Understanding by Design, Chapter 7

I'm a little behind, both in reading the chapters and in posting my thoughts about them. Part of this may be because I'm not happy with most of my assessments (which are the topic of chapter 7 & 8). Either my students find them too difficult, or they seem too trivial, too memorization-based to me.

The goal is to "convict" students of understanding specific goals or standards, using a "preponderance of evidence" from assessments that probe those goals/standards. Most traditional paper-and-pencil assessments probe simpler knowledge and skills, rather than deeper, structural understanding. Not that a student with real understanding wouldn't do well on them, but it's possible for a student who does well not to have that deep understanding, just by having memorized the surface skills. To probe for understanding, we need to see if kids can apply their understanding to at least marginally new situations. In my classes, this usually results in students complaining (during the test) "You didn't teach us this stuff!" as if they were monkeys trained to jump through a thin blue hoop and completely baffled by being asked to jump through wide red hoop. Getting students past this is a major goal for the upcoming year...

Before I can get there, I need to plan the evidence I'm going to collect. Let me start with the difference between velocity and acceleration (a major stumbling block for many students). What would provide evidence that a student understands the differences?

• Choose correct formula for a situation
• Correctly label a situation (verbal description, video, graph) as constant velocity or changing velocity/acceleration
• Solve traditional problems
• Sketch graphs for constant velocity and changing velocity/acceleration from verbal description, label, or video
• Analyze other rate problems (including the house painting problem)

Wiggins & McTighe say that assessments should be designed around problems, rather than around exercises. (A problem in this usage is like an actual soccer game, while an exercise is shooting drills or dribbling drills.) What problems are related to velocity? Last summer I started working on a problem revolving around an elementary school across a very busy street from a park. I was thinking about asking students to try argue for/against the need for a pedestrian bridge to allow elementary students to safely get to the park for recess/science class. Another possible problem might be train or bus scheduling: if I need to provide bus service along a certain route for a certain number of passengers, how many buses, leaving how often, moving at what average speed, etc. (And why do buses clump up, anyway?) I suppose network traffic and download speeds are an extension of that idea. (Dan Meyer's "Boat in a River" is probably at least as good an intro to velocity as the Modeling Physics two-buggy lab. But that's how to teach, not how to assess, and that's supposed to wait until later in the process.)

There's also the idea that assessment should provide a scrapbook, rather than a snapshot, of what students know. Having students assemble the scrapbook/portfolio also asks them to develop their self-knowledge/meta-cognition so that they can recognize good work when they see it. Teaching that is way harder than getting students to recite Newton's Laws...

Understanding by Design, Chapter 6

Chapter six focuses on "Enduring Understandings." There's a bit about the difference between understandings and factual knowledge. So, "The specific heat of water is 1cal/gK" is factual knowledge while "Coastal areas have milder climates than landlocked areas because of water's high specific heat" is an understanding. Just as with Essential Questions, the essential-ness of the understanding depends in large part on the lessons that make up the unit. If we're not teaching for conceptual change, the best-written understanding becomes a factoid to be forgotten after the exam.

Understandings also don't have to be phrased in a way that will be clear to students. In fact, if an understanding is too clear, it might not be worth focusing a unit on.

The prompt for writing EUs is "Students should understand that" rather than "how" or a fact (even an important one). So here are some initial thoughts on understandings for physics, some of which may not be suitable for a first course taken in 10th grade (15-16yrs old).
Students should understand that:

• we can describe motion with words, pictures, graphs, and equations.
• if we know the initial conditions and the acceleration as a function of time for a classical (macroscopic) system, we can predict its future.
• forces are interactions between objects or between an object and a field.
• many physical quantities have direction as well as magnitude.
• the "natural state" of motion is constant velocity, not constant position.
• velocity is the rate of change of position, while acceleration is the rate of change of velocity.
• gravitational forces, static electrical forces, and light intensity all decrease with the square of the distance from the 'source'.
• momentum gives us a way to describe collisions even when we don't know the forces or the forces change too quickly to be useful.
• objects have energy based on their motion and position, which gives us another way to describe them.
• light is both a particle and a wave: the observed behavior depends on the test done.
• moving electrical charges cause both electrical and magnetic fields.
• energy can be transferred between objects and transformed between types, but some is always lost as heat (disorderly, atomic-scale kinetic energy).
• different substances respond at different rates to changes in thermal energy.

Honestly, we spend the majority of our time in Sophomore Physics on the first seven of these, even though the last six are arguably more interesting.
What are your thoughts?

