The Spirit of SBG

You want switch to standards-based grading, but, for whatever reason, you cannot. Do not worry. All of the strengths of SBG can be done within a traditional grading system:
  1. Shift from tracking by chapter to tracking by concept.
  2. Allow opportunities for students to show growth.
  3. Don’t grade homework and practice.
  4. Provide timely and effective feedback.
  5. Spiral concepts throughout the curriculum and your assessments.
  6. Give shorter, more frequent quizzes.
  7. Assess what you value.
  8. Provide clear goals and expectations for performance.
  9. Encourage risk taking, failure, iteration, and experimentation.
  10. Do what works best for your students and your situation.

A traditional system done in the spirit of SBG  is much, much better than an SBG system done poorly. (Trust me, I’m speaking from experience!)

Project Work: Group or Individual?

Thanks to Chija Bauer for prompting me to write this post:

For the last several years, I’ve allowed students to work together in groups on their end-of-year projects (a self-designed lab investigation). The rationale was that students would be able to do much more complicated experimental designs with two, three, or four people than with just one. But in the end, I was never satisfied with how it worked out. Often the experiments were simple enough that they could have easily been carried out solo. Or two students actually did the project and then added the name of a non-contributing friend (or two) to the report.

One solution I’ve tried is to require individual reports. This usually ends up with group members submitting identical “individual” reports. Which leads to phone calls, discipline, cries of “I didn’t know we couldn’t do that.” etc., etc. It’s a battle I don’t enjoy fighting, so I don’t find this solution to be successful for me (though your mileage may vary).

This year, each student must do their own unique investigation. All students are now fully immersed in the experimental design process. Sure, some of the experiments require an extra pair of hands, but students have been enthusiastically helping each other out. Jack might be the cameraman for Jill’s terminal velocity experiment. And then Jill might release the cart at the top of the ramp for Jack’s conservation of energy experiment.

Some students have stated that if they work together to collect data, then they should both be able to analyze that data for their projects. My response to this is that they must have unique data sets. Take Jill’s terminal velocity experiment. She’s looking at the effect of mass on terminal velocity by dropping nested coffee filters. Jack is using a camera to film the falling filters so Jill can analyze the videos in LoggerPro. Now Jack is not allowed to use Jill’s data, but Jack could investigate the effect of surface area on terminal velocity or simply repeat Jill’s experiment using jumbo coffee filters or cupcake wrappers instead. And in the end, Jill and Jack can compare conclusions and come up with a mega-conclusion that ties together both experiments.


Sometimes, however, the project work must be done as a group because that’s the only feasible way. I had to do this in my Conceptual Physics class this year for our model defibrillator circuit project and our modified bike light generator project. I did not have enough equipment (or storage!) for each student to have their own circuit kit or bicycle.

Both of these projects came from the Physics That Works curriculum, and I used their solution to this problem of group project vs. individual work. The solution is that the project has two parts: a group component and an individual component. For example, for one project, each group had to modify a bike light generator so that the headlights would light even when the rider wasn’t peddling, yet wouldn’t add more batteries to the landfill. For the group portion of the project, students worked in groups to design and build such a circuit for their group’s bicycle. And everyone in the group received the same grade for that part (25% of the overall project grade).


For the individual portion, each person had to submit an annotated circuit diagram (25% of the project grade) and give a mini-presentation to the class (50% of the project grade). I’ve posted my rubrics below:

Even the way the mini-presentations are handled by the authors of Physics That Works is genius. Students are given several choices for topics for their mini-presentation, but the caveat is that, as group, no two students can do the same mini-presentation and that two of the mini-presentations must come from the two required topics and the others come from the elective topics. For example, for the bike light presentations, these are the options:


Ideally, the mini-presentations would be tied together in one large presentation for the whole group, but each student would only be graded on their contribution.


What are your solutions to the group project vs. individual work dilemma?

Labs, Notebooks, and Reports: For What Purpose?

Today was Senior Seminar: a day-long school event where seniors get breakfast, BBQ lunch, yearbooks, and attend workshops about upcoming college life. So all my seniors were not in class today, which gave me some time to reflect. I was thinking about how best to use lab notebooks and lab reports next year.

