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.
Continuous Everywhere but Differentiable Nowhere 
Sam,
This is great. Are you doing this with both calculus and alg II? If you’re doing this with Alg II, and not grading HW, will you still do binder checks? I’m doing SBG with my freshman, but I still want to give them some feedback on organization, and was thinking of doing binder checks similar to what you described last year, with no grades. Not sure if this would be effective or not.
Hi John,
I’m only doing this for Calculus this year, for various reasons not worth listing them all. The big two are (1) the other teacher teaching Algebra II is new to our school and she has a really crazy full plate for someone who is new, so I didn’t want to overwhelm her, and (2) I wanted a “safe” place to try it out and non-AP Calculus is perfect because we don’t have to get to everything if it throws off the pacing.
If it works well, I would have to have a serious talk with my department at large if I wanted to do it for Algebra II.
It’s going to be weird, because in Algebra II I am going to be doing the same thing as last year — binder checks, less frequent assessments, no retests. It’s going to be cognitive dissonance.
I think if you required binders and gave them feedback, even if not for a grade, you’ve at least introduced them with an organizational system they might be able to use in future years. Like, you’re saying: lemme show you one way to do things. For freshman, I think that’s especially important. Sometimes they’re a mess, because they just haven’t been taught how not to be.
Sam
your entire assessment for the class doesn’t ALL have to be SBG. i think i remember dan meyer saying that he still gives regular unit/term tests. i’m making “skill quizzes” that are sbg, and i’m going to give them chapter/unit tests that are given by the rest of the department. i feel like that’s a good balance of grading based on the standards and grading higher-level thinking.
That I know. I am definitely giving a serious midterm and a serious final exam. Seniors don’t get final exams, so my kids are going to be VERY upset.
As for the higher level thinking, I am going to probably do 2-3 days worth of problem solving each quarter (similar to https://samjshah.com/2009/11/23/genesis/), where I have them do writeups and grade them on specific skills.
I am hoping after doing this for a year and getting a sense of the routine and what it’s all about, to find ways to tweak it to better reflect the synthesis, higher level thinking, etc., pieces. I guess I realized I don’t teach too much of that without SBG anyway.
Sam
I love the reassessment email! I’m just starting to work on something like that.
This year I’m trying a tweaked version of SBG. Original grades stick in the gradebook, but final reassessment grades go in as an additional quiz at the end of the unit. I’m hoping it will get kids to study hard the first time, but also keep working at the skills they don’t get. And this seems to record information better than averaging old and new quiz grades.
So the message is, you are expected to get it right the first time through, but you are also expected to keep learning if you don’t.
Thank you for sharing your process and thinking. I’m just starting to develop/figure out how to move toward more SBG and this will help me get there.
Sam,
You clearly articulated the process for the students and I like how you’ve included both the pros and the cons on their end of the system. I finally settled on a similar strategy for incorporating problem solving into the course, but I may steal the write-up idea.
Is your calc class taken only by seniors? At my school, grades play a big role in future placement, so the students and parents are very competitive. It is a challenge to redirect the focus to learning. I’d love to hear your thoughts on that.
Pam
My course is only taken by seniors, so future placement isn’t a problem.
If I were doing this for Algebra II, my initial reaction is that students would automatically be placed in Precalculus. Students who want to jump to the accelerated track — I’d ask those who were interested to come to a special meeting near the start of the year. Then I’d clearly lay out all they’d have to show me they have the ability to think abstractly, be on the ball with assignments, synthesize material, articulate mathematics, etc. I’d probably have a set of concrete things they could do to show me their ability to work at this higher level. If they can complete that checklist (which would include academic and behavioral things), and get super high grades in the class, I’d have evidence they could succeed in a faster paced, more abstract, course.
That’s my initial thought. Like the one I had just from reading your comment. So it’s very unrefined.
But you know my mantra: you have to be clear, consistent, and fair. This seems like, if done well, it could do all of those things. And allow kids who want to move to do more than just “ask” — they’d have to be motivated enough to show you.
Sam –
Thank you for articulating this so clearly! I love your packet and your materials and plan to adapt them. You rock.
You’re super welcome. You know the teacher mantra: beg, borrow, and steal!
Sam, this is great. The handout is so completely and utterly you, and it makes me happy that you have no problem showing yourself to your kids from Day 1. I just hope that you wear an engineer’s hat while going over this in class.
On a more substantive note, I’m kind of glad that a lot of folks are doing the details of SBG in their own ways. My system will use the top two grades to determine a skill score— mainly because I want kids to think that they can only gain by doing the assessments. But as long as each has his/her justification, then I say go for it, connect four.
