0. A few students I taught in Algebra II last year came up to me this year and told me that they’re using my binder system in their math classes this year to stay organized. One wants to show me his binder to see how organized he is now. Organization was his Achilles Heel last year. Just hearing that was vindication enough. Because I’d guess about 1/2, eh maybe 2/3, of my Algebra II students last year came to me unorganized. They just had never been taught to correct and organize their work. I had hoped to introduce them to a skill that they might find helpful in the future. So hearing that caused my chest to puff up, my heart to swell. It may indeed have been a heart attack. But what a glorious way to go.

1. I suspected that I would experience cognitive dissonance, because I’m doing Standards Based Grading in Calculus, but not in Algebra II. That — indeed — has panned out. The one SBG-style change I’ve made in Algebra II is that I’m entering things in the gradebook by topic now for Algebra II (e.g. “Compound Inequalities” and “Absolute Value Equations”). At the very least, I can see very quickly in what areas each kid is successful, and similarly, where each kid needs to work.

But here’s the rub. I’m so transformed in the way I’m thinking about student learning, and what assessments mean, and what grades mean, that I am already frustrated that I don’t have a good response to the Algebra II student who comes to me upset about their test grade. Last year, I would have calmed the kid down, and had a talk about the causes of what might have gone wrong. Studying poorly? Not following things in class? Not enough sleep? Whatever. And then we would have made a plan for the next assessment. We were always looking together towards the future.

And that conversation is important. Because part of being a teacher, and highlighted by SBG, is that students need to be hyperaware of their own learning, and proactive in their approach to it.

However, when I’m having these conversations with students this year, I want to also say: “Oh, you’ve figured things out? Prove it. So what if you got a C on the assessment. Show me you know it, and I’ll have your grade reflect that.”

3.  One of my concerns before embarking on the SBG express (woot! woot!) is that I wouldn’t know how to grade on the SBG system. What a 4 is versus what a 3 is versus what a 1 is. But you know what? That’s actually not hard at all, with my rubric. Whenever I get stuck, I ask myself: “From what they’ve written, what level of understanding do they have?” That question settles it. I have a copy of the rubric posted at my desk, and there’s a poster of it hanging in my classroom. To reinforce the importance of the rubric, I photocopied it on the first assessment, so students could refer to it.

4. I’ve raised the bar in calculus. It used to be that on an assessment I would give a bunch of problems, to suss out a level of understanding. Like, I might ask students to find the vertical and horizontal asymptotes, the x- and y-intercepts, any holes, and the domain to the following three rational functions: , and . Now I only give one question on the skill, but it tests all I need them to know. That would be the last and hardest rational function, in this case. And to get a 4, I demand perfection.

5. In calculus, I don’t feel any of that “guilt” when a student does poorly on an assessment [1]. You know that moment when grading a non-SBG test, and there’s a question worth 5 points, and you see that the student factored correctly but couldn’t do anything else… and you know if you were being honest with yourself that you shouldn’t give any points, but you think “oh, maybe I’ll give one point just because the student showed me he/she could factor.” You know the thought. Right? RIGHT?!? Well, I have those moments. (FYI: I always go with that is right, rather than what is in my heart.)

With SBG, all that moral teetering goes away. My heart and my mind are finally in sync. I give a student what they deserve and then say “You’re there, you need to be here. Let’s help you find a way to climb that mountain.”

6. Students have started reassessing. So far, not a lot, but I anticipate next week to have — oh, I don’t know — maybe 10 or so? (Reminder: I teach less than 30 kids in calculus.)

7. I tried groupwork & presentations  in Algebra II. It failed. Probably worth another post, if I feel like writing about it. Nothing really exciting. I tried to teach absolute value inequalities by having students muck around and come up with patterns and then generalize and come up with general procedures. I was impressed with the students’ abilities to get to where they did. But it was my organization of the groupwork, and my facilitation, and my rushing because of time pressure, that made it less efficacious than it should have been.

8. I got two really nice emails since school has started: one from a college counselor who said I wrote really great college recommendations, and one from the head of the Upper School who said I had really great course expectations for my students. It’s amazing how a few kind and genuine words can go a long way.

9. Three photography students are putting up an art instillation throughout the school. It’s an amazing idea. They are having faculty each write a short paragraph about why we teach. Then they take photographs of us and post them around the school with our blurb. I had my fashion shoot today, and I’m excited to see what results. If you are so curious, you can read my paragraph here:

Initially, I became a teacher because I loved mathematics so deeply that I wanted to share its beauty with others.. Since I started teaching, though, I’ve come to love something else. I relish the delicious challenge of getting someone who doesn’t know something to actually know something. The thought of changing someone’s view of the world… jut a little bit… therein lies the new thrill.

