I think everyone has made some very valuable comments. However, I think there are times we are missing the forrest because we are looking at the trees. For example, discussing how the student can not answer the question correctly is a tree. Any student can give an answer that is not detail enough if you don’t say that is not what you are looking for in an answer. When was the last time you gave an assessment and you didn’t explain what was acceptable?

Basically, I think the forrest is the power of video to remove cultural or reading biases and achieve evidence of conceptual understanding. I teach in an inner city high school where there are 28 countries represented. In addition to this high english as a second language population, most students are two to three grade levels behind in reading. However, reading and cultural bias should not be a factor in determining of the mathematical or science concepts. We should strive for assessments that eliminate these factors. While video removes these filters, it also demands a demonstration of conceptual understanding that we were not able to achieve with a word problem. I don’t know about anyone else, but this makes me EXCITED!

I know Meagan wanted to problem to require the students to show the meaty math but I think it actually does. Too often in math class, we have students complete the steps of math without ever explaining what the answer means. What better way to get to the meat of math then to apply what the answer. Why not take it a step further and have the students explain how a change in certain numbers changes the outcome of the stuntman!

I love this blog!

Assessing them, I’d say each has its role and you have foolishly listed them in order of increasing complexity.

Option 1:

This is a primitive problem, one that I would put in on-line homework to be sure they have done the reading. What makes it the most basic of problems is that it gives you all of the numbers needed to apply Fdt = mdv, and nothing else. No distractors of any kind.

Option 2:

I think this tests the concept, but not conceptual understanding. What I like about this version is that it has an excellent distractor in that the only number given is irrelevant to the impulse-momentum theorem. It dangles bait that suggests work-energy (or even work-impulse) in front of the student. Although you mention time, the student has to CHOOSE between time and distance when analyzing the problem. Force is not mentioned at all, so its importance has to be recognized by the student.

True, it is too wordy, but that can be fixed. Could even have a drawing.

Option 3:

The only difference between Option 2 and Option 3 is that the student has to identify all of the key variables from knowing the theorem, not from the quantities given in the problem itself. (BTW, that could make this version easier because students should start from the theorem rather than the data, so they won’t waste time trying to find some way of using the distance given in Option 2.)

I won’t go so far as to say that it does a better job of testing conceptual understanding, because it tells them which principle to apply. A better question would simply ask why the stuntwoman survives, letting them choose the one that is most relevant. After all, an expert would look at the question and say “this is usually used as an impulse-momentum problem with a known speed, but conservation of energy is the best way to determine the ratio of the height of the crane to the height of the air bag if I know I can land on my back.”

Comment:

No mention of your rubric. Is choosing the height of the crane part of your ideal answer?

Off topic digression:

Firing an automatic weapon is a much cleaner example, and these days I usually have several students (both male and female) in any given class who have extensive experience with fully automatic weapons and can share with the class their experience of average force resulting from a series of impulses.

You could use this video to introduce the topic, by showing it at the beginning of the unit and facilitating a discussion about just where the miscommunication between customer and customer service rep is coming from.

For assessment, you could use this video at the end of the unit, asking students to explain who is in the right–customer or customer service rep–and why, and/or determine how much the customer would think he owes and how much the representative would think he owes if some other given quantity of data was downloaded.

Also, I like your example of a conceptual & back-of-the-envelope mathematical question. I’ll have to think about using more of that sort of question in my classes. And you’re right on when you say students need practice/modelling before they feel comfortable with similar “less helpful” questions.

1) The force is applied for a long time because of the air bag. The i-m theorem is F dt = m dv, so the stunt person will survive.

1/4. You don’t mention that the long time of impact results in *less* force. Stating the formula without further explanation is insignificant. In general, if you apply a force of a longer period of time you have a greater change on momentum.

2) The stunt person takes some time to stop after they land on the air bag.

0/4. The stunt person would also take some time to stop if they hit the pavement. You need to talk about the differences between these times and what the implications for force are.

3) The force on the stuntman will be relatively small because the stunt person slows down gradually due to the airbag.

2/4. You’re correct, but you’re not making reference to the I-M theorem. Add another sentence to the effect of “The stuntman will experience a large change in momentum as he comes to a stop, a change which according to the I-M theorem is equal to (average) force times time, so the larger t is the smaller F will be.”

4) The i-m theorem is F = m dv/dt, and the airbag increases dt, and therefore decreases F.

4/4. Though this answer is brief, it’s clear you’ve been able to precisely describe the mathematical/conceptual basics of the physics going on in the video.

5) The i-m theorem is F = m dv/dt, and the airbag increases dt, and therefore decreases F. If the stunt person landed on the sidewalk, they would stop almost instantly — dt would be very small.

4/4. Only thing that I would consider adding is “dt would be very small, making F very large.” to the end, but is a 4/4 answer already in my book.

6) The airbag reduces the acceleration experienced by the stunt person.

0/4. This is true, but you need to explain *how* it reduces the acceleration–and explanation that would involve the I-M theorem–and also how lower acceleration translates into reduced potential for injury.

7) A given change in momentum (stunt person coming to a stop) can be accomplished by a large force over a short amount of time (side walk landing) or a smaller force over a longer amount of time (air bag landing).

4/4. It’s fine that you don’t state the I-M theorem as a formula, because you’ve stated it with words. Your additions in parentheses connect the formula to the video, demonstrating understanding.

I teach woodshop/science/technology in a school for neurologically-different kids and I’m going to give your three options my decidedly un-scientific sniff test.

Option 1 becomes nearly impossible for students with neurological issues – students with major reading comprehension issues will have trouble matching formulas to numbers, parsing the importance and relationship between those numbers and then just solving the equation. I could probably train my students to answer this type of question correctly – but if I change the pattern, my students’ neurological differences will trip them up, no their understanding of the physic concept.

I have similar issues with Option 2. Various writing disorders, such as dysgraphia, turn smart, articulate scientists into reluctant learners. Again, my assessment method runs into a neurological difference before it runs into a student’s understanding.

Option 3 gives the students a visual prompt to respond to in a low key way – written essay, orally if the time allows & even a physical demonstration. In this coming year, I’ll be asking for a physical demonstration of the principle (the wonderfulness of small class sizes). An example of the impulse-momentum theorem in woodshop: A student trying to hammer a nail into a board which is held in their free hand, not secured to a workbench/ground/etc. It is nearly impossible to hammer a nail into a board that way because your hand moves with the hammer blows, extending the time of impact and lessening the amount of force transferred to the nail head. My middle-schoolers would make that connection.

–Mr. Patrick.

@luke: Yes, in many of your “answers” I see students who kind of understand the material parroting back something I said in class. I call this the spaghetti method — throw a bunch of ideas on the test and see what sticks. This is where I favor Frank’s idea to include back-of-the-envelope calculations to apply the math to their understanding of the video.

On the aspect of video-as-assessment, I say “bravo”. But then, the deck was stacked in favor of video, wasn’t it? For the sake of assessment, I need to put this video in each kids’ hands to play and replay as needed. When they need to. Hmm, I wonder what tech I could do this with most economically.

Excellent job! I love your explanations behind the three potential problems that you provide. Now, I am wondering how I can make this work on the elementary level (fourth grade). For instance, how could I do this for a topic like place value?

Ross