OK, lets asume you are correct. Some people just can’t do math. Not their fault. Lets grant that. But why should those people qualify to be a teacher? I can’t throw a baseball very well. Lets grant that it is an inherent problem with my body. Is it reasonable for me to be able to get a job as a major league pitcher? Some people, through no fault of their own, simply can’t do some jobs. Not everyone can be a movie star or an airline pilot or a farmer. Or a teacher. That is the way the world works. Though perhaps the field of education is broad enough to allow lots of people to be teachers even if they aren’t able to pass CBEST. Just like being a movie star, or at least a movie actor, doesn’t require great looks.
It is a separate issue if today’s education system fails to educate people who could be a qualified teacher and as a result we exclude those people from the profession.
There is a political angle to this, because the group of people who can’t do math tests for cultural reasons is biased towards Blak people, but the facts aren’t biased, it’s a real effect.
I wouldn’t be surprised if a good 25-30% of the accountants I work with couldn’t pass this sort of test. There isn’t a day that goes by when I don’t read an email from a controller or a VP of Finance and think, “how the fuck did you get your bachelor’s degree, much less a high ranking job?”.
My point is, this kind of staggering, dumbfounding lack of education is by no means limited to the public sector.
Can you provide any evidence for this? I did the test. The questions are simple and also quite practical: the kind of basic math skills that are useful in everyday life. I would be highly skeptical that people who can’t do the test somehow know how to do the math.
I can think of three things it could mean when people “can do the math, they just can’t do math tests”:
They have something like test anxiety, which interferes with their ability to do what they otherwise could.
They’re taking tests that are poorly designed. (With a well-designed test, there’s no real difference between “doing the math” and “doing the test,” because doing the math is precisely what the test asks you to do.)
They really can’t do the math (at least not unless it’s presented in one specific format that they’re used to).
I’m a math teacher. I can testify that there are students who can grasp solving mathematical problems in situations that make sense to them, but have trouble grokking word problems. The issue is that the education system thinks of “theoretical - practical” as a dichotomy where things are either entirely abstract, or entirely concrete, where in reality it’s a scale. “Word problems” are not “practical math”, they have at least one level of abstraction, and for some students getting past that abstraction is hard. And sometimes the education system doesn’t help them learn the skills necessary to grasp the meaning of word problems, it just hammers into them “word problems are meant to be solved by magically guessing which approach to use and what numbers from the problem to plug in where”.
One of the core problems of math is that fairly early on it becomes like learning about a completely new world at the same time as you are learning a completely new language to use to describe that new world. And some students never comprehend the finer points of the mathematical language, or the finer points of the mathematical world. They are basically stuck in acting like a Chinese Room for math.
Can you give examples of students solving math problems in situations that “make sense to them” ?
I would say many of the problems in the test are pretty practical and involve situations which could easily happen in real life. Like:
“If Gabriela needed to buy 9 bottles of soda for a party in which 12 people attended, how many bottles of soda will she need to buy for a party in which 8 people are attending?”
If college graduates struggle with problems like this, I think you have a real problem.
And in a job context, employees will often have to analyze numbers which are at least as abstract as the word problems in that test. You don’t have the luxury of only doing math which “makes sense” to you.
Hmm, having done more than a few tests in the old days, I always found that the sample questions were only indicative of the easier test questions. However, I have no experience with this test.
Again, and as a separate issue- I want to point out that test-takers who could afford to buy a prep course did much better on the tests.
If someone for instance is doing wood work, they’ll be able to figure out scaling, the use of Pythagoras to get a square corner, the best use of materials etc. etc. And if you know that you can use that basis to explain the mathematical language for the approaches they use.
But if you give them the world problem you present they’re more likely to go “She should just buy 9.” or similar. And it’s not something that could easily happen in real life, because buying soda for a party is an exercise in approximation.
You could somewhat easily make it a situation that could happen in real life, but even if it is something they have direct experience with, the textual description is a layer of abstraction that requires a learned skill to interpret. Yes, for a large part of the population that skill feels like it’s just innate, but that just means you learned it easily at an early stage. It is also a skill to turn it into an equation and some students may have made it through this level of questions by manipulating the quantities in their head, thought taking the trouble of writing it out was annoying, and then been unprepared for more complicated problems and deciding that math is just stupid and not for them.