What do you mean “engineer’s hat”?
I’m guessing a train engineer’s striped hat, so you can shout “All Aboard the Knowledge Express!”
I’m having a hard time with the idea of SBG. The group of people who read this blog seem very thoughtful, so I’m hoping you can address my concerns. Here’s the crux of the matter: I strongly believe that content skills are NOT the main goal of high school math education. Sure I want my students to learn some math, but what I really want is for them to become good problem-solvers & good learners in general. (I currently teach geometry and Algebra II. Other than the handful of students who become mathematicians & math teachers, none of my kids are ever going to have to use most of the specific content I teach. Those kids will learn the content again when it becomes necessary. (How many of us relearned a topic in order to teach it? Certainly me.) By the way, I might feel differently about the central importance of content if I taught elementary school; I really, really want my students to be able to add 2 numbers in their everyday life.)
SBG seems to focus on whether students have mastered particular skills. Where does problem-solving come into this? I know Sam mentioned this concern, but I don’t think problem-solving is a topic in and of itself; rather, it’s how I approach the math content on a daily basis – both in class & on assessments. (For example, one of the problems on the test I gave today had the hint: “you really do know how to solve this problem.” Answering the question involved solving a system of equations & factoring a quadratic equation, but nothing about the question itself made that obvious. In asking this question, am I assessing students’ skill at solving systems, their skill at factoring quadratic equations, or their ability to look at a problem and figure out how it relates to the mathematics we’ve been studying? I’d say all three, but I don’t know how that 3rd piece fits in with standards-based grading.)
When it comes to allowing re-assessments, I worry that we de-emphasis the need to meet deadlines, an incredibly important life skill. I know some people have talked about this, but I think the conversation changes a bit if your main goals are problem-solving & life/learner skills, rather than content. It’s also worth noting that I have a similar “work on it until you get it right” approach when it comes to homework. I check in homework each day, but I only correct & grade it for correctness on the day of the unit test; in other words, I expect students to go back & revise their homework until everything is right. There is a learning process in my class, but the test is the “deadline” at which point I expect full understanding.
Hopefully my underlying question is clear amidst this rather long comment; I really am curious what people have to say. I should also probably point out that I work at an extremely high achieving school. My students would do well on standardized tests even if I barely taught them any content this year. I’m wondering how relevant my situation is to my beliefs about what matters…
I think you bring up some very good points. My biggest concern about SBG is the lack of problem solving skills being integrated in the system — at least the way I am doing it. I will have some problem solving days each quarter, but I’m going to really focus on the way students attack and write these problems up. But for the main part, I’m really focused on discrete skills and written explanations — not innovation.
Those decisions are a product of many considerations. Some majors ones of these include (and this is me being frank):
1. I’m a new-ish teacher, I’ve always taught this way, and I have my doubts about being able to teach problem solving on an everyday basis. I don’t just don’t know how I could do it, because I haven’t really seen models more than Exeter (and Jim Wysocki, who modified Exeter’s curriculum). Basically, the idea of doing this scares the bejesus out of me. And I don’t have full confidence that I can get my kids to know the skills by teaching mainly through problem solving.
2. No one in my department focuses on problem solving in their courses. Although we might all agree with your sentiment (“I strongly believe that content skills are NOT the main goal of high school math education. Sure I want my students to learn some math, but what I really want is for them to become good problem-solvers & good learners in general.”), I don’t think that my department agrees with this in practice. We’ve made this huge shift in the past two years to codifying the curriculum, and it is codified by individual skills. (This is a school-wide initiative.)
3. Instead of problem solving, I have decided to focus on concepts and the ideas underlying them (so many skills talk about explaining concepts, or why sin(1/x) doesn’t have a two sided limit at 0). Sometimes we have to make decisions about what to value, and this is what I’ve decided to value.
I’m totally at peace with my decision this year. But I hope that in the future I can find ways to teach more about problem solving. But if I were you, I’d ask Shawn Cornally (at Think Thank Thunk) his thoughts about this — because I suspect he teaches a lot of problem solving through the way he gets kids to investigate.
I do have a response for this thought: “I worry that we de-emphasis the need to meet deadlines.” I have thought about this a lot, and here’s where I’m at. My kids are seniors. At my school, by this point, they know the stress and consequences of a high stakes deadline-based environment. By their senior year, I’m confident they’ve been trained to know the importance of deadlines. With that said…
I see SBG as teaching them something else. Especially with not grading homework. It’s going to SHOW them concretely what happens when they focus, when they do their work, when they put in the effort on the front end… versus the consequences of what happens when they don’t.
