Andrew Busch

Starting at a new school with a new team, everything is up for grabs—this week, it’s how we assess student learning. I’ve got a lot of questions tonight and decided to write them down. I don't think I have any answers. That seems par for the course lately. 

In Unit 1 of Algebra 2, we spent 2 days doing retakes for the unit 1 quiz. After students got the quiz back, we had a “mastery” day where they fixed their mistakes on the quiz and worked on practice problem associated with the learning targets they had trouble on. Then, because so many students had trouble with linear programming, we had a retake day. One the one hand, that's cool that we're giving time for revision and improvement. On the other hand, we reassess every one of those standards again on the test. What if, instead of having a re-quiz, we replaced quiz learning target grades with the test learning target grades? We’re already separating out our learnings targets in the grade book. It would be easy enough to figure out which learning targets we needed to update with a conditional statement on a spreadsheet. We could get at least one of those days back for a rich task or an investigation. Maybe even two. 

I'm also rethinking the whole quiz halfway through then test thing we do in math class. After the quiz, students have the opportunity to reassess the learning targets they struggled on. In my department, we don't allow retakes after the unit test. That's a department decision. The number of quizzes we give in a unit is up for grabs though. What if we did two quizzes and a test with no quiz retakes? I like assessing the learning targets twice to show improvement. Since the test already reassess the learning targets from the quiz we could count it as the retake. If a student struggled on learning target #4 on quiz 2 but they rocked out learning target #4 on the test, we could replace the grade entirely. Of course, that begs the question of what happens if they do worse on the question. Maybe we average the two? Obviously, they didn't understand it as well as we had hoped. Every learning target gets assessed twice and we give weight to the later understanding.

One of the difficulties I see with this method is that a student who did poorly on the first quiz need to wait several weeks until the quiz to see his or her grade improve. For students who struggle to make eligibility requirements, that's a really long time to wait. Hmmm, I'll have to keep thinking about this. 

If we decided to move forward with a model like this, we would need to restructure our unit timeline. I need time to grade the 2nd half of the unit quizzes, get them back to students, have them make corrections, and give them time to ask me questions. I don't just want to sit around in class and wait though. Maybe we could start new content before the unit test? 

I wonder if something like this might work:
Week 1 after finishing Unit 1
    -Start Unit 2
    -Unit 1 Test 
Week 2
    -U2 Quiz 1
Week 3
    -U2 Quiz 2
Week 4
    -Start Unit 3
    -Unit 2 Test

What do the rest of you do about re-assessing standards students miss?

Yesterday at work a couple of us from the Algebra 2 team were talking about how to best put our grades into the grade book. Since we were offering quiz retakes just on the learning targets students missed, we ended up deciding we would put the grades for each learning target as a separate grade. It would take more time on the front end but, since we were already breaking down the information anyway, it would make putting changed quiz grades into the computer easier. And, there was the bonus that students and parents knew what learning targets they were doing well with and which ones they needed some help on. Then a colleague down the table piped up, “Your team is doing standards-based grading, huh?” After starting a denial, I realized it was mostly true. Our Algebra 2 team is stumbling headfirst into a modified SBG model.

Accuracy Checks:
Based on the work of people like Ron Berger (Leaders of Their Own Learning), we set defined learning targets (objectives) for each class period. We then have one or two "accuracy checks" on the learning targets we think the students will have difficulty on in a week. An accuracy check is basically a graded exit ticket on a specific standard. Think one question or two question quiz. If I have time in class, I have students grade each other’s work. Students may choose to retake them as often as they like until the unit test.

Assessments: 
Like most schools, we have a quiz halfway through the unit. Each question on the quiz assesses a specific learning target from the unit. We write the learning targets above each question or group of questions so the teachers and the students know which objective we’re attempting to assess (new for us). After each quiz, we started compiling data about how each of our students did on each of the learning target (new for us). Along with the accuracy checks, this allows us to target our interventions for each student. Then we aggregate the data for all classes. Specifically, we are looking for 80% for 80% of our students. Basically, we’re calling it good enough if 80% of our students are achieving what we’ve defined as mastery (80%). 

