if I don't understand it, I can't help them resolve the cognitive dissonance of their incorrect approach, which means that my work is not complete.

But in general, this is the type of feedback that seems to pay the most dividends. The kid is right there with their work, we can have a conversation, I can see if they are able to implement my feedback and give more or of a different kind, as needed, or ask them to work on a related problem. This is really the best case scenario in feedback world for me.

Feedback on homework:

Things start to get real hazy real quick when I'm looking at a kid's work outside of class and my feedback is now provided in written form or via a conversation with them the next day. Will they have time/inclination to do anything about my feedback? Without the option of a conversation, I have to make a guess, which I suspect is often not great, about their thinking and the amount/level of information to provide back and how to do that in a way that opens thinking rather than closes it. Honestly, I don't have any evidence that students get a ton out of the written feedback on their homework assignments. I've thought about building in class time to have students read the feedback on their assignment from the previous day and do something with it (since homework is turned in digitally and feedback is provided digitally, I have no idea how thoroughly students would be reading my feedback otherwise), but it seems like I could just use this time to talk to students of concern about their work or have the class do a problem related to an issue that I saw on many papers. We already go over homework questions in class before it's turned in and the answers are provided in advance, so presumably, they know if they are understanding the material. If I'm very concerned, I would rather email a student or talk to them in class or ask them to work with me outside of class. Spending lots of time writing comments and then flinging them into a black hole of ??? doesn't seem like the best use of my limited time. But not providing feedback on homework also seems wrong. So I'm at a bit of an impasse here. I've moved some of my homework grading (especially for bigger projects) to in-person conversation and in an ideal world, I would be able to do that for all of my grading, but time with students is a precious commodity.

Feedback on assessments:

This type of written feedback seems to go better than homework. I think that there are a few components that have made it more successful:

1. Students perceive assessments to be more summative and take feedback on them more seriously. They know it's a check of their understanding that will more directly be reflected in their grade (grades as motivation.... laaaaaame, but I'm not sure how to get around this... I have to produce some sort of grade at the end, and I like homework to be purely for feedback so that leaves assessments for grading). As a result, they read comments more carefully and are more motivated to figure out their mistakes and learn from them so that they can show more understanding on the reassessment.


2. I separate the feedback and grading parts to help students focus more on the feedback initially. When I grade assessments, I only write comments/questions (and try not to say too much since I know I'll be there in person to continue the conversation). I record their SBG grades on the assessment in the online gradebook only a day or so later, based on the research that showed that when students receive written comments and a grade on an assessment, they basically ignore the comments and only look at the grade, and that this is not helpful for learning. Getting back their assessments with comments only helps to keep the conversations on concepts and learning only, not on grades, as well as encourages students to work together with less comparison to others. 


3. We spend class time correcting quizzes, usually in groups that are either assigned randomly or by common error types. The quiz corrections are an assignment that is collected, they are not for "earning back points" (I don't actually understand what that means), but they are required in order to reassess. I ask students to analyze their error (did they misunderstand an aspect of the concept? execute a procedure incorrectly? make a careless mechanical error?), as well as redo the problems on which they made errors. Based on my thinking around this issue, going forward, I'd like them to also state what they plan to do to make progress on the issue identified. Michael seemed to think that identifying the type of error is not particularly helpful to students, but I think that when followed up with a "next step," it is maybe more useful?


4. I think that more students actually know what they should do to make progress with assessment feedback. They've done a lot of work with the concepts being assessed. They can talk to peers to understand other approaches, they can talk to me, we can schedule a meeting outside of class to work together, they can refer to online resources organized by content topic to review a concept or procedure, they can do practice problems from homework assignments and previous reviews related to this concept so the feedback is both more closely connected to a concrete goal and to ways of reaching that goal. 

So my main questions right now are:

1. How can I make feedback on homework more useful in helping students change their thinking?
2. Are there ways to improve both my in-class and assessment feedback?
3. How can I move more of my feedback to conversation and away from enigmatic notes that try to strike just the right balance of tantalizing hint/information-giving and hook to motivate kids to want to look at their homework again and rethink their approach, but that mostly get ignored or scanned quickly and not attended to? Did I mention that writing tons of feedback on homework assignments takes a lot of time???
4. Are there aspects of feedback that I'm not considering?

