Benjamin Dickman
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Argument for and against giving two different grades at the end of a course
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8 votes

I recall an undergraduate thesis presentation on grade inflation at a particular liberal arts college in the United States (completed for the Department of Economics). The thesis can be found here; it ...

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What is a healthy and effective way for a math educator to evaluate his or her performance?
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10 votes

One place to look is in the following source: National Research Council. Evaluating and Improving Undergraduate Teaching in Science, Technology, Engineering, and Mathematics. Washington, DC: The ...

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Is there a good age/level to start learning mathematical proofs?
11 votes

With regard to Math Education literature on proofs: a person to look to is Eric Knuth (Google Scholar). However, it may be more fruitful to shift from talking about writing (formal) mathematical ...

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How shall we teach math online?
3 votes

Here I broach only the case in which students have consistent internet access; the more general case is clearly much more difficult. Moreover, this answer is written for the present context, i.e., a ...

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How do blind people learn mathematics?
10 votes

Update for JMM 2020: See the potentially relevant blogpost here. The post begins: I am interested in how blind people learn mathematics at any level, but particularly before college. Math is often ...

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Are degrees of polynomials illogically defined in elementary algebra, intermediate algebra and college algebra courses?
2 votes

I do not believe that this is a concern that would surface, or be worth surfacing, in the courses named by this question's title. In my reading, the question is analogous to worrying about whether you ...

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How do you attract more math majors at a liberal arts college math department?
6 votes

I wrote to a professor of mathematics at a liberal arts college that has, in recent years, found great success in attracting more math majors. Here are lightly edited excerpts from the two emails I ...

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What does the research say about direct instruction vs. student centered approaches
3 votes

I suggest reading the AMS blog posts about active learning [which I think can serve as a suitable substitute$^{\star}$ for what you refer to as "student-centered"] for which the 2015 series ...

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Quote to show students don't have to fear making mistakes
4 votes

I appreciate Ben Orlin's "Math with Bad Drawings" post about Andrew Wiles, for which the theme is not mistakes but rather being stuck. I have the sense that it contains some relevant content ...

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Are there any math journals or magazines with math problems for middle school or university?
5 votes

The various journals listed in the MSE question here can help with the university portion. These include, but are not limited to, the journals: The American Mathematical Monthly (AMM) College ...

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Pedagogical considerations behind current order of presentation of trigonometry
7 votes

I disagree with the notion that the unit circle approach preceding the triangle approach should be, if it is contextualized historically, "baffling." To this end, I suggest two pieces if you are ...

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Would a 1990's educated person need additional content knowledge to tutor high school mathematics today?
5 votes

I gave an earlier answer [to a rather different question] in which I pointed to the Regents Exam Archives. One approach that you could take would be to look over a few tests from the 1990s as compared ...

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why did common core remove so many topics from Algebra II?
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4 votes

The Common Core State Standards for Mathematics (CCSSM) provides a list of standards that should be covered; the inference that a topic not mentioned in the algebra strand should, therefore, be ...

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Why is absolute value difficult?
9 votes

I am writing this based on pure observation (e.g., entering year four of teaching this topic to secondary school students, and having co-taught a minicourse for teachers on absolute value functions$^\...

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How to work with polynomials in difficult classes?
4 votes

Have you looked into Desmos for possible resources? In particular: How about the Marbleslides activities? I'm not sure whether this satisfies the criteria in your case (specifically: I do not know ...

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Desmos Assignment: Make a graph that does this
4 votes

Edit (June 2019): I used this final project with minor tweaks again this year. You can find links to some of the output for Spring 2019 - both students' graphs and write-ups - here and here. I used a ...

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Examples of Innumeracy
26 votes

Re-Re-Edit (May 2019): Found in a selection of tweets here but pasted as images to preserve. Credit for the first one goes to @lizardbill and to the rest to @GeneticJen: Re-Edit (Jan 2016): Perhaps ...

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Jason Padgett's "Struck by Genius"
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23 votes

Edit 2: This story continues to reappear periodically in mainstream media; this month (April 2019) it was featured in a BBC Feature story here. The article title is: The violent attack that turned a ...

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How to explain fractions to 7 year old kid
3 votes

With regard to this question: Any ... books I can buy which can help me to explain this? Here is a specific book recommendation, which is a source that I have personally found helpful: National ...

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Algebra 2 textbooks that incorrectly claim that all solutions of polynomial equations can be found
12 votes

At the moment, I can answer bullet point two: Are there any high school textbooks that explicitly acknowledge that the methods included in the text are not adequate to solve all 3rd and 4th degree ...

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In what grade do kids (New York, US) learn common differences?
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5 votes

The linear function component is covered early(ish) in Algebra 1, and quadratic functions are covered towards the end of Algebra 1; so, the former by 7th/8th grade and the latter - if at all - by 8th ...

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Why do inequalities flip signs?
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40 votes

I'm slightly concerned that Is there a mathematical reason (like a proof) of why this happens? is a purely mathematical question, but since you write "we just warn students" I will assume that ...

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What to include in an "elevator pitch" for an undergraduate statistics class
3 votes

Here is the course description I wrote for a (high school) class on Statistics and Probability. I think you could modify it ever so slightly if you are covering Statistics, specifically, and that it ...

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Appropriate journal for an article on practical mathematical teaching
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11 votes

Edit: See also the PDF linked here: Wikipedia has a list of mathematics education journals; I happen to prefer the list of mathematics education journals compiled here, as they are provided along ...

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Has Benezet's teaching experiment ever been reproduced?
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9 votes

You can find some further studies that cited the original writing on google scholar: link Mahajan (PDF) remarks that: Etta Berman, one of the teachers in the program, studied it for ...

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What are standard (or good) textbooks for undergraduate graph theory?
0 votes

The book that I used was Applied Combinatorics by Alan Tucker. There is a preview available for free on google books, link. Here is part of the table of contents: [FWIW: I mentioned this same book ...

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Source material to study number theory?
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8 votes

I've heard very good reviews of the 2017 book, "An Illustrated Theory of Numbers" by MH Weissman. The book's main site is here; a write-up, along with some reviews, by the American ...

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Examples of Research Level Math Discoveries Done by Undergraduate Students
2 votes

One certain source can be found by looking through winners of the Morgan Prize, which is awarded for mathematical research by undergraduate students. Besides the wikipage linked above, there is also ...

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What is most motivating way to introduce Fermat's Little Theorem
8 votes

I wrote an article for NCTM's grades 8-14 journal, The Mathematics Teacher, which is about building towards ${\rm F}\ell{\rm T}$ by thinking through ways in which the following statement can be ...

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Experiences with Venn diagrams as didactic tool for factors, GCD, LCM?
6 votes

I have a worked example on MSE here in which I cite (RE: your comment on pointers to articles): Feldman, Z. (2014). Rethinking factors. Mathematics Teaching in the Middle School, 20(4), 230-236. ...

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