Scaffolding questions on tests

[hutchphd]

OMG

Mentor's Note: The first 18 or so posts have been split off from a previous thread at the request of the participants: https://www.physicsforums.com/threads/mechanical-physics-coefficient-of-friction.1051397/

 

[kuruman]

Never seen that assumption before
https://en.wikipedia.org/wiki/Free_body_diagram

It's not really an assumption but a convenient way to find the net force. It relies on the idea that any vector that is not the position vector or related to the position vector, e.g. torque, angular momentum, etc., can be translated parallel to itself for purposes of calculating vector sums, components, angles between vectors etc. This becomes relevant in cases where the system can be treated as a point mass.

Indeed, the Wikipedia article that you provided as reference states in section Modeling the body:

A body may be modeled in three ways:​

​

a particle. This model may be used when any rotational effects are zero or have no interest even though the body itself may be extended. The body may be represented by a small symbolic blob and the diagram reduces to a set of concurrent arrows. A force on a particle is a bound vector.​

$\dots$​

(emphasis in bold is mine).

Now you have seen it. I have found it useful to students who are beginning to learn how to use vector addition and a FBD to find the net force.

 

[malawi_glenn]

Now you have seen it. I have found it useful to students who are beginning to learn how to use vector addition and a FBD to find the net force

I do that too, but I do not call them FBDs

 

[kuruman]

I do that too, but I do not call them FBDs

OK, I'll bite. What do you call them? (Just for future reference.)

 

[malawi_glenn]

OK, I'll bite. What do you call them? (Just for future reference.)

I call them nothing special. Not everything needs a name. Forces are not "pure" vectors, because they have a point of action. In particular, if one is allowed to parallell transport force vectors in a FBD then torques and rotation will be problematic for the students is my experience.

 

[hutchphd]

I agree but I have found the "opposite" to be true. I always encouraged and demanded that the vector addition not be done on the free body diagram because of the point of action issues. Adding vectors heel to toe is limited to a separate space "where the vectors live". Then the axial vectors particularly can be added with less confusion.

 

[malawi_glenn]

Yes, I show students to write to separate diagrams. One FBD and one "vector diagram"

 

[kuruman]

In particular, if one is allowed to parallell transport force vectors in a FBD then torques and rotation will be problematic for the students is my experience.

I agree and that is why I made I drew the line when parallel transport is permissible in post #23:

It relies on the idea that any vector that is not the position vector or related to the position vector, e.g. torque, angular momentum, etc., can be translated parallel to itself for purposes of calculating vector sums, components, angles between vectors etc.

I think we agree on everything except on what to call a force diagram in which forces acting on a system have been translated parallel to themselves. I say "FBD" you say "nothing special." I think it would be confusing to ask students on a test to "Draw nothing special showing all the forces acting on the block and use it to find the acceleration."

 

[malawi_glenn]

I agree and that is why I made I drew the line when parallel transport is permissible in post #23:

I think we agree on everything except on what to call a force diagram in which forces acting on a system have been translated parallel to themselves. I say "FBD" you say "nothing special." I think it would be confusing to ask students on a test to "Draw nothing special showing all the forces acting on the block and use it to find the acceleration."

Are we trying to be funny? :)

I do not even explicitly ask students to do draw FBDs on tests. I just ask them to find either the acceleration or the velocity after a certain displacement and so on, no "stepping stone" questions. However, they should know that drawing a FBD is part of a well motivated solution for such a question.

Perhaps "FBD of the CoM" is a good description of such FBD where you place all forces as vectors starting at the CoM?

 

[kuruman]

Are we trying to be funny? :)

Not intentionally. I find that "stepping stone" questions are useful for assigning letter grades to percentages of total scores on a test. If three or four stepping stones are ordered in increasing complexity, then students who cannot even take the first step, get a failing grade. My belief is that "I don't know how to start the problem" should not be a barrier to a student's performance on a test. If my goal is to measure how much a student can do and a student doesn't know how to start a problem, I have a null measurement. Anyway that's my philosophy.

 

[malawi_glenn]

My belief is that "I don't know how to start the problem" should not be a barrier to a student's performance on a test.

Well that is another discussion. But I have national guide lines to consider. Scafolding should be done in class not on tests

 

[hutchphd]

With apologies @malawi_glenn that seems to me a very silly answer. There are many different ways to construct a test and they are no more equivalent than the students are identical. To define exactly what a test should look like assumes knowledge that I most certainly lack.

 

[malawi_glenn]

With apologies that seems to me a very silly answer. There are many different ways to construct a test and they are no more equivalent than the students are identical. To define exactly what a test should look like assumes knowledge that I most certainly lack.

as I wrote, I have national curriculum to consider. There are no scafolding on those questions.

 

[hutchphd]

You have guidelines that rigidly constrain the tests you give? Interesting.

 

[malawi_glenn]

You have guidelines that rigidly constrain the tests you give? Interesting.

The final test "course exam" and those tests are quite brutal. If I have scafolding questions on my midterms etc pupils will feel that I somehow misled them. I give them scalfolds in class, and before each exam I give them a collection of exam questions so that they can prepare well. Never I have had a pupil who said "the course exam was not like midterm tests" when I started to make my own midterm tests more like the course exam.

