Young Americans are dumbs

[GaussLaw]

Yes, I would need to link the longitudinal studies for that. But the quality of teachers overall is shockingly poor - the C students from third rate schools as it were. When speaking to some of them, and reading their prose, the literary level they have is pathetic - and frightening. That has been my anecdotal experience, and what I have read elsewhere over the years.

As a physics teacher at a somewhat decent suburban high school, I concur with you greatly.  But the term "prose" is far too kind for the rubbish they write.  "Alphabet soup" is a better term for it.  They can't write in complete sentences and it's nearly impossible to discern whatever they're trying to convey.

[GaussLaw]

To all interested, I have conducted an item analysis on my last cumulative physics test that I gave my class, consisting primarily of 11th graders of average academic abilities. 

The following questions were missed by more than 50% of the students:
13. A catapult fires a projectile at a speed of 50 m/s 30 degrees above the horizontal.  What is the initial horizontal and vertical speed of the catapult? 
18. An object with mass 8 kilograms experiences a force of 20 N applied to it.  What is the acceleration of the object?
22. Find the angular momentum of an object with mass 7 kg, radius 2 meters, and velocity 10 m/s. 
27. Find the equivalent resistance of a 2-ohm resistor and a 7-ohm resistor connected in parallel. 

Anyone with any kind of physics background would realize how easy these problems are. 

Sigh.......it's nearly impossible to teach my students anything even remotely resembling physics.  They just refuse to learn or take responsibility for themselves, and they're fed this narrative that they're "so special" by their parents.  It's sickening.  It's not the unions that are the problem; it's the parents.  They just refuse to hold their kids accountable for anything.

[GaussLaw]

To all interested, I have conducted an item analysis on my last cumulative physics test that I gave my class, consisting primarily of 11th graders of average academic abilities.  

The following questions were missed by more than 50% of the students:
13. A catapult fires a projectile at a speed of 50 m/s 30 degrees above the horizontal.  What is the initial horizontal and vertical speed of the catapult?  
18. An object with mass 8 kilograms experiences a force of 20 N applied to it.  What is the acceleration of the object?
22. Find the angular momentum of an object with mass 7 kg, radius 2 meters, and velocity 10 m/s.  
27. Find the equivalent resistance of a 2-ohm resistor and a 7-ohm resistor connected in parallel.  

Anyone with any kind of physics background would realize how easy these problems are.  

Sigh.......it's nearly impossible to teach my students anything even remotely resembling physics.  They just refuse to learn or take responsibility for themselves, and they're fed this narrative that they're "so special" by their parents.  It's sickening.  It's not the unions that are the problem; it's the parents.  They just refuse to hold their kids accountable for anything.

Cumulative tests highlight another difficulty. Many students assume that either there is a sheet of potential equations or there are a select few equations to memorize; equations they are told in advance to memorize. I don't know if you did either of those for your test, but I don't. As such easily half a class of calculus-based introductory students would get all but 18 wrong.

Problem 13 combines trigonometry with vector kinematics. Students have trouble combining the information from the two disciplines though they can follow it easily enough. The critical thinking skill to mix two fields to solve a problem has been lacking for many years.

Problem 22 might see half get it, but many students won't know whether the radius is of the object or of the trajectory. A lot of science problems require reading to get the context, and students expect to be handed a specific formula and then numbers to insert into the formula.

Problem 27 requires remembering both the formula and distinguishing the definitions of series and parallel. Students who didn't memorize the formula won't try to derive it, but they will usually make a guess that is more likely to something along the lines of the simpler series formula.

Problem 18 would break 50% at the college level primarily because the formula is one of direct division. The wrong answers would occur for those students who want to multiply rather than divide because they'll guess it's one or the other, or they'll get the units wrong or leave them off entirely.

I think the theme is clear. More work needs to go into earlier grades on how to synthesize knowledge, not just repeat it. To bring this back to political discussion, the math standards of the Common Core have significant parts designed to address this issue.

Common Core, in my opinion, is good about encouraging problem solving.  However, it eschews traditional computational algorithms that are a necessary prerequisite for problem solving.  Without a good "number sense", it's very hard for students to get comfortable with problems.

With regards to my physics class, I put cumulative questions on most of my exams and give a good number of truly cumulative exams because it's very difficult to get my students to retain information without a test.  Part of the problem is that my students have a hard time with the basic math.  I have to drill them on division, algebraic manipulations, and especially quadratic equations (even basic ones like x^2+5x+6 = 0).  Since math and physics are in the same department, we as teachers try to work together to make sure the kids are as solid in math as possible.  Thus, I just can't spend that much time on theoretical physics concepts and am generally teaching formulas, problems, and methods that are accessible to students at this level. 