Using Canvas to coordinate written feedback

Yesterday, @druinok asked for suggestions on providing more written feedback to many students quickly.

I wish I had the time to give my students more written feedback without a grade attached. How do you fit it all in?

— Druin (@druinok) April 15, 2017

It turns out that we both use Canvas, an LMS, at our schools. There are a lot of features about Canvas that are not the most user-friendly, but in terms of giving feedback to students quickly and easily, it's been really helpful. Here's how I use it:

1. All work that I collect from students passes through Canvas, including work that is not graded, but is just for feedback. I create an assignment with either a link to a pdf for problem sets or to a Google doc for projects/written reflections
   
   
   

2. Students complete the work either in their Math notebook or in a Google doc (for projects/written reflections). But all work is submitted digitally. The student's view has an electronic submission button. Most of my students have the Canvas app on their phones and can submit by snapping a photo of their written work. Those that don't have the app take a picture with their computer camera and submit it via the web version of Canvas. I remind students to submit their homework to Canvas after we go over homework questions in class.
   
   
   




3. In grading mode, I see the photo each student took, mark the assignment Complete or Incomplete, and type written feedback. If the assignment is graded, I indicate their level of proficiency and sometimes comment on the specific objectives graded (we use Standards Based Grading so students don't see points, only learning objectives and levels of proficiency).
   

4. The system is quick - I can go through all the work submitted by students, type or copy and paste comments, and click on levels of proficiency if I'm grading the assignment. Students see the feedback on individual assignments and can also look at feedback from past work, chronologically or organized by learning objective.
   
   
   
5. I love the fact that students have access to all of their Math work in their notebook at all times - there's no longer the loss of time in turning it in, waiting for me to write feedback, and then getting it back, accompanied by the inevitable loss of someone's work and of me lugging piles of papers back and forth from school. There's no longer a question of whether something was turned in or what the feedback on that work was. We can both always easily see a chronological record of the feedback given over the course of the year and track progress. If I ever create a portfolio system for summative assessment, all of the student's submitted work is already digital and organized.
   
   
6. The one drawback that I wish Canvas provided is the ability to annotate directly on student work. If I want to draw a student's attention to a particular problem, I have to write a note that says, "In question #2, look at..." instead of just circling question #2 on their paper. When students upload their files in pdf format, Canvas has an internal marking system that activates and allows you to annotate, highlight, and type directly on the page. But for most students, this would add an extra step of converting their picture to a pdf and uploading it in that format, and I would rather make homework submission as simple as possible. So for now, this is my system.

Student meetings for formative assessment

This year is going by in a blur, but I did finally squeeze out a few minutes to blog about something that I've tried this year that I'm really liking. Based on a description in the book, "Creating Cultures of Thinking," I implemented something that the book calls Individual Feedback Sessions (I just call them "regularly scheduled meetings," but sure, pick the fanciest name you think you can get away with), which were created by a teacher profiled in the book. His explanation of this strategy is here, but the gist of it is:

1. Schedule 20 minute bi-weekly meeting with each student (he recommended meeting with 2 students at the same time, which I would do if I had a more typical class load). I meet with students before school, during lunch, during their free periods (if they overlap with mine), during tutorial, and after school.
2. Discuss work that the student has turned in during the last two weeks (since the last time you've seen them). Go through their work with them in detail, giving verbal feedback. Either you or the student records a summary of the feedback (I put comments in the online gradebook and ask students to also write some notes in their notebook).
3. Discuss the student's overall progress in the class, how they're doing incorporating feedback from previous sessions, and ask for questions about the content and for feedback on what you can do to support them better. Follow up on any issues that have come up in class with that student.

I have a schedule of meetings posted on the class page so students know when we're supposed to meet. For students who need a bit of an extra reminder, I have an automated email that emails them the day before our scheduled meeting. It is more work. I do have a much busier schedule during the school day as a result with almost no "free" periods. BUT, I do virtually no grading at home (other than quizzes, which I like to grade more quickly than a 2 week window would allow) AND I feel like students understand my expectations, really hear my feedback, and develop stronger self-advocacy and ownership of their learning. 

