# Do teachers and books target more apt students?

Do math teachers, mathbook writers AND math textbook writers generally target students who show a math aptitude initially? Are students who show lack of interest weeded out? I remember seeing the movie STAND and DELIVER with Edward James Olmos (forgive the spelling), where he was a high school teacher and he wanted to teach calculus to his grade 12 students. The faculty was against him but he managed to make his students proficient in Calculus; A LOT of them initially disliked it. Why can't calculus be taught in grade 12 or 11?

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Calculus is taught in grade 11 or 12 a lot of the time. –  Ryan Reich May 10 at 16:10
Your post seems to contain three questions. Could you make it more focused, and also clarify what you mean by "target" and "weeded out"? –  Trevor Wilson May 10 at 16:37
Do teachers and textbook writers 'target ' or favor students who seem to understand concepts 'faster' than others? Those who are unclear or frustrated by 'standard' explanations are 'weeded' out meaning LESS of an effort is used to find out what they are unclear about. And Differential Calculus should be treated as MORE than an introduction in Grades 10 and 11.. –  user128932 May 15 at 6:17

## 6 Answers

Yes. In many places, students who are more capable get more resources allocated to help them excel. The textbooks do not discriminate between different students, but the teachers can, and quite often do.

It is not unheard of for 9th graders to take Advanced Placement Calculus BC. It's just a matter of how ready they are to take the course. I don't think that anyone is really neglected, it's just that the "smarter" kids get put into more advanced classes, which get more resources, allowing them to do even better. It comes down to ability more than anything.

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I'm confused about your conclusion "It comes down to ability." The rest of your post seems to aim at the conclusion "It comes down to resources!" –  Chris Cunningham May 12 at 14:53
I saw a news broadcast recently with Scot Pelley (forgive spelling) talking about some study casting doubt on S.A.T. scores and maybe I.Q. tests. THE study implied (I think) just as many student who did $average$ on the S.A.T. scores and or I.Q. graduated from good colleges as those who did well on the tests. Also there may be ALOT of people who can think well BUT are not good with the time limits of testing. –  user128932 Jul 13 at 5:52

It's not necessarily the case that people are trying intentionally to target a certain type of student. However there is evidence that certain traditional methods of mathematics instruction do cater to certain kinds of people and it is not as simple as selecting for the more apt students.

In the process of learning, students form ideas about what mathematics is and who they are in relation to it. Many get an impoverished view of mathematics because of an approach that focuses on certainty, having a single answer, rigid procedural action (so-called "machine agency"). Some decide that this inaccurate view of math is just what they're looking for for themselves and their future. Others want a future in which they feel they can express themselves in their work and use their interpretive, meaning-making ability. Not surprisingly, those people think math is not for them.

So, it turns out you're not getting the most "apt" students, and it's not necessarily intentional targeting.

For more details, and references to that evidence, see this other MESE answer:

How to handle the situation when you made a stupid mistake in front of the class?

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For whatever reasons a student finds limits to understanding a subject like Math shouldn't Teachers and Math-book writers have the goal of teaching anybody no matter how many times a student says 'I don't get it'? Maybe this shows clear explanations and methods to find clear explanations for ANY given student are MORE important than the hundreds of exercises that are imposed upon a student. I think a clear explanation of an important concept should be valued MORE than a 'proof' of that concept. –  user128932 May 15 at 6:28
@user128932 - Writers and teachers may very well have that goal. It is not the case that everyone is aware of the consequences of the methods they choose. Part of what math education research is for: to understand the consequences of the things we do have some control over in the classroom. In the case of the research I linked to, you can see the consequences are not just about understanding. Another insight is that "good explanations" from teachers are not what makes education good. To super-over-simplify, student explanations are probably a lot more important. –  JPBurke May 15 at 16:35
@user128932 - To pull this point together: the way you talk about clear explanations shows an (unsupported) assumption that good teaching = good explanation. But what outcome do we want? From person to person, this may differ. However, many people value understanding over proficiency with procedures (for example). So, a question: are clear explanations from the teacher what bring about understanding in students who are struggling? What if it turns out that explanations sometimes get in the way of student understanding? –  JPBurke May 15 at 16:47

No, they aren't. That said, some subjects are genuinely difficult such that even the clearest writer cannot simplify concepts further. You cannot distinguish your readers in a text. Authors attempt to narrow the prerequisites for learning their area to their bare minimum, which may not account for the true amount of background knowledge and/or mathematical maturity (often invoked) necessary for dealing and struggling with the naturally presented difficulties.

As for your anecdote regarding calculus in grades 11 and 12, I am not from the USA but I believe this stands: it's not about age but about readiness and willingness to work through the concepts. I feel that whoever learns calculus earlier than usual is better prepared and nurtured to do so than most people, not that they are more capable than anyone else.

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It is just that someone talented/very interested will be able to learn even from an awful book or teacher, and that teaching those is a lot more fun than dealing with the bottom fifth of the class. Given Sturgeon's revelation, and teachers being just human beings explains your observation.

