Joel Reyes Noche
• Member for 7 years, 10 months
• Last seen this week
• Naga City, Philippines

It is possible to teach real numbers in elementary school before even rigorously defining them by using what H. Wu ("The Mis-Education of Mathematics Teachers," Notices of the AMS, vol. 58, no. 3, p. ...

Try objects that often occur in pairs but are distinct from each other: forks and spoons (or forks and knives), left and right shoes, salt and pepper shakers, and so on (where each fork has an ...

If your students have learned some statistics, then you could point out that the normal distribution's probability density function uses this double exponential. $$f(x)=\frac{1}{\sigma\sqrt{2\pi}}\exp\... View answer 25 votes (My answer is just a guess and not based on any formal research.) I suspect the absolute value function may be difficult to understand because it involves "negative numbers that aren't negative." ... View answer Accepted answer 24 votes One practical reason for choosing a Taylor Series approximation of a function over the function itself is if you are able to compute using only the four arithmetic operations. For example, if you are ... View answer 24 votes I make the statement "If it is raining, then I have an umbrella." Did I lie? If it is raining and I do not have an umbrella, then I lied. If it is raining and I do have an umbrella, then I didn't ... View answer 23 votes If your main interest is to provide a role model that students can identify with, you might want to look at Danica McKellar. According to her Wikipedia entry: McKellar studied mathematics at UCLA, ... View answer 22 votes If a teacher has taught the course before, and has asked questions that are free-response (not multiple-choice), then the teacher can look at the incorrect answers previously given by the students. ... View answer Accepted answer 20 votes I suggest you discuss the Seven bridges of Königsberg problem (the problem that essentially started the field of graph theory), then discuss the Three utilities problem. For each, discuss the problem ... View answer 20 votes \times\ \ +\ \ 4\quad 2\quad \omega\quad 9\quad a\quad 1\quad i\\ x\quad t\quad y\quad z\quad w\quad g\quad q\quad l\quad j View answer Accepted answer 18 votes This is a problem for some English language learners: The triangle on the left is also a right triangle. View answer 17 votes I would use the (real) number line. First introduce the concepts of positive numbers (distance to the right of zero) and negative numbers (distance to the left of zero). Then introduce the concept ... View answer Accepted answer 16 votes If the expression were, say, 48\div 4\times 12, there would not be much disagreement (multiplication and division are performed from left to right). But an expression such as 48\div 4(12) results ... View answer 16 votes You might want to read Kline (1973). I haven't read the book, but according to Wikipedia, In 1973, Morris Kline published his critical book Why Johnny Can't Add: the Failure of the New Math. It ... View answer 15 votes The American Mathematical Society provides posters promoting awareness of mathematics, its beauty, and applications. Here's a quote from the AMS Posters website: "Students frequently ask when ... View answer 15 votes Chvátal's art gallery theorem, a visibility problem in computational geometry, was proposed and proved in the 1970s. \left\lfloor n/3 \right\rfloor guards are always sufficient and sometimes ... View answer 14 votes The problem with the word "solution" is that it could mean the final answer or it could mean how the final answer was obtained, so I suggest that you don't use it. How about the following? Clearly ... View answer Accepted answer 13 votes From Wikipedia: The identities (bc)^x=b^xc^x and (b/c)^x=b^x/c^x are valid when b and c are positive real numbers and x is a real number. But a calculation using principal branches shows ... View answer 12 votes Underwood Dudley answers the question "What is mathematics education for?" in this article from 2010 (Notices of the American Mathematical Society, vol. 57, no. 5, pp. 608-613) (even though ... View answer 11 votes The standard that you link to (ISO 80000-2:2009) seems to be not available for free. That is, in order for me to follow the standard, I have to be able to read it, and in order for me to read it, I ... View answer 11 votes One way to see if the student understands the commutative property of addition is to have "fill-in-the-blank" questions such as$$2+3=3+\_\_2+3=\_\_+22+\_\_=3+2\_\_+3=3+2$$View answer 11 votes I allow students to have one index card of notes during their exams. I believe this allows me to test for understanding and skills that are more important than the ability to memorize. I also ... View answer 11 votes Some universities (like mine) are accredited by a third party agency. One of their requirements for a university to be accredited is for it to have an "updated set of reference books" where "updated" ... View answer Accepted answer 11 votes I think your question is good, but a little vague. When you say "how many problems," would ten easy problems be counted the same as ten difficult problems? If exactly the same problem was ... View answer Accepted answer 10 votes One way to introduce group theory to a general audience is to talk about how to flip a mattress so that it is in "a different position each time, so as to pound down the lumps and fill in the sags on ... View answer Accepted answer 10 votes If you continue the operations until$$\require{cancel}\frac{x}{b}=\frac{c}{b},\qquad\left(\frac{x}{b}\right)b=\left(\frac{c}{b}\right)b,\qquad x\left(\frac{b}{b}\right)=c\left(\frac{b}{b}\right),\...

The problem with $(4x+7=6x+2)-6x$ is that there is no subtraction operation that involves subtracting a term from an equation. Subtraction involves subtracting a term from a term. So the correct ...

If you use LaTeX to prepare your documents, there are many packages that automatically randomize the order of choices in multiple-choice questions. One recently updated package is esami. (This ...