You see, this year in college-prep physics, students recorded lab work in spiral-bound graph-paper notebooks. They taped a rubric next to each lab. I collected their notebooks, lugged them around, marked their rubrics, and returned their notebooks. All 51 of them. For each lab. (I could have simply collected one notebook from each lab group, since the other notebooks in the group were usually identical — right down to the conclusion, awkward sentences and all.)


I’ve gone through various other incarnations of notebooks, reports, whiteboards, packets, etc. in my 15 years of teaching. My handwritten reflection for what to do next year are below. I think it captures the best of all those previous systems while still maintaining a reasonable workload.

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  1. I stamp the lab notebooks during class as evidence that the student was present in lab and participating — brief design, measured data, calculations, and graphs. These are the things that will be identical from noteb0ok to notebook anyway. I won’t be picky about proper format because I’d rather have them spend most of their time taking and analyzing data than worrying about the notebook looking picture-perfect. Also, students who are absent would be required to come during a free period or after school to perform the lab. (I’ve never done that before. It could be overwhelming. But I also think it sends the wrong message to a student that they can just copy the data from a partner.)
  2. Students write a post-lab reflection. After we’ve had our post-lab class discussion to tease out the concepts, idea, models, relationships, etc. from lab, I’d ask students to summarize what they’ve learned, what questions they had,  and what they found to be (in)effective about the lab. I wouldn’t grade this either, but I think taking the time for solo sense making and summarizing is important. This could be done on an exit ticket, in the notebook, or online.
  3. Students write a formal lab report. I think that effective communication of a scientific experiment is important. My failure this year was trying to do it simultaneously in the notebook. How to make a table and graph and put it into a report is an important skill. How to best represent the data is an important skill. How to make a scientific argument based on evidence is an important skill. But reading 50 lab reports about 6 times per quarter is awful. So I’m taking a cue from my freshman writing professor. He set up a rotating schedule in which just a few students submitted an essay each week, based upon one of the books we had read. I think doing it this way would lead to fewer reports to look at each week, thereby allowing me to give more effective feedback. Plus, I’d have fewer copied reports since I’d have just one student from each group-turn in the report. So if there are 3 students in each lab group (A, B, and C) then all the As would turn in a report one week, all the Bs the following week, etc. Hopefully the schedule will allow for 2 write ups per student each quarter in order to show growth.

What’s your system for lab work?

An “I-hit-publish-too-early” update: Of course, none of this directly addresses what I feel is the most important issue with lab work: how to assess the scientific inquiry process. I’m reminded of AAPT’s Goals of the Introductory Physics Laboratory and Eugenia Etkina’s Scientific Abilities.

“Is it getting hot in here?”

The other day in class, we were having a discussion about stars and color and temperature. But since most of the kids were looking silently at their laps, I knew their interest was fading fast. (Which is surprising, since they voted by a landslide to study astronomy in the 4th quarter.)

So to get the kids’ attention, I got up on the teacher desk at the front of the room. Then I stood on my hands and farted fire. No, I didn’t merely light one on fire. I literally farted fire. (Lucky for me, I keep a change of clothes at school — just in case.)

And the biggest reaction I got was from a student, who, without even  looking up from his lap said, “Is it getting hot in here?”

And then another said, “What’s with the sudden breeze? Can someone close the window?”


It seems that, at this time of year, any attempt at whole-class discussion is a recipe for failure. Any advice?

Learning Analytics

MOM: Billy! Billy, I got an email today from your computer-based math class. It’s your Learning Analytics Progress Report. Please come inside, dear.

BILLY: Uh oh.

MOM: Let’s see. It says here: you pick choice C too often; you spend more time working on even numbered problems than odd ones; you watched 3 videos all the way through, and rewound portions of 5 other videos. And last, it says your answer patterns most closely match those of women over age 25 who live in Canada and prefer One Direction over Justin Beiber.

BILLY: Does it say why I’m struggling with algebra?