This last quiz it was very apparent we needed to reassess one of the learning targets. Students from every teacher struggled with it. We then allow students to retake just the learning target they missed on the quiz (new for us). In order to qualify for a retake, the student must fix the mistakes on the quiz and then do 3 practice problems correctly. They must do this for each learning target they would like to retake. 

Each team member is in charge of helping create the assessments. We take previous assessments and align questions to learning targets. Then we discuss the quiz or test together as a team. We don’t quite know what to do with the test data, yet. We know which students are struggling with which learning targets but we don’t have any way of doing anything about it that the team agrees on. We don’t allow retakes of the test in Algebra 2. Maybe that will change, maybe it won’t. We’ll see.

Homework: 
I called this a modified standards-based grading model because we do count homework and we currently don’t currently allow retakes past the unit test. Tests and quizzes are worth 70%. Accuracy checks are 20%. Homework/practice is worth 10%. Though it’s not much of the overall grade, missing assignments in the grade book are a strong motivator for students (and parents) alike. 

For homework, we allow students to turn in any completed assignment up until the unit test for full credit. We had quite a bit of back and forth on this. I’ve used all sorts of options at the secondary level: no credit, 1/2 credit one day late, 10% per day, etc. This is new to me. Late work handed in whenever for full credit? It... stretches me. However, as the team discussed the point of homework being practice with a particular topic, we all agreed we would rather the students do the work than not do the work. So, full credit it is. 

I didn’t originally vote for all of our changes this year. But as a team, we made a decision and everyone is expected to woman up and toe the line. After a month under the newly revised system, I understand more of what my students know this year than any previous year in teaching. Granted, it’s more paperwork than I prefer but that’s a tradeoff I’m willing to make. 
 

For as long as I’ve a teacher, I’ve struggled with isolation. Mostly, that’s because no one was around. I taught in poor rural communities with tiny schools. I never taught the same classes as other teachers in the building. Even when I did move to the big city, I was still the only math teacher for my grade level. This year all of that changed. I left my job in Boulder and accepted a position at my local high school. The school is big… for me at least. My department has 17 people. My biggest department ever before this was 5. Our Algebra 1 team by itself has 5 teachers. The Algebra 2 team: also 5 teachers. Now that I’m no longer alone, I need to figure out how to be part of a team.
 
Here’s a rough overview of how teams work at my high school. Each content area team—for me that’s Algebra 1 and Algebra 2—meets together once a week to discuss what’s going on, walk through the lessons for the week, and work out any pacing issues. During the week, we partner with another teacher to co-plan a lesson. Because of modified block schedules, each content area pair plans for about one class period each week. I only need to be creative and insightful once a week for each different prep!
 
I looked forward to this moment for over a decade. Now that it’s here, I find the transition harder than I expected. It’s not quite clearly defined how much freedom I have to deviate from the group lesson. We keep all the classes on the same pacing. This means all Algebra 1 classes teach the same lesson on the same day. That’s really new to me. I’m used to doing whatever I feel like whenever I feel like it. Granted, the lessons in my new school aren’t handed down to us from on high. Our teams create them. However, it’s really hard to teach someone else’s lesson.
 
I feel unsure about how much room I have to modify the lesson to make it my own. Can I rearrange the order of the lesson? Can I substitute out examples? If so, how many? Can I scrap the way they approach it and come the learning target from a different angle? But if I do that it starts to feel like I’m off doing my own thing and not part of a team. And, if I modify every lesson, I start losing the time-saving benefits of being part of a team. I also struggle with how to ask the modification question in a way that doesn’t make it seem like I think the lesson my teammates created is trash. Just like wearing someone else’s clothes feels strange, teaching someone else’s lessons feels...uncomfortable. It's just off.
 
This transition to a different way of teaching also brings up some of my professional insecurities. I come to this position with lots of ideas for how things should be approached: technology, classroom setup, lesson ideas. It’s unreasonable for me to bring all my ideas to a group of people who don’t know me from Adam and expect them to incorporate all of it into how they normally do things. I get a seat at the table but I don’t get to take over the conversation. I get that… but I really like some of these lessons. What if they don’t want to do them? My ego is having trouble even before they’ve said ‘no’. I’ve invested so much blood sweat and tears pushing my teaching in this direction that it’s hard to step back and try another way.
 