Grading papers at home by myself vs. interacting with an actual student about their actual work...
You do the math

Doing this has made it possible for me to assign better problems. I have been using IMP Problem of the Week tasks in my teaching for a long time, but every year, after grading a few write-ups, I became quickly overwhelmed by the sheer volume of grading (how the heck do English teachers do it??) and stopped assigning them. This year, I have already assigned four Problem of the Week write-ups for every class. And graded them all with students. And seen tremendous growth in their ability to describe their process and reasoning. Yes, I do think it's a valuable skill for students to learn to interpret written feedback from teachers, and I plan to do some of this in the second semester (perhaps, I provide written feedback first, then we meet and student explains how they understood it). But in terms of actually understanding and learning from feedback, in person conversations are waaaaaay more effective. Especially when I'm asking students to do mathematical work that they are not used to doing (writing about process, explaining reasoning, providing evidence, using formal notation and clearly annotating work, etc). Overall, I do think it takes more time, but it's much more fun for me and results in more learning for students so I think it's worth it. 

As the semester winds down, I am starting to ask students to give feedback to their own work and to the work of their peers so this is definitely not my only model for feedback. And as always, I'm curious to learn more about others' approaches and ideas on this.

Goals for 2015-2016

I find these goal-setting types of posts pretty helpful. Ideally, I will actually go back to this and reread it at some point into the school year. Maybe when we do the #1TMCthing check-in at the end of October? I just reread some of the goals that I had set in previous years and it's pretty hit and miss in terms of how much I actually accomplished. My main concern is that I have too many goals and it's maybe unrealistic that I will be able to accomplish all, but what's that terrible saying that I've seen in a bunch of classrooms that doesn't actually make any sense? Oh yes...

That literally makes no sense. The stars are farther.


Anyway, without further ado, my goals for the 2015-2016 school year!!

Grading/feedback

• Give back quizzes with feedback only, share the grade after class (we will have an SBG online gradebook this year that will hopefully make that easier), as described in this post by @mythagon.
• Students must correct original quiz and demonstrate evidence of work/learning done in order to reassess. They may not reassess on the same day. Still debating whether I want to put a limit on the number of attempts. I thought about making all of the attempts count (with a weight making the later attempts count more), but decided that this is not in the spirit of SBG.
• Teach students how to use feedback effectively. This was from @pegcagle's session at #TMC15 and is my official #1TMCthing that I have publically promised to follow up on this year. One way to do this is to give back feedback mixed up and not attached to assignments and have students in each group try to figure out which feedback should go to which person. Another idea that I want to try is to have students exchange papers and coach each other on what to do with the feedback they received. Last year, I did a bit of peer feedback prior to turning work in to me, with some success. I need to make this a more consistent part of my class.
• Incorporate homework and classwork into students' self-assessment of their practices. Last year, I asked students to do this for projects, but I would really like a portfolio each unit with self-assessment that is more global and includes homework and classwork with linked examples of their work as evidence. This idea is based on a post by @jacehan.
• I really need to get homework and projects graded more quickly so that students are getting feedback at a time when it's still useful to them. I got bogged down with grading big time last year, and I need to be better about staying on top of it. Update: after reading "Creating Cultures of Thinking" a few weeks ago, I would like to set up individual meeting times with each of my students outside of class every 2 weeks (we'll see if the schedule supports this) in order to discuss their progress in the class and go over their projects and reflections with them. One of the ideas in the book that I found really fascinating was that instead of thinking about time as the most limiting constraint, as we usually do, we can instead think about energy... what feels energizing and what feels draining. It might make sense to change something that takes less time, but is draining with something that takes longer, but energizes you. The example given was grading papers at home, which can be exchanged for in-person meetings with students with the paper graded in real time and written feedback accompanied by in-person interaction. I would like to try this model, knowing that it will mean trading off some time, but hopefully, will feel less painful than grading projects late at night.

