Benjamin Dickman
• Member for 7 years, 10 months
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## 185 Answers

8 votes

One source you might look to is the following Master's thesis: Dickey, G. (2004). A Historical Approach to Teaching the British Columbia Mathematics Eight Course. In particular, see the literature ...

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8 votes

For already TeXed documents, I have generally attached them to threads in the discussion forum. As an example, I did this with a proof sketch of the Cantor-Bernstein-Schroeder Theorem using a .docx ...

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8 votes

Edit: You might consider Klain and Rota's (1997) proof of Buffon's noodle problem as a somewhat general example that can be used to resolve (the better known) Buffon's needle problem, and also to ...

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8 votes

Edit (4/29/14): A popular media piece in the New York Times on rent division gives a great example of how Sperner's Lemma can be used for fair division problems (as related to cake cutting, the ...

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8 votes

Quoting Wikipedia: The adjective quadratic comes from the Latin word quadrātum ("square"). Summarizing succinctly: Consider objects of side-length $a \in \mathbb{R}^{+}$. $a^1$ gives the size ("...

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8 votes

With regard to the education literature (note that this is not specific to mathematics education) Keith Sawyer writes about the paradoxical balance of improvising in the classroom and having ...

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8 votes

A related example that comes to mind at the (strong) secondary level is Yellow Pigs Day at Hampshire College; this includes David Kelly's focus on the number 17. At the (undergraduate) tertiary level,...

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8 votes

A good math curriculum to check out for Pre-K to K is Big Math for Little Kids. You can find some information about it in this interview with co-developer Herb Ginsburg. Ginsburg is also working on ...

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8 votes

I think there are several good problems that can be explored (e.g., using the Moore method) by beginning with a word or term and trying to axiomatize it. I happen to think that assembling several of ...

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8 votes

Outside of what is found in refereed journals (which one can generally find by just searching Google Scholar) a good source - if you have access - is ProQuest's "Digital Dissertations." ...

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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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7 votes

I am not quite sure if this answers the question in the body of your post, but here is how I have motivated the search for a closed form regarding these summations. Summing the first $n$ counting ...

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7 votes

If I were to cover the Fibonacci Sequence in introducing sequences to Calculus students, I would probably avoid some of the more obscure properties. I would focus on what early Calculus students ...

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7 votes

Here is my attempt to answer your question, if not directly, then at least in spirit! I am specifically responding to the following: Many students see no beauty in this subject, only fear and a ...

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7 votes

With regard to "mathematics as story" in the context of mathematics education, one place you might look to is the work of Leslie Dietiker (google scholar) on mathematics curriculum as story. For ...

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7 votes

(Summary: I would suggest exploring it flexibly, but ensuring students also know the "rigid" version.) Rather than directly addressing Euclid's algorithm for the $\gcd$ of two whole numbers, I ...

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7 votes

I have TAed several content courses for graduate students in mathematics education. In this respect, my interactions with students may differ from the scenarios faced by others who have served as ...

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7 votes

First, a direct answer: Yes, there is work in mathematics education connected to Gadamer. One soure for such studies is articles by Brent Davis; more generally, google scholar yields such ...

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7 votes

Perhaps this historical example fits the bill: Khovanova, T., & Radul, A. (2012). Killer problems. American Mathematical Monthly, 119(10), 815-823. The piece was published earlier on the arXiv ...

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7 votes

Literature: Unfortunately, I have never seen a study that compares these two approaches to teaching Calculus (nor did a cursory search through ProQuest and Google Scholar produce anything of import). ...

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7 votes

There are a lot of resources for problem solving online. One place to look is MIT's OpenCourseware; see their Problem Solving Seminar: Course Description This course, which is geared toward Freshmen, ...

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7 votes

(Sorry if my answer is as offensive as responding to a question about Coca-Cola with data about Pepsi!) There are certainly some lesson plans around looking at statistics for M&M colors. For ...

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7 votes

I'm not exactly sure what's being asked here, since you say you want to to learn how "to do advanced math," but also that you "want to try algebra and trigonometry, to play with equations." I can't ...

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7 votes

Your question is in fact three questions. Is there a good solution? Do you ask your students to give explanations for true-false questions? How do you deal with the issues raised above? My answer ...

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7 votes

In terms of researchers who I am personally familiar with: I would recommend work by Orit Zaslavsky. From her NYU-Steinhardt bio: Orit Zaslavsky's research focuses on mathematics teacher ...

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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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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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6 votes

Edit [12.16.17]: A write-up concerning a few of the problems below was accepted for publication in NCTM's grades 8-14 journal, The Mathematics Teacher. It is slated for publication in Fall 2018, but a ...

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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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6 votes

I recommend a newer Calculus textbook, which was published earlier this year: DJ Velleman's text, "Calculus: A Rigorous Approach" (link; also mentioned in my answer to MESE 11971). In the introduction,...

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