It’s teaching them to break things down into what they know and what they don’t know, think about the process of continual improvement, and think a little meta cognitively about their own learning process.
Those are my immediate uncensored thoughts. They’re probably a bit unclear. (I’m so tired now!) And they probably don’t address your concerns satisfactorily. I pretty much have come to the conclusion, from reading about a zillion blogs, that each school context and culture is different. Some things resonate with some and some things don’t resonate with others.
I REALLY appreciate your comment, and I hope others take the time to think about the good points you raised, and comment.
Sam
Fascinating thread this is.
I am not teaching at the moment and SBG is not at all big in Australia BUT I am compelled to comment here….please indulge me.
Rightly or wrongly, teachers are obliged to come up with a grade. Ideally, the grade is justifiable as well as useful. From what I can gather, SBG is very logical in doing this. Particularly in maths, it makes sense to use categories (standards) due to the multiple strands.
That said, I also think problem solving is very important as this lesson I had, inspired by @dcox21 shows. I have had students good at problem-solving but let down by below-average numeracy and reasoning skills.
The problem with problem-solving is that it is very hard to objectively grade. In real life, there is often no right or wrong way to solve – just a way, which in most contexts, need to be logical and justifiable. Rounding up the circle, the latter are skills easily mapped to specific content, eg SBG.
Maybe another way of looking at this question is the good old process vs product debate. Process is important and there are ways to assess it (Problem or project based learing resources abound). Usually though, process skills are ‘judged’ or graded via the final outcome – mirrors real-life most of the time. Still, if you really want to grade problem-solving, you could. Personally, I think it’s more a skill to encourage rather than graded…sort of like homework…but that’s another topic again.
I hope this helps somewhat.
On the de-emphasis of deadlines:
1) While meeting deadlines is an important life skill, it is sometimes (often) not as important. Many deadlines are flexible, and faced with a choice of a crappy product now or a much better product a day late, many people (even bosses) will choose the latter. On the other hand, some deadlines are hard and fast, and even for flexible ones there is a limit to their flexibility: accepting a better product a day late will not usually translate into accepting a better product a year late, after you’ve been fired for not getting done what you needed to and someone else’s poor quality work has made it through to the finish line instead. In fact, determining what type of deadline one has is its own important life skill!
2) Even SBG has some firm deadlines: end-of-quarter reporting of grades to the district! And many SBG teachers have set up some system to guide student responsibility so students are not leaving everything to the last minute: whether it be only re-assessing one (or two) skills per day, or not seeking help with a skill the same day you assess, or requiring demonstration of work/practice done leading up to reassessment.
3) While meeting deadlines is a key life skill, equally (or even more) important are independent self-directed learning, setting your own goals on your way to a deadline, and keeping trying until you have reached a goal. A math professor I studied with in college would always say that failure is the only way we truly learn anything. And this skill of persistence in the face of failure, learning from your mistakes, is perhaps the most important skill I wish to teach my students. Even though it’s not on my SBG skills list :-), the very nature of SBG and re-assessment seem to promote this continual striving to get better instead of being satisfied with mediocrity.
4) On a personal note [and this is my first foray into SBG — so I do not speak from experience and will likely be reprimanded by the SBG police ;^)], I’m grading this year as 1/2 SBG skills quizzes, 1/2 projects. In the projects, students will demonstrate applications of key math skills, some degree of critical thinking and problem-solving, understanding of connections within math and between math and other subjects, and their ability to meet deadlines (some narrow flexibility provided via lateness penalties)!
Hi Katherine,
I agree w/ you about the content/problem solving aspect. I’m a science teacher and that’s pretty much all we ever talk about and we get boring about it. As a side note, that’s mostly BS. Most of us drive content like nobody’s business and give lip service to “inquiry.” I’ve been in quite a few science class (my own not excluded) and content is still king. I’m not saying it’s right, I’m just saying that the true “I use my content to teach XYZ important life skill” teacher is rarer than we like to admit to ourselves.
So here are my responses. 1. about problem solving 2. about deadlines
1. There are separate issues here. One is can you teach problem solving skills separate from content? Two is how do we assess the skills of problem solving? I think the answer to the first one is no, at least not easily. Transfer sucks. Problem solving skills should be embedded, but explicit, in your content.