10. I have to be cautious about SBG. I love systems. I have to make sure that SBG doesn’t just become a system of test, reassess, test, reassess.  It’s not something that students should feel is mechanical. But a process that students go through to learn about themselves, as people and as learners.  And armed with that, they can be proactive and achieve anything. (Sappy, I know.) So here’s a reminder for myself: talk explicitly every couple weeks or so about what we’re doing in this class. It’s not a system. It’s not a system. It’s not a system. It’s a philosophy.

[1] That’s not to say that I don’t think about my teaching, and my teaching’s role (both positive and negative)  in my students’s learning. That’s a given. I’m talking about something else.

For those of you who have secretly been giving dirty looks to me, because you’ve been in school forever, and I’ve been on summer vacation forever: hey, I’d do the same. But lucky for me, those looks can stop, because we officially have started classes. Today. Of course we have tomorrow (Thursday) off because of Rosh Hashana. But then we have classes again on Friday.

I’d like to talk about how I introduced the new grading system in calculus. Basically, the answer is: I took a little from each of you. Not only in the development of the system, but how I talked about it. We had a meaningful back and forth a few times, where I asked them some key questions, and got them to reflect about the system.

Here’s the general setup – in words. I’ll include my slides at the end if you want to go through them.

Students come to the classroom, see the seating chart projected on the smartboard, and sit down. They have at their desks large index cards which they make a little “name tent” so I can learn their names. I talk with them as they arrive, and I get them in a boisterous and joking mood. I’m already in a giddy mood anyway, so this isn’t hard. I’ve taught a bunch of them before, and I know others from this thing or that.

Then we go into the course. I talk about historically the problems students have had with calculus — from all teachers I’ve talked with. The big thing separating kids from calculus is a giant mountain of ALGEBRAIC SKILLS. I talk to them about how we’ll work around this by doing algebra bootcamps for the first semester. (I’ve written about this before, I hope, right? I can’t seem to find it in the archives… hm…) I talk about how calculus is actually quite simple — just a few basic conceptual ideas — but the thing that bogs students down is not being super solid with the algebraic undergirdings. So we’ll just get the relevant algebraic skills out of the way beforehand so we can focus on the calculus in each unit.

I then polish off a few logistical things (e.g. no eating and drinking in the classroom, since it is a designated lab classroom), and then I intentionally lie to my kids.

Here’s where the magic comes in, I believe. I have to lie to my kids, for the new grading system to make sense. I had to raise their anxiety about the course, to mimic the anxiety they’ve had for all their other courses. I want to play on their emotions. It’s a little cruel, I know.

So I made up a fake grading system: 90% assessments, 10% homework. 3 tests per quarter, so each test is worth 30% of their final grade. I make it a point to tell everyone that there are no retests.

I talk about how “THIS IS CALCULUS” and “IT’S SERIOUS BUSINESS” and “IT’S HIGH STAKES.” I also talk about how I don’t want to make it high stakes because I’m a meanie, but rather, I feel obligated to get them prepared for college.

I actually am super convincing, if I do say so myself.

I really emphasize that this is a do or die class, but I do so with some humor. They all laugh at the right places (see the slides below for full effect), but I can tell some of them are freaking out.

I tell them the date of their first assessment is in two weeks.

And then I ask for thoughts.

(Crickets.)

Then, when the pause is pregnant enough, when the tension is just about at its height, I say “JUST KIDDING.”

They don’t know what I mean, so I explain to them that everything I told them was a lie. I tell them that we’re not going to be grading that way, and that I just wanted to make a point — which they’ll see later. Then I asked Shawn Cornally’s question:

“What do you do if you bomb a small quiz?”

I also got some priceless, heart-breaking, answers, like Shawn did:

“Crumple it up and shove it in my bag, hoping to never see it again”
“Shrug.”
“Forget about it.”
“Mope.”

Of course, I got some non-depressing answers too, like “Meet with the teacher” and “Go over the material again at home.” Some kids know what they think I want to hear — so these responses could be that. But I know some of these kids, and some genuinely have a lot of these learning skills down already — about being proactive and on top of their learning continuously.

So I talk about how them not learning material they missed hurts me, because I am a math lover, and I want them to know everything! And I want them to have the opportunities to learn things and be recognized for that.

Then I introduce the grading system. Pretty much how I outlined in the handout. I explained how it worked, I explained the wonders of it, I explained how it’s about them learning how to learn effectively, not just getting a zillion second chances.

I talk about my own concerns with it: the amount of work it’s going to be for me, the fact that I’ve never done it before. And then I get them to talk about their thoughts about the system. What they like about it.  That goes easily. We also talk about the meaning of grades.

