(Image credit: **drewleavy**)

I talked to someone recently about first aid training, and they expressed their frustration at how ineffective first aid training usually is.

Unfortunately, according to my friend, many people who teach first aid actually have very little practical experience using first aid. As a result, the agencies that are responsible for first aid certification give their instructors "idiot-proof, deadly boring, text-filled presentations" to use in their training so that every first aid course is at least minimally useful. According to my friend, instructors are expressly prohibited from using their real life experience and telling stories of themselves actually using first aid, and also from explaining the reasons behind the protocols used in first aid. Further, most people taking first aid training have little to no interest in first aid themselves, they are almost certainly required to take a first aid course as part of retaining certification in their line of employment.

It occurred to me that this situation is remarkably similar to the position that we find ourselves in mathematics education, at least in the k to 12 level. Mathematics teachers often lack experience either making mathematical discoveries, or even applying mathematics as might an engineer or physicist. Consequently, curriculum is packaged in such a way so that nearly anyone can follow the text and make sure the students get at least a minimally effective mathematics background. We aren’t prohibited from using stories to relay our experience in mathematics, but we often have pretty frustrating limitations on what mathematics we can teach, and at the end of their k-12 program, how our students will be assessed. Finally, almost none of our students is really interested in mathematics; most of them are in our courses because they are required to be there.

Fortunately, first aid training is occasionally successful. My friend suggested that about 80% of the time, people who have first aid training are more useful in an emergency situation than people without the training. At my school, a 6th grade student, **learned the Heimlich maneuver during a recent first aid training, and then used it to save the life of his mother two weeks later** (An aside: according to my friend, the **correct response when someone is choking**, after encouraging them to cough, is 5 sharp blows to their back with the heel of your hand, right in the middle of their shoulder blades, followed by abdominal thrusts, then CPR if they fall unconscious). Not teaching first aid is obviously not an option, even when the programs are usually limited in effectiveness, but I wonder, what would happen if we let people who were highly experienced in using first aid have a bit more flexibility in how it was taught?

In the same way, our mathematics education is not a complete disaster. Many people go on from their subpar mathematics education to be able to use mathematics in a meaningful way, and some of those people even make new mathematical discoveries. However, the surest proof **I have** that our system is less than adequate is the enormous number of people I have met who will happily admit that they were terrible at mathematics, hated it, and now never use it.

The question that I think defines my career as a mathematics educator is, what can we do about this issue? It is of limited use to complain about a problem, especially one as well discussed as mathematics education, without proposing some sort of solution.

What if mathematics educators who had actually used mathematics to solve problems, or had developed new areas of mathematics, had more freedom in how they were able to help their students learn mathematics? If someone has significant experience in topology, number theory, mathematical modelling or any other area of mathematics, why not let them teach this area of mathematics to their students, perhaps leaving out some other area of our curriculum so that they would have time to do so. What if we taught mathematics in such a way that our primary goal was to inspire our students into further study of mathematics?

Hi David,

I think this is a really insightful post – thanks! Likewise, I think it’s a tragedy that significant numbers (most?) students never get even a glimpse of why mathematics is beautiful, and grow up hating the subject.

A nice program which has been in place in Australia for the past few years is the “Mathematicians in Schools” program (link: http://www.mathematiciansinschools.edu.au/ ) which means some students get to interact with professional mathematicians, and of course there are many passionate teachers of mathematics, but I wish that every student could be exposed to beautiful mathematics, presented by a teacher who is doing more than teaching straight from the syllabus.

Cheers,

Nathan

p.s.: Although this is my first comment, I regularly read your blog, and highly enjoy your thoughtful writing on the topic of mathematics education.

I have always thought of myself as a mathematician (even as much as an amateur as I am) who teaches, rather than just a teacher of mathematics. I spend at least part of my time thinking about mathematical problems and improving my own understanding of mathematics, and I honestly think that we should give all teachers time to learn more about their own subject area.

I completely agree with that. Unfortunately, in Australia all of the political discussion at the moment is around how to provide financial `incentives’ to teachers, with the idea that their teaching will magically improve and students will do better on standardized tests, rather than investing in training.

My biggest concern with mathematics education is not at the high school level, where most mathematics teachers are knowledgeable and interested in mathematics (although, as you point out, limited in what they can teach by rigid syllabuses), but at the primary school level where there are many mathematics phobic teachers presenting mathematics straight from the syllabus in a dry way, so passing on their phobia to their students.

As a mathematician who has worked in an industrial setting and who has taught at the college level, I can tell you that there is a bit of a disconnect between the two worlds. It’s not that the mathematics taught in school is not useful, it’s that — in defense of academic programs — problems in industry can be complex, unwieldy, and time consuming.

Contextualizing mathematics should and can be done. In the classroom setting, “project-based” problems can be presented as lighter version of real industrial problems. And I think this can be very valuable for students at all levels. This requires a little bit of effort and ingenuity on the math instructor. Probably a fair compromise would be to bring in a guest speaker every so often and have him/her work with the classroom instructor to devise appropriate exercises / projects (of course, there are plenty of schools that do this).

The burdens faced by industrial mathematicians, are not just the mathematics. They are other things like budgets, timelines, regulations, corporate bureaucracy, etc. (University professors face similar non-mathematical burdens as well (publish or perish, as the old saying goes).) Students should be made aware of this.

I recently gave a talk to a high school English class (yes, English) on the importance of communication and presentation of technical matters. We are in an interconnected world, not just socially, but by academic discipline as well. Our pedagogy should reflect that.

-Manan

I absolutely agree on all of your points. I don’t think the purpose of our classes is preparing students for future classes, rather our purpose is to help them learn how to think. Decontextualized mathematics and entirely too-straight-forward questions that lack the messiness of real life do not either help prepare our students for life, or give them as much opportunity to learn how to think as they deserve.