Posts
* Monday (45 minutes): position-time graphs, learned through facts and a graph-matching exercise. Homework is about position-time graphs.
* Wednesday (90 minutes): velocity-time facts and graph-matching exercise; acceleration facts with demos using the PASCO visual accelerometer; demonstrate free-fall acceleration with a motion detector. Homework is about velocity-time graphs.
* Friday (90 minutes): motion diagrams with a 10-Hz dot machine; make a position-time graph from the dot machine output; use two slopes of that graph to find an acceleration. Then, two quantitative demonstrations with the projectile launcher and algebraic kinematics. Homework is about the definition of acceleration.
* Monday (45 minutes): finish dot machine lab, correct any issues with the first homeworks. Homework is several algebraic kinematics problems.
Then on Wednesday we're moving into equilibrium of forces. (Those of you who have taken my workshops might be confused - for my upperclassmen, I start the year with equilibrium of forces, and then move into kinematics in the style above. But for 3rd formers who are more at home with real inquiry from the beginning of the class, I dive into motion.)
How, you might ask, does this minimal treatment lead to deep understanding?
Well, it only kinda does right away. It's the long-term re-visitation of these concepts, the integration of kinematics into problem solving with other topics, that truly ingrains deep understanding. Yet, my students average a full two points higher than the national average on the AP Physics 1 exam. They're getting kinematics just fine with my approach.
I use fact sheets, and demand direct reference to the facts on every problem.
A big part of why students struggle at first with understanding motion is that they rely on their prior knowledge. I mean, AP physics students are generally at the top of their class. They are used to half-listening in math or science class, then using their natural talent to reach in the direction of an answer or written justification.*
*Then they're used to using their debate skills to argue why their answer is technically correct and should earn points.
A big part of why students struggle at first with understanding motion is that they rely on their prior knowledge. I mean, AP physics students are generally at the top of their class. They are used to half-listening in math or science class, then using their natural talent to reach in the direction of an answer or written justification.*
*Then they're used to using their debate skills to argue why their answer is technically correct and should earn points.
I don't provide the class with a lot of facts; but those facts get directly to the point of kinematics concepts. And direct reference to these facts will lead students to correct answers and justifications... if the students can be arsed to use them.
Here are the facts. No justification is accepted unless the student has quoted at least one of these facts nearly verbatim. (When there's a numerical or semi-quantitative problem using the constant acceleration equations, those equations are used instead of these facts.)
And yes, really, these facts and a week of experiments/demonstrations/practice is all that's necessary to dive into kinematics. In my next post, I'll explain how I use the acceleration facts with demonstration to stamp out misconceptions.
Definitions
Displacement indicates how far an object ends up from its
initial position, regardless of its total distance traveled.
Average velocity is displacement divided by the time
interval over which that displacement occurred.
Instantaneous velocity is how fast an object is moving at a
specific moment in time.
Position-time graphs
To determine how far from the detector an object is located,
look at the vertical axis of the position-time graph.
To determine how fast an object is moving, look at the steepness
(i.e. the slope) of the position-time graph.
To determine which way the object is moving, look at which
way the position-time graph is sloped.
A position-time slope like a front slash / means the object
is moving away from the detector.
A position-time slope like a back slash \ means the object
is moving toward the detector.
Instantaneous velocity is found by taking the slope of the
tangent line to a position-time graph
Velocity-time graphs
To determine how fast an object is moving, look at the
vertical axis of the velocity-time graph.
To determine which way the object is moving, look at whether
the velocity-time graph is above or below the horizontal axis.
An object is moving away from the detector if the
velocity-time graph is above the horizontal axis.
An object is moving toward the detector if the velocity-time
graph is below the horizontal axis.
To determine how far an object travels, determine the area
between the velocity-time graph and the horizontal axis.
On a velocity-time graph it is not possible to determine how
far from the detector the object is located.
Most everyday motion can be represented with straight
segments on a velocity-time graph.
Acceleration
Acceleration tells how much an object’s speed changes in one
second.
When an object speeds up, its acceleration is in the
direction of motion.
When an object slows down, its acceleration is opposite the
direction of motion.
Objects in free fall gain or lose 10 m/s of speed every
second
Greg- I am inspired to drastically shrink my own AP class' kinematics curriculum . Gaming out how that would impact my current other units, do you consider this coverage to also include projectile motion? Or do you discuss this later? Or not at all since projectiles seem to have a negligible effect on the AP exam? Thanks!
ReplyDeleteRyan, I do cover projectiles, in an additional one or two classes. For my upperclassmen, I begin the year with a week or so of equilibrium problems - thus, they know how to break a force into components. So projectiles become a review of this process, since they need to break velocity into components. And once they can break velocity into components, projectile kinematics becomes just an extension of one-dimensional kinematics.
ReplyDelete(For my 9th grade, I start the year with kinematics, and THEN I move into equilibrium and N2L. So, I come back to projectiles after we finish discussing N2L problem solving. The same pedagogical principle applies, though, that we're reviewing the idea of breaking a vector into components, but in context.
Hi Greg,
ReplyDeleteI absolutely love your blog - as a 10 year veteran aspiring AP Physics teacher.. heh heh.. I am always looking for new hacks, tweaks, and general ways to get better. I have been trying to move toward inquiry and have had a bit of success in lab, and I love the philosophy of engaging the students in hands on work and demos as much as possible. I am feeling a sense of eager exhilaration and freedom at the possibility of reducing my formal treatment of kinematics to a mere two weeks, but I'm wondering about handing my students a sheet of facts - as you alluded to above, it feels a bit like it flies in the face of wanting them to build a deeper understanding. Can you maybe say a little more about how you revisit this later to build the enduring understanding? It is something you do deliberately, or does it just come from the study of later topics organically? I'm trying to see the flow as it comes up later - maybe unbalanced forces - for example, would you then look at the motion and have them sketch graphs commensurate with a given scenario? Or something like that?
Lisa, it’s organic... I guess the best way to think about it is that kinematics becomes fair game as part of any physics problem that comes up. The N2L practice requires a reinforcement of the definition of acceleration, and then of kinematics. So many problems use kinematics to find acceleration, and then N2L to find the value of a force; or vice-versa. That right there is a “review”. Projectile motion is next, which is just kinematics but twice. Circular motion allows us to consider the conditions under which we can use “speed = distance / time”. Momentum problems often have a kinematics component, say after or before a collision. Our labquests produce velocity- and position-time graphs, which must be read in order to get useful data out; and we use these for momentum, energy, all kinds of labs. Lots of opportunities. Each time, the students have to use their fact sheet and their (originally hesitant) skill in kinematics problem solving to do kinematics *in context*, not just as something Mr. Jacobs told them to do for homework. An so the concepts stick. By year’s end, kinematics is second nature.
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