There are so many ways to fail in math, so many ways to learn bad approaches, and very hard, with the available resources in your average classroom to deal with more than a couple of students with challenges while also teaching all the middle of the road students and a high achiever or two. And giving students work at the wrong level can reinforce their bad ideas about math. Do that for several years and you get a lot of “I just can’t do math students”, but you also get college students who can pass a basic math test by cramming a limited set of methods right before a test, but who don’t understand what they are doing, and don’t retain the knowledge.
OK. Even simple word problems will have some small level of abstraction. But if students and even teachers cannot handle that level of abstraction you have a serious problem. People face real-world situations with greater levels of abstraction all the time: as employees, tax-payers, borrowers etc. If you can only solve math problems in a tiny number of contexts, you are not functionally numerate.
I agree that teaching basic math skills is harder than it looks especially for weaker students. Which is why I think that more time should be spent in high school reinforcing those basic skills with classes in numeracy, personal finance etc rather than moving fully to more advanced math topics which are often of limited practical value for the average person.
Again, it’s not just math. They are also failing the reading and writing portions.
I don’t think this is a new problem, or one limited to the U.S. In the 1980’s the government of Alberta instituted a ‘writing competency exam’ because of complaints that nearly illiterate students were being admitted to college and even graduating without decent writing and reading skills.
The test was dead simple: There were a number of topics you could choose from, all of which were relatively generic. All you had to do to pass was write a 400 word essay on one of the subjects. You weren’t graded on the quality of your content, but merely that were able to string together a 400 word commentary that had less than two or three spelling errors or grammatical errors, with paragraph breaks in appropriate places and a conclusion. The main thing was that you started with an opening paragraph and maintained a coherent thread for 400 words. That’s it.
You had to pass this test by your third year of college or you had to drop out. You could take it as many times as you wanted, as I recall. Two years after the test was put into place the universities panicked because so many students were still failing it that they were going to lose a large number of students. So the test was quietly dropped and never mentioned again.
I was a grader for these tests and can attest that a failing test meant you were pretty much unable to express yourself at all with the written word. A sample failing test would look something like this:
"My esay is on Dogs. One topic was pets. Dogs are pets. Some dogs are not pets.
On dogs, I wood say dogs are good pets but a dog can be more and a dog that is not a pet could be wild or i guess just running around but those dont count. If you loose a dog it is still a pet though. This has been my esay on dogs."
I made that up, but it’s very close to the quality I saw on dozens of essays I graded. These were students already in college.
The only conclusions I can draw from this are:
Our educational system doesn’t work very well for a lot of people.
We are sending way too many people to college, and our standards are too low.
We are graduating people who are incapable of doing the work they are supposedly qualified for.
The teacher exam failures leave me with the same thought I had at the time: How are these people graduating from high school, let alone being accepted into college?
I agree with you 100%. If there is one thing that creates these “passed high school math, knows no actual math” students its the system that thinks the right thing is give them extra help to get Cs in statistics and precalc instead of working on fundamentals and genuinely practical math.
Although all the reasons for not being able to do tests are relevant, what I specifically was thinking of was the known, demonstrated effect that test performance depends on how well you think can do on the test, and the known, demonstrated effect that Blak Americans do badlly on math tests because they think that Blak people do badly on math tests.
This creates systematic discrimination, which is bad in itself, but also is of particular relevance when you are trying to provide cultural balance in your teacher workforce for pedagogic reasons.
The known, demonstrated effects are general, and demonstrated under research conditions. I don’t know how relevant they are to this test, and this demographic. But at first glance, this seems to be exactly the kind of test and the kind of demographic where it would be relevant. And the quoted numbers indicate that something is causing an obvious racial bias, of which this may be one factor.
I agree that the test covers grade-school maths, and grade-school teachers should be able to do it. But when you are using a test for certification, you don’t have the luxury of just saying “they should be able to do it”. You should/must put some thought into what you are actually testing.
I repeat: I agree that the test covers grade-school maths, and grade-school teachers should be able to do it.
In the interests of fighting ignorance, I point out that the known problems with this kind of test may also be an issue.