The answer to number two is trickier. What are you looking for? Are you looking for something like this: http://coxmath.blogspot.com/2010/06/problem-solving-rubric.html or more general habits like this: http://mathteacherorstudent.blogspot.com/2010/09/habits-of-mind.html
The first one is easy. You include that in your standard. So in order to master whatever skill, they also need to represent it in four ways (or whatever you want) The second is harder. I don’t have an answer for that one. You could assess those as a separate standard but I don’t like doing that. I try to make those habits explicit and visible but I’m not sure that it needs to go beyond feedback and practice.
Personally I advocate a slightly different approach to SBG based on topics, more here: http://alwaysformative.blogspot.com/2010/07/playing-whole-game.html It might be more what you’re looking for.
Last point, “am I assessing students’ skill at solving systems, their skill at factoring quadratic equations, or their ability to look at a problem and figure out how it relates to the mathematics we’ve been studying?”
I’m assuming a standard 87% score doesn’t let kids know whether they need to work at factoring, solving systems, or just identifying the context. You could take that one problem and give feedback on all three parts. That’s the simplest difference between trad and sb grading.
As for the deadlines thing. Nyates314 is spot-on.
Katherine:
Thankfully, we’re all secretly doing the same thing. We are all trying to emphasize thinking above memorization. The intricacies of SBG are hard to layout in a blog post, but when the system is enacted with real students, the benefits of student self-assessing and learning how best they individually study are staggering.
The thinking skills question is a good one, but in the end no assessment scheme will create or ruin that for you. You’ll have to admit, that while skills are not the most important, as they really won’t be used that much later in life, that they are in fact vessels for carrying these larger abstract ideas. That’s why SBG is so important. A student must come to grips with their misunderstanding of some specific content on their own, because that’s the only way to convey the thinking skills we all covet for our students.
Finally, it’s not about the assessment. It’s about what you do to get the kids the information in the first place. Using SBG doesn’t stop you from doing an investigation or creating a rich project. It does, however, focus the outcomes of that project for the students in a meaningful way.
The final point that has come to light for in my fairly extensive implementation of SBG is that when we think we are teaching thinking skills or responsibility, we are often just assigning grades to things that students are forced to do, and there is no real learning going on (i.e.: Notebook organization). Sadly, the final currency of the school system right now is grading. I suppose SBG just uses that system to its advantage by saying, “hey, want a better grade? You’re going to have actually figure out how to know and retain something.” You’re right that the content doesn’t really matter, it’s just a delivery system.
Hope that helps. If you’d like to read more about SBG and some fairly common questions/objections to it, feel free to check out this article (sorry for the self promotion, Sam.)
http://101studiostreet.com/wordpress/?p=673
Another thought is that there’s nothing stopping you from including “Problem Solving” as an entry in a SBG grading system. You could ask challenging questions that require making connections between real-world problems and content that’s already been mastered, and separate assessing the problem-solving analysis from the lower-level skills they use.
I doubt that’s a perfect description, but maybe it inspires some ideas.
I dunno, maybe it could even be a separate data point that is calculated by looking at how students did on problem solving assessments / questions over a number of different quizzes, etc.
I think my ideal would be a world in which assessments could be tagged in my gradebook such that one assessment might go towards “Graphing Trig Functions” and “Problem Solving”, while another is “Logarithms” and “Communicating mathematical ideas” or something like that.
Thanks for all the thoughtful answers to my questions. For anyone who’s interested in thinking about how to integrate problem solving into their everyday classes, read Intellectual Character by Ron Ritchart. It’s all about “habits of mind” and emphasizing process & thinking skills in the classroom.
I don’t see problem-solving as it’s own topic, or as something that should (or can?) be assessed on its own. In terms of content skills, you can break things down into discrete concepts, but I think that misses some of the point: in a sense, it’s telling kids to not see the forest for the trees. I just read Jason Buell’s post about using SBG with topics, and it does sound a lot like how I feel. (I’d have to read more, and think more, about how it would actually look in my classroom, but the reasoning definitely resonates with me.) I think I believe that students truly understand a concept only when they can not only deal with skills individually, but when they can also put those skills together & think about the details within a more holistic situation.
I’m also wondering what implications SBG has for our “non-assessment” time within the classroom. Has anyone ever thought about how SBG-like their daily, formative assessment is? I haven’t. I wonder if thinking in terms of SBG might guide how I respond to students in class, even if I don’t want to use SBG in a formal grading system. Because I do agree with the basic premise that specific feedback is (in general) better, even if I also feel that focusing exclusively on specific feedback causes us to lose something important.