I use a standards-based assessment system in my classroom. Assessments are marked based on evidence of conceptual understanding using a pretty extensive rubric. Most of my students are new to this idea, and it’s a struggle for them to understand.

The students who struggle the most are often the ones who have had some success in traditional math classes, where grades are based more on the ability to perform algorithms, procedures, and calculations fluently. Assessing for understanding requires that they not only are able to perform procedures correctly (which is of course still important), but also show evidence that they understand the underlying concepts. This is incredibly frustrating for students who are able to learn procedures without understanding why they work. 
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It’s also tricky for me, as a teacher, to illustrate why this is so important. On a recent precalculus assessment over vectors, some students produced interesting responses that, sometimes within the same student’s test, made me think a great deal about this difference, and provided me with some great fodder for explaining it.

​Context:
The learning target for this assessment is N-VM.A and B: Represent and model with vector quantities and perform operations on vectors. I knew the students needed some scaffolding for the process of adding vectors. It is complicated, with many opportunities for errors. It’s also a great example of the kind of problem where you can do the calculations absolutely correctly without having any understanding of what you’re doing: just give me some formulas for r and theta, and I’m golden, right? Well, not really, especially when you have to figure out the angle at the end. There might be a bunch of “rules” to teach students about when to subtract from 180, add to 180, ditto for 360, but I don’t use ‘em, or know ‘em: in my opinion, you really have to understand what you're doing to reach valid solutions on these problems. I don't know a better way to show this understanding than visual models.

The point I made repeatedly while working this through with three sections of students was this:

• It would be very difficult to confidently answer the last part (the angle) without a visual model.
• It would be nearly impossible to show evidence of conceptual understanding without a visual model.
• You should use a visual model when answering these questions so that you can be confident your answer makes sense.

So, I had an assessment with three different vector addition problems. One was a “naked numbers” problem (here are two vectors; add them together), one was a classic word problem (two tractors pulling on a tree stump in different directions with different forces), and one was a bit more of a problem (navigating a course for a boat that accounts for the current of the water). I suggested that students focus on one of these and do it well (I only give them 25-30 minutes to complete these assessments).

​These are just a few examples of how interesting assessing responses can be when you look for understanding and reasoning rather than right or wrong. I’d love to hear opinions from anyone who would like to discuss.
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But back to the students. I’m only giving them written feedback on this assessment, no grade (we take two assessments over every topic, and this is just the first). I’m hoping that sharing these responses with the students next week and having them do a little assessment or comparison of their own work will help make the point clear: using the right algorithms, even if you do it well, isn’t enough to prove that you understand the concepts.

How this all translates to grades
I have to give a percentage grade, there’s no way around it at my school. This is sort of the hardest part for me. My last school was an IB school, so I used historical data from IB exams to set up my system there. It’s a much more forgiving system, in terms of percentages, than the classic American system where 60% is the minimum passing grade. I’ve done a lot of blog reading about this, and I think I’ve got something I can work with:

Grading Scale (what I put in the grading system)
0=0%
1=50%
2=70%
3=85%
4=100%

Weighting
10%: Practice work (includes homework, classwork, etc, and is pretty exclusively completion grades)
65%: Summative assessments
20%: Cumulative exams
5%: Awesomeness
Awesomeness, you ask? Yeah, this is something I threw in to try to keep kids on their toes.

• It’s not extra credit - I expect all of my students to show some evidence of awesomeness.
• It’s intentionally vague - I don’t know how they’re going to be awesome, so they will have to come up with what this looks like, and convince me, on their own.
• It’s probably different for everyone - Are you a great artist? Love writing poetry? Like tinkering or building? Spend all of your free time on the computer? OK, do something awesome for math class with that.

This might be a complete failure, but I’m curious to see how it comes out, and I think keeping it at 5% keeps the stakes low.
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So, by the time parents come in for back to school night on Tuesday and hear about this, I’ll have presented it to all of my students as well. I expect some pushback, but I’ve thought about this for a long time now, and I’m feeling confident and ready to support my position clearly. Wish me luck! And, as always, let me know what you think.