The types of lessons I teach and how I approach concepts are, in some sense, a professional identity issue. I see myself as a certain “type” of teacher. It’s taken me a lot of hard work to transition from the type of teacher I was into one that I’m mostly proud of. I like the hands-on approach. I like experiments. I like the mess. The possibility of giving up those previous ways of doing things threatens how I see myself as a teacher. Relying on the people around me for part of my professional reputation is hard. Those types of changes will take some time to get used to.
 
Giving up some of my independence is hard. It forces me to think of others and not just my own preferences. It forces me to re-evaluate what's important. It forces me rely on other people. That’s how teams work. Deep down, it is what I want.
 
We are better together. Always. Even if it's hard work.

One of my perennial issues as a secondary math teacher is how to keep track of student progress on learning targets before a test or a quiz. I needed a quick and easy tool to which allows me to sit down with student groups, look at work or listen to conversations, and start checking of who understands and who still needs help. This could even work for gathering data from exit tickets. Realistically, I'm not checking more than one or two learning targets for the day. Actually, I can't even imagine checking more than one. Right now, I have eight learning targets loaded into the sheet. ...I'm not sure why. Maybe I can use the checklist for the entire unit's learning targets but the horizontal scrolling may end up getting in the way. 

Here is a link to my Formative Assessment Checklist. Feel free to make a copy. 
Note: The embedded document here shows the "values" of the cells (i.e. True or False). In the actual tool, these are checkboxes. I don't know why the preview has any blank cells. That's just plain weird.
Extra Note: I suggest making a "clean" copy of the checklist before you use it. Here is a link to my unused copy. 

This is not meant as a comprehensive standards-based grading tool. It's not meant to be a one-stop anything. I need a tool which allows me to track learning targets for each student and which can export a CSV file to upload into either Schoology or Infinite Campus. This does that. 

I also don't think it's realistic for me to assess every learning target for every student every class period. I'm pretty certain that only happens in books and education Twitter chats. I'm hoping the little information I do gather will help me circle back to students which need more help before a summative assessment. 

If you have any suggestions or ways you've changed the tool to make it work better for you, I'd love to hear about it. 

This is huge! I made the push for discussions because I wanted to up the engagement level in my class. Now you mean to tell me it counts as assessment too?! Whoah. In reality, this would probably work better if instead of whole-class discussions I had student groups working at stations. Extended group work sessions isn’t a primary way I run my classroom. It happens every couple of days, but it’s not my go-to method. Mostly because I enjoy the whole-class-as-a-community aspect of the way we do problems. But, if I did more group work, I could observe more students as I went around the classroom. I have yet to figure out how to strike the right balance. Any ideas you might have would appreciated. 

My primary difficulty with using observations of students as assessment is my own ability to recall everything that happened. Initially, I bought into the school of thought that says formative assessment is only about getting a pulse on student thinking. It’s supposed to be light and nimble--only good for a day or two. Address student misconceptions quickly and move on. At least that’s how I read the advice from Wiliam and Leahy. 

However, after a few months I found myself having significant misgivings about the process. Yes, I did address individual and group misconceptions within a day or two of the lesson. But I couldn’t remember who struggled with particular concepts from previous chapters. That meant I couldn’t check up on kids who were maybe a bit shaky with a requisite skill for the new topic of the day. I don’t have a fix for this.

Standards-based grading seems like the way to go, except that I get overwhelmed when I think about creating a system to keep track of all the information. What I really want is someone else to make the system for me. I want to carry a tablet around the my room and checking off which students are progressing on a standard and which ones still need work. Basically, I want something like Bullseye for Education but a little more nimble and without the subscription fee. I’d gladly pay $20 for an app that did that.

