Brendan W. Sullivan
• Member for 7 years, 10 months
• Last seen this week

I'm not sure how well this suggestion would fit into your specific course set up, but I want to share something that has been helpful for me in other contexts: I like to set a general theme/...

This sounds like a method described in the following paper as second chance grading. The logistics are slightly different (less frequent exams with groups of topics, as opposed to weekly quizzes) but ...

Background: In my senior year of undergrad, I was a TA for our school's "Fractal Geometry" course, having worked with the professor before on a research project in fractals. We followed some ...

In general, issues with abstraction and axioms can boil down to losing the ability to visualize what's going on. I'd suggest appealing to visual/tactile intuition as much as possible, especially in ...

I study pursuit-evasion games on graphs, so I will recommend using the cops & robbers game as a way to introduce graph theoretic terminology, concepts, and examples. It should also keep the tone ...

I will share what I have been doing. I cannot claim this is popular, nor that it is necessarily the best, feasible option for everyone. But I know that when I started searching online for suggestions, ...

I second Sue Van Hattum's suggestion that you should not be so concerned with how large the $n$ is where the pattern eventually fails. I'll go one step further and recommend an example where that $n$ ...

I have no evidence to back this up, nor do I know how I could obtain such a thing. But I strongly believe this is a vocabulary issue, and I would like to see the term "series" phased out of usage in ...

I always provide the following example whenever a student assumes what they want to prove: Suppose 0=1. Then 1=0 must be true. Then we can add both equations to deduce that 1=1. This is a true ...

I've noticed a few issues when students solve problems of the form, "Find the inverse of this function", and not all of the issues are necessarily because of the students' misunderstanding of what an ...

How about the Tower of Hanoi puzzle and finding the optimal number of moves? This link describes the recursive solution procedure and a proof of optimality using induction. https://proofwiki.org/...

I think the Squeeze Theorem can provide a good opportunity for this phenomenon. The example I describe below arose in a Real Analysis course for upper-level mathematics majors that I taught this ...

I would emphasize the algorithmic nature of a construction over the ad hoc nature of a sketch/drawing. Tell your students that a construction must be accompanied by a specific sequence of steps (a "...

I believe option #2 (teach both and methods for choosing) is best. I'll try to illustrate with examples. $\displaystyle{\sum_{n=1}^\infty \frac{n}{n^2+1}}$ The intuition (which most students see ...

First, I think this is a great question for this site because it made me question how I teach uniform continuity in my own classes and sent me on an exploration for better ideas. So, thanks! Now, to ...

I suggest the probabilistic method in combinatorics and graph theory, for a few reasons: This will introduce the students to other mathematical concepts that they may not be aware of already, but you ...

One application is infinite series, since they are characterized by their sequences of partial sums. First, use the Cauchy Criterion for Sequences to establish a similar result for series. Then, use ...

I suggest using rational functions. Students are used to evaluating limits of rational functions because such examples are prevalent in most calculus courses. Moreover, I think the work required to ...

This may seem strange to offer an answer to my own question after just a week, but I did find a useful resource that may be helpful in addressing the issues described in my question. This week, I have ...

I'm trying to find more problems suitable for early college students (students who know algebra and calculus) that involve translating words into mathematical notions, [...] problems which seem ...

I suggest having a class discussion about formal logical phrases and symbols, and how to translate those into natural English. For example, your student wrote this For a and b to be relatively ...

Since a precalculus is, by its nature, designed to prepare students for calculus, I recommend gently introducing students to the concepts of calculus using the tools they already have. In this case, ...

Perhaps you can make the topic "applicable" by comparing it to some popular social media posts of the form, "How many triangles are in this figure? Only geniuses get this right!" Take a $5\times 1$ ...

Student Research Projects in Calculus Cameos For Calculus I particularly like the first one because the authors include with each project a description of how long it may take a student, any issues ...

Other answers suggest sticking to the definitions and just teasing out their logic carefully. I agree that this is a good method and you should mostly stick to this. @Behzad's answer with the picture ...

I teach, essentially, a "math course for non-math students who need to fulfill a college requirement" and have found great success with topics that don't seem like math to the students but certainly ...

I teach undergraduate students (ages ~17-22), with class sizes ranging from 10 to 30. I have come to realize that students will have their phones with them no matter what, so it would be unnecessarily ...

I don't believe students subconsciously misread the notation as an exponent with a word in front. I think they are not sure at all how to read the notation! When using logarithms (whether in a basic, ...

This one might take some extra massaging to make it "mathy" (re: "half" and "part" and "some"), but I like it as a fun twist on Abe Lincoln's classic (which @...

I believe this depends on how clearly the counterexample is stated. Consider this claim: $f:\mathbb{R}\to\mathbb{R}$ is continuous $\implies f$ is differentiable. Imagine a student, let's call him ...