28 Colleges and High Schools to Use Personal Robots in Class

Math is fun for me, but the word fun means different things to different people, and often has the connotation of being easy. Math is challenging, and that’s part of the fun for me.  It might be better to focus on playing with math. Don’t try to put a ‘fun layer’ on top of it; instead, find ways to approach it that are playful. And, like little children totally absorbed in their play, dive in!

I’m working on a book, Playing With Math: Stories from Math Circles, Homeschoolers, and the Internet, in which we see 35 authors’ different ways of playing with math, and the communities they form to do that.

I think the best first step is to honor children’s innate curiosity, and to find ways to engage them, with their consent. (Schools are headed in exactly the wrong direction these days, I’m afraid.)

+1 for pointing out that math skill is not something you are either born with or born without. I recall reading (maybe in Liping Ma’s book?) that this is a pecularly Western notion; in Eastern countries there is no concept that some people are born without the ability to learn math well. 

It seems like perhaps the key is getting across to kids that math > repetition, not math = repetition. 

Great post.  Math can certainly be fun, even for the most resistant student.  From about the seventh grade through the college algebra course I had to pass as a freshman to be done with the subject forever, my brain would simply shut down when confronted with numbers and equations.  I wasn’t stupid; I simply I hated to think mathematically and justified it by falling back on the idea that I lacked the innate talent. 
Then I met my partner, who is a math professor at a big state university.  She does away with algorithms in as many places as possible and emphasizes critical thinking rather than drill-and-practice.  The point she stresses is that there are many ways to come to a solution, and the process can be as important as the solution itself.  Maybe this is old news to the math crowd, but her approach blew my mind, and I now take her quizzes and look over her notes for fun (not even joking).  Looking at it as a puzzle rather than a collection of steps really flipped a switch for me in terms of both enjoyment and comprehension.
One last note on the school culture you mention–the students who are most resistant to my partner’s approach?  Future teachers, who gripe endlessly about having to work and think, rather than simply regurgitating the algorithm.

Not sure that is a very precise question. Of course, any subject should be made interesting and engaging to attract students to want to learn, but “fun”?  I had a “phobia” about math in HS and college even though I was in a major (biology) that required calculus I and II, I barely made it through. Now several (plus several more) years later I feel like I could do a lot better. I think the instruction was too linear or word-based. I couldn’t understand the concepts because I couldn’ t visualize them or see change in motion. Partly that was the lack of good math video instruction back in the 70s, my teachers stood at blackboard with chalk, erasing with one hand and writing with the other. Now you can go on you tube and find awesome instructional videos that really help learners visualize math and that helps a lot with statistics and calculus. But “fun” is too fuzzy a goal, things are fun when you are good at doing them so the question presents a tautology. And you are brought back to the pertinent question of how can we make learning math more intuitive or approachable so students feel empowered. The fun is a consequence of understanding, so start there.

You thought  to a person who is not proficient in math and wanted to understand “the beauty of math” that the example of a “non-intuitive fact from stochastic geometry (the relative spread of mass on multi-dimensional distributions that has an application in
statistics concerning the observation of outliers in the multivariate
setting)” was going to do the trick?? Interesting.

No wonder she dropped the question quickly. I think you might want to revisit the need for “f’un” question above.

I have a philosophical question that gets at the heart of mathematics and the human mind all at once:

“What is a number that man may know it, and what is man that he may know a number?”

Not sure that is a “fun” question but I have always thought it was interesting to contemplate. And, if anyone has an answer, please send along.

Have you seen Conrad Wolfram’s Ted talk on computation and teaching kids math with computers? (http://www.ted.com/talks/lang/en/conrad_wolfram_teaching_kids_real_math_with_computers.html) Interesting idea. Instead of making computation by hand fun, he wants to teach kids to use computers for that so they can spend their time on stuff computers can’t do (which is more important, and more interesting). Not sure I buy it completely. Would be interesting to hear what a mathematician thinks.

I run into the same cultural problems with music theory, even within the broader discipline. Lots of professional musicians get by without theory (largely because they were taught it poorly, so it didn’t stick, and without application, so they didn’t care) and pass their apathy or disdain on to their students. I’m fortunate to be in a department where the other full time music faculty send the message that it is important, but I think that’s somewhat exceptional. I wonder if it’s similar for math. Do teachers of other subjects talk down the importance of math, as well? (For what it’s worth, I don’t!)

My elementary school aged kids go to a school (private) that is best known for its math program.  The interesting thing is that the curriculum follows the same focus as your partner is using at the college level.  For instance, multiplication is taught with a focus on what it really means. My kids were never given times tables to memorize, instead they were given lots of of “word problems” which the principle of multiplication is necessary to solve. They were also given lots of matrices to count out and work through in the second grade to show how multiplication is a short cut to lots of addition (a concept that did not get exposed to explicitly until my fifth semester of college math in my linear algebra class). While it was disconcerting to me since I still clearly remember those flash cards from elementary school, the approach is remarkably effective.  Both of my kids state that math is one of their favorite subjects.  Also, we regularly give them math problems to solve from the real world, and can see that the approach clearly works.  They both can solve reasonably complex problems in their head and do not find real world applications of math intimidating at all.

