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In many universities there are honors math classes. For example, instead of having five "mixed" Calculus I sections they arrange one "honors" class and four "ordinary" classes.

How effective is this? What are the arguments for and against such arrangements? Is there any research showing the effectiveness of such an approach?

My personal view (from teaching in a regional university) is generally against the practice. I prefer all "mixed" sections, thinking that the presence of well-prepared and gifted students among the general group of students helps both. I also think honors credit are better to be given to students who work on a project with a professor in a personal setting.

Edit:

In USA the terminology of "honors" is used to refer to classes of well-prepared and motivated students who take the same course at a higher level. There are no standard terminology for what I referred to as "mixed" or "ordinary". Typically no adjectives are used, or they may be referred to as "non-honors". Sometimes terminology such as "STEM College Algebra", or " Calculus for majors" etc. may be used to note a course with higher standards than the average.

The expectations from an honors class varies very widely.

Maesumi
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    There is lots of research at K12 levels that math works better if you find find a way to effectively teach students of different levels together. But I think it's different once you hit college. – Sue VanHattum Mar 20 '24 at 22:01
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    Would you say that the presence of mediocre and disengaged students among the general group helps both? – Sneftel Mar 21 '24 at 10:53
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    Is this generic terminology in English-speaking countries, or specific to one of them? – Tommi Mar 21 '24 at 11:35
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    @SueVanHattum How does that (the K12 part of your comment) work e.g. if you have some 12-year-olds still counting on their fingers while others have discovered and are working their way through their parents' boxed set of Newman's World of Mathematics? – shoover Mar 21 '24 at 16:12
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    I think those are both outliers. (I hope the finger counters are, anyway.) Check out the research Jo Boaler did. – Sue VanHattum Mar 21 '24 at 17:54
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    As written this question can't really be answered, because you haven't told us what you mean by "effectiveness". What do you want university calculus courses to do effectively? – Greg Martin Mar 21 '24 at 19:28
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    @GregMartin Correct. But I did not create the system either. Someone else thought it will be great to have an honors course. What were their objectives and rationale? Were the goals achieved? – Maesumi Mar 21 '24 at 20:30
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    @SueVanHattum a lot of these kinds of studies test the higher-level students on grade-level math after combining the classes, which completely negates the point they're trying to make. Of course if good students are tested on easier material, they'll do better. That doesn't mean they' – Esther Mar 21 '24 at 22:14
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    @SueVanHattum Finger-counting doesn't mean you can't do maths: it's just a sign you're struggling with addition tables. – wizzwizz4 Mar 21 '24 at 22:24
  • https://www.reddit.com/r/Teachers/comments/1bjjfjk/memorizing_your_math_facts_is_controversial/?utm_source=share&utm_medium=web3x&utm_name=web3xcss&utm_term=1&utm_content=share_button – shoover Mar 22 '24 at 01:41

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My undergrad university had an honors math program and the point was to prepare students for top graduate programs in math. The content was far more rigorous/intense than the regular classes, which I don't think would have provided adequate preparation.

Justin Skycak
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    I agree. I graduated well before the whole 'honors' thing started. Both freshman first-semester physics and linear algebra math had advanced sections of courses explicitly intended to break away from the other sections after the midterm to head on their own, more rigorous way for the rest of the year. You signed up for a different course number initially, and if you were not doing well by the midterm you were switched into the regular section. Basically everyone who ended up majoring in physics was in that section, so it worked as designed. – Jon Custer Mar 20 '24 at 17:22
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    Yes, these are different courses with different goals, so it doesn't make sense to combine them. Although we could debate whether "honors calculus" is the right name for it. – user1149748 Mar 20 '24 at 17:38
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    I was in an honors math program at U of Mich in the 70s. (There were actually 2 levels of honors! I was in the top level.) I was doing analysis in my very first calculus course. (I was very good at math, but certainly unprepared for that. I was the only one in my class who hadn't taken calculus in hs.) But yes, preparation for top graduate programs. – Sue VanHattum Mar 20 '24 at 18:09
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    I took honors calc I for the first semester because I had gotten AP credit for the first semester of calc and didn't feel like jumping right to the second semester (and/or maybe it wasn't offered in the fall; it was a small school). Honors calc worked through Spivak and did a lot of theory and proofs. Regular calc, whose book I have forgotten but may have been Thomas, covered the mechanics of the calculations to prep us for engineering classes. – shoover Mar 21 '24 at 16:17
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This can play out very differently depending on the setup of the educational system that you're in. When I was an undergrad at Berkeley in the 80's, honors classes were much more rigorous than ordinary classes, they were only intended for students intending to major in the subject, there was an entrance exam to get into them, and they used a different textbook. But at the California community college from which I recently retired, honors classes were expected to use the same book and cover the same material as non-honors classes. Any student could enroll in an honors class, and there were explicit rules saying that an honors class was not supposed to have more work or more difficult work.

If one was to measure the effectiveness of such a program, how would it be defined? By whether students gain self-esteem and have transcripts that look more impressive? By how they do on a standardized test? By how many of them end up having research careers?

kjhgsldkjh
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    What differentiated an honors class from the other sections? – Sue VanHattum Mar 20 '24 at 22:00
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    @SueVanHattum The honors section could differentiate and the other section couldn't. – Thierry Mar 20 '24 at 22:06
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    @Thierry: The honors section could differentiate and the other section couldn't. --- Although I'm sure this was intended as a bit of hyperbole humor, a very slight revision is probably true in many U.S. colleges/universities: "The honors section could differentiate from first principles and the other section couldn't." (By "first principles", I mean by using the limit definition of a derivative.) – Dave L Renfro Mar 21 '24 at 11:11
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How effective is this?

Mathematicians have difficulty understanding how the practice of requiring nearly everyone to take calculus leads inevitably to disastrous results. In fact, they have difficulty even realizing this is happening, after seeing it every day for over half a century.

Since this kind of subject matter is being taught to students who are not there out of any desire to understand this subject, but who are there in order to get an impressive grade, the result is that mathematicians have given up on the impossible and undesirable task of coercing people to understand, and instead they teach them to execute algorithms with no understanding. And it is those who work the hardest at that, who end up in "honors" courses. The mathematicians who organize these see that those students aren't really better than the others and the whole thing isn't working, and at least have enough sense to abolish such "honors" courses.

As for gifted students, they learned calculus before their first year at university.

It is unethical to design the curriculum for the purpose of extracting the few lumps of gold from a few tons of dust. If mathematics is to be taught to broad masses whose interests are in other subjects, it should be designed to teach them things they will understand and things they will use. Otherwise those broad masses of students are being abused and defrauded.

There are some universities at which the "honors" classes may work they way those who design them hope they will work. And it is very difficult to tell which universities those are without talking to people at each university and knowing which questions to ask. You can't tell from university web sites or any sort of published information.

Michael Hardy
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  • mathematicians have given up on the impossible and undesirable task of coercing people to understand, and instead they teach them to execute algorithms with no understanding. Disagree. The task is neither impossible, nor undesirable. It is just damn difficult, especially in the so called "mixed" class. Honors classes where the students are pre-selected according to their abilities (even if those are just the abilities to work hard and nothing beyond that) are easier and more pleasant to teach and you can go both deeper and further in them. – fedja Mar 30 '24 at 21:35