Questioning
Once students start talking sometimes they need a little help. But I need to be careful--it needs needs to be unhelpful help. I want to help a student expand on his or her response without giving hints about how to solve the problem. I want to be interested in the child’s thinking and what that says about his or her understanding (Wiliam and Leahy, 75). So, I stole a bunch of questions from Steve Leinwand. ​

I made posters (8.5”x11” landscape--not really “posters”) of each one and put them up in my room so I could see them and the students could see them. I use them often enough in class that students troll me with them. “Mr. Busch, how do you know….? Can you explain that?” It usually isn’t until they get to “Can you draw me a picture?” that I know I’ve been had. 

After several weeks of prompting students to explain their thinking using the same questions every time, they begin expecting them. After a semester, I rarely needed to ask the questions anymore.

Think-Pair-Share
Another one of my many problems is that I want to move too fast through the content. When I ask a question to the whole class, they often don’t have enough time to process what I want them to process before I’m calling on someone to give it a go. This happens even when I give them wait-time. Think-pair-share slows down the call-and-response cycle and allows more people to have their voices heard. I ask a question. Students have some time to think about the question by themselves with no one talking into their ears. Then, students share their rough-draft-thinking with each other. They aren’t sharing complete solution processes; they’re sharing what they’ve noticed about the problem and how they might attack it. This part is key, every student gets a chance to verbalize his or her thinking. Does every student talk every time? Not even close. But it’s a step in the right direction. 

During the ‘share’ time, if I have the time, I walk around the room to listen in on conversations. It’s a great way to get a feel for how well the students understand the new material. 

After the conversations simmer down I chose a group to present (share). Sometimes I do this based on the types of strategies I heard students using. Sometimes I use randomized cards with students’ names on them. Either way, one or more students go up to the front of the room and present their initial solution strategies for the problem. The class gets a rough draft or a starting place to begin revision process. I get to hear students’ thinking and evaluate their understanding based on my objectives for the day.

Interviews and Show Me
In the The Formative 5, Fennel, Kobett, and Wray introduce a couple more ideas that, in my first read through, seem like natural progressions of the Observation. By asking good questions, a teacher can dig deeper into what a student or group of students are thinking. Not particularly earth-shattering but I appreciate someone smarter than me making explicit why dialogue in the classroom is so important. Students learn from each other and I get insight into how they think. Here are some short quotes to explain the basic premise of each of these tools. ​​

Like with Observation, my issue isn’t with the strategy, it’s with documenting student thinking. “We suggest that you complete and maintain a brief record of the student’s responses and your feedback to the student either during or right after the interview” (Fennel et al, 52). The researchers had some good suggestions about using technology to capture students responses. One of which was to use Explain Everything to capture student thinking (Fennel et al, 57). I want to have documented progression of my students through the standards, I just can’t seem to get my crap together enough to create a system to make it happen. 

I think this is where the importance of community comes in. I was the only teacher in my building making this particular push last year. Yes, I had wonderful colleagues to bounce ideas off of. Somehow it’s different when you don’t have people who take the same risks as you. It’s like jumping off the dock into cold water. You’re more likely to do it with a friend by your side. ​

​Rough Draft Thinking: Formative Assessment Like a Novice - Part 3
 
Rough Draft Thinking
My push towards teaching math through rich tasks revealed a problem in my classroom--students didn’t want to dive into the math, they wanted to get the right answers. I had to work on creating a classroom culture which valued risk-taking more than correct answers. This shift has been central to my professional work for years. In order for the whole process to work, students needed to feel safe in our classroom community. Normally, it took a couple of months to get students to believe I actually wanted to know more about their thinking than whether their answer was ‘correct’. In years past, most students were willing to present their partial solutions by about November. This past year, that happened late August. For real. The change: I started the year with ‘Rough Draft Thinking’ paired with ‘No hands up, except to ask a question’.
 
It started with a PD session over the summer. I don’t remember if it was the end of the year or the beginning of the year. I do remember not having classes to teach that week. Anyway, I was sitting with a group of Humanities teachers and they were talking about how in a semester they only get a couple of essays or projects done. Instead of asking students to turn in lots of different essays, they ask the students to perform multiple rough drafts on every essay. The conversation went around the table about how these different teachers deal with the various problems they encounter with the process. I can’t think of a word that was said after that. I was fixated solely on the sheer amount of revisions. These students are putting down initial ideas and then reworking them over and over and over again. Really, that’s what life is like. We try something and it doesn’t work and then we try it a different way. Repeat the process for 80 years. But in my classroom, we didn’t revise anything.
 