Class culture

• Continue using daily random groupings and whiteboarding, as described by @AlexOverwijk to increase student participation and engagement. Based on a Twitter conversation with @fnoschese about gender balance in groups, in which he discussed the research that groups in which there are as many or more girls as boys have higher performance outcomes for girls than groups in which there are fewer girls than boys (single gender groups are okay), I will be tweaking the gender ratios in my random groups to help make them more balanced, if needed. But not always. It depends. Basically, it's on my radar, but I'm not 100% sure that gender always trumps other status issues and I really do believe in the overall benefit of visibly random groups.
• Continue my policy of having students volunteer to participate in class discussions, with the caveat that each person must participate at least once or they must start the next day's discussion. In addition, when groups report out, I can call on any member of the group.
• Introduce talking points and exploratory talk ideas into class discussions, as described by @cheesemonkeysf here and as described in a similar Visible Thinking routine called Micro Lab. Teach language of argumentation and mathematical discourse, as described in the Claim-Support-Question Visible Thinking routine.
• Continue assigning bi-weekly reflections as a way for students to reflect on their learning and also to build community and feelings of connection. Move from reflections that are only about learning and affect to reflections that also dig deeper into mathematical concepts and connections. Incorporate reflection questions into daily homework or exit tickets to have more formal processing opportunities and feedback on thinking routines and classroom structures and how they are impacting student learning. 
• Build student-student connections to strengthen class culture. I really enjoyed the activities that @sophgermain demonstrated in her session on restorative justice, which facilitate student-student connections in the classroom. Some examples:
• There are two circles of students facing each other, a question is asked and each person speaks for 1 minute on that topic (examples of questions and topics below), then one circle rotates to a new partner and another question/topic is asked.
• Making one circle for the class and popcorn or going around the whole circle sharing on a particular topic or to give appreciation to someone.
• Have students write their names on a piece of paper, then distribute randomly and each student must write something nice anonymously about the person whose paper they received. Can repeat this multiple times and then return to the original person.
• Ask students to share at the end of a task who was helpful to their learning and how. 

Homework

• Be more intentional about homework. I blogged about this here already, but I'd like to assign fewer homework problems, spiral it in more intentional ways, and always provide answers in advance and worked solutions from students' own work after we discuss homework in class. Homework will be organized into three sections: Review (questions/problems relating to old material), Reflect (processing questions relating to new material, connections between content), and Reach (deeper/harder questions from mostly old material).
• From @bowmanimal's post on homework, I'm going to ask students to give themselves feedback on their homework and emphasize it as a learning tool. I normally tell students to limit themselves to 45 minutes per assignment and then provide a day every 2 weeks that is a designated catch-up day when they are expected to go back to old assignments that were not finished and put more work into them. I will do this more explicitly this year.
• I am still playing around with how I want to handle homework questions. I tried using a Google form, as described by @z_cress, last year, and it was a bit hit or miss. Quite a few students simply didn't do it and of those that did, many filled it out too late for it to be useful in my planning of the next day. In @pegcagle's workshop, she discussed using entrance tickets as a way to assess which homework questions are worthy of discussion and to anchor that day's learning, with questions like, "Which homework problem was the hardest for you? Which homework problem was the most interesting?" I definitely like giving groups a few minutes to discuss homework questions together and asking students to present solutions to problems that many are wondering about or that are especially important, but am still working on how to do this efficiently and in a way that maximizes everyone's learning. I definitely treat homework as a vital part of class, with questions that bring out connections between topics and that preview new content or skills that will be useful in that day's learning.
• I will continue having students turn in pictures of their homework digitally while keeping an organized notebook. I really liked that students had access to all of their work and that I didn't have to track papers last year.

Other

• I would like to emphasize organization a bit more. Ideally (if I can make myself do this consistently), I would like students to create a table of contents at the front and number pages in their notebook. I was reminded of Magdalene Lampert's structures for student notebook writing in @sgnagni's post describing the sections that she had students create (Date, Problem of the Day, Experiments, and Reasoning). For my high school students, I am thinking something like:
• Date
• Questions being investigated
• Tasks/Mathematical Work
• Summary and Reasons
• I would like to continue giving students 5 or so minutes at the end of each class to organize their written work and complete the summary section of their notes. I started doing this halfway through the year last year and students felt that this was very helpful in solidifying their learning, especially if much of their work had been done on whiteboards and they wanted a record of their thinking for that day.
• I will spend more time planning tasks in anticipating student responses and how I will treat them. I did too much of this on the fly this past year, and while much of the time, it went okay, I am starting to see the benefit of spending more time on advance planning. I would also like to provide rubrics for all projects in advance. I did this sometimes and always got positive feedback when I was able to do it.

