Benjamin Dickman
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What did math educators think about the transition to widespread classroom use of calculators?
6 votes

Googling "NACOME" 1975 calculators seemingly leads to the report that you mention: Hill, S. (1975). Overview and analysis of school mathematics, grades K-12 (NACOME Report). In Washington, DC: ...

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Definition of the term, equation
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6 votes

Your question is, in some sense, purely mathematical: What is "the" definition of an equation? You identify two different definitions, so I do not know if any single one of them can be ...

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Subtraction Methods in School Mathematics
6 votes

For the United States, I suggest as a resource: Karp, K., Caldwell, J., Zbiek, R. M., & Bay-Williams, J. (2011). Developing Essential Understanding of Addition and Subtraction for Teaching ...

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The meaning of equal sign in unit conversion
6 votes

You write the following: Obviously, the question is about what fraction of what is shaded. More generally, the question is about unit conversion in disguise. I believe what you have recorded here ...

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Motivating Mathematics Movies
6 votes

There is a list at The Mathematical Movie Database that includes (for some of the entries) the relevant time stamps and dialogue. I found the site by looking for one particular movie: It's My Turn (...

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Justifications for: Why learn mathematics?
6 votes

Edit (Feb 2016): Since the OP mentioned Hacker's Algebra opinion piece in the NYTimes, perhaps this is a good place to point out his most recent follow-up in a similar direction (I exclude here my own ...

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Which math subjects should I know well to tutor competitive mathematics?
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6 votes

I know they contain algebra, geometry, combinatorics, and number theory, but is there any other well-defined subject that is tested in these competitions? Consulting Gelca and Andreescu's (2007) ...

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Are there any video games/app to teach children at age 3-4-5?
6 votes

(Migrated from the comments.) Here are three specific suggestions: Teachley (company page) Tiggly (company page) Bedtime Math (wikipage) I mentioned the first two in an earlier answer to MESE 750; ...

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The interplay of memory and mathematical performance
6 votes

In light of your edited "more general" question, I thought I would make a few remarks. Historically, an early treatment of the subject of reasoning by analogy can be found in work on Gestalt ...

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Learning vs. Development in Practice as a Math Educator
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6 votes

You have asked three questions, and, in mostly answering the second, my response is already quite long. For now, let me not broach the third question about consequences of the distinction in practice. ...

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How to convey the meaning of "mathematical maturity"?
6 votes

This question is tough to answer since I do not know the course you have in mind; I am imagining something that involves proof-writing, possibly naive set theory, and, more generally, the ability to ...

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How to deal with answers containing completely off-topic/random/very wrong arguments?
6 votes

I think an important consideration in deciding how to grade something is to ask yourself whether the answer even makes sense. I mean this in the more formal use of the word sense making in Mathematics ...

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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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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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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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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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Calling on students by name (who do not volunteer) in math classes
5 votes

I emphasize from the beginning of the year that mistake-making is to be expected; the specific language that I use can be found in MESE 11794. I believe that by ensuring this is a norm from the ...

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Requirements to learn calculus
5 votes

From Velleman's Calculus: A Rigorous First Course: As to the content of the first chapter, it includes (but is not limited to) the following: decimal notation, integers, rational numbers, irrational ...

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Everyday Example Problems for Solving Linear and Quadratic Equations
5 votes

Here is a real-life example that I used in a class with some success. The enrollees were middle school and high school teachers, who were in their first year of teaching (not having arrived with ...

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Is there a framework to study the mathematical competence in problem-posing?
5 votes

The answer to your question is yes. Check out the recent textbook: Singer, F. M., Ellerton, N. F., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. ...

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Approaches to Teaching for Questions Around Partitioning Space
5 votes

Since Joseph O'Rourke, in his response, has linked to the lazy caterer's sequence, let me also mention its three-dimensional analogue, the cake number. In this case, we are dividing three-dimensional ...

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Teaching advanced math using books with cartoons
5 votes

Edit: There was a relevant talk just last week (with some names that may be worth following up on) entitled Visual Learning and Teaching (and headlined with: Cartoons Can Teach Science). I see that ...

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What are some places to publish pedagogical articles about teaching undergraduate mathematics?
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5 votes

The links you've already provided (especially the second one) are quite good. The top journal, I'd say, is the Journal for Research in Mathematics Education (JRME). Depending on the content of what ...

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Examples for reasoning by analogy going wrong
5 votes

Given $ax + b = 0$ with $a \neq 0$, I can find a formula for $x$. In particular, we have $x = -b/a$. Similarly, for $ax^2 + bx + c = 0$ with $a \neq 0$, I can also find a formula for $x$. In ...

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Playful problems in mathematics
5 votes

There are many examples of games that children play (in the same way that kids might enjoy mazes) which have deep mathematics underlying them. An oft-cited example of this is the game of Hex: In the ...

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When is it a good idea to avoid talking about why something works?
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5 votes

Framework for Concept Introduction: A general framework can be adapted from the Zone of Proximal Development or ZPD, which is an instructional concept (due initially to Lev Vygotsky) that continues to ...

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What are some best practices for creating student groups?
5 votes

You seem to be asking about within-class grouping by ability, but there is a fair amount of literature about what happens when the entire class is grouped by ability, e.g., when mathematics classes ...

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Is there a program like ALEKS for mathematical logic?
5 votes

The most relevant piece of software of which I'm aware is called Proof Designer. Proof Designer is a Java applet that writes outlines of proofs in elementary set theory, under the guidance of the ...

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What different ways do people use to show students that $\mathbb{R}$ is uncountable?
5 votes

There might be better or worse choices depending on how you actually build up $\mathbb{R}$. Are you using Dedekind cuts? Are you using (Cauchy) convergent sequences of rational numbers modded out by ...

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Is Peer Instruction suited to mathematics classroom?
5 votes

There is an emergent literature around peer tutoring used for mathematical instruction in urban settings. A nice article to begin with is: Walker, E. N. (2007). The structure and culture of ...

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