That is why I do not use scafolding on tests.

Imagine when you are to get your drivers licence and have to ask the examiner how to turn on the engine.

If we could have a new thread, I can translate my latest exam to show you how it can look.

 

[hutchphd]

Now I understand your reasoning and it makes sense! I'm not at all sure I agree with the rigidity of the structure. I believe I prefer the less monolithic US approach.

 

[malawi_glenn]

Now I understand your reasoning and it makes sense! I'm not at all sure I agree with the rigidity of the structure. I believe I prefer the less monolithic US approach.

Every system has its pros and cons.

 

[kuruman]

If we could have a new thread, I can translate my latest exam to show you how it can look.

I reported post #22 by @hutchphd and asked that the thread be split at that point into "STEM Education and Teaching." See you there.

 

[malawi_glenn]

I reported post #22 by @hutchphd and asked that the thread be split at that point into "STEM Education and Teaching." See you there.

Alright, here is my latest physics test, for third year high school in sweden. It is the third test and covers harmonic motion and waves. The previous two tests covered: (first test) - torques in equilibrium, projectile motion in two-dimension, circular motion. (second test) - magnetism, charged particles in homogenous electric and magnetic fields, electromagnetic induction. The fourth and final test will be an exam which covers these three tests and some basic modern physics (such as photoelectric effect, hydrogen atom, blackbody radiation).

As you can see, I have to give points graded with certain skill levels. I have not made this up, this is part of the Swedish school system.
One could see the E-C point questions as stepping stone questions. For instance the later problems, where there is skill level A points awarded, it is fairly easy to start by finding e.g. the spring constant in question 9, or the wavelenght in question 10. The "weaker" students does not do this, they just see "oh, this is A-level question let's not bother with that one".

There is however some changes going on here. In maths, the level points will be removed on the test and only the teacher will know afterwards which questions were supposed to give A-level points, C-level points and so on. There are pros and cons. Weaker students are used of being hand held also on the exam. The level points is a guide for them to know what to focus on. But, as mentioned, they do not push themselves trying the A-level points. The brighter students have an opposite strategy, they often skip the E-level questions and save them for the last 10 min of the test, resulting sometimes in a very sloppy approach and mistakes.

Another result of the level points, is that there will be many questions on a test. The course exams has like 20-24 questions in 4 h time.

I often include "answer only" questions, and multiple choice, because about one third of the course exam will be composed of such questions. Also each test I make has some kind of "explain" question. There is usually one or two of those on the course exam.

Also note "formula book" is allowed. In here, many many formula are given, but perhaps not all the constraints. For instance "work" is only written as "W = F⋅s".

Here is the test

Test time: 120 min.
Allowed aids: graphic calculator, formula book, ruler.
Unless otherwise stated, motivate all your solutions with e.g. which formula are used and/or figures.
Remember that your answer should have correct significant figures and units.
------------------------------------------------------------------------------------------------------------------
Maximum points for the entire test (E/C/A) is 9/8/7 (24p in total).
Preliminary limits for test grades: E - 7 p total, C - 12 p total (min 4 C/A), A - 18p (min 4 A).
--------------------------------------------------------------------------------------------------------------------
All situations plays out near the Earth's surface and without air-resistance, unless stated otherwise.
--------------------------------------------------------------------------------------------------------------------
1) Two point-like rods A and B are dipped through a water surface and generate circular waves with wavelength 3.2 cm. The motion of the rods is harmonic and the two rods are in phase with each other. The figure depicts all lines between A and B where the surface of the water moves up and down the most. Find the value of BP − AP. (2/0/0)

2) A block weighs 610 g and can move without friction along the ground. The block is attached to a wall by a spring and undergoes horizontal harmonic motion. The diagram shows, as a function of time, the position of the center of the block as measured from the equilibrium ( y = 0 ). Find the spring constant. (2/0/0)

3) A loudspeaker is assumed to emit sound isotropically. At a point Q located 2.0 m from the loudspeaker the sound intensity is 32 µW/m².
a) What is the power of the sound generated by the loudspeaker? Answer only. (1/0/0)
b) What is the sound level at the point Q? Answer only. (1/0/0)4) Rubert has made his own gym, inspired by the classic “muscle maker”.