Grading Systems

I'm not fond of traditional, points-based grading, but I'm not confident with standards-based grading. I've been reading Marzano and Understanding by Design and @DataDiva's rubrics wiki and following the #sbar physics/math axis on Twitter. In an attempt to work out some of the kinks in my understanding, I'm trying to work through not just the curriculum objectives for the course (Basic, CP, and Honors Sophomore Physics all use the same objectives), but also the grading.

The first topic is Constant (or average) Velocity. It doesn't get its own unit in the curriculum: it's part of the Kinematics & Dynamics unit that takes up the entire first semester. Here are the Learning Objectives from the district curriculum:

Learning Objectives

The student will:

• Transcribe raw experimental data into graph form.
• Interpret graphs for physical meaning.
• Show an understanding of kinematics by solving appropriate kinematics problems.
• Distinguish between the position time patterns of constant speed and accelerated motion.
• Show an understanding of dynamics by solving appropriate dynamics problems.
• Apply the concept of inertia to real world situations.
• Explain the relationship between the mass of an object, the forces exerted on it, and the resulting acceleration.
• Identify the equal and opposite force pair which exists in any interaction, including inverse square relationships.
• Handle quantities which involve direction as well as magnitude by using vectors.
• Describe circular motion and the forces necessary to maintain it.
• Become knowledgeable with the universal nature of gravitation and subsequently state its implications.
• Combine kinematics, dynamics and vectors to analyze projectile motions.

Here are the objectives I think apply to constant (or average) velocity problems:

• Interpret graphs for physical meaning.
• Show an understanding of kinematics by solving appropriate kinematics problems.
• Distinguish between the position time patterns of constant speed and accelerated motion.

And now my revisions of those standards into something I hope I can give to students and use as a basis for designing assessments and grading them:

1. Graph experimental data:
3. Create appropriate position-time and velocity-time graphs from verbal or visual descriptions of motion.
3. Solve appropriate kinematics problems:
1. Find average velocity given change in position (displacement) and change in time (duration).
2. Find change in position (displacement) from average velocity and change in time (duration).
3. Find change in time (duration) from change in position (displacement) and average velocity.
9. *Combine skills to solve more complex problems.

I've left out the standards that don't apply. The asterisk marks an "advanced" standard I don't expect my Basic students to reach.

I haven't included the rubric for 3.i., because, frankly, I'm not sure how handle it. It's something that my students frequently have trouble with, so I think I want it in the standards for their consideration, but I don't know how to assess it, other than to throw multi-step problems at them and see what happens. Students who can't handle multi-step problems generally take two random numbers from the question step and stuff them into a formula, which should be handled by the rubric for 3.a.-c., right?


Here are my attempts at 'student' solutions for an old test question:

So, questions: Should I collapse standards a-c into one for feedback & grading purposes? Which rubric should I use? How can I improve the rubrics? Are the distinctions between levels clear? Any other advice?

Thoughts while reading Understanding by Design, Chapter 5

Essential Questions, as used here, are open-ended, transferable, interesting, and appropriate to the audience.

I don't think I need to come up with different questions for classes at different levels. If I'm doing it right, the questions I use should be questions that could be used productively at many levels, including actual research. If I phrase the question well, it should be accessible to all of my students.

On pg 110, "No question is inherently essential." The same question can be rhetorical or essential, depending on context and intent. I've noticed this in classes. Sometimes when I ask a questions that I hope will be thought-provoking, my students look as if they're trying to recall a pat answer from the textbook or waiting for me to answer my own question. I think they're used to being asked rhetorical questions. I need to set up my questions better, so students realize that they're being asked to think!

"Skills are means, not ends; the aim is fluid, flexible performance." (pg 113) I think this goal has been lost in the testing craze. We test skills and implicitly tell kids that the skills are the goal, or that performance on the test is the goal, when the real goal is performing outside of school.

I think the current sophomore physics curriculum needs two overarching questions, one having to do with motion/force and the other having to do with energy. But maybe one about energy would be enough, if I can figure out how to weave mechanical energy into the first half of the course. That might also ease the second semester time crunch.

Possible Essential Questions for Kinematics:

• How can we describe motion? How accurately?
  
• What are forces?
• Can we predict motion and change of motion? How? How accurately?
  
• What causes motion/change in motion?
• What causes change?
• What assumptions do we make to make sense of the world?

I'm sure these aren't perfect, but they're a start.