College Readiness and Advanced Placement

I never did AP (non-US high school), so I'm somewhat shocked by the implication that AP math doesn't test algebra, trig, etc.? Only calculus? I would have expected a more well-rounded approach.

To address Pam's comment: AP tests, to my recollection, are subject-specific. That is, you can take a test in AP calculus, for example, and it'll test calculus, not other math. (It's been a loooooong time since I took any AP tests, so I could be misremembering.)

The thing is, they're not like SATs or GREs, that are generalized to apply to as many students as possible (at least in theory, but that's another discussion). You take a class in that particular subject area, and are tested basically on the material from that class.

I took a huge battery of AP tests, and IB as well, though ultimately it didn't make much difference: I was a music major and there's only one music AP test. I was the only student in my high school who took it, and my score wasn't quite good enough to get me out of basic theory (in retrospect, probably a good thing as music theory at the college level is quite a bit more sophisticated than what you get in most high schools, if you get it at all).

I can say, though, that even after all these years, my algebra is still pretty good. I chalk this up to having taken it twice: the first time, I flunked.

More than three decades ago when I went that route it seemed to work well. The few of us freshmen who placed into the middle of the Berkleyintro physics sequence, had a huge challenge, but be all got caught up in time for the first quarters final.

Since the schools are teaching for the test, it is clear that the tests must somehow also include proficiency with the fundamentals. Kinda sounds a little like sports&music continually drill the basics, until perfection is acheived.

Perhaps the schools can still admit students based on AP scores, but
should give any students who want to place out of the basics a test which covers proficiency in the basics. Otherwise I imagine a lot of smart -but underprepared students will struggle and transfer into another field.

I'd say that even the students who can do algebra don't really understand algebra. That is, a lot of the various techniques and "tricks" and so forth of algebra can be separately memorized, but once you understand what you're doing they all start to make sense.

For example, I see students in my non-majors class sometimes talk about "cross-multiplying." I have to catch myself and remember what that is. It disturbs me a little bit that they've memorized that as something that they're allowed to do when the equation has this pattern. If you understand algebra, both the concepts of a symbol standing in for a value (known or unknown), the concept of multiplication and division of expressions, and so forth, cross multiplication becomes just something obvious, a special case of a more general technique.

Too many students get through by memorizing the tricks they need to know in order to get through the tests. This does not serve them well later when they get stuck with a professor (like me) who wants to assume that they actually got something out of their high-school math classes.

Practice is definitely part of it; they need more practice with algebra. But they need also to learn how to understand what it all means, to have a deep enough understanding of it that the techniques are no longer a bag of mysterious tools, but a bag of tools that are used as shortcuts, but which could be rederived easily enough if necessary.

I have been helping my daughter with her AP calculus. She is taking it as a junior. I took it as a senior many years ago. She took it because her older sister did.

She is terrible at algebra, and is it showing in her AP calculus performance. I have helped through many problems where her hangup was algebra.

AP tests (at least those with which I am familiar) emphasize a "cookbook" approach to solving problems. First, you recognize which formula out of the 22 you've memorized apply to this problem, then you plug the numbers or symbols you're given into F = ma or Gauss's Law, and then you choose the best answer. This applies most strongly to the math and physics tests, but I saw the same sort of thinking in the biology, computer science and even American Government exams.

It's hard to write a test which doesn't work this way, at least not a standardized test one can give to thousands of students across the nation and score by machine. It's not even a wholly bad idea: knowing which equation to use is, after all, a valuable skill. It does, however, mean that you are stuck testing the kinesthetic level of thought instead of the iconic or symbolic (to adopt Jerome Bruner's terminology; see Gonick's Cartoon Guide to Non-Communication for details). Also, more generally, the pressure to "teach to the test" means that anything which can't be tested in this fashion won't be taught: symbol manipulation, history of science, debunkings of pseudoscience (nobody takes down perpetual motion machines in AP Physics) and so forth.

More than three decades ago when I went that route it seemed to work well. The few of us freshmen who placed into the middle of the Berkleyintro physics sequence, had a huge challenge, but be all got caught up in time for the first quarters final.

It works fine for some students. I took AP calculus in high school, and skipped the first semester or two of the calculus sequence in college, and that worked out all right.

I think, though, that there are far more students taking AP math now than there were in 1989 when I took it, and there were probably more then than ten years earlier. Many of those additional students don't have a solid understanding of what they're doing, and that's what creates the problem.

