Education Bookcast

In this episode, I review a paper from the Foreign Service Institute (FSI) about language learning and teaching. The key insights are eleven: Mature adults can learn a foreign language well enough through intensive language study to do things in the language (almost) as well as native speakers. "Language-learning aptitude" varies among individuals and affects their classroom learning success (but at least some aspects of aptitude can be learned). There is no "one right way" to teach (or learn) languages, nor is there a single "right" syllabus. Time on task and the intensity of the learning experience appear crucial. Learners' existing knowledge about *language* affects their learning. A learner's prior experience with learning (languages or other skills) also affects classroom learning. The importance of "automaticity" in building learner skill and confidence in speaking and reading a language is more important than has been recognised by the second language acquisition field since the 1980s. Learners may not learn a linguistic form until they are "ready", but FSI's experience indicates that teachers and a well-designed course can help learners become ready earlier. A supportive, collaborative, responsive learning environment, with a rich variety of authentic and teacher-made resources, is very important in fostering effective learning. Conversation, which on the surface appears to be one of the most basic forms of communication, is actually one of the hardest to master. If a learner has passed a certain threshold of proficiency in a language, then attrition of their knowledge over time is very low. However, below that threshold, learners tend to forget their language relatively quickly with time. During this episode, I discuss each of these points, and provide a personal point of view with reference to my own experience of learning multiple languages over the years. Enjoy the episode.

I wanted to share some things I learned from my trip to the US this summer, and what my own experience of running maths circles has been like so far. This episode includes: Discussion of the Summer Math Circle Institute; Tips and techniques learned from the Institute; My own experiences of running maths circles; Potatoes with added sugar; What you should and shouldn't assume about students; Why Math Circles (sometimes) work; Why Bloom's Taxonomy is upside-down; and The role of the teacher in having a vision for the students in his/her care. Enjoy the episode.

Interview with Robert Kaplan, co-author of Out of the Labyrinth (the book we looked at in the previous episode), co-founder of The Math Circle, and the man behind the Summer Math Circle Institute course (which I attended this summer).  Robert Kaplan tells of his colourful background, his experiences starting and running The Math Circle, and the recent explosion of interest and growth in maths circles in the favelas of Brazil. Enjoy the episode.

This is a book that I have more of a connection with than many of the others I cover on the podcast. I first bought a book by these authors when I was 17, and didn't read it until literally ten years later. It was a fascinating recreational maths book. I then discovered that they were involved in alternative maths education, and that they had even set up an organisation for this called The Math Circle. This book relates their experiences of running Math Circles, their philosophy and approach to maths and maths education, and some pointers as to how to set up a Math Circle of your own. Two questions may come to mind. Firstly, what is a Math Circle? Robert Kaplan summarises it as "a conversation, among equals, about math". Secondly, has there been any education or psychology research on maths circles and their effectiveness? I have been looking for this for a long time, and have asked a lot of people deeply involved in the scene, but I am yet to find out about any studies done about them. So, short answer, apparently not. The word on the street is that they tend to be highly beneficial to students, but that they are "risky" in the sense that, as with any conversation, you don't know what it will be like until you have it. There are maths circles that flop, and there are those that shine. More shine than flop, but there is always the risk of flop. In this episode I discuss the book, and the following few episodes relate to the Math Circle Summer Institute, a weeklong course I attended in the US where Robert and Ellen Kaplan share their wisdom and help teachers to learn how to run maths circles for their own students. Enjoy the episode.

Have a go at some of these: An athlete's best time to run a mile is 4 minutes and 10 seconds. How long would it take him to run 5 miles? It takes one orchestra one hour to play a symphony. How long would it take two orchestras to play a symphony? On a ship, there are 13 goats and 12 sheep. How old is the captain? Among schoolchildren, the most common answers to these questions are: 20 minutes and 50 seconds; half an hour; and 25 years old. Hence the title: where are these thoughtless, silly answers coming from? The bizarre and somewhat frightening thing is that this is a well-attested finding in many different countries and schools. School students predominantly seem to think that anything involving calculation, in the classroom at least, is a matter of doing a simple arithmetic operation on the numbers given, without any kind of sense-checking or thinking about the real situation behind the numbers.  This strange phenomenon demands explanation, not to mention fixing. In this episode, we look at several articles concerning this issue, why it's there, and what to do about it. Enjoy the episode.

Dr Amanda Serenevy is a mathematician and mathematics educator, focussing on outreach through the medium of Math Circles, and on teacher training. This episode appears as number "27+" because the previous episode, Consider the Circle, was about how Amanda rescued a young girl from a terrible time with maths at school.  She is the founder and director of Riverbend Community Math Centre in South Bend, Indiana, which works to improve mathematics education within the local community. She runs teacher training courses throughout the year, both to help teachers with their pedagogy, and with their knowledge of maths itself. She also has many local children and young people come to her Math Centre to engage in mathematical activities, the most prominent of these being Math Circles. In summer, she is the main organiser of the Summer Math Circle Institute at the University of Notre Dame, which is a course for learning how to run Math Circles, and is the place where I met her. She also finds time to spend almost two months a year in Navajo Nation helping to run maths outreach programs, including a three week long summer camp. She did her undergraduate degree in mathematics at the University of Indiana at South Bend, and her PhD in dynamical systems at Boston University. Interestingly, she declined academic positions at university in favour of doing more maths outreach, and so her choice of career is very deliberate, and she is committed to her cause. From getting to know Amanda personally, I can say that she is both very personable and very dedicated to her work. It is easy to see how much positive effect she is having on her community, particularly on the children who have clearly gained so much from her help, guidance, and activities. While she has a thorough understanding of the problems with maths education in her country, she somehow isn't completely disillusioned, which is a feat in itself. I was greatly privileged to be able to shadow her for a week while in the US and pick her brains about maths, education, and why America is such a strange place. Enjoy the episode.