Don't believe what Hollywood shows you. A modicum of knowledge in a given area (or just a bit of common sense) will show innumerable howlers in your random film. I'm not saying it can't happen; but if it was reasonably common, it won't make a good story...

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Was the movie 'Stand and Deliver' based on a true story? Other than this movie there have been hardly any good and inspiring movies that have something to do with Math. –  user128932 May 15 at 6:33

The text itself isn't the issue. In my opinion, student's aptitude fits a bell curve fairly well, and the struggle for teachers is to keep that lowest 1/6 passing, while not losing the top 1/6 to boredom.

In my school, the advanced track has calculus as an offering for seniors (12th grade). I also see seniors who are struggling with algebra, of basic trig. A student's problem on solving simple trigonometric operations is an example of this. The text and the teacher are expecting students proficient at basic manipulation, yet, the teacher will likely need to pause to give this a review.

An answer to that question (Chris) suggests that mastery isn't the right expectation. My opinion is that his response is correct and forms the basis of the full high school curriculum. i.e. that a certain fraction of class time spent on review reduces the amount of new material that can be delivered.

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Maybe the issue is that clear and fascinating explanations of Math concepts do not seem to be promoted as much as accurate proofs of some theory. Why aren't there awards for the most fascinating and clear and elegant explanations of a theory or principle. Even if the theory has 10,000 proofs one of them might involve an interpretation that is clear and elegant EVEN for amateurs or students. There should be contests for the clearest elegant explanation of a theory. –  user128932 May 15 at 6:41

Do teachers and books target more apt students?

I am shocked at people either saying or implying that the answer is no.

I have discussed this topic several times with my former fellow students and to me it's quite obvious the answer is yes.

In first grade everyone, except for a few rare exceptions, learns the material. This is the kind of success rate any normal academic school should aim at.

In university, only a handful of people learn the material properly (and not just passing). How can people claim that the courses aren't out of the average students reach? They are so by definition. Arguments such as "students just don't study" aren't good because students don't study in first grade either, yet they learn.

With respect to books, the same happens. Take a regular mathematics book about a subject you don't know and you (unless you are one of those handful of people) will struggle. Take a non-regular mathematics book like How to Prove It: A Structured Approach and things are very different. You can actually read this book like a novel. The level of detail is actually adequate for someone who doesn't know anything about it.

Picture yourself teaching a group of thirty people how to turn your water heater on. Would you really believe that you're teaching was adequate if only two or three people really learned it and ten somehow managed to 'barely' turn it on while the others simply couldn't? The difference in difficulty between turning a water heater on and learning calculus is of no concern here, results are what matter.

Throughout my rationale I basically assumed that students should be learning without studying at home. I do not commit to this view, but if you reject it, I still maintain my position. If one removes people who don't study at home, there will still be a huge amount of people failing. (I can't support this claim with evidence, this is just something I observed during my undergraduate degree).

On a more personal note, I had good grades throughout my BSc I had good grades, but I had to work hard to get them, so did my most of my friends who had good grades and I know about lots of people who worked hard and didn't get good grades. Wouldn't you expect, if you pick one of the best students, that he/she would be someone who learns easily? This isn't so...

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I don't understand your comment about studying at home and not studying at home. In my experience (both as teacher and as student in the U.S.), learning is mostly expected at home in high school (but doesn't always happen; perhaps the top 20% can get by without doing this, and the bottom 20% will not get by and will not do this), and learning is strongly expected as an undergraduate (the often-cited rule being roughly 2 hours of outside class study for each hour of class; math tends to be higher than this, and some faculty will suggest 3 hours). In graduate school almost all is at home ... –  Dave L Renfro May 21 at 14:32
@DaveLRenfro From your comment I can't realise what you don't understand. In response to your comment, I reiterate: "If one removes people who don't study at home, there will still be a huge amount of people failing. (I can't support this claim with evidence, this is just something I observed during my undergraduate degree)". –  Git Gud May 21 at 14:37
It's been my experience, in the U.S. at least, that academic standards rise very sharply from high school to college. Indeed, this seems to be all I heard from teachers when I was in high school, with comments like more than 3 or 4 misspelled words in a 5-10 page term paper ment a letter grade penalty (this was mid 1970s, before spell checkers) and professors expecting you to learn almost everything out of class. (The movie The Paper Chase comes to mind, although this was for law school.) If anything, I thought college was much easier than I had been led to believe. But that's me ... –  Dave L Renfro May 21 at 15:06
There are alot of great teachers in many fields; it usually takes an enthusiastic teacher to make a boring and/or tedious textbook understandable and not like one of those VCR Owner's manuals no one wants to read. I think textbooks should be written so they don't always need a 'super' teacher to make them clear. We should not only value great thinkers and writers but ALSO great $explainers$ –  user128932 Jun 14 at 13:51