Where I'm coming from
I got my teaching license in 2003. None of my coursework for teaching, including my student teaching, had anything to do with standards. 
Then I got a job outside of the traditional school setting, out of the loop as far as current best-practices and educational reform were concerned. I kept this job for 8 years.
In 2012, I got back into classroom teaching by landing a job at brand new international school in China. The leadership of the school was pretty progressive, and decided from the beginning to go with the most current research-based practices.
I still remember the staff meeting where we were introduced to Standards-Based (SB) Grading, Assessment, and Reporting (I'm going to use SBG, SBA, SBR, and try to explain why I differentiate later). Few of the staff (some with much more experience than I) knew about or had much experience with SB anything, and it was kind of a shock to most of us. Oh yeah, BTW, this meeting happened AFTER two or so weeks of instruction, AFTER some of us had already distributed syllabi, grading scales, etc. I had no idea what anyone was talking about - the only grading I knew was percentages and ABCs. I cried in the bathroom that day...
Pretty quickly, watching others struggle with this, I came to the understanding that my lack of experience was an advantage. I didn't have to deal with, or unlearn,  years of assessing any other way, I just had to get my head around doing it this way. I was also the only secondary math teacher in the school, so I had an incredible, and often intimidating, level of freedom in developing my curriculum and classroom practices. So I bought in, did the work, and started learning. 
Needless to say, I learned more through the experience of teaching than I ever had in any class about teaching. I learned more through personal research, struggling with frustrations, searching for my own answers, than I ever have from professional development. After five years with this school, I feel like I have a relatively good grasp on the idea of SB, although I'm still struggling with the practice and implementation.

Where I am now
As far as I can tell, so is everyone else. I ask educators and administrators about their implementations whenever I can, and I read a lot of blogs and articles on the subject. Over the last five years, only one educator I've spoken with said that his school had "completely figured out" SBG; further conversation revealed that what he really meant was that his school had aligned a 1-4 grading scale with a percentage grading scale in a way that the majority of teachers, students, parents, and other stakeholders accepted.
Everyone else tells the truth; it's a journey, a learning process that no one seems to have nailed down completely yet. There are great ideas out there, but there doesn't seem to be anyone (other than that guy) who's willing to say they've got all the answers and they know exactly how it should be implemented.
I like to separate SB, especially when it involves grades, into three areas that help me think about my own practice. These distinctions are mine, from my experience, and may be different from others'. (they may also be wrong! :)

• Assessment (SBA): This is the spirit of the whole thing. You start from a standard, make it into a learning target, and design instructional activities (formative assessments) and summative assessments by which students can show that they've met those targets. Teachers assess the degree with which students have shown proficiency.
• Grading (SBG): This is the method by which teachers assign a category, or grade, to represent a student's level of proficiency. 1-3, 1-4, 1-5 scales are common, rather than letter grades, and each level comes with a descriptor (my last school used Emerging, Approaching, Proficient, Exemplary) and they usually reference a rubric which tries to explain what each level means. SBG also makes little or no use of formative assessments (homework, quizzes, classwork) in calculating the final grade, focusing instead on a student's performance on summative assessments. This is where the big controversy with students, parents, and teachers who are used to traditional grading scales and levels. It also seems like every school is coming up with their own (different) way to address this discomfort.
• Reporting (SBR): This is the report card, the way student progress is communicated to students, parents, other schools, etc. My last school had us report on content domains from the Common Core as well as and overall "grade" and a narrative paragraph (yeah, report cards took a long time).

​Where I'm going
Earlier this summer, I participated in an assessment workshop for AERO which gave me a whole new way to think about the standards, and I really want to write a post about it later. The shift that's rolling around in my head involves using clusters (not specific standards) to come up with targets, and couching the targets in the four claims from the Smarter Balanced Assessment Consortium.

In a few days, I'm heading out to start a new job in Pakistan! I don't know everything about how things work there, but I don't think they're using SBR yet (kind of a relief to me). They use percentage scales and letter grades for reports, but I've been reading a lot on how other teachers are doing SBG within their own classrooms, even if it's not a school-wide practice, and even if they eventually have to show a letter grade. Overall I don't think I can do assessment any other way, so SBA will be a part of what I do no matter where I teach. 

If anyone made it this far, thanks for reading. I hope to keep posting on this journey, reading about what others are doing, and refining my practice.


People who've helped me think about this (not an exhaustive list, INPO):
Follow the links for some great posts on SBG
Michael Matera
Dan Meyer
Dane Ehlert
Jonathan Claydon
Nora Oswald

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