48

All four of your options lead with "They are told..." Consider asking the student questions instead. At the very least, this shows interest, and they may end up catching their own mistakes as they try to explain to you what they had glossed over in their own heads. When I have the opportunity, I like to challenge my students to explain EVERY step of their ...


37

When I'm the instructor for the course, I remind them of the time and location of my office hours by writing it on the board at the beginning of every lecture (if you're not the instructor, you can ask the instructor to do this). It sounds like overkill, but in my experience part of the reason students don't attend office hours is because it's just not a ...


33

I'm not completely sure how well this addresses the question, but here is my best response. A few years ago I was teaching a Methods course for preservice secondary math teachers. Over the course of the semester there was a fair amount of griping, not about my course but about the other courses they were required to take, and in particular about their ...


31

This is indeed a challenge, especially for adults. Three suggestions, none of which is a panacea. (1) Emphasize a growth mindset. Make it clear to them that learning math is a skill accessible to everyone, with effort. It is not only accessible to those with a mythical "math gene." (2) Compare understanding the abstractions of math and its notations as ...


30

First of all, I believe this question is quite similar to the question "How to give homework for integration technique?". I avoid the temptation of repeating my answer for that question. Instead, I try to give an answer from a different angle based on a recent experience I had in a numeracy class with adult students. One of the questions I asked was inspired ...


25

Allow me to contribute from the student perspective. I've taken College Algebra classes three times at three different levels and schools due to unusual circumstances. To make things even more interesting, I started out as an English Lit major, and later became a computer programmer. First, you have already realized that confronting the students in an ...


24

A recent Times article titled Americans Are Bad at Math, but It’s Not Too Late to Fix offered an example - A&W's "Third Pounder hamburger failed to catch on because During focus groups, the company discovered that customers believed they were getting less meat. Because the “3” in ⅓ was smaller than “4” in ¼, “customers believed they were being ...


24

Talk to math teachers as you would talk to any other professional with whom you share a common interest (the education of your son). Note, I have addressed this to respond to you specifically in some areas, and I have had to make some assumptions in some places. I did this, in part, to try to make this answer more generally helpful (because the title is so ...


23

There's the Verizon "0.002 cents versus 0.002 dollars" mishap, wherein an unhappy customer calls to complain that he was billed 0.002 $/kB after being told the rate is 0.002 cents/kB. The confusion is perhaps deeper than expected.


22

Most of what you learn in school isn't directly useful. When I was in primary school I was taught the difference between warm and cold-blooded animals. I've never used that information; should I not have been taught it? Another example is that in any English-speaking country you still have to take English courses even after you speak the language fluently....


21

Re-Re-Edit (May 2019): Found in a selection of tweets here but pasted as images to preserve. Credit for the first one goes to @lizardbill and to the rest to @GeneticJen: Re-Edit (Jan 2016): Perhaps this does not quite qualify, but I was rather surprised to spot the following question (#6 in the image below) in a recent airplane Mensa quiz: (Side-note: #2 ...


20

Here is some text from the paper "Teacher Characteristics and Student Achievement Gains: A Review" (Wayne and Youngs, 2003): Three analyses take advantage of the detailed teacher data in NELS:88 on degrees. The analysis by Goldhaber and Brewer (1997a) illustrates the key finding most clearly. No differences were evident when the authors examined ...


20

I was unofficially advising a student the other day who told me "I am struggling, but I know more than my friends in the class." This was the excuse she used for not attending meetings of a popular study group. How could she increase her grasp of the subject if her friends couldn't help her? An answer to this question (if not the answer, as I believe there ...


20

A 16 year old once told me that he has no need for mathematics since he wanted to become a lawyer. I told him that he wouldn't make a good lawyer if he jumps to such conclusions without first collecting all available evidence. So what evidence is there? I have a book in front of me: Mathematics, Physics and Finance for the Legal Profession by Ashley ...


20

Even without explicitly introducing the language of "linear maps", "vectors", and so on, you can still develop matrices as a shorthand for such maps, thought of as exchange rates. Example: Machine A can make 3 sprogs and 2 sprakets a day. Machine B can make 1 sprog and 3 sprakets a day. We summarize this data in a table of values: $$\begin{bmatrix} 3 &...