SBG: Assessing Mathematical Practices

In an earlier post, I wrote about the challenges of giving meaningful feedback without using grades as motivation. But now, I am thinking about the challenges when grades are part of the picture. Over the summer, we put together a set of mathematical practices (a mix of aspects unique to our school, Common Core, Park School's Mathematical Habits of Mind, and work done by Avery (his post on Mathematical Habits is here), who teaches 5th and 6th grade Math at our school). The five main categories are

• Investigate, Explore, and Play
• Represent
• Reason
• Communicate
• Growth Mindset

Within each one are four sub-categories and four "levels:" Emerging, Developing, Strong, and Leading. 

Mathematical Practices 14-15

This template formed the backbone of my feedback this year. Every chapter has its own content objectives, but the practices continue the entire year and are consistently being used by all of the Upper School math teachers.

In order for this to be useful to students, most assignments had a content component, which was assessed separately, and a practices component. No assignment included all of the practices, but each one included at least a few. I would let students know in advance which practices I would be assessing with a particular assignment/project. Sometimes, there would be a self-assessment component first ("highlight the level you think you have demonstrated for each practice assessed on this assignment and give evidence for your conclusion."). They would get back a rubric with the appropriate cells highlighted, along with comments and suggestions for improvement.

Pros: very specific and detailed feedback, it was very clear to students how highly the practices were being valued, they understood them better as they continued to self-assess and get feedback on them over time, they began incorporating the language of the practices in their overall reflections on the course and in their work for the class, and they demonstrated progress and growth over time

Cons: there are so many sub-categories and so much detail that it took a while before students were really clear as to what each one meant, it took an almost unreasonably long period of time for me to do each assessment and justify each rating, compiling all of this in a non-formulaic way for a final semester grade was a Herculean effort that I don't know that I can ever undertake again, and the sheer volume of feedback that this resulted in for students, families, and advisors was overwhelming and therefore not practical in the long run

The main change that I think we will make for next year is to eliminate the sub-categories. They can be there in the background if we want to make reference to specific aspects of each practice, but always including each one is just too much. I would also like to build in more time for students to revise their work and make improvements on a project they've gotten back rather than waiting for the next project or paper in order to improve. I'm currently in discussions with other 10th grade teachers to use the last week of the school year as a time for students to put together a portfolio that will include one paper or project from Math, History, English, Science, and World Language from earlier in the year, but revised and improved to incorporate the feedback and learning that has taken place since then. I would love for revision and iteration to be a regular part of the learning cycle in all of our math classes and for feedback to be a step along the way, not the end.

I also need more regular ways to give feedback to students on practices that are not always assessed on projects, such as ones having to do with their growth mindset and collaboration and contribution towards class. There is so much already to plan, assess, and give feedback on that this one definitely slips through the cracks. But I keep reminding myself that if I want something to be a vital part of the class and for students to make progress on it, I need to regularly assess it, give feedback on it, provide explicit instruction on how to improve it, and ample opportunity to revise and iterate and apply it again and again. It makes sense to me that quality is way better than quantity here. Decreasing the number of practices, but assessing them more often and with depth, clear feedback, and explicit instruction and mentoring of students to move them along the spectrum is much better than spreading myself thin.

Homework Folders - Made 4 Math #5

I think I skipped a few weeks there, but hey, that's just how I roll. Anyways, today's Made 4 Math post is basically the only original thing that I've ever thought of for teaching. I mean, literally ever. I take the "beg, borrow, and steal" mentality of teachers everywhere to a new level, which is why I am so proud of this one idea that is my very own. It came about because my biggest difficulty in teaching (and life) is organization. Loose papers are my kryptonite. So this is my system for keeping kids' homework organized. I buy 4 sets of colored folders ($0.10 each at Office Depot), one set for each of my classes, 7 folders per set.

Each folder will hold the work of one group. I generally have between 4 and 6 groups of 4 students per class, but I buy a few extra folders in case one rips or a kid loses one (more on that later). The groups are based on the kids' seats - the desks are usually arranged in groups of 4. 

The folder is labeled with the kids' names and the class and period number. When we change seats, I just stick a new label on top of the old one and write the names of the new group on it.

The folder has two parts: "In" on the left side is where kids turn in their homework and "Out" on the right side is where I place graded homework. One of my group roles is a Materials Manager. This student's role every day is to pick up his or her group folder from the magazine stands that hold all of the folders.