Rubert is quite poor so he has only one spring. This spring is attached to a wall from which he can pull it outwards horizontally. Rubert needs to pull with the force 340 N in order to hold the spring still extended 0.40 m from its natural length. How much work did Rubert perform when he stretched the string in this fashion? (1/1/0)5) The figure depicts a light ray hitting the boundary between oil and water. The light ray will continue in the water.
a) What is the angle between the normal line and the refracted light ray in the water? (2/0/0)
b) Describe the path of the light ray if the angle of incident is 70.0°. (0/2/0)

6) Rebecca is shining light from a laserpointer at a transmission grating with 1200 gratings per mm.
The wavelength of the light is 404 nm. How many maxima can she observe at most on a flat screen? (0/2/0)

7) A tube is 0.79 m and is open in one end and closed in the other. Inside the tube a thin lawyer of sawdust has been placed. When the loudspeaker generates sound waves with a certain frequency f
the sawdust has moved quite a bit at three locations, indicated by the arrows in the picture below.
What was the frequency f of the sound used in this experiment? (0/2/0)

8) Adam has bought a “perfect” bouncing ball from NASAs webshop. The fact that the bouncing ball is perfect means that there is no loss of mechanical energy when it bounces off the ground. Can the motion of this bouncing ball be described as harmonic motion? (0/1/1)9) A PASCO-smart cart with mass 0.480 kg is rolling frictionless on a horizontal track. The velocity of the cart is initially v = 1.6 m/s to the right, see picture below. The cart is moving towards a spring break with negligible mass. The spring break is attached to a wall. The construction of the spring break is such that the spring can never be extended beyond its natural length, it can only be compressed. You may assume that the spring in the break has its natural length when it does not have any contact with the cart.

The cart obtains contact with the spring break at the time t1 and has stopped completely at the time t2. Between t₁
and t₂ the cart travels 6.0 cm. Then, the spring will cause the cart to move to the left. The cart finally leaves the spring break at the time t₃ and has there yet again the speed 1.6 m/s.

Estimate the total time for which the cart had contact with the spring break. (0/0/3)

10) Two point-like rods A and B undergo harmonic motion in phase and generate circular water waves. At the points P and Q one observe maximas. There are two more maximas being observed between P and Q. How many nodal lines are there on the line AB?(0/0/3)

 

[hutchphd]

Interesting test. I will ask questions haphazardly as they occur to me.
How is this test scored? For instance is question1 answer only? Otherwise it seems a nightmare to grade (nice ideas though). What does the designation (2,0,0) mean ? ....I'm sure I've missed the obvious.

 

[kuruman]

I too would like to know the answers to @hutchphd's questions. In addition, to that I would like to know some more about the constraints imposed by the Swedish school system. Do they issue guidelines that teachers have to follow? How much latitude does a teacher have to deviate (read reinterpret) these guidelines?

For example, I see that most of these problems require the use of a calculator. In my tests, I eventually adopted the philosophy of not asking questions that require the use of calculators. That's because I observed students spending too much time pushing buttons on their calculators trying this and trying that instead of thinking about the problem. In problem 9 for instance, I would replace the numbers for the mass, velocity and amplitude with $m$, $v$ and $A$. That would force students not to spend time finding a number for the spring constant, which is not needed anyway. Hopefully, students who have been paying attention, when I told them that a spring-mass system is equivalent to uniform circular motion seen edge-on, would immediately write down the answer as the length of the semicircle divided by the speed, $t=\pi A/v.$ Those who don't see the shortcut can do the long way after recognizing that the time required is half a period. Having said all that, my question is, "Would I be able under the Swedish school system ban calculators and ask questions that expect answers in symbolic form?"

The level points is a guide for them to know what to focus on.

The underside of this is that if a student only partially understands simple harmonic motion and sees an A-level question it, he/she will avoid it as expected. Wouldn't it be better to ask individually "scaffolded" questions and let students decide how much in each they can or cannot do? I see this "guide" as a self-fulfilling prophecy. Anyway, I understand that if that is the system that you have to work under, that is what you have to do. I am just trying to understand it.

 

[malawi_glenn]

Interesting test. I will ask questions haphazardly as they occur to me.
How is this test scored? For instance is question1 answer only? Otherwise it seems a nightmare to grade (nice ideas though). What does the designation (2,0,0) mean ? ....I'm sure I've missed the obvious.

I can provide a complete score card as well. Question 1 id scored like this:
1 E point for setting up BP - AP = an integer times wavelenght.
1 E point correct answer with units.

Only problem 3 is "answer only" you can see it written in the test header.

The point levels I can also explain 2,0,0 means two E skill points 0 C skill points and 0 A skill points.

E is the lowest passing grade. It is "basic understanding and problem solving"
A is the highest passing grade. It is "advanced understanding and problem solving"
C is in the middle.

@kuruman I sometimes have some questions on the test where they are just required to provide algebraic answers and such. The problem 9 was actually from my "booklet" but in there I asked for an algebraic expression for the t2 - t1 (time it takes for the cart to get zero speed).

Hopefully, students who have been paying attention, when I told them that a spring-mass system is equivalent to uniform circular motion seen edge-on, would immediately write down the answer as the length of the semicircle divided by the speed, t=πA/v.

I have such students yes, but because that relationship is not written in their forumula book they need to motivate it.
In this way, students who "remember things" are "punished" - like it or not. Same with students who "remember" that the range of horizontal projectile motion is $L = v_{0x}\sqrt{2H/g}$ get score withdrawn.

Regarding usage of calculators and such, it is the same on the math course exams - lot of things to be calculated numerically. Swedish school agency incoorporate more and more of these problems in their final tests. Also, in the math courses, students are supposed to learn basic programming since a few years ago...

I will get back and answer your other questions later. Now I have to make dinner for my family.