All in all, these students have parents that don't make them study or do homework.  I see that as the ultimate root.  This makes it very difficult for me as a teacher to get good results from these kids.

[GaussLaw]

To all interested, I have conducted an item analysis on my last cumulative physics test that I gave my class, consisting primarily of 11th graders of average academic abilities. 

The following questions were missed by more than 50% of the students:
13. A catapult fires a projectile at a speed of 50 m/s 30 degrees above the horizontal.  What is the initial horizontal and vertical speed of the catapult? 
18. An object with mass 8 kilograms experiences a force of 20 N applied to it.  What is the acceleration of the object?
22. Find the angular momentum of an object with mass 7 kg, radius 2 meters, and velocity 10 m/s. 
27. Find the equivalent resistance of a 2-ohm resistor and a 7-ohm resistor connected in parallel. 

Anyone with any kind of physics background would realize how easy these problems are. 

Sigh.......it's nearly impossible to teach my students anything even remotely resembling physics.  They just refuse to learn or take responsibility for themselves, and they're fed this narrative that they're "so special" by their parents.  It's sickening.  It's not the unions that are the problem; it's the parents.  They just refuse to hold their kids accountable for anything.

These are really easy questions. How my physics teacher from junior year would ask them:
13.   A catapult fires a projectile at a speed of 50 m/s 30 degrees above the horizontal. Find the distance traveled and the total time before it hits the ground.

18. A car with mass 1000 kilograms is traveling at 20 m/s applied to it.  After 10 seconds it collides with another car weighing 20000 kg traveling the same direction at 10 m/s. If the collision is perfectly elastic, calculate the resulting velocity of each car.

22.  A round ball with radius .5 m is rolling down a slope of angle 30 degrees. Calculate its velocity <moment of inertia for a sphere given on test>

27. A circuit with 8 resistors in both series and parallel given (too lazy to draw it now). Find the power across resistor x.

I'm proud to say that with the possible exception of question 22, I can still do these problems a year later.

And re: math in science, I really do think that people shouldn't be taking physics until they've taken at least trig and some sort of calculus involving integrals and derivatives. With the knowledge that by integrating distance you get velocity, and by integrating velocity you get acceleration, and by integrating force you get energy, kinematics literally becomes a breeze. Yet without understanding the concept of integration of shading in the area under the curve, the laws become haphazard, and it becomes much harder to understand the concept behind memorizing equations. Also, I could not imagine someone doing banking angles, forces at an angle, and acceleration down a non-frictionless ramp without trig.

That's quite impressive.  Is that an AP Physics class or an Honors Physics class?  Those are pretty complex problems.  The elastic collisions one is a real pain as it involves annoying systems of equations and complex circuits can be pretty challenging.  If I gave those problems to my students, they would fail miserably.

[GaussLaw]

AP Physics B (we don't have honors- just regular, AP B, and AP C- the latter of which I don't think I'm currently capable of mastering)

One of my favorite questions from last year appeared on the first test- if you drop a rock down a well and here it 3 seconds later, how deep is the well? In order to solve it you need to incorporate both freefall acceleration and the speed of sound.

Part of me thinks that in 8th grade or 9th grade they should make it part of the curriculum to understand the concept of derivatives and integrals- just the idea that it is possible to find the rate of change of a function at a certain point and the area underneath two points, and maybe some basic examples of each.  On the other hand, knowing kids, that might not be a good idea.

I assume your Physics C teacher makes the class harder than the exam, but I have no doubt you'd do well on the AP Physics C exam (at least Mechanics)  based on what you told me.  While our school doesn't have an AP Physics course now, I have studied the required material for it.  Physics C Mechanics is 20% kinematics, and merely knowing the basic kinematics equations and the calculus component is enough to ace that.  Since a 5 on Mechanics only requires ~55%-65% of the points depending on the year, one would only need around 50% of the remaining types of questions right.  Some basic knowledge of dimensional analysis, net forces, momentum, and kinetic energy (which I'm sure you've covered), and you'd easily get a 5.  

As a teacher, I am curious how your teacher would teach Physics C.  The level of difficulty of many of the problems you described are far more in line with C than B by most teachers I've talked with (I'm certain you attend at a much, much, much more rigorous high school than the one I teach at in central Missouri though).