As I mulled over the revision process in life, I decided to steal the “rough draft” concept from the humanities and apply it to math class. When I asked students to present their thoughts, I would ask for their rough draft thinking. For the first month of class I’m sure I sounded like a broken record.
- “I’m looking for your rough draft thinking on this not a final solution method.”
- “When you present, you’re giving us a place to start the solution process; you’re giving us a rough draft. Then, the rest of us get to be good editors and start the revision process.”
- “If you get it right the first time that means I’m not giving you challenging enough problems.”
- “Mistakes are evidence that the work I gave you was tough enough to make you smarter” (Wiliam and Leahy, 81). I even made a poster out of this one.
 
All of my comments before and after students presented initial solution strategies were about lowering the stakes of failure in my classroom. I wanted to make it so getting something wrong the first time was completely expected (Wiliam and Leahy, 172). That’s how life works--even in math class.
 
No Hands Up, Except to Ask a Question
What this idea doesn’t do is solve the problem of only 4 or 5 kids raising their hands to answer questions in each class. For pretty much all of my professional career I’ve asked a question to the class and then called on students that raise their hands. With some well positioned think-pair-share opportunities and group-work I had it workable. Mostly. After reading multiple authors talk about the benefits of cold-calling I decided to give it a try. I cut up index cards into fourths and put students’ names on them. Rather than calling on students with hands up, I pulled a card from the top of the deck. Wiliam and Leahy call this: “No hands up, except to ask a question” (Wiliam and Leahy, 65).
 
I tried this way back when I was a new teacher. It went horrible. No, I don’t think you understand--words cannot express how much I disliked the process. It caused unnecessary disciplinary issues when students would get defiant and refuse to participate. The students fought me tooth and nail to go back to just raising their hands. I hated it. This time, thankfully, things went differently. There was zero push back on me calling on students who didn’t know the answers! None. I can’t believe it. When a student didn’t know what was going on I asked them to give a starting point for the conversation: How might they approach the problem? What information do they see that might be relevant? ‘IDK’ isn’t an option if you’re called on--you have to help the class move forward somehow. By lowering the cost to participate in class most students were no longer fearful of getting called on and every student was willing to participate. They knew they were only being asked for their rough draft thinking. Getting it wrong was expected. They only needed to give the class a place to start the revision process.
 
We had another mantra in class: Be kind. Be brave. I stole this from another math teacher. If memory serves me correctly, she got it from the new Cinderella remake. Whatever. To help create the culture of low risk participation we talked about ‘Be kind. Be brave.’ as students walked up to the front of the classroom to present. We did this at least once a week for the entire year. It’s probably excessive but I wanted to keep it as a norm in our classroom. No matter how the outside world treats people, in my classroom kindness is king.
 
Okay, here’s how it works. Students who are presenting need to be brave. It’s nerve wracking to present a solution process which you know is probably wrong. It takes guts no matter how low the risk bar is set. Be brave.
 
Students who are listening need to be kind. We have no clue how the person presenting feels. Whether they look nervous or not, we don’t know what they’re thinking. Even if they are people who normally don’t mind talking in front of groups, they could be having a bad day. We need to be kind because we want to be a safe community for sharing ideas. If you make an unkind remark about someone’s presentation, I’ll ask you to leave immediately. There can be no laughing, or snickering, or giggling. At all. It doesn’t really matter whether it’s directed at the presenter or not. The presenter will feel like it is. No questions asked. No warnings. We will honor each other’s ideas and critique them with care. Be kind.
 
Unexpected survey results
 
At the end of the year I gave a 5-minute survey about my classroom culture. Here are the results from the survey. When asked about using “No hands up except to ask a question” students were quite positive with 85% saying they liked it. I asked several questions about whether students felt safe contributing to the classroom discussion and whether or not students felt like I valued their thought process more than the “correct” answer. Though both questions came out to about 94% in favor of what I was trying to do in my class, only one student responded ‘no’ to both of those questions... and he was angry at me for recommending he repeat the class. So, take that with a grain of salt. That means the students who didn’t feel safe contributing to whole class discussions did believe I valued their thought process more than whether they were right. The students who didn’t believe I valued their thought process still felt safe contributing to group discussions. Weird and unexpected.
 
