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0

I'm not in education, so take my answer with a grain of salt. I am merely approaching this from a perspective of someone who is really frustrated with how mathematics is taught. Mathematics is a tool we use to understand the universe. If you want to make math more engaging, it would be useful to actually show how one could use math to solve problems. For ...


3

It's about the learning experience. An issue with project based learning is the need for objective grading isn't going away. Since the first semester of mathematics is what serves to filter out under performing students there is a desire to have an unmovable bar. Without it you get grade inflation. This isn't to say there can't be projects. You just have ...


2

I'm an engineer who really likes and uses mathematics on work and daily life. Myself, I would try to make the course as much self-contained in classes, but still stick to some written material the students have access to. This allows the subject to be more complex and extensive while keeping down the difficulty settings. I'd prove theorems as much as ...


1

Select and use an open textbook. Students who wish to use a physical textbook will be able to get a copy run off and hole-punched at a local print shop, then put in a binder, for far less than the cost of a conventional textbook. You will save your students a pile of money and there are enough available options that you should be able to find something ...


7

Without directly answering your question, you don't seem to have the background you need to be "improving" the undergraduate experience yet, and have some work to do. I think you're right in sensing that your question is too general Don't talk about the "difficulties in forming such a course", and spend your initial time finding out what aspects of the ...


9

Given 100% control, I would have one-to-one instruction. One instructor meeting individually with each student. That instructor can change the approach, the speed, the order of topics, the method of instruction, based on that individual student. But of course hiring (and training) enough instructors for that is probably way beyond any reasonable budget. (...


4

A lot depends on what you plan to use the bachelor's for. If you plan to go to grad school, than go crazy and take a bunch of hard upper div classes. I really caution AGAINST grad school in pure math though (for you, based on your evident aptitude level). Even for stars, this can be quite a daunting pyramid--how many of the people here are tenured profs ...


3

When an inexperienced student sees $a=b=c$, I'd assume that both $a=b$ and $b=c$ are clear but the transitivity that yields $a=c$ might not be obvious. That's why I'd focus on this hidden equality when reading it out loud, by not just reading the equation (your first option), but rather saying "a, b, and c are all equal" or "a, b, and c are the same number" ...


1

I think how you read (and write) them depends on how they are being used. $$ x^4 - y^4 = (x^2- y^2)(x^2 + y^2) = (x - y )(x+y)(x^2 + y^2) $$ is fine but pedagogically $$ \begin{align} x^4 - y^4 &= (x^2- y^2)(x^2 + y^2)\\ &= (x - y )(x+y)(x^2 + y^2) \end{align} $$ is better. More important is dealing with this common misuse of chained equals ...


8

I think it is very possible to have real, meaningful research projects at all levels. As an example, I had 2 of my students in Calc 2 work on a project which started with the idea "Can we define a tangent circle instead of a tangent line?" They started by finding a formula for the center and radius of a circle given three non-colinear points: https://www....


5

Perhaps a research project could be replaced by an independent study project. The idea is to learn more math, in a more independent way. The student would still have to produce something to show what they've learned (although if the teacher found it easier, they could instead require an oral explanation of the content learned). I learned a lot on the ...


3

Opinion: I think they get enough exposure to writing reports in other subjects. Think the time is better used for drill and exams, than for writing a report. The one benefit might be learning to search the literature, but even that is probably much better done in history or science where, although rather difficult, the papers are still comprehensible. (...


3

My opinion on this topic has vacillated a little through the years, but for the most part, I've always spent time on background information about mathematical and statistical information because I firmly believe that doing so encourages an increase in student understanding and recall. I believe it also helps students feel less stressed in my classes, ...


5

I'll quote a few short things from the (fantastic!) articles shared in comments by Dan Fox and user1527. Morris Kline in 1954 wrote: What have we been feeding the liberal arts students? The almost universal diet has been college algebra and trigonometry. I believe that these courses are a complete waste of time... Kline proceeds to outline a plan ...


6

Here are some problems I see with asynchronous self-paced instruction. Let me begin by first setting forth some assumptions I have about what self-paced likely entails. Instruction is automated: the content is largely produced asynchronously to your use. You are not directly interacting with a teacher. Instead, you are likely watching little tutorial videos ...


2

This is a little later than the 1950's, but it's been a while since your question was asked. I used to teach math at the Ohio State University in the early 1980's and even then, anyone getting a B.A., who were basically the students with non-STEM majors, were only required to take one basic algebra course to complete their degree. If I recall correctly, the ...


6

Usually, "self-paced" or "personalized learning" courses are managed via technology. An interesting review of the current state of the industry was published yesterday (as I write this) at Technology Review by Natalie Wexler: A 2019 report from the National Education Policy Center at the University of Colorado on personalized learning—a loosely defined ...


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