In the teaching of physics, we have been learning about student difficulties in kinematics. So far, we have mostly

• Examined, interpreted, and discussed artifacts of students’ written work in kinematics
• Read and discussed research articles describing student difficulties in learning kinematics
• Read and discussed teacher accounts about the teaching and learning of kinematics
• Worked through problems and curriculum designed with knowledge of student difficulties
• Applied knowledge of student difficulties to generate example student solutions

There have been four broad categories of things we’ve examined in context of student learning about kinematics.

• Student being capable and being in habit of mind to discriminate concepts that similar but different.
• Student being able to relate representations of motion to actual motions, and relate kinematic definitions to actual ways of observing, determining, and measuring
• Students being able to verbally interpret the meaning of kinematics concepts and use those interpretations to reason about an object’s motion.
• Students having a “flexible” tool kit of strategies, representations, and mindsets for engaging in problem-solving that goes beyond substituting into equations.

Yesterday, we began work in consolidating parts what we have learned. Our first consolidation activity was to create icons, diagrams, drawings, situations, phrases that represent each of the different kinematic distinctions that need to be supported as part of learning. Here are examples of what we came up with.

Interval of Time vs. Instant of Time

“An 8 O’Clock Class” vs “An 8-hour long Class”

(Both are miserable, but for different reasons)

Position vs. Change in Position vs. Distance

Position vs. Velocity

Average vs Instantaneous Velocity

Acceleration vs. Velocity

Going 60 mph for 4 seconds

Going “0-60″ in 4 seconds

One group tried to put everything into one diagram with a GPS, either as something embedded in one snap shot, or something concerning what’s change from one snap shot to next.

Following this activity we discussed a few of the instructional ideas we had encountered for helping students to distinguish these concepts as part of their understanding of kinematics

• Being explicit about these distinctions (rather than shoving them under the rug or hoping they will come along for the ride)

The shortcuts, omissions, and ‘simplifications’, which are meant to reduce complexity are not conducive to understanding; they are specious, and they make genuine understanding extremely difficult. (Arons, “Teaching Introductory Physics”, pg. 24)

• Being aware of subtleties in language (e.g., “at” often indicates instants/locations and “for” often indicates durations/distance ), and pressing for specificity in language (i.e., asking “What it is ?” when students use “it” instead of naming quantity specifically)
• Using problems that require students to make such distinctions (e.g., problems where objects don’t start at origin; problems with information given as both distances and positions or clock-readings and elapsed times).

• Requiring students to explicitly articulate the difference themselves verbally and in writing (coming up with examples, analogies), like this one from Physics by Inquiry

• Requiring students to consider and respond to faulty reasoning in which such distinctions are not made (similar to one’s we’ve seen in Physics by Inquiry)

• Requiring students to respond to and argue in context of potentially ambiguous situations (e.g., kinematics traffic court)

Anyway,that’s a quick brain dump. There’s a whole lot more for us to consolidate and reflect on, and so much more for us to learn…. how will we ever get there?