An Open Letter: To Andreas Schleicher, OECD, Paris
Heinz-Dieter Meyer and Katie Zahedi, and signatories – 5th May 2014
Heinz-Dieter Meyer and Katie Zahedi, and signatories – 5th May 2014
[Reposted from multijimbo.]
I have been a teacher for many years now; in fact, we’re now rapidly approaching the point at which I’m thrice the age of my students, rather than merely twice. I teach 2 very different things. On the one hand (which I can write without violating the basic tenets of the Number Liberation Front, as I’m using ‘one’ not as a number but as an adjective, I suppose), I teach mathematics to undergraduate university students, and on the other hand, I am 1 of the instructors in the University aikido club. I’ve been thinking recently about the commonalities and differences between the 2 types of teaching.
There is an obvious difference between the 2. To practice aikido requires physical contact. Someone grabs me, or attempts a strike, and I need to do something rather quickly. (Or is it quite quickly? Having lived in 2 countries where the use of ‘quite’ and ‘rather’ is different, I am now very confused and can’t remember which is the current local usage.) The end of a good, active aikido session can be sweaty. This physicality leads to a directness in teaching. When I’m being thrown by a student, I have the opportunity to feel exactly what they’re doing, right and wrong, which I can then feed back to them immediately.
Mathematics, on the other hand, can be done in isolation. (And to follow a random train of memories, this brings to mind Ms Shearer, my 6th grade teacher, with whom we spent a session listening to Simon and Garfunkel’s I am a rock, I am an island, and discussing how people cannot exist in isolation, as they remain part of the cultural in which they grew up.) Also, mathematics rarely involves physical combat. Not never, mind you, just rarely. In terms of teaching, though, mathematics teaching is a bit more at a distance than aikido teaching. Part of this is that mathematics classes tend to significantly larger than the aikido classes I teach. Also, a good, active mathematics class rarely ends in sweat.
Even so, there are for me some deep and significant similarities. These are things that no doubt are similar to the teaching of many things, but hey, this is my meditation. The similarity I would like to focus on here is the lead-a-horse-to-water phenomenon that is regularly, and sometimes almost brutally, brought home to me in both teaching fora.
In both aikido and mathematics, there are some basic, fundamental ideas that underlie everything that we do, and that I try to bring out and illustrate as much as I can through my teaching. This is after all, in my mind at least, what a teacher should do. I have spent time studying how to do particular things, learning from my contemporaries and those who have gone before, and I can use the miracle of language to take what I’ve learned and provide my students with some short cuts, so that they can get farther along the path a bit faster than me.
In aikido, 1 of these basic, fundamental ideas is that at any moment in a technique, I should understand where my balance is and what is happening within both my own centre and my partner’s centre. The way I like to try and embed this idea into my students’ brains is to have them go slowly through a technique, paying attention throughout. But this requires that the student is willing to do the technique slowly, and alas not all of them are. So I talk, I demonstrate, I cajole, but in the end, I cannot force. Ultimately, I cannot teach anything. All I can do is to provide guidance for my students on how they might learn and provide them with an environment within which they can learn.
In mathematics, the basic, fundamental idea on which I like to focus is that each statement, each assertion, needs to come from somewhere. With each question, we have to start with things we know to be true and work out from there. Part of an undergraduate mathematics education, and indeed mathematics education before university, is to provide students with a collection of facts, procedures and processes that we know to be true. Mathematics does not come from nothing. Mathematical facts do not spring full-grown from the head of Zeus. Rather, mathematical facts are the product of accretion and accumulation (and this is where the sweat comes from). We have just come to the end of the semester, and as in all previous years, I have the evidence that some of my students listened, and some didn’t.
So, what to do? There is nothing to do besides persist. Some students listen and some students don’t, but I have come to believe that it is these larger things, these fundamental ideas, that are by far the more important things that I teach, far beyond the individual techniques of aikido or the definitions, theorems and examples in mathematics. And so we persist. As Samuel Beckett once wrote, ‘Try again. Fail again. No matter. Try again. Fail again. Fail better.’
From Charles Walkden, University of Manchester:
The Imitation Game Cryptography Competition: www.maths.manchester.ac.uk/cryptography_competition_the_imitation_game
The film’s distributors asked us to get involved in the publicity and promotion for the film by running a one-off on-line `Imitation Game Cryptography Competition‘, www.maths.manchester.ac.uk/cryptography_competition_the_imitation_game.