19

My thinking is that it is just so damn useful for students to be aware of these tricks. The examples/exercise should allow them to develop a sense of when and how it is helpful to simplify an expression in this way, BUT also when it is NOT necessary. Leading up to it by looking at fractions. Should the students write a rational number in the form $3\frac17$ ...


18

There are a few strategies that are supported by experimental research which I will share here, but they all have to do with stereotype threat. I am sure there are other types of anxiety related to math which would not be helped by these strategies. First, the wikipedia article on stereotype threat is fairly comprehensive. It describes some studies that ...


18

I really like this answer given by John Green: https://www.youtube.com/watch?v=x78PnPd-V-A "School is not about you! School does not exist for your benefit or for the benefit of your parents. Schools exist for the benefit of me. The reason why I pay taxes for schools even though I don’t have a kid in school is that I am better off in a well-...


18

(I am a woman in my last year of a PhD in low-dimensional topology, I'll be a postdoc in the fall, and I have research aspirations. I'm mostly trying to articulate how I got to this stage in my life. In a real sense, my answer shouldn't matter very much since the many things that keep women away from mathematics clearly didn't work on me too well, or on the ...


18

Let me offer a different type of response, a student's answer to a problem. The question offered the height of a building, the equation for distance of a falling object, and asked to calculate the time till a rock dropped off the building would fall to the ground. The student used his calculator and the answer was 900 seconds. I asked if that was right, ...


18

Ah, yes. My sympathies... maybe the question should be moved to another site, but, pending that... and/but the U.S. environment will not change significantly any time soon, for many reasons. I have my own acquaintance through my kids with better-quality [sic] U.S. education, at the supposed high end. In that context: first, also I am acquainted (through ...


18

Perhaps: The discovery a year ago of a new tiling of the plane by a convex polygonal tile, found by Mann, McLoud, and Von Derau (the latter of whom was an undergraduate at the time of the discovery): Here is a nice article on the discovery in The Guardian, by Alex Bellos. As Alex says, the problem has been studied for $100$ years now, since Reinhardt in ...


17

Some possible approaches: Challenge the student. A possible reason why the student is having "off-topic" interests is that the student doesn't find the "on-topic" things interesting (he "thinks" it is too easy) or that the student doesn't see the point of the topic (he lacks a vision of the big picture). So the thing to do would be to divert the student's ...


17

There aren't many new theorems in old subjects that are accessible to undergraduates. However, as others have mentioned, there are many relatively new subjects within mathematics that are accessible. These include: Graph Theory, which really dates back to Dénes Kőnig's 1936 textbook. Many of the fundamental results were proven in the 1930's, but many ...


17

When I teach courses, I usually see the majority of my students in office hours at least once a week. Here are some strategies for promoting office hours: Get a room. My office isn't nearly large enough to accommodate 10 students, and students who have to wait outside don't feel welcome. By reserving a classroom or other large room, I make sure there's ...


17

Flatland by Edwin Abbott Abbott It's a story about a 2-dimensional being's encounter with a three-dimensional being. (Well, there's a class(?) allegory at the beginning, but you can skip that.)


17

Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter is a book about Mathematics, Art, Music, Computer Science and Artificial Intelligence. It alternates story chapters and descriptive chapters. In my opinion the most valuable parts of the book are: a very understandable presentation of Gödel's incompleteness theorem. a good discussion of ...


16

I think there is no clear answer, although there has been some research on this topic. I remember one study which focussed on gender differences of university math students: Mischau, A., Blättel-Mink, B., Daniels, J., & Lehmann, J. (2004). Doing gender in mathematics: indications for more gender equality in German universities? Bielefeld: IFF. The ...


16

In the first place, it is "only" common course-naming conventions (and the AMS and NSF subject classifications) are to blame for the impression that there is some meaningful schism between something called "pure" and something called "applied" mathematics. Second, as noted, as much as anything people rationalize their own limitations or failings by blaming ...


16

In searching for information about hours of work per week by teachers at the secondary vs. tertiary level (for an earlier question) I came across a nice report by Scholastic and the Bill and Melinda Gates Foundation. A summary-type page can be found here; the full report (pdf) can be found here. (From the same study) A nice summary of "teachers on teaching" ...


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