Then I ask them: what might make this system hard for you.

They come up with some great things: retention, grades going down, no classroom engagement grade to “buffer” their grades, etc.

I then introduce the idea of how their quarter grade is calculated: it’s all skills. And how homework isn’t included in their grades (though it is required). I ask them again: what difficulties or situations do you think might arise with this?

They again are really thoughtful and realistic in their responses: all variations on “I might not do homework.”

I then pace around the room, saying histrionically “I’ve told you my big concern for me — the work involved. Now I’m going to tell you my concern for you…” I lay out a story about it being 10 or 11 at night, and they have two or three unfinished assignments. They decide to forego the homework in calculus because “well, Mr. Shah might give me a disappointed look, but he isn’t grading me on homework.” And how there is a chain effect, with how things can quickly build up. Procrastinators beware. And how I’m here to help, but “WITH GREAT FREEDOM COMES GREAT RESPONSIBILITY.” Yadda yadda yadda.

Three comments, of quite a few, that were said by students that stood out for me, were:

“Mr. Shah, I want you to know: this is the best first day presentation yet!”

“Wow, this just makes so much sense.”

“Did you come up with this idea on your own?” (No.) “Where the heck did you find this thing?” [I said on math teacher blogs. I saw some snickering.]

Then I pretty much dove into, verbatim, David Cox’s spiel about knowledge, community, and sharing.  I even stole the pictures.  And this quotation from his blog:

I love my kids, but I also love the fact that I think this form of grading makes sense to them, philosophically and emotionally. I don’t know what will happen as this gets implemented. But I suspect I have gotten the buy in because of this first day presentation.

Full presentation here:

I’ve now introduced my Standards Based Grading system to the following people:

1.) My chemistry teacher friend, whose opinion I trust and respect the most on all matters pedagogical. (This isn’t hyperbolic. She beats all y’all, blog and twitter friends!)

2.) The learning specialist at my school (I had to give her a super brief and inarticulate overview)

3.) The Upper School head of school (read: principal)

4.) My department head.

And I will soon be talking to the senior class dean.

Why? I’m not about to embark on something so different, in terms of how things are done at my school, without ensuring the support of those people who will, or might be affected, by this change. Also, I was just darn excited about it and wanted to share with them what I have decided upon.

What was really heartening was that people really seemed to understand it, and interested to see how it actually panned out on the ground. As you know, I’ve been thinking and reading — from y’alls blogs — about SBG for a long time. And it took me a while to finally “see” it [1]. But because of that struggle, and thinking through all the drawbacks of SBG (logistical and pedagogical), I was able to deftly and confidently field all the questions I was asked. And more than anything, I was really heartened by the serious interest and great questions coming from the Upper School head. The last few days have made me really proud to work at my school.

So without further ado, I am posting what is my final version of the introduction to the new calculus grading system.

There it is.

Some decisions I had to struggle with to make:

1. Rubric goes from 1 to 4, not 1 to 5 if a student attempts a problem. Because as @jlanier said on twitter, you don’t want to give yourself a middle option so you can straddle the fence.

2. I decided to not include homework as part of the grade. I’m scared of students not doing it, but part of teaching them involves them seeing for themselves that doing homework [read: practicing problems] is a necessary skill to be fully confident with (and to retain older) skills. I am, however, still requiring students to do homework, and they need to keep it neat and chronological. That’s because if they are doing poorly, I may want to point out the fact that they haven’t done the homework, or haven’t done it well, that I can use their work as a jumping off point for a conversation, about what’s working for them and what isn’t, in their learning practices.

3. I have problems with the fact that everything is so broken down. Where’s the higher level thinking? Where do students draw connections themselves? Unfortunately, when I thought about these questions, I realized that I rarely introduced or had students work on higher level thinking questions in calculus before anyway. We did bits and pieces here and there, but nothing super consistent. We did do a couple 2-3 day problem solving marathons with formal writeups.

I think each quarter, I will do these problem solving marathons and writeups, and simply break down the skills associated with these problems and writeups, and grade them. Having them broken down into individual skills is fully in line with the SBG plan.

4. Because I’m scared of having too much work to do — and I have so much non-math related things on my plate this year — I have limited the times and the number of skills students can reassess.

5. To get students to think about their own learning processes and styles, what works for them and what doesn’t, I’m having students reflect on why they might have done poorly, and what they did to rectify the situation, before they can reassess. As my Upper School head said, “you’re coaching them in metacognition.”