When asked about whether this class helped them become more confident math students, about 64% said yes, 31% said there was no change, and 5% said they were less confident. I so wish that 5% didn’t exist in my classrooms but that’s the reality. Some students did worse in my classes than in previous classes. What’s interesting here is that the breakdown between my Algebra and Geometry students was about the same.
 
What?!
 
Okay, let’s give a little background for why this blew my mind. I teach middle school. My Geometry students are spectacular math students--they are all at least 2 years advanced (some of them 3). I expected them to be very confident in their math abilities. As it turns out, they weren’t. That the introduction of rough draft thinking helped them just as much as it did my Algebra students was completely unexpected.
 
After sitting with the results for a couple of days it started to make sense. These students are the ones who are excellent at memorization and abstraction. They have no difficulty moving symbols around like musical chairs until someone says ‘stop’. Having a math class which intentionally put sticks in the spokes of the memorization bicycle is super frustrating for them at the beginning. It calls into question what being “good” at math looks like.
 
Rough draft thinking decreased the stress of needing to understand content the first time through or getting all the answers right the first time in order to be ‘smart’. Slowly, my wicked smart kiddos began to disassociate speed and correctness from intelligence. It took time but it happened. That’s a win in any teacher’s book.

P.S. - If you're interested in learning more about rough draft thinking in math class, I know Amanda Jansen is doing research in this area. Give her a follow on Twitter (@MandyMathEd).
 
P.S.S - It’s crazy to me that my classroom played out the research of Jo Boaler and Carol Dweck this year.

This past year, I focused most of my extra time on getting better at formative assessment. Because, why not? I decided to approach the subject like a novice--instead of making my own “to do” lists, I started by reading.

Here are the books I either read for the first time or reread this year:

1. Embedding Formative Assessment: Practical Techniques for K-12 Classrooms by Wiliam and Leahy
   -I would definitely recommend this book! It's very much worth the read.
   
2. The Formative 5: Everyday Assessment Techniques for Every Math Classroom by Fennel, Kobett, and Wray.
   -I'm still undecided on this one. I found it helpful and frustrating at the same time. On the one hand it helped expand my ideas about what I can use as assessment in my classroom. On the other hand it was frustrating because it advocated collecting all the data coming in but the sheer scope of the data was overwhelming. On top of that, it did nothing to give ideas on how one could go about quickly collecting and organizing the data.
   
3. 5 Practices for Orchestrating Productive Mathematics Discussions by Smith and Stein
   -Oh. My. Goodness. This book changed how I teach. This year was my 3rd time through the book. It's that good.
   
4. Principles to Actions: Ensuring Mathematical Success for All by National Council of Teachers of Mathematics
   -This book is a great reminder about what best practice looks like in the classroom. Well written and backed by research. Every other sentence has a footnote. I'd recommend reading it with a group of people. It was hard to do on my own.
   
5. Implementing the Common Core State Standards through Mathematical Problem Solving by Gurl, Artzt, and Sultan
   -I wouldn't recommend this book. I appreciated the effort and the concept but the execution of the book left me wanting more. Maybe it's that I expected better problems. It felt like going through the harder problems in each section of a textbook. It was okay but it doesn't really come close to the things the Math Assessment Project, Open Middle, Visual Patterns, *insert 4 or 5 more excellent resources here*, are doing.
   
6. Teaching Math with Google Apps: 50 G suite Activities by Keeler and Herrington
   -I appreciated the effort but I didn't get into the book. There's some good pointers in here, but nothing earth shattering. I guess that makes sense--there's only so much Google Apps can do. Since I'm not an early adopter of technology (I'm more of a 'wiling to be convinced' person) I'm probably not really the intended audience for the book. So, take this with a couple of grains of salt.
   