R. Hanson, National Assessment Reform – Where are we now? The De Morgan Gazette 5 no. 5 (2014), 33-39.
This short report summarises the pending changes to national assessment at 4/5, 6/7, 10/11, 15/16 and 17/18. It attempts to list the key concerns about the reforms and to describe the likely imminent calls for modifications.
It can also be downloaded as a word document here:
National Assessment Reform Where are we now 1 Sept 2014
If you have any questions you can contact the author.
Mobi Snoodles, September 2014 Newsletter
Hi, I am Moby and I bring you the news about Natural Math. Send me your questions, comments, and stories of math adventures at firstname.lastname@example.org
In this newsletter:
Math coloring pages and other activities to try
BugFest is a big annual celebration of insects and crustaceans at the North Carolina Museum of Natural Sciences, attracting some 35,000 visitors to its hands-on learning centers – for example, to explore fractals in nature at our table. We miss you already, BugFest friends, and hope to see you again next year! Huge thanks go to the amazing kids who liked our activities so much that they taught them to others. The two most popular activities at the BugFest were insect-themed coloring pages and origami.
As it happens with most viral stories in social media, the provenance of this picture (at one point published in chinaSMACK) is hard to trace:
From BBC http://www.bbc.co.uk/news/education-29342539 :
Low-level, persistent disruptive behaviour in England’s schools is affecting pupils’ learning and damaging their life chances, inspectors warn.
The report says too many school leaders, especially in secondary schools, underestimate the prevalence and negative impact of low-level disruptive behaviour and some fail to identify or tackle it at an early stage.
Source: Poll conducted by YouGov for Ofsted, http://www.ofsted.gov.uk/news/failure-of-leadership-tackling-poor-behaviour-costing-pupils-hour-of-learning-day
This is one of many low-level school issues that affect undergraduate mathematics teaching. In a mathematics lecture, weaker students are more prone to “loosing the thread” than in most other courses. Also, students for whom English is not the first language, in particular, most from overseas are more sensitive to the signal-to-noise ratio than natives, and, at a certain level of background noise, their understanding of the lecture becomes seriously degraded. In my opinion, this is one of many neglected issues of undergraduate mathematics education. I in my lectures always insist on complete silence in the audience (and usually start my first lecture with a brief explanation of the concept of signal-to-noise ratio).
Children born to mothers who have low levels of thyroid hormones during pregnancy tend to do worse in maths in early primary school, a study says.
Dutch researchers tracked 1,196 healthy children from birth to age five, having recorded their mothers’ thyroxine levels at 12 weeks of pregnancy.
They then looked at the children’s test scores for language and arithmetic.
Those born to mothers with low levels of thyroxine were twice as likely to have below average arithmetic scores.
However, the scientists – led by Dr Martijn Finken at the VU University Medical Centre in Amsterdam – said the five-year-olds’ language results were no different.
The maths results were the same even after taking into consideration the child’s family background.
Read the whole article.
Many mathematicians believe that that their brains continue to do mathematics during sleep. A paper
Kouider et al., Inducing Task-Relevant Responses to Speech in the Sleeping Brain, Current Biology (2014), http://dx.doi.org/10.1016/j.cub.2014.08.016
Proves that brain continues in sleep some mental activities of the day.
From the summary of the paper:
using semantic categorization and lexical decision tasks, we studied task-relevant responses triggered by spoken stimuli in the sleeping brain. Awake participants classified words as either animals or objects (experiment 1) or as either words or pseudowords (experiment 2) by pressing a button with their right or left hand, while transitioning toward sleep. The lateralized readiness potential (LRP), an electrophysiological index of response preparation, revealed that task-specific preparatory responses are preserved during sleep. These findings demonstrate that despite the absence of awareness and behavioral responsiveness, sleepers can still extract task relevant information from external stimuli and covertly prepare for appropriate motor responses.
The paper generated a huge response in mass media: BBC, New Scientist, NBC News. It is mentioned in this blog because the study of brain activity is relevant to mathematics education. A naive question: do our students get enough sleep?
Stories about mathematical circles from Moebius Noodles: