I believe that standards-based grading, at its fundamental level, is only changing your gradebook so you grade individual standards. However, this change forces you to face realities about a traditional classroom that you can’t ignore and that you are forced to react to.

If this piece were only about the implementation of standards-based grading, it’d be indispensable. If you’re thinking about making a constructive change to how you grade and treat your students, you should read the Schneider’s how-to guide.

But it’s also about changes Schneider made from year one to year two in that implementation, which makes it rarer and more valuable among all the SBG literature you can find.

But he also diagnoses how this one change to assessment then rolls along and affects every other aspect of his classroom. Curriculum, homework, relationships, the definition of math itself – nothing is spared. Assessment is only the first domino.

It’s the best examination of the classroom as a thriving, codependent ecosystem I’ve read in a long while.

Another question I thought was typical showed two spinners that would give you random numbers from 1 to four. It wanted to know the probability that the sum of the two would be a prime number. I drew a complete blank, until I realized I could easily write out all 16 combinations and just circle the ones that resulted in a prime number. That more clearly took mathematical reasoning, problem solving and content knowledge.

I like the question, and I like the direction it should push math curriculum. But I’m also aware that if even if kids have been taught probability, if they haven’t been taught it in a way that encourages flexible and resourceful problem solving — rather than pulling numbers out of stereotypical word problems and following procedures — they will be completely screwed.

I’m glad parents, policymakers, and stakeholders are taking these exams (or shortened versions of them) and reflecting on their results. But again we should be careful not to write expansive prescriptions for what we teach kids based on the test results of grownups. The proposition, “A middle-aged bureaucrat hasn’t used algebraic expressions in three decades and turned out fine therefore we shouldn’t teach algebraic expressions to fourteen year-olds” has yet to be nailed down for me.

Five swimmers compete in the 50-meter race. The finish time for each swimmer is shown in the video. Explain how the results of the race would change if the race used a clock that rounded to the nearest tenth.

You should take a tour through the Smarter, Balanced Assessment Consortium’s released items, make an opinion about them, and share it here. California is a member state of SBAC, one of two consortia charged with assessing the Common Core State Standards, so I’m comparing these against our current assessments. Without getting into how these assessments should be used (eg. for merit pay, teacher evaluation, etc.) they compare extremely favorably to California’s current assessment portfolio. If assessment drives instruction, these assessments should drive California’s math instruction in a positive direction.

The assessment item above uses an animation to drive down its word count and language demand. It’s followed by an expansive text field where students are asked to explain their reasoning. That stands up very well next to California’s comparable grade five assessment [pdf]:

• Elsewhere, we find number sense prized alongside calculation (here also) which is a step in a very positive direction. (ie. Our students should know that $14.37 split between three people is between $4 and $5 but it’s a waste of our time to teach that division longhand.)
• I’ve been assuming the assessment consortia would run roughshod over the CCSS modeling practice but on the very limited evidence of the sample items, we’re in good shape.
• The assessments do a lot of interesting and useful things with technology. (Reducing word count, at the very least.) I only found one instance where the technology seemed to get in the way of a student’s expression of her mathematical understanding.

I can’t really make an apples-to-apples comparison between these items and California’s current assessments because California currently has nothing like this. No constructed responses. No free responses. No explanation. It’s like comparing apples to an apple-flavored Home Run pie.

Featured Comment:

Candice Frontiera:

Next thing to explore: Technology Enhanced Item Supporting Materials [zip]. [The “Movie Files” folder is extremely interesting. –dm]

1. The student knows that first attempts are rarely perfect, and often require serious revising.
2. The student wants expert feedback on work that is established and based on research and the literature.
3. The student knows that his learning is not tied to class time or any other arbitrary unit of time or space.

Assessment is too complicated for any of us to do any more than say, “We’re trying to optimize for a certain set of values,” and then make those values explicit. Standards-based grading involves some compromise, but I don’t know of another assessment strategy that optimizes the values that Shawn’s made so explicit here.

Let’s say he wants to assess the impulse-momentum theorem, which is the theorem that explains why boxers roll with punches rather than against them. ie. If you double the duration of the impact, you halve its force. (Cut me some slack here, science-buds. Everybody knows I have no idea what I’m talking about.)

He gave me permission to share with you three versions of the same assessment of a student’s understanding of the impulse-momentum theorem. Let me invite you to assess the assessments in the comments. List some advantages and disadvantages. Ask yourself, “What is each option really assessing?” Greg will be along shortly to offer his own commentary and to assess your assessment of the assessments.

Option 1

An 80 kg stuntman jumps off of a platform high in the air and lands on an airbag. The stuntman hits the airbag with an initial velocity of 45 m/s downward. 0.1 s elapses between the moment the stuntman first touches the airbag and the moment the airbag completely deflates and he comes to rest. Assume that the maximum force that the stuntman can experience and survive is 39200 N. Does the stuntman survive the fall?