He or she passes out the graded homework from the right side of the folder to each member of the group and after the group or class goes over homework questions, the Materials Manager inserts everyone's homework papers into the left side in numerical order (each kid in the group is assigned the numbers 1 through 4). My gradebook is set up so that the kids are listed in the order of their groups and their assigned numbers so entering grades is a snap, straight from the group folder. It also means that I never ever ever lose homework - it just moves from the left side of the folder to the right side. I don't have to use any class time to collect or pass out assignments, and if I want to know if a kid turned in their homework that day, I can find out very quickly. I also like that it turns over responsibility to the students.

This also allows me to easily keep track of work for kids who are absent. When I pass out any worksheets or problem sets in class, I pass out a copy for the absent kid too and the Materials Manager puts his or her name on the sheet and places it in the right side of the folder so that it's ready for the student when they return to school. 

The best part is that almost all of the other MS math teachers at my school have adopted this system so now I don't even need to take the 5 minutes I used to explain how it works or remind students to not put any papers on my desk or try to hand them to me (I literally tell students that if they hand me a piece of paper, there is about a 90% chance that this paper will never be seen again by human eyes).

One more logistic thing - I added a responsibility for the class leader (a job that rotates each week) to check at the end of class that all group folders have been returned to their container so that no one walks off with one. Before I added that, I had a group folder disappear for good about once every two years, which is still probably a better statistic than how often I lost homework before I started using this system. Hopefully, this is useful to some new teachers out there, and I'd love to hear how you handle homework organization in your class.

Thoughts on homework

Some recent discussions on twitter and on google plus got me thinking about my own homework policies. An Alfie Kohn article that I had read back in grad school and now reread as a result of these discussions posits that homework at any level is at best, useless, and at worst, actually detrimental to learning. In my Algebra classes (which is primarily what I've been teaching the last two years), I give about a page's worth of homework four times per week. Students are expected to check their odd answers at home, mark the problems that are incorrect, and fix them if they can. At the start of the next class, students check any even problems (usually only one or two of these), and discuss with their group the problems that they did incorrectly, but that they couldn't fix on their own. Then, as a class, we discuss any questions that the group couldn't resolve, as well as problems that I just thought were interesting or that bridge to the next lesson. Students turn their homework into group folders and get back their graded homework from the previous day.

The first thing that I do with a homework assignment is determine whether every problem was attempted, the answers checked, and incorrect problems were corrected in a way that demonstrates understanding. I look at the work and write notes if the thinking demonstrated was creative or elegant, or on the other hand, unnecessarily laborious. If there are skipped steps in work or problems that are incomplete, I circle the problem number. If there are errors, either of understanding or careless in nature, I circle and make a slash through the problem number. Each homework assignment is worth 3 points, and I grade based on how well I believe the student understood the lesson. A score that is less than 3 means that I want the student to correct that assignment and turn it back in to me (they will need to fix the circled and the circled & slashed problems). A student can correct and turn in work as many times as they want until the unit is over. They can ask me or other students questions in class to get help with an assignment or they can see me outside of class (there are designated times in the schedule for students to meet with teachers). Almost every assignment, whether it scored a 3 or not, has comments on it that I want the student to read and think about.

Homework is about 20% of a student's grade in my class, but I find that there is a very high correlation between homework grades and grades on quizzes, tests, and projects for most students. (Yes, there are exceptions... for those students that legitimately don't benefit from the homework because their in-class work is sufficient, I handle homework differently.) At the beginning of the year, students are not great at checking and correcting their work on their own. I emphasize homework corrections as a way to understand their errors and deepen their understanding, but I push them in the direction of checking their work and learning to ask for help before they turn their assignment in so that they ultimately are not dependent on me for going through their work and giving them feedback.

One of the pros of my system is that students take homework seriously. They know that I look at every problem and that I use it to assess their understanding of the content. I think that the detailed feedback they get on assignments and the emphasis on correcting and understanding, rather than just completing, is helpful for their learning. The main con of my system is that it takes so darn long for me. I do spend about 30 minutes per class per assignment (this varies between 45 min at the start of the year and 15 min at the end of the year). I also wonder if it's a helpful system if their future Math teachers treat homework very differently (most of the high school teachers either spot check a few problems a few times a week or collect homework at the end of the unit and grade on completion or sometimes, don't count homework at all), but my goal is that by the end of the year, it is internalized and seen as helpful for their learning so that they will continue to do their best work regardless of how it is graded. And isn't that the point of most techniques and habits of mind that we teach?