Studies on the change in effectiveness of pedagogical practices over time
Are there any studies that have investigated this question?Why certain pedagogical practices that used to be effective up to a few years ago, may suddenly become less or even no longer effective?I am...
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A better example of a logical implication
(Updated)An example of a logical (material) implication that is commonly used is: "If it is raining outside, then the ground is wet." The problem with this example is that it could be seen as a causal...
View ArticleWhat is the pedagogical justification and history for using mnemonics to...
There was previously a question/rant here on MESE about why so many are still using the PEMDAS/BODMAS/BIDMAS/BEDMAS mnemonics to teach order of operations. The question was deleted (still viewable by...
View ArticleAverage Rate of Change isn't/is Statistics
I have the common misconception in my business calculus classes that the Average Rate of Change, say from $x=1$ to $x=5$, is the statistical average of the rates on the four unit intervals $1$ to $2$,...
View ArticleActivities that encourage students to create or evaluate mathematical notations
I'm looking for references about activities that encourage elementary school students to create or evaluate mathematical notations. do you know any?
View ArticleWas math education following a western trend?
After some research on the recent history of math education in the U.S., from the new math movement to the beginning of the 21st century, I understood that the historic flow of the math education...
View ArticleFighting math phobia with history
After years of experience in some area of expertise, you can easily forget how difficult it can be for the uninitiated to grasp some fundamental concepts, and, indeed, people often edit out of their...
View ArticleWhat are some good books on mathematical pedagogy?
I suspect that; just as one must "do" mathematics to learn mathematics, one must have practice teaching mathematics to become a great mathematics instructor.Still, a good book on mathematical pedagogy...
View ArticleBooks that every aspirant mathematician should read
I am a student and I would love to become a research mathematician one day.So I would like to ask you---experts in mathematics but also ineducation---what are some influential ($\star$) books that I...
View ArticleCan we avoid confusion over using "let" as a quantifier?
I've encountered the following misunderstanding.I pose a question (to undergraduates in the U.S.), for example:Let $P$ be a polygon of $n$ vertices.Is it true that every triangulation of $P$has the...
View ArticleHow to teach pure mathematics to a well-educated adult who did badly in maths...
My partner is a PhD student in philosophy and has recently developed a keen interest in learning pure mathematics. I am doing my best to teach her (I'm a pure maths PhD student myself) and it is...
View ArticleBetter proof for a proposition when a proof is already available [closed]
What is a much better proof in mathematics, is it need to be a much more advanced one compared with the proof already available or a much simpler one? I think you can challenge a proof in two different...
View ArticleStudents can't seem to grasp the intent of tangent lines and getting general...
BackgroundI'm informally helping a few students with college Calc 1. This isn't the first time I've aided people with calculus, and so they've sought me for help, though I don't consider myself to be...
View ArticleIs this a viable Calculus 1 question?
A person is standing next to a hot air balloon. At the same time, the person starts moving away from the balloon at 5 ft/sec and the balloon rises straight into the air at a rate of 12 ft/sec. Is the...
View ArticleRole of history of mathematics in contextual teaching and learning
To get a deeper understanding of mathematics conceptual teaching and learning is supposed to be a much better approach than factual teaching and learning processes. Since the conceptual approach is...
View ArticleIdentifying Trigonometrical proofs
How can we identify trigonometrical proofs from geometrical proofs, do we have purely trigonometrical proof of Pythagoras theorem as claimed by two high school students...
View ArticleWhat can I do when advanced undergraduate and/or early graduate STEM students...
I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control,...
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Educational resources commonly address slant asymptotes. Why not general...
Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes."...
View ArticleImportance of complex numbers knowledge in real roots
Many students question the importance of complex numbers in real life. We can find many important applications of imaginary numbers in Engineering field and physics. This question is not related to...
View ArticleBridging the gap between students' intuitive problem-solving abilities and...
Seeking guidance on how to assist students who possess a solid grasp of problem-solving concepts, allowing them to intuitively arrive at solutions, yet encounter difficulties when it comes to...
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