6. Only the latest skill score counts. I had some debate — highest of the last two scores, average scores, etc.? But I came down on the side that skills have to be retained. And historically except for final exams, I never really taught, demanded, or tested retention. So this is a huge shift.

7. I am going to try to assess most skills twice. But it’s not going to be possible for all.

8. Most importantly, I’m going to go slowly with this, and run with the punches, this year. I’m not worrying about being perfect, or having the perfect skill list, or finding the perfect questions for assessment. Maybe I do have too many skills, and I should chop the list in half? Maybe I am not focusing on integrating problem solving, or making two levels of problems (easy and hard), or intending to change most of my old smartboard lesson plans or what I do in class? I’m going to take it slow, get kids in a routine, get myself in a routine, see how this works out. And once everything is smooth sailing, then I’ll worry about tweaking the system.

[1] The three big “click” moments that got me on board, and then totally shifted my outlook with this:

1. Grades can go down — and retention is part and parcel of this grading scheme.
2. You have to take the most recent grade.
3. I want all my kids to earn As.

You want to know something I realized about myself and my transition to Standards Based Grading? It’s something I’m kind of embarrassed by, but I’m glad I recognized it so that I can be super conscious about it.

It’s that one of my big fears, something I couldn’t articulate until now I couldn’t quite place my finger on it, is that all my kids are going to do really well. That I’m going to have all 4s and 3.5s for all my students’ final skill grades.

I work at a school full of motivated kids. These kids are largely motivated by grades. [1] I’m  pretty sure there will be tons of reassessment, until students have 4s on everything, or almost everything.

I think something I’ve been proud of is having a pretty solid distribution: a couple As, a bunch of Bs, a few Cs. I don’t know why I’ve taken pride in this — I think having that distribution showed me I was challenging students the right amount, pushing them as a whole. [2] And although I always told my students I’d be happy if they all got As, and I think I would have been because I don’t make my courses easy and I would have been impressed that they all rose to the occasion, I would have also felt like I wasn’t making the course challenging enough for them. Does that make sense? I’ve always used my grading  distribution to let me know if I’m making the course the appropriate level to challenge my kids without having any of them drown.

So when people say Standards Based Grading is a total reorientation in terms of the way you think about the classroom, I realize this is exactly the sort of thing they mean. Because I’m ashamed to admit that one of my secret worries is that all my students get 4s on everything I teach. I don’t want to be that teacher that always gives As. *shiver*

I’m glad that I’ve recognized this secret fear, because it is TOTALLY AND UTTERLY DUMB. SERIOUSLY DUMB. LIKE SO DUMB. If I didn’t recognize this monstrosity in my subconscious now, I would have sabotaged my whole year inadvertently. Yikers!

Hello, earth to Sam, the point of this new grading system is to focus on getting the most amount of kids to know the most amount of material (and also, importantly for me, to teach kids independence and study habits that work for them). And I’ve made a rigorous set of non-fluffy standards. And if my kids can achieve mastery and retention of those standards, I’m going to toot my own horn as loud as I can. I want to capitalize on the motivation of my students to do well.

So now my new mantra is: I want to be the teacher who gives all As, and I’m going to do everything in my power to make sure my students know that I want them all to get As, and do everything in my power to encourage them to use their newfound SBG freedom and independence to get those As. Because my As in this new framework will mean something. Because my course forces mastery and retention. Because my course is rigorous.

Wow, huge realization.

PS. I have a smaller fear that I won’t know how to grade students well, even with my list of skills and my rubric. Not that I won’t be consistent among how I grade students — I am scrupulous about that now. But that I have assessment questions “good enough” that they can reveal to me the various gradations of 4, 3, 2, 1, 0 from the rubric. I think that’s something I’ll pay attention to as the year goes on. It’s something I have to see in action to see if there is some tweaking to do here.

[1] Many care about their grades more than they care about learning. Although both are sort of tied up, they are not synonymous. But regardless, it does lead to kids actually learning stuff.

[2] I’ve also had a serious problem with teachers who always tend to give As to students.

Soon-ish I will be writing and putting up my entire Standard Based Grading system, and possibly my rationale for making the choices I did (e.g. how I decided on a 4 point scale instead of a 5 point scale). For now, though, I thought if some of you were still trying to finalize your system and were looking for a rubric, I made one that I feel pretty happy about:

I wanted to create something that would work for routine plug and chug problems, some more multi-step problems, and some “explain this” problems. I also know I’m going to be doing some major “holistic” grading — in the sense that I am not going to take off this many points for this mistake, that many points for that mistake. I’m going to look at how the student performed on one or two questions testing the same skill, on the same short assessment, and give them a holistic grade for that skill. I think this rubric allows for that pretty well.