I had AP English, which prepared me in no way for college English. Decades later I realized that the point of AP classes is that the teachers get paid more.

The SAT Math and SAT II Math 2C test symbolic manipulation on the harder problems, where they ask to solve for one variable in terms of several others. So maybe there should be a requirement to get a 700 on the SAT Math, or perhaps 650 on the SAT II Math 2C, in order to take intro mechanics. Failing that, they take a remedial course concurrently.

personally, I did great on the AP calculus test through sheer luck after a marginal calculus history in highschool. Getting placed out of mechanics in physics was no problem, but going straight into calculus of several variables and diff eq. for my math classes left me struggling. I got through it much more by knowing rules than by understanding rules. If I had just done the full sequence of calculus classes freshman year it would have slowed down my physics courses by one semester (due to math prereqs), but I would have struggled much less in physical chemistry and general relativity courses later on ... and probably retained more after graduation.

My undergrad, regardless of how well you did on the AP Calc AB or BC exam required you had to have at least one semester of basic calculus. For those who did well on the BC exam they had a special one semester experienced calculus course. For those who did well on the AB test they took a year long experienced course. For those that did alright-poor on the exam took the traditional calculus course. The reason for this was that they wanted students to have a skill set beyond being able to test well. As for algebra, shouldn't these students who take calculus in high school take two year of algebra prior? I took algebra in 8th grade and then took an honors adv. algebra in 10th grade. Adv. Alg. was a requirement before taking trig which was a requirement to take AP Calc.

I've been teaching biology at a high-minority, public university for over three decades and I think that Rob Knop and Blake Stacey are right on. Your students probably had the needed algebra but understood little about it. They just memorized algorithms. I think there are two reasons why the problem is unlikely to get better.

Many states are moving algebra I into junior high and they are also requiring more students take the course. Any course taught that early to that many students is going to be taught to the lowest common denominator; memorize this stuff so you can pass the test. When the students get to algebra II, the basics are already lost. It has been so long since your students had the material, it has been long forgotten. That is just the nature of memorized information.

All states now have some version of high-stakes testing because of federal requirements. It's anecdoatal evidence but it's what I consistently hear; the teaching emmpasizes what will help students pass the test. Teaching for understanding takes a back seat to teaching to the test.

My students come to freshman biology with a lot of memorized facts but they understand very little of it. They can list the steps in mitosis but they have no idea what the genetic consequences of mitosis are. Go to meiosis and even biology majors are clueless.

College readiness is something more than what can be easily captured on standardized tests, even the AP test. But standardized tests are what both political parties see as the cure for ailing education. Your problem is unlikely to go away soon.

I have a slightly different suggestion. Algebra should be introduced earlier and taught for a longer period of time. Back when I went through school, Math seemed to stagnate at about 4th grade. By then we had learned the basics of addition, subtraction, fractions, decimals, etc. and spent the next 3-5 years doing variations of the same thing. Okay, in fifth grade we learned about bases other than 10. The basic concepts of algebra should be moved into elementary school. It's not much of a jump from the silly, non algebra based word problems that students start doing by 3rd grade, to some very basic algebra concepts. That way, there's plenty of room for trig, geometry, and optionally calculus in high school. (I know that I could have used a stronger trig foundation)

I'll add a "me too" on the algebra problem, but I attribute it more to the use of graphing calculators and "high stakes" testing than AP classes, since I see all of those characteristics in my CC students. The problem is that the TI-83 will only do y(x), not x(t) or a K(T) rate equation so they just don't do a lot of symbolic math in our CC algebra classes or in HS classes built on a similar high-tech model. Similarly, the emphasis on passing a HS competency test means they teach to a certain style of multiple choice exam where there is zero critical thinking and very little in the way of word problems. They freeze up when a problem does not give them a number for each thing, because the concept of just making up a symbol "m" for an unknown mass is alien to them. They never got math problems with too much or too little information.

I will add something else: skimming rather than reading. I discovered the technical name for a certain out-of-fashion technique (close reading) from some non-science blogs I follow. Test prep emphasizes skimming and guessing by comparing foils back to the text. Eight years of that, and you will have difficulty seeing the details in physics problems and turning them into your own words and equations. I have written about this in the "close reading" articles grouped under the "teaching" category on my blog, and will be writing more about that when I get some time since I now see examples of it all over the place.