Option 2

A stuntman jumps off of the top of a crane extended high up in the air. Below him is an airbag–a large inflatable cushion that has a thickness of 3 meters. When the stuntman comes into contact with the airbag, the impact deflates the airbag over a period of time, compressing the airbag from 3 meters thick to 0 meters thick while slowing him down to a stop. Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive.

Option 3

Explain, making reference to the impulse momentum theorem, why the stuntman is able to survive the jump.

In addition to the material I facilitated on instructional design, the staff at Colchester High School wanted to work on their implementation of standards-based grading. Happily, they had already agreed on the fundamentals:

1. We should assess students on what they know now, as opposed to what they knew when we first assessed them.
2. Assessment should be atomized to the point that it empowers teachers and students in their remediation.

This left me all the creative, interesting parts. We talked about reporting methods for keeping students apprised of their progress, both individually and as a class. We talked about the effect of SBG on retention. Then we picked a concept and had pairs come up with a score of 1, 2, and 3.

We debated productively about marginal scores – when a 2 turns into a 3, specifically – and concluded that, in a system this forgiving, we’d rather underestimate a student (who could return to improve her score whenever, wherever) than overestimate her.

We discussed, afterwards, how to construct valid, manageable assessments. I gave them four test questions, each of which, in its own way, invalidated what it claimed to measure or was unmanageable at scale. I’ll leave them here. Feel free to kick them around in the comments.

Alex:

The trouble with the two-step equation problem is that it’s also an intimidating decimal arithmetic question. If a student fails it, you don’t know which skill needs work.

Erick:

The issue with the Law of Sines / Cosines problem is that you do not have to use the Law of Sines / Cosines to solve it. A student can get those right WITHOUT using the Law of Sines / Cosines, especially the 30-60-90.

Also, the concept is too broad. If a student has a 2/4 on “Law of Sines / Cosines,” how do you know which one to remediate?

“Quadrilaterals” is also too broad a concept. If a student has a 3/4 on “Quadrilaterals,” do you know what the student knows about quadrilaterals? Which ones she understands and doesn’t?

We decided “Linear Pairs of Angles” is too small a concept. If every concept were this granular, we’d have several hundred concepts to manage by semester’s end.

Who is better at Doodle Jump? Mike or Dan? Why?

The first semester ended, not with a bang, but with two days of canceled class… because you can’t be too careful with those Santa Cruz tornadoes. and two days of hasty final exams. My remedial Algebra class spent a lot of time this semester on what California calls computational fluency and what I would rather call the awesome descriptive power of numbers.

Which has meant, thus far, everything from times tables to proportions to infographics all leading to the motivation for the question above: when your friend is being kind of insufferable about how good he is at Doodle Jump, you can use numbers to shut him up!

It is a feature not a bug, in my opinion, that Mike and Dan can draw their own self-serving conclusions from the same set of numbers.

The concept checklist, in theory, is where students track their progress towards mastery. They write down concept names in rows as we test them and then record their scores (on a four-point scale) along that row, one after the other, each time they retake a concept quiz. I log only their highest scores in the gradebook and whenever they record two perfect scores on a concept, they never have to take that concept again.

The concept checklist is a mess. I run through the same script every year, illustrating the same process with better and more precise visuals every year to no avail. The process confuses students. The process puts students farther from meaningful self-assessment not closer. I saw another checklist crumpled in the trash last week and figured it out.

Their highest score matters much more to me than the specific ordering of low scores preceding it. So forget the earlier low scores. Students add length to the bar as they improve on earlier scores. This checklist design is consistent with our class ethic that “what you know now matters to us more than what you used to know,” whereas the other design maintains a permanent record of “what you used to know.”

So here’s an updated attachment.

BTW: Reader Jacob Morrill does me one (or two or three) better with his adaptation, which is superbly designed:

I have underrated the assessment question, “what’s wrong here?” I need to do more of that. It isn’t that tricky, though it is tricky to deliver that assessment visually, as Bill has done here. It’s trickier still to rip that visual from a kid’s show, packaging the whole assessment in the sort of scientific put-down of children’s entertainment that appeals directly to the inner misanthrope I keep loosely tethered on a fraying leash.

Comments are closed here. Tell Bill what’s wrong over there.

Mr. Meyer, where does this go in PowerSchool? Because I check and my grade doesn’t change.

Christy, next to her, jumping in:

It doesn’t. I checked. But I’m sure he’d take away points if we didn’t do it.

Which, um, isn’t exactly true.

Perhaps I’ll mention some day before the end of the year that none of the classwork they’ve done all year long has had any direct positive or negative effect on their grade, that the only direct effect of their practice has been on the level of waste material in our recycling bin.

That admission might provoke an interesting conversation about the point of the practice. Or it might provoke riots.

More likely is that I’ll chicken out of that conversation until a student distributes printed copies of this blog post to the entire class. That will be fun.

[BTW: It took five weeks, it turns out, for a student to call me out.]