It may sound like something out of a stand-up-show by any comedian in the world. But it may also be a phrase very close to the heart of mathematics. Did you ever notice… that when you have been out travelling and returning home, suddenly the newpapers and TV shows are full of references to the place you just had been to? Where on earth were these news stories before you went there?
I just got home from a very nice travel back and forth to Bratislava, staying at a nice hotel called Ibis Bratislava Centrum Hotel (do I get a discount for promoting work here?). And on the train to work today I flipped through an article I have had lying on my desk for I don’t know how long, In praise of lectures, by T.W. Körner (click here for a pdf). I didn’t have much reason for having this paper around, other than the fact that I used a lot of Körner’s writing on Fourier Analysis 15 years ago for a thesis. And the point of departure was the Ibis, a sacred bird to the Egyptians. I had read this before, but since Ibis made no recollection in my mind, I just scanned those lines quickly and moved on. This time, I googled the bird, read about it, made a review of the Ibis hotel and also got thrown back with some nice memories.
It seems that what we experience in life will dictate how we control our awareness. It could be people we meet, places we go to emotionally or geographically, things we perceive with our senses in one way or the other. This may not be very shocking, I mean, in what other ways could our inclinations for learning something be working with us?
I think all kinds of education work in much the same way. As a teacher of mathematics I can not jump into the minds of my students and twist their brains into what I want them to look like and how I want them to act and work (and I believe, metaphorically speaking, we have all tried to jump into the minds of our students!). If I tell a thirteen year old pupil that the parameter in front of x will vary the slope of the graph of the linear function y=ax+b… then he might say “fine” and move on with his life. I know I would. Instead I could give him a very simple GeoGebra file to tinker with. For instance the standard one where you have gliders to control a and b in the mentioned expression. I could still do the mistake of telling him “Look, as I alter the parameter a, the graph slope changes accordingly”. I still don’t think this will stick to his brain, although a picture might do a better job than my words alone. And of course, the picture can also be improved, something I tried doing on a blog post on my Norwegian blog here.
Better still, I could ask him to alter a (and b) with the gliders, and have him tell me what happens. That would be the equivalent of my travel to Bratislava. The stay at Ibis Hotel pointed my awareness in that direction. I can also point the pupil’s awareness in the right direction and help him make sense of his discovery.
One of my favorite authors when it comes to books about mathematics, must be Mike Ollerton. We use some of his books as curriculum on our courses within teacher education. For example, we used Inclusive mathematics on one of our master courses in mathematics education.
Mike Ollerton has written several books, and you can find most of them (I guess) on Amazon and other sites.
This book is just what the title says – it contains 100 starters for mathematics classes. They are more or less grouped by topic, although some activities might fit in everywhere. I have just read through this book, and I must say I found several new tips, activities and tasks that I could and will incorporate into my own lectures at the mathematics education department. I wasn’t able to find the solutions to all the activities as I read along, but I did some, and some where also what I would call classics of mathematics.
You must have a very bad imagination if you don’t find many activities to adopt to your classroom in this book! 🙂
Ollerton’s pedagogical way of thinking is quite clear from seeing these activities. It’s not about givint the students questions and tasks, but rather activities and problems. Some of the ideas might not even have a specific answer to be found. The activities are also expanded upon by providing hints for how the teacher could take the ideas even further.
I’d like to mention one little tip that my students liked very much. My students arrive by bus mostly, and there are always one or two buses that arrive late, and some students who have to wait a couple of minutes. I then gave each pair of students five die as they arrived, and instructions to throw them all once. The problem is to make use of the five numbers in order to arrive at 100 in one way or another. They can use plus, minus, division, multiplication and parentheses as they like. There appeared to be something within this activity that made them sit there thinking quite hard. Could all throws result in 100? (Of course not, five ones can not be made into 100). How many hundreds can be made? (Well, with 6 to the power of 5 possibilities I doubt that that is easy to find out). Perhaps if we also included powers…
I highly recommend this book for anyone teaching or learning or being interested in mathematics. You can order it quite cheap from Amazon og Play.com
Former colleague, present mathematician (and part wizard) has his blog at http://naylors-in-norway.blogspot.com/. Mike Naylor is an American who are living in Norway with his family for a couple of years. He works at the National Mathematics Centre here in Trondheim, and writes about all things Norwegian, Mathy and creativity in his blog. So take a look!
Sometimes, the mathematics scream at you, begging to be calculated… This lovely parabola was sent to me by my studet, Ekaterina, and you can check my GeoGebra uploads to see the neat function it describes, here.
Teaching mathematics in mathematics education, I now and then have lectures on the mathematics found in nature. I rather like this subject and enjoy finding new ways of attacking the problems in there. I must say, that I don’t think I have seen a nicer illustrations of the phenomena og Fibonacci numbers and golden sections, than can be found in the video below. It has been circulated from YouTube for some time and I hope you will enjoy it too.
My guess is, it serves nicely as a kind of repetition of the concepts for students already familiar with them.
I have had plans for a while… making a lot of exercises just by providing pictures. It’s quite hard finding the “math moment” visually in order to empower your tasks. But I am getting better, both at using my mathematical lens and also at capturing it on media.
Here are some samples – what would be nice questions to ask about these pictures?
I don't know if I qualify as a researcher (actually, I know I don't), but at least I WORK as a researcher within higher education. I am a lecturer in mathematics in Norwegian teacher education. This blog will show some of the thoughts, software products, scientific tidbits and ramblings I encounter in this area of work. I hope you leave some comments in the... comments field.