A lot of the learn the mechanics, but not the reasoning problems may be due to poor grasp of subject matter by the teachers. When my kids are stumped inmath and ask me for help, I always hear something like
why can't the teachers explain it to me like that -or something like it. I'm afraid it takes someone who both understands the material, and has the patience to carefully show WHY they are doing it this way to do the job. Given the low pay/esteem of pre-college teaching it is hard to see how this can change.

A secondary problem, which is especially true for math is that students need to be motivating to learn extra stuff on their own. I did that because I had a keen interest in science. Math cannot really be taught, it has to be learned via interested effort. The only one of my three high-school kids I can get to do that is the one who wants to write computer games...

The algebra problem is one I encountered in industry too. Many people graduate with technical college degrees and still don't understand algebra. This is a tool that anyone doing technical work needs. No algebra means essentially no statistics, which means (among other things) limited ability to test products and determine effectiveness of work strategies. Being able to regurgitate problems on a test bears no resemblance to how an educated person utilizes algebra in the real world (or at least, the ones who actually know how to use it).

And even outside of the technical world having some intrinsic knowledge,as ossposed to cookbook following can save your bacon. I can remember a car dealer trying to get me to take a loan (at 2% higher interest than savings) trying to convince me that I'd be ahead to borrow from him, at leave my money in the bank. Even though I didn't have the time to dissect the fallacy embedded in his "marketing" tactic I had confidence that he was wrong. I suspect cookbook mathematicians would fall for that trick any day of the week.

I am with Tonyl move Algebra up earlier. 6th & 7th grade math were a waste of time. Jump into Alegbra for most students at least by 6th grade if not sooner. Do two years of algebra in middle school so students learn the basics.

I'd rather they knew algebra well and didn't have half-ass calc. e^{i\theta}=cos (\theta)+i sin(\theta) should not sound to them like I am speaking in tongues......They are great with their graphing calculators, but take them away and (#%_&_&*$%$*&%_&%_$*%&$(%&+##$%%%# is oftentimes what we get.

The standard deviation for a high school physics class (in my state, Ohio) is larger than the mean I do believe.

Of course if they were aware it was legal to read other books other than the required text, and that all books have indices in the back to help find things......ah thats another rant:-)

I'm currently a senior, and I'm in 3 AP classes (Calculus, Physics C Mechanics, and Chemistry). I plan on taking 4 AP tests, so that includes all of my classes and Physics C E&M.

Personally, I think AP is great. The actual class work isn't too much harder than high school work, which at times feels incredibly slow and painful. And yes, most of the kids who take AP classes should not even be in them. But thats true of all kids, in all classes. I've had people my class ask me how to find moles once they know molarity and volume. This is 3/4 into the year, in AP chem. They've taken to memorizing the formulas, but without having a clue as to how to apply them.

But these people don't do well on AP tests. Typically, they don't take them. I anticipate that I'll do well enough (4 or 5) on my tests to move onto multivariable calc and either sophmore physics or advanced freshman. Without the actual tests, the AP classes would be useless. Most of the people I know who have taken the tests recieve 3s, which few colleges accept for credit.

So, my view is that the AP tests are generally good. GPA isn't a very good indicator of how well someone is going to do in a subject, but if someone recieves a 5 on the AP tests, you can be sure that they will be well prepared for their subject.

How many of the students you talk about actually recieved high AP tests scores? I think maybe they just took the class, and learned nothing, which is typicall.

As an aside, let me tell you about our calculus classes. I've heard people talk about how they can do calculus, but they can't do algebra. And this is perfectly alright, because calculus is "hard". Most can't manipulate equations at all, unless they're perfectly set up. For instance, whats the derivative of x cubed times the square root of x? My friend was at loss. In his senior year, he still had not learned you can add exponents. Thats the state of our math education.

"Personally, I think AP is great. The actual class work isn't too much harder than high school work..."

You just made the point of the original article. Classes like that don't prepare you for ones where you have to do 5 to 10 hours of homework and write a 5 page lab report each week. You would be much better off taking my physics class as a dual-enrolled student than your AP class. You would get a full year's college credit for a year's work at a college pace.

I took calculus (all of it, through calc III) at a local CC while in high school. There is no comparison between that experience and what kids from AP programs have learned.

I tend to agree with Dr. Pion that part of the problem is one of "teaching to the test." I took a large number of AP courses when I was in high school 20-odd years ago. Back then, the teachers were not (or at least not solely) engaged in teaching to the test, and so my AP experience was generally a good one.