I haven’t quite finished everything that I want to. Here’s the list of books I’d still like to read:

1. I’m currently in the middle of Leaders of Their Own Learning: Transforming Schools Through Student-Engaged Assessment by Berger, Rugen, and Woodfin
2. Differentiated Assessment and Grading by Wormeli
3. How to Grade for Learning: K-12 by O’Connor

I started off working through Wiliam and Leahy’s book during endless elementary soccer practices. It was so good it pretty much served as the basis for my plan for the year. I made a list of tools I wanted to implement and then would try out one or two new ‘tools’ every month to try to cement them into my regular classroom practices. Once I got deeper into the other books, there was a little more conflict about what types of tools were best and how or if to collect data (preview of upcoming Wiliam vs Fennel cage match!). Early on in the year, it was all just figuring out how to turn ideas into actual boots-on-the-ground-daily-routines in my classroom. Trying to change deeply embedded ways of doing things made me feel like a new teacher--all awkward and self-conscious in ways I haven't felt in years.

Here's a quote I loved from my reading: 
“Teachers are frequently told what they should do, but they are usually not provided clear guidance on how to implement it in their classrooms--theory triumphs over practice” (Fennell et al, xiii).

Of the 5 areas involving formative assessment (below) I spent the majority of my year with the first two. I dabbled a bit in the others, but didn’t really have a lot of success with them.

1. Clarify and sharing learning intentions and criteria for success with students.
2. Engineering effective classroom discussions, questions, and learning tasks that elicit evidence of students’ learning.
3. Providing feedback that moves learners forward.
4. Activating students as owners of their own learning.
5. Activating students as instructional resources for one another. (Wiliam and Leahy, 11; Fennell et al 7)

For the purposes of this post, I only want to talk about the first one: “Clarify and sharing learning intentions and criteria for success with students.” In normal person language, I think it’s roughly translated as: ‘What do I want my students to learn?’ and ‘Do students know what I expect them to learn?’.

I started out each unit by breaking the unit into standards which I would cover in the lessons/activities. I did this for almost the entire year *self-congratulatory pat on the back*. I then posted learning targets at the beginning of every lesson… for a couple of months. Like the first time you do anything, there are so many things I would do differently. I stopped posting learning targets at the beginning of the lessons because I felt like it didn’t make any difference to my students--at all. Actually, that’s not true; I thought it was worse than what I was doing before. The way I implemented it, it felt like something for my students to copy down and we never talked about it again. I realize now that students didn’t take ownership because I never made it a point to circle back to the standards at the end of the unit or even had them self-asses the standards as we went along. It’s obvious in retrospect but I only figured this out the week before Spring Break.

Next year, with a couple of small-scale tweaks, I think I can get more buy in from everyone involved. I need my assignments and my assessments to consistently circle back to the learning targets. If I don’t take time to show how important they are to me then students won’t think they are important either. I’m thinking about starting with tests/quizzes and the review material leading up to tests/quizzes. Every test and quiz question could be linked to a standard. That way, when students need to do retakes they know what they need to study and I have a better idea about the types of interventions I need to make. Better yet, if my review assignments were linked to each of the standards, the students would be able to self-assess the standard and ask better questions. I said small-scale tweaks but we are talking about rewriting every test and quiz I give. Maybe I need to jump in both feet with one class rather than trying all of them at once.

Some of you are probably shaking your heads slowly and queueing up multiple posts you’ve written on standards-based grading. Here’s where it’s probably worth mentioning that I basically did contortions to not do standards-based grading this year. Like an idiot. I was trying to follow the road marked out by my books. Different authors had very different views on collecting and organizing student data. The way I understood Wiliam and Leahy’s advice was to not take down data about individual students. The point of formative assessment was to get a pulse on how the class was doing and to pinpoint individual help for either day of or next day interventions. If individual students had issues, you could address those issues over the next couple of days but there wasn’t any point in keeping information past a couple of days because the problem would have been addressed. Initially, it the system worked fine for me. But then, after a month or so, I wanted to circle back to issues students were having to make sure things were really okay. For the life of me, I couldn’t remember. Sometimes I remembered the students but I didn’t know what the exact issues were anymore. Other times, I remembered the misconceptions but was fuzzy on which particular student had them. Not helpful. I probably misunderstood the book.