A very short episode about an article written by a young girl concerning her experiences with maths. At school, she is faced daily with the same worksheet, always refusing to do it. Her teachers continue to give her the sheet every day for months, keeping her out of the normal classroom. She becomes resentful and angry at maths and at school, and continues her protest of inaction. When she discovers Math Circles, a different approach to maths education, then she stops feeling neglected and starts, gradually, to engage. With time she not only gains confidence in the maths she is "supposed" to know, but also discovers mathematics as a field full of things to explore - and things she is capable of exploring. Having gained confidence and understanding from Math Circles, she eventually graduates from high school and enrols in university. (A happy ending, one presumes.) We will be talking a good deal about Math Circles, so this little story makes a good anecdotal introduction to their potential benefits. It sounds a bit like an advert, but Eliza Vanett is a real person who really underwent these experiences and volunteered to write this herself. You'll hardly see adverts for Math Circles on television. Enjoy the episode.

What do you think of mathematics? Is it: a sterile tool for accounting? boring, mindless, and annoying stuff your teacher makes you do? an anarchic, psychedelic adventure? If you answered 1., mathematician and teacher Paul Lockhart vehemently disagrees with you. If you answered 2., then Lockhart understands your plight. If you answered 3., then you really know what maths is. A Mathematician's Lament is a short book all about misconceptions, and how the system propagates them into an insurmountable monster hiding the true nature of a cherished art form. Kids in school hate maths lessons. Why? Because they're not really doing maths! They're engaging in a hollow imitation of it (if they're engaged at all), where memorising formulae takes the place of imagination and reasoning.  He starts us off with a parable about a musician, and another about a painter. Imagine if everyone thought that music was those little marks made on the page of music books, or that painting a fence is the epitome of what it means to be a painter. This is the situation that mathematics finds itself in today. Very few people know about the true nature of doing mathematics, and there is no cultural corrective for the mistaken view propagated by the bulk of the education system. This is why Paul Lockhart laments. This book was originally published in abbreviated form as an article of the same title, which is very close to my heart. I've read it about six times so far if not more, which is more times, I think, than I've read any other publication. I have a lot to say about it. I hope that it will reach a wide audience. Enjoy the episode.

Over the past century, women have been gaining rights and prejudice against women has declined. Although many would argue that there's still a way to go, the progress is undeniable. Why, then, do men still outperform women in a number of intellectual domains? In this episode, we look at several articles that try to answer this question for one cognitive domain in particular: chess. Chess is a good domain to test for a number of reasons: There is little subjectivity or ambiguity in deciding who is a better chess player. In chess, you either win or you lose (or draw), and there's no arguing about it. This isn't the same in most other domains, such as art, literature, music, or scientific research. In chess, it's what you know, not who you know. You don't need to have a professional network or be well-liked to win chess tournaments. You just have to play the game. This is different to other domains, where your career can depend on the judgements of others, and women or other groups may suffer from the effects of a "glass ceiling". There is a lot of data on chess. For the top few hundred male and female chess players, we know who played who; when; at what event; what the exact moves were; and what the result was. This helps our analysis greatly. So, why do women tend to worse in chess? Are women less interested in chess? Is there some hidden psychological bias or prejudice that is holding women back? Is it just some sort of statistical artefact? Or are men simply cleverer than women? All these theories and more are discussed in detail. Enjoy the episode.

I write a little blurb like this for every episode, but I feel that some books hardly need any introduction. This is one such example. Malcolm Gladwell is one of the most celebrated journalists and writers of the early 21st century, and his book Outliers caused a splash in people's thinking about success. Why? One answer is that it popularised the idea of the so-called "10,000 hour rule", initially discovered by K. Anders Ericsson, concerning how much "deliberate practice" it takes to become a world-class expert in any field. "Popularised" is the key word here, as several others were writing the same thing, but when Gladwell writes, everybody reads. And, for the most part, everybody believes. (So another answer to "why did the book cause a splash?" would be "because it's Gladwell, and he's famous, and everybody likes him.") The strange thing is, the 10,000 hour rule makes up a minority of what he writes about in his book, but people seem to often forget the rest of the ideas. Since we've already seen the power of extended deliberate practice described in other books (Bounce, Genius Explained, and The Talent Code), it's actually these remaining ideas where we find Gladwell's unique contribution to our knowledge of the development of expertise. And it has a message with is quite at odds with the spirit of the 10,000 hour rule. Gladwell's unique yet oft-forgotten contribution, then, is the idea of success as being a gift. He's not talking about talent, which he more or less rejects by reference to the aforementioned 10,000 hour rule, but about life circumstances. You don't choose where or when you are born, or the culture you are born into, or the state of the job market or of national demographics or of technology as you are growing up, and yet these very factors have a profound effect on whether somebody is successful. Would Bill Gates have become so rich were he born in Burma instead? Or in the 1920s? Or in fourth century Phrygia?  Although some of Gladwell's historico-cultural musings can be somewhat open to doubt, in several places he gives evidence strong enough to convince even the careful reader that something funny is indeed going on. In this episode, I hope to help you see where he might be onto something, and where we need to be wary of the potential of his masterful storytelling to obscure his shaky arguments. Enjoy the episode.