Plus, I need something I can point to, since my teaching mantra is: clear, consistent, and fair.

Without something I can point to, I would be failing on all three counts.

Guess what, ma? It’s taken me half a year of mulling, some cajoling from the “inspiring ideological cult”, and the realization that even though I think I’m teaching responsibility, I could be doing way better. So here I am, naked, standing before you… wait, no, that’s not right at all. I have clothes on. Scout’s honor.

Here I am, standing before you, newly self-inducted member of the Standards Based Grading (SBG) cult.

I can’t roll it out for Algebra II next year, but I am plunging — head first — into standard based grading in Calculus.

I made a list of skills that I taught last year — maybe it’ll be of some use to someone out there:

This ordering and skill set probably won’t be changing much for the upcoming year. But it will definitely have to be rewritten for the SBG skill/topic list.

I wasn’t going to blog about my SBG system until it was done, but someone (forgive me, for my mind is weak, and I have forgotten who) mentioned that it might be useful to watch the process unfold. Plus, I have a bunch of questions.

Here’s what I’ve definitely figured out:

1. I am going to assess most skills/topics twice.

2. The skills/topics I won’t assess twice are mainly “explain this idea, statement, or claim (using words, diagrams, tables, graphs)” questions. (Students can reassess those questions on their own, if they want.)

3. Students will have to email me by Sunday night to be able to reassess during study hall on Tuesday, and students will have to email me by Wednesday night to be able to reassess during study hall on Friday. This way I have time to prepare for these individualized reassessments, and students won’t have to individually work on tracking me down.

4. I am not going to be including homework in their final grade.

5. Students keep a binder with all their assessments in it — so students can have them to study from, and I can ask them to see them if I need to.

Here are where I still have to make decisions:

1. Do I want my gradebook to have skills listed, or topics listed? This is a big one! David Cox says this is a false dichotomy, and I can buy that — because skills and topics are really part of the same tangled net. Or two sides of the same coin. Or some other cliched metaphor. But I guess I still think in these different terms. A list of skills, and a list of topics, seems very different to me. Skills tend to be more specific, while topics tend to be more “umbrella”-y. I am leaning towards skills, because that’s where I’m comfortable.

2. Do I want a bunch of short assessments given frequently, or regular (longer) assessments? I think I’m going to go with the shorter assessments, even though it is going to be harder for me to do because I usually have a plethora of students (read: more than 50%) with extended time. I have to figure out a way to not spend too much class time on these assessments.

3. When I give assessments, I might have a few problems testing various cases of something. For example, I might put four problems asking for the limit of rational functions at infinity. Or eight derivative problems asking to apply various skills (e.g. product, quotient, sum, difference). How do I combine these multiple problems into one score? I’m leaning towards a holistic approach, using the rubric, and a lot of feedback.

4. Do I require students to demonstrate/explain to me what they have done to fix gaps in their understanding, in order to be able to reassess? Would setting up the expectation that they need to have done something before they reassess, and then having a place on the reassessment for them to write what they’ve done to fix gaps in their knowledge, be enough?

5. A student’s grade on a topic/skill will either be the average of the last two scores they earned, or the average of the top two of the last three attempts. I’m leaning towards average of the last two scores they earned.

6. Do I allow myself to throw “old” skills on assessments? Like, if students are taking an assessment on derivatives, and I throw on a limit question, is that kosher? This rubs me the wrong way. When I did this in Algebra II in previous years, I told my kids I when I would be including older skills, and I would give them a general idea of what the problem would be on (e.g. absolute value equations and inequalities).  Does that seem like a fair compromise, or is that spoon-feeding too much? I am leaning towards including older material, but with a general warning. It just rubs me as being fair and clear. And I do want students to know that retention is important.

7. Should some skills/topics be worth more than others? I’m thinking of making almost all skills/topics worth 5 points, but I think I might highlight a few and make them worth 10 points. Specifically, I’m considering something like: “Apply the sum, difference, product, and quotient rules for derivatives.” Alternatively, I can break it into two 5 point skills, making one “Apply the sum, difference, product, and quotient rules for derivatives of basic functions” and “Apply the sum, difference, product, and quotient rules for derivatives of more complex functions.”

8. Even though I am not including homework in a grade, I do want students to keep their homework organized someplace, so we can refer to it together. I want it to be powerful — when a student doesn’t do well on a skill, and then we can look it up. If they haven’t done the problems, it will be clear what they need to do to improve. If they have, we can use that as a starting point for a discussion of why they didn’t do so well. So how do I get them to keep their homework, and keep it organized?

So there is where I am. Providing any and all advice and thoughts in the comments would be SUPER welcome!

Always,
Sam