Benjamin Dickman
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Using terminology for the different concepts of rational number
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You can find a discussion of these considerations in: Chapin, S., & Johnson, A. (2006). Math matters: Grade K-8 understanding the math you teach. Sausalito: Math Solution Publications. ...

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Common Core, threat or menace? Or maybe ok after all?
10 votes

Edit (7/17/14): You can find a very informative flow chart about CCSSM here to show dependencies among standards. At the time of posting, the page covers the standards included for K-8. If by "...

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Conceptual Mathematics by Lawvere & Schanuel as text for bridging course?
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In case you have not yet seen it, I thought I would draw your attention to (what is currently) the most recent issue of the American Mathematical Monthly, and, in particular, the article: Leinster, ...

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Real-World Applications of Logic
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I think a good real-world example for an undergraduate course on logic is to discuss the following: The source of this is: McGee, V. (1985). A counterexample to modus ponens. The Journal of ...

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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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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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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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SMSG: Did any school districts actual teach the curriculum as planned and what were the results for the teachers and students?
9 votes

Your question is twofold: (1) Did any school districts actual teach the curriculum as planned and (2) what were the results for the teachers and students? At the moment, I have an answer for (1): ...

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Why is distribution prioritized over combining?
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9 votes

This grew a bit long for a comment. (My first note is similar to Alexander Woo's remark about factoring polynomials; perhaps he intended "polynomials" to subsume the case here, in which we add ...

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Wiggins' question #12
9 votes

I think you might find some value in Raymond Wilder's classic textbook Introduction to the Foundation of Mathematics. A free copy is archived here. Here is a short excerpt from p. 10 of Wilder's text: ...

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Was there an SMSG (New Math) "Algebra 2" text?
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Update: I had believed not, but see Paul Stanley's response above. A good source for information about twentieth-century textbooks on algebra and geometry is: Donoghue, Eileen F. "Algebra and ...

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What caused the (relatively) recent popularity of set theory?
9 votes

My very incomplete understanding: I know from Henry Pollak (first-hand, but mentioned briefly here and in an article below) that one of the driving forces behind SMSG (with whom New Math is often ...

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What can be done to instill good habits in students?
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9 votes

One thing I have done is to have taken the courses I have helped with (Teaching Assistant, Course Assistant, Research Assistant, Instructor) very seriously. A summary of my approach to TAing and ...

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Are puzzles a good way to interest pre-college students?
9 votes

(This is more an extended two-part comment than explicit answer.) Part one. Finding "puzzles" (often with a mathematical flavor) is not too difficult. Martin Gardner is probably the main go-to, but "...

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Is there any math text reader device to help children who cannot see?
9 votes

Edit: There is a related meta.MO post here. (This MESE thread is linked to in a comment there.) Check out this link and, if applicable, you might consider contacting some of the professors involved. ...

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What are some fun/nonstandard examples of arithmetic/geometric series?
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9 votes

The classic examples of the first $n$ natural numbers, first $n$ even numbers, and first $n$ odd numbers are all nice introductions. Here are some pictures I created to help explain them using blocks: ...

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What universities in the United States have Spanish-language mathematics classes?
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9 votes

Excerpt from a 2011 Insider Higher Education article (bold text added by me): In an effort that some are calling the first program of its kind, Georgetown College, a Christian liberal arts college in ...

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Should Eisenstein’s criterion be taught in high-school?
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I maintain that what you want to focus on is sense making (MESE 1) (MESE 2). If you can present Eisenstein's criterion as a way of tackling such problems that helps to promote students' critical ...

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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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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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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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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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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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What is the name of this discipline in mathematics education?
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What is the name of this subdiscipline in math education? In one of the comments, Dave L Renfro has a reference to Piaget, whose work was primarily done with younger schoolchildren. With respect to ...

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Complex numbers in high school
8 votes

Complex numbers are also taught in China. I observed a mathematics classroom in Nanjing, Jiangsu Province, China in 2008-09 for students in their penultimate year of secondary school (their high ...

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What do you look for in a student presentation?
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8 votes

I have students present (in classes ranging from grades 7 to 12) and use the following rubric. It is not original, and googling various snippets suggests to me that it has been pieced together from ...

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Mathematics Education Graduate Program List and Rankings
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8 votes

Update (2016 Mar 9). The OP asks (emphasis added): Is there a guide to selecting a math education graduate program, including a reasonably comprehensive list of programs? Here is a List of Links ...

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Method for teaching factorization
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8 votes

One way this is sometimes done is with factor diamonds. (Google or google image: factor diamond method. Here is a sample result.) In your question, you gave the example of $a \times b = 2$ and $a + ...

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Dividing by zero
8 votes

Having recently covered this topic in a course for pre-service elementary school teachers, I thought I would write a bit about the somewhat subtle difficulties entailed in tackling this question. I am ...

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Moving From Rote Learning To Creative Thinking
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8 votes

The question is very broad, as you surely realize, since you broke it up into six sub-questions (which are also very broad!). In order to attempt an answer, I will have to send you on a bit of a ...

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