Young Americans are dumbs

[muon2]

Here's an opposing view:

You must be logged in to read this quote.

This brings up an important distinction in cohorts. Torie started by comparing the 55-65 cohort to the 16-24 group. The Sandia report is correct that the statistics of falling scores are best described by an expanding pool of test takers, but that compares students graduating in the 60's and 70's to those graduating in the 80's. That's essentially comparing today's 55-65 year-old cohort to today's 45-55 year olds. That doesn't get to a question of whether there are differences going forward.

I claim there is, though with the caveat that it is a narrow statistical slice. However, my findings have been echoed by others in higher ed over the last decade.

I have the opportunity to teach a broad slice of students fresh out of high school at a generic state university that is not selective. It is not unusual for me to work with 300 students a year that is well mixed with urban, suburban and rural backgrounds. Like many I often reuse questions and sometimes whole quizzes so I can norm a class in one year to one taught a few years before. Based on test scores and written course evaluations there is no doubt in my mind that graduates in the last decade lack a set of critical thinking skills that their peers had in the decade before.

What is most different is the way classes have to be taught in this era of evaluative testing in high school. Students are taught a broader array of topics to insure that they've covered the subjects of the standardized test, but give up the depth that is needed to tackle unfamiliar but related fields of knowledge. For example, I find students in introductory courses today are far less comfortable with science questions that require knowledge of relationships between concepts, but instead expect science questions that test the ability to follow a script that churns out a number from a calculator. In my experience there has always been some fraction of the students for whom that statement was true, but it was less prevalent at the beginning of this century.

Now let me pull this back to the OP article about middle class incomes. As you might guess some students who faced conceptual questions but wanted scripted exercises will come to complain. I would then ask them if they want to be engineers or other professionals to critically analyze a problem are they aiming for a job as an entry-level technician who only needs to follow a script. In general they all prefer the salary of the engineer, yet as we continue to talk it becomes clear that their high school has not prepared them for real problem solving. The culprit was the form of the test that was used to assess their school and the teaching designed to create success on that test.

[muon2]

So comparing the 45-55 cohort to the 16-24 cohort would be comparing apples to apples, in a way the 55-65 cohort to the 16-24 cohort would not?  When did the test taking pool stop expanding?  Is there any reasonable accurate way to "correct" for the "noise" of the expanding pool factor?

Thanks for your anecdote Muon2. That was very interesting. My anecdote is that I find that there has been a material decline in literacy skills in my lifetime. Folks who have spoken English all their life, as their first language, in general just don't seem to me to have the vocabulary and writing skills that older cohorts fitting in that category seemed to have.

Somewhere by the late 90's most schools had reached the point where everyone was taking the ACT or equivalent to assess how well the schools were teaching. At that point the expansion essentially ended. The best way to control for the expansion is to select a particular socioeconomic group that already had high test-taking rates and use that to benchmark the larger sample.

I found part of my anecdote particularly interesting since with 200-300 students a year over a span of more than a decade some of the trends have statistical relevance.

[muon2]

Did the SES of you class composition stay the same more or less over that period, Muon2?  That would be the other perhaps distorting factor, if it exists, that would need to be corrected for (as you suggest, when it comes to test scores).

As far as I can tell my class demographics have changed little in the last 20 years. That's one advantage with data from classes at a generic (non-flagship) state university. They are relatively inexpensive and are intended to accept most students from the state with a HS degree. There are substantial remedial classes designed to bring students up to par if their HS program was lacking in English or math. So any demographic shifts would be mostly be due to shifts in the region of the state itself, and IL has not had a lot of growth to change the numbers over the last two decades.

[muon2]

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.

[muon2]

I find that the context often makes the problem harder. I could reframe question 18 as follows. I don't think this would improve the rate at which students solve it.

You look up some specifications for your little Smart Car and find that it has a mass of 800 kg with you inside. From the specifications you also determine that when you step on the gas the engine supplies 2000 N of force to the car. Find the acceleration you would feel under those conditions. Bonus part - how does that compare to the acceleration you would experience in free fall?