The school’s theory is that the biggest problem with math instruction is drills.  What good are they if the kid does not learn the underlying mathematical principles or how to apply them?  Thus, at this school, kids never get anything other than word problems in math class, fractions are first taught by sending them loose with a ruler to measure everything in their world and reinforced by by cooking class since cooking is the most common place in life that fractions show up etc.

 The way I posed the question to the acquaintance was:

“Imagine a circle inscribe in a square.  Outside of the circle but inside the square there is some area.  Now imagine a sphere inscribed in a cube.  Outside the sphere but inside the cube, there is some volume.  In fact, the volume outside the sphere is more than proportionately larger than the area outside of the circle.

Imagine there can be additional dimensions more than three.  As we consider the analogues to circles and squares in higher dimensions, the increase in proportional excess area / volume (let’s call it mass) increases more than proportionately for each additional dimension.

In statistics if you have many random variables and think about them following a distribution, it’s interesting to consider that they lie in a geometrical setting where more mass goes to the corners.”

I could go on, but I was assuming my original post was read by math folks and wrote in short hand.

Although your question may be interesting to a philosopher who thinks about numbers, this question is not particularly mathematical and I don’t think answering it would give someone an appreciation of mathematics because that’s not the kind of question that mathematicians deal with.

One of the things that the Udacity computer science course I took did very well was create a “need to know” prior to covering the material. They didn’t just jump into a discussion of hash tables — we reached a point in the course where we couldn’t continue on this interesting problem (writing a working search engine) without having a more efficient form of storage. So when hash tables came up, there was a context for it. 

We in mathematics do not do such a good job of creating that “need to know” prior to introducing material. We tend to do drill/practice first and applications later — often MUCH later — and hold out the promise of applications, or at least a meaningful context, as a sufficient reason to keep drilling and practicing. I just don’t think that is a sufficient reason anymore. 

Oh, and another thing, I tend to feel that many people, both in their personal lives and in their professions, probably don’t really need any more math than basic arithmetic, a little algebra and some statistics. Seems like there is a tendency, these days, to say “OH! You GOTTA HAVE MATH THROUGH CALCULUS!”  While I commend people who do go that far in math, many of us just don’t need that much. 

Kids love to master . . . anything: riding a bike, playing ball, using a computer, learning to read. Learning any kind of math can become an accomplishment (from addition/subtraction to calculus) if presented well — and if any kind of applications can be made, all the better.

Some of the most interesting mathematicians I’ve ever met were guys with high-school educations in a sheet-metal shop, who could take a flat piece of metal and make a connector that would like a square duct with a round one. By contrast, I’ve met engineers who complain that they’ve never used most of the mathematical tools someone insisted they learn. Could it be that our schools are partly responsible for adults’ mathematical indifference?

I have two scientific degrees and have have spent many, many hours solving math problems.  In my last semester of my last degree, I had to take an advanced econ class.  To make a long story short the class was the study of economic formulas.  The Prof taught the class how to read a mathematical formula, just like reading this sentence.  Why after years and years of school was I just now being shown that math could be read?!  That class, which was not in my major, which was taken only to fulfill a requirement opened my eyes to a world that I had never seen before.  What’s worse was why were the business majors of all people being exposed to this life altering knowledge? ;-) Over in the proper science department math was, and as far as I know is still being taught as a number of rote steps to be followed to achieve the correct answer.  

Don’t you GET IT people math is a LANGUAGE!  Once you can read, …. oh once you can read the world is open in ways you can’t imagine.  

Fast forward, now I work in education, but not in a teaching role.  When I ask teachers, curriculum people, principals, why don’t we teach math like a language? I get blank looks.  Why, because to them math is a number of rote steps to be followed to get a correct answer.  I guess there is just one Professor in the world that knows how to teach students to read math. So sad. 

I strongly agree with the use of “flow” over “fun”. I’m merely using the word that was kicked around in the article. 

One of my deans, a mathematician, claims that in the Netherlands and the US, students could opt out of math at age 14, whereas in Belgium all students had to take at least an hour or two a week until 18. In the Netherlands and the US, there is a problem of “math anxiety,” especially among girls, whereas in Belgium, he claimed, as far back as the 1940s there were more girls than boys in math all the way through the doctorate.

Yep. That’s one of Danica McKellar’s projects. I applaud her for her efforts. Does anybody have a sense of what kind of difference this is making with the perception of math, especially among girls? 

“Imagine there are additional dimensions…”  I think you stopped the mental gears from grinding right there. Who imagines multiple dimensions? I mean among people with lives who don’t study math or physics. I am not trying to be critical but, once again, to the “acquaintance” who did not understand math but wanted to understand its beauty, how does this help? You believe that rigamorle is any easier to contemplate? You might assume (incorrectly) that this article was read mainly by math folks but you are just joking at this point I take it. If your “dumb downed” version of the beauty example above is any indication of how you presented it to the questioner then the same problem is still apparent. Hope that wasn’t a first date question-answer exchange. To a non-mathematician, your geometry example is not interesting to consider in the least. So good luck explaining the beauty of math, hope you get a lot more mass into your corners.

I also wonder if “need to know” should shape which subject areas are emphasized.  With cash registers and pre-packaged items, some of the traditional “story problems” used to teach small number calculations seem a little archaic (Q: if 12 eggs cost $2, how much does one egg cost. A: have fun trying to buy one egg at the supermarket).  Meanwhile I use set theory all the time, and am amazed at how many otherwise educated people don’t get it.