Pretty much, I think fate has my road marked to try some modified form of standards-based grading next year in one of my classes.

​My next post will start detailing some of the particular formative assessment tools I tried.

Factoring trinomials has been the bane of my existence as an Algebra 1 teacher. It's not that I don't like it... actually, that's exactly it. I'm not a fan. Don't get me wrong, as a math teacher, I completely see the usefulness of seeing the roots to a polynomial function laid bare before me. However, for the amount of time and effort we put into teaching Algebra 1 students factoring quadratic functions when the a-value isn't one, I don't see a lot of payoff. Plus, most of my students just see it as shuffling numbers around until someone tells them to stop. Kind of like musical chairs with factors. Not helpful.

Rather than continuing to use an obviously losing strategy, I let desperation lead me to something else this past February. I convinced my school to buy me a classroom set of Algebra Tiles off Amazon. I also found a great set of online Algebra Tiles. This is my first year ever using these things. I'm still figuring it out.

I started using them as soon as we started the chapter. We started out with multiplying binomials. Normally, I would just use the area model and the distributive property. Here, I forced students to use algebra tiles. Forced. They moaned and complained. I persevered because I knew what came next: factoring. Now that we were attempting to find the factors of a trinomial, we used algebra tiles to create the area model and find the side lengths. I did zero teaching on this at first. Instead, I used the introductory lab at the start of my book's lesson. I had to do some serious reformatting and added a couple of questions but it went really well. Much better than I expected. Here is a link to the file if your interested: MS Word, PDF.

Once students figured out how to create the rectangles everything started to click. We were even able build rectangles with side lengths (x-3) and (x+4) which require adding zero pairs to the initial tiles. Very cool. At the end, I asked them to try and generalize our findings. How do you know a trinomial is factorable? You can create a rectangle out of it. The side lengths of the rectangle are the factors of the trinomial!

We were even able to extend this to when the a-value isn't equal to one. That's the biggy. I forced  students to use algebra tiles all the time. This is the first time students started making the connections without me having to be explicit about it. After a couple of days, they were begging for a better way. Algebra tiles were great and all but they were too much work and when the numbers got big you needed to pile all the individual sets together to do it. Students begging for generalization in Algebra 1? That's a win. 

As part of the Algebra 1 standards for comparing distributions, if you haven't checked out the Math Assessment Project stuff, you're missing out. Their card sorts are the best. I use Representing Data with Frequency Graphs and Representing Data with Box Plots. However, by this time in the year my students are done cutting out cards for me. Time for a little Desmos Activity Builder help. Here's my Desmos card sort version of Representing Data with Frequency Graphs and Representing Data with Box Plots. It worked quite well.

And, as a little bit a fun practice, we create frequency graphs and box plots of our class heights. It's amazing how when students gather a bit of data all of a sudden you have buy-in for a solid 30 minutes of work.

We just finished up our circles unit in Geometry. I had one more day before a long weekend. Rather than jumping into something new, we did a little bit of math art a la Desmos. I gave them a quick directions document with some review of families of functions they might want to explore. Then I set them loose. I gave students a choice whether or not they wanted to work on their drawings after the class period ended. That was not the assignment. Some students decided to go all out!

Are you ready? I don't think you're ready. 

BTW, I linked the pictures to the actual Desmos pages. You're welcome!

The moon revolves around the planet in this one!

I base all of the trigonometric functions/ratios in the unit circle. We use this activity as an anchor for our future discussions about all sorts of things: the graph of sine and cosine, how we create triangles within the circle, and even sine being the distance from the x-axis and cosine the distance from the y-axis.

I overheard multiple conversations between students who noticed the rate of change both sped up and slowed down. They were convinced they were doing it wrong. That's the kind of dissonance I'm looking for!

Here is a complete write up of the lesson.

Original problem by Robert Kaplinsky. I use the problem directly after we learn about special right triangles in Geometry (45-45-90 and 30-60-90). Lot's of great overlap between Algebra and Geometry here. Lot's of great opportunities for students to present different solution methods.

Here's the slide deck and handout I use with my students.