But the box-checking factor that Chad discussed in an earlier post also comes into play. Many students, especially in elite schools or districts, feel compelled to take these courses in order to appear competitive on their college applications. Add in the bonus points that many schools give in GPA computations, and the too-frequent result is AP classes like Edi's, where many (most?) students cannot really handle the material. This is not a new phenomenon by any means; it was already happening in humanities/social science AP courses at my high school when I was there.

My solution would be to avoid putting so much reliance on multiple choice tests and instead focus on longer problems which require students to actually demonstrate competence in the subject matter. If AP exams are similar to what I took back in the day, they are actually not nearly as harmful as most standardized tests.

I agree that AP is nothing that it promises to be. But AP to me isn't the class, its the test. There is no other way to show I know the material than to take an AP test. Colleges would rather see you score a 4/5 on an AP test than to get an A in an AP course. They know there's grade inflation, but the tests are calibrated so that its representative of how you would do in an actuall college level class.

It isn't all multiple choice, and its a fairly difficult test. So, I think AP isn't as harmful as one thinks. The kids who take AP courses but not the tests won't get out of those college courses anyways, but for the rest of us, its the only way to show that we can do college-level work.

According to my acquaintances who teach high school math these days, the hardest part is convincing the kids to even do ANY homework in the first place. The teachers don't even bother with assignments anymore, because the kids will just copy off one another. (The more resourceful kids will find a computer program and/or java applet online to do it for them). So they end up giving a weekly or bi-weekly test, largely as a semi-ineffective way of motivating the kids to even open the textbook. There's no penalty anymore for NOT doing any homework. With grade inflation so problematic these days, literally nobody fails.

(The ironic part is that they don't even have standardized testing here).

The main problem is that essentially the k-12 school system is "run by the inmates" these days. Kids can get away with literally telling teachers to "fuck off" in their faces, with impunity. There's no penalty for bad behavior in schools these days, short of a kid bringing a machine gun to school and killing everybody in sight. Kids can literally get away with anything these days.

If a teacher insists on "old school" type of work habits and discipline, they better have a very good lawyer representing them. Teachers can't even touch any kids these days, such as pushing them out of the classroom for bad behavior, without the risk of being sued and/or being reprimanded by the teacher's union or guild. Basically it's the "kiss of death" for a teacher's career if they have any reprimands these days. In summary, discipline is largely absent or very ineffective for anything these days.

Teachers will also get fired if they fail too many students and/or if the final grades are too low. Even in dealing with the bad behavior of kids, they can't even send them down to the principal's office anymore. Whenever kids are sent to the principal's office, they get sent straight back to the classroom the next minute. (That is, if the kids are NOT escorted away by law enforcement in handcuffs). Administrators have largely "washed their hands" off of the situation.

It's almost next to useless in even calling the kids' parents these days, in reporting and/or dealing with bad behavior. Many parents will typically respond with things like:
- "So what?"
- "My kid isn't the problem. You the teachers are the problem!"
- "Fuck Off!"
- "Don't bother me. Go fuck yourself!"
- "Where the hell did you get your teaching license? From a crackerjack box?"
- "Fuck You!"
- etc ...

The other big occupational hazard is dealing with violent students, who are willing to physically assault their teachers. Even with metal detectors everywhere, guns will still get through. The teachers with a reputation for being "strict", will frequently get beaten up by their students or even possibly gunned down. (ie. These particular teachers have to be constantly watching over their shoulder).

With work conditions like this, it's no big surprise that hardly anybody wants to be a k-12 teacher these days.

"The kids who take AP courses but not the tests won't get out of those college courses anyways".

There is the problem, what I call a failure to comprehend the concept of prerequisites. The reason for getting a 4 on the AP exam is not to "get out of a class", it is to demonstrate that you have learned the material well enough that you will still know it 6 months from now when you have to apply it in another class.

Now I suspect that Edi (based on other comments) knows better, but the "cram and forget" style of test prep one often sees is what results in kids in calc III who can't solve a simple algebra word problem without studying for it. When we require trig or calculus as a prerequisite, we expect you to "know" it, not "have taken" it.

The concern expressed in the original article above, and repeated by other professors here, is that the kids who just "take" an AP class are under the illusion that they have had a college course. The same can be said for ones who pass it, as Steven Zucker at JHU has pointed out. (Google him, and read the "orientation material" section "told to my calc III class".)