Benjamin Dickman
  • Member for 7 years, 10 months
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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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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?
Accepted answer
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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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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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?
Accepted answer
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?
Accepted answer
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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Has Benezet's teaching experiment ever been reproduced?
Accepted answer
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?
Accepted answer
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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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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How can I help a student who has a "wrong" kind of enthusiasm?
8 votes

First, a response to a particular excerpt: I admit it's hard because often she's enthusiastic about things I'm enthusiastic about myself, and I actually like to chat with her about the Riemann ...

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Recommendations for free, basic resource on discrete probability for a discrete structures class?
0 votes

I recommend examining the site Seeing Theory to see whether it suits your needs. There is a corresponding text draft (link) on which the authors are actively seeking feedback. It is a free, basic ...

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Introducing an axiomatic method to high-school students
2 votes

I suggested back in MESE 11836 the following example from RL Wilder: With regard to the question here: Does anyone have any suggestions for a simple illustration, which ideally the students could ...

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Good Examples of Questions to have Students Ponder Over Without Paper
2 votes

Matt Enlow recently posted a wonderful collection of problems on twitter in his tweet here. He links to the "More Questions than Answers" pdf on dropbox here; it is a compilation of 100 math problems,...

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How to Write Steps of Solving Equations?
5 votes

Since I recently had a math teacher from another institution observe me during an Algebra 2 lesson and comment positively on my notation ("I'm going to steal that!") here is a worked example:...

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Should I tell my students that math is hard for me?
9 votes

I've long read - perhaps misread - the following comment from Einstein as lacking empathy: (What use is: Oh? You have a headache? I can assure you, mine is worse!) I feel as if sometimes teachers' ...

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What is the required mathematical background of a US elementary school math teacher?
8 votes

Here are the requirements for Teacher Certification in Massachusetts: The Massachusetts Teaching and Certification Resource Become a Teacher in Massachusetts An image pasted from the latter link: ...

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Is algebra unnecessarily quadratic intensive?
6 votes

Here are some brief [and admittedly inchoate] thoughts, as I'm not quite ready to invest in writing a formal essay about your very important question with respect to what an Algebra 2 course should ...

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How to teach abstract algebra for the first time?
3 votes

Some years ago I worked as a "CA" (Course Assistant) for preservice/inservice teachers taking a first course on Abstract Algebra (mostly group theory, with a bit on rings and fields towards the end). ...

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