MOM: (shrugs)

Also: The Soaring Promise of Big Data in Math Education by Dan Meyer

Video Analysis of a Bouncing Ball


Nothing earth-shattering here. I just wanted to share the activity we worked on today, which was an introduction to quantitative energy conservation by doing a video analysis of a bouncing ball. (Up until now, we were only doing qualitative energy pie charts.) Here are the handouts and the video:

The graphs from the analysis are just beautiful:

HeightTime VelocityTIme EnergyTime

Lots to talk about in those graphs!

Feel free to edit and reuse the handouts as you see fit. They’re not perfect, but I figure it’s better to share them than having them collect dust on my flash drive.

PS: I’ll sheepishly admit that I don’t do the whole suite of paradigm labs in the Modeling unit to mathematically derive the energy equations from experiments. But we do some simple qualitative demos/experiments to discover what variables would be in those energy equations. We start by talking about how the further a rubber band is stretched, the more energy it stores. Then we launch carts into a rubber band “bumper” (i.e., big rubber bands from Staples and two C-clamps) to qualitatively see the energy stored.

In doing so, we see that the cart’s kinetic energy depends on its speed and its mass. (Or is it weight? What would happen if we repeated the experiment on the moon?)

For gravitational energy, we can repeat the experiment, but have carts rolling down an incline. Or use the rubber band to launch the cart up the incline. I’ve also dropped balls into sand and looked at the depth to which they get buried. Either way, we see that gravitational energy depends on height and weight. (Or is it simply mass? What would happen on the moon?)

For elastic energy, we already know it depends on the distance the rubber band is stretched. Then, we can swap out the rubber band in the bumper with a stiffer/looser one to see the effects of the spring constant on energy stored.

Then, after we predict what the energy equations might look like, I just give them the actual energy equations, or have them look them up. (Gasp! See Schwartz’s A Time for Telling, aka Preparation for Future Learning.)

So, modelers, what am I missing by not doing the full-blown energy paradigm labs? How do you introduce the quantitative energy equations?

Algebra, Fractions, and PLNs

Which is more difficult to teach/learn: Algebra or Fractions?

Last week, I was a guest at Discovery Education’s “Beyond the Textbook” forum. During one of the breakout sessions, my group (Christopher Danielson, Angelia Maiers, and Chris Harbeck) got to discussing about how hard it is to write math curriculum and that no digital textbook would be worth its weight in bytes if it didn’t acknowledge that. Christopher Danielson wrote a great blog post which both summarizes and expands upon that discussion.

To illustrate that most non-math teachers don’t quite get the nuances involved in science and math instruction, I asked Angela which concept she thought was more difficult: algebra or fractions. She answered algebra without hesitation. And I said I felt fractions were more difficult. I said that my 8-year old son has no problem with algebra: 5 + [_] = 7. What goes in the box?

But what does 3/4 mean? Is it 3 objects out of 4 objects? Is it one object split into 4 pieces, but we only care about 3 of those pieces? Is a ratio of 3 things to 4 different things? Or is it division and we are taking 3 objects and splitting them evenly to 4 groups? Is is 75%? Or is it 0.75?

Angela was blown away by this discussion and wondered how other people (math folks vs. non-math folks) would respond. We decided to conduct a little experiment. We would both ask our PLNs the same question and compare responses. My prediction was that since my PLN tends to have a math and science focus, the majority of my followers would say fractions are more difficult. And I predicted that Angela’s PLN, which is more broad than mine, would say algebra is more difficult.

Here are the results:


I was correct in my predictions, but I was surprised at how my PLN was much closer to a 50/50 split rather than a 2:1 split like Angela’s. Here’s the raw data —  it’s interesting to comb through the responses to read why they chose algebra or fractions:

Many people said fractions were easier because they are concrete — you just slice up some pie or look at a Hershey bar.

I’ve singled out two thoughtful replies on Angela’s Facebook page below. Jodi’s is great because she polled her second grade class:


And Susan’s is great because she sees the many possible meanings of a fraction:


What do you think? And do I think fractions are more difficult because I am misunderstanding something about the nature of algebra?