[muon2]

I find that the context often makes the problem harder. I could reframe question 18 as follows. I don't think this would improve the rate at which students solve it.

You look up some specifications for your little Smart Car and find that it has a mass of 800 kg with you inside. From the specifications you also determine that when you step on the gas the engine supplies 2000 N of force to the car. Find the acceleration you would feel under those conditions. Bonus part - how does that compare to the acceleration you would experience in free fall?

I fail to see how a Smart Car would engage their interest.      For that matter an approximately ¼ gee acceleration would be somewhat pathetic even for a Smart Car.  (As an aside, I think it would be more useful to define the standard gee as 10m/s² rather than as 9.80665 m/s².  Easier to use and anyone who needs a more precise figure than 10m/s² probably needs to use the local gravity rather than the genericized standard gravity.)

But more seriously, would anyone in the "real world" ever make a calculation like that? My point was not simply that we ought to provide a context, but provide a context that motivates students.  Most word problems fail seriously on the motivation point and an unmotivating context may well be worse than no context at all.

I picked the Smart Car only so I could easily scale the two values in the original problem. Not many cars have a mass as low as 800 kg. You are free to pick any other vehicle you like.

If you aren't trying to estimate how many g's of acceleration occur when you hit the gas, then I expect that there is probably no real world example to help the students. That's one of the things that makes acceleration so hard to teach - students don't have a real world feel for the concept.

[muon2]

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.

Math needs are evolving, and teaching expectations have to as well. In this age of calculators and the internet there will be less need for computational skill beyond one digit manipulation. Instead the premium will be on people who can properly set up the information to supply to a computer and make estimates to have a sense of what the computer's answer ought to be. It's not the removal of number sense, but the type of number sense changes in this paradigm. For example our western European tradition does operations from the least significant digit to the most significant digit to improve calculation accuracy. However, when using a tool, whether a calculator or going back to the abacus, a better and older method starts with the most significant digits.

Physics for non-physicists becomes more about concepts and relationships between physical variables than plugging numbers into an equation. If you are familiar with the force concept inventory it is is a good example of conceptual questions. For non-physicists the goal becomes correctly predicting an approximate result and avoiding errors in conventional wisdom. That helps when physics concepts appear in other fields.

[muon2]

Acceleration need not involve the understanding of derivatives, and when I teach it to life science majors (eg pre-meds) it doesn't. There are two generally important concepts that acceleration embodies, and those are often applicable to work outside of physics. One is the idea that the rate of change of motion is not the same as the motion itself. Slowing down from 80 mph to 40 mph in 10 sec is not as harmful as going from 20 mph to 0 in 2 sec, since it's acceleration that can cause damage not speed. The other idea is that net forces don't cause velocity, they cause acceleration. So setting up a display to minimize damage from acceleration is related to minimizing forces that are out of equilibrium, and the same principle applies if the display is set up in a moving truck.

[muon2]

I see it's been long enough since I had to worry about the terminology I goofed.  When I said differentials earlier, I meant differences  (i.e. ∆x's and not ∂x's).  [By the way, I would think 20 to 0 in 2 sec shouldn't normally cause harm as it's under half a gee.  Possibly for a baby who doesn't have any support in the direction of the acceleration, but certainly not a healthy adult.]

nb. you are correct that half a g isn't very harmful to people. I was only comparing that to a higher speed but less acceleration.

[muon2]

Speaking of the Common Core, at least one citizen thinks it's a superhighway straight to Hitler. And what is a means for a local board to put on end to the verbal flagellation? Yes, you guess it - go into executive session!  

Ironically NY has had state mandated standards leading to its Regents Exam for probably longer than any state. NY has modified those standards and the test it gives many times over the decades. I suspect the citizen needs to take up his issue with the NY state education establishment circa 1878 to get satisfaction as to why his local board is using standards developed to collect data on student performance and to insure some level of equivalence among districts.