Anonymous on 4 January 2015 at 22:49 said in response to my post:
Anon: My comments are on a few themes which appear within the paper. They are stand-alone, selected on the basis of curiosity, and do not necessarily present a coherent over-arching argument.
“…the winning strategies in such games were typically based on identifying the underlying algorithm instead of being “misled” by the story.”
This is very true, and I view it as a result of the human tendency to simplify or reduce puzzles to their essence.
YD: I would prefer to say the “pragmatically relevant essence”… Yet there is also another tendency that is unfortunately systematically suppressed by the system that I am criticising: The tendency to comprehend and delve into the essence of anything/everything.
[To appear in the LMS Newsletter]
There are now an increasing number of movies where mathematics plays an important role. Usually we are let down by the parts featuring the maths because the makers of the film have little knowledge about our subject. So it is a real pleasure to review x+y a beautiful film where the mathematics is carefully done but not in a way that will put off a non-mathematical audience. The director is Morgan Matthews who also made the BBC4 documentary Beautiful Young Minds about the Mathematical Olympiad and the film is clearly based on this documentary. This documentary can be seen on Youtube.
The main character is Nathan. From the BBC synopsis
Preferring to hide in the safety of his own private world, Nathan struggles to connect with people, often pushing away those who want to be closest to him, including his mother, Julie. Without the ability to understand love or affection, Nathan finds the comfort and security he needs in numbers and mathematics.
Even though there are similarities between this film and the documentary, the main story line is totally fictitious. Near the beginning, Nathan, who has Asperger’s syndrome, is involved in a car crash which kills his father to whom he was very close. He is then mentored by his maths teacher Martin Humphreys, who when young had taken part in the Mathematics Olympiad. He was diagnosed with multiple sclerosis but also has other problems to do with self worth and soft drugs and ended up being a secondary school teacher.
Humphreys recognizes Nathan’s abilities and persuades him to enter for the Olympiad. He goes to the preliminaries in Taipei.
One of the scenes where there is actual maths is when Nathan is brought to the board to explain how to solve a problem. This involves playing cards which can be face up or face down.
Nathan’s solution is to model this with binary arithmetic involving 0s and 1s and he then turns the problem into an arithmetic one which is easy to solve.
In Taipei he meets Zhang Mei, a girl on the Chinese team. The film concentrates on two relationships. One between Nathan and Zhang Mei and the other between Martin Humphreys and Julie.
The scene moves from Taipei to Cambridge where the Maths Olympiad takes place.
There is real pathos in the final scenes. One where Nathan finally opens himself up to his Mother, and another when Nathan and Zhang Mei while travelling back from Cambridge by train see a rainbow and the viewer feels that their relationship will last. At last, Nathan feels and understands love and affection. Some critics have thought that this ending is too soapy, but if you see the documentary on which this film is based, the rainbow really was there!
One should also mention the excellent cast. Nathan was played by Asa Butterfield, Martin by Ralf Spall, Julie by Sally Hawkins and Zang Mei by Jo Yang. A lovely film where mathematics plays a central role.
Book review by Richard Elwes:
Open a typical book on the theory of pedagogy, and all too often one is confronted by a morass of impenetrable and, one often suspects, unnecessary jargon. So it is a particular pleasure to read Ken Bain’s “What the Best College Teachers Do”. The book is the outcome of a fifteen year study in which Bain and colleagues identified and analysed around a hundred excellent teachers at US Colleges and Universities. Through extensive observations, discussions, and interviews with the teachers and their students, Bain arrives at a range of conclusions regarding the practice of good teaching. His findings are laid bare in a series of straightforwardly entitled chapters: “How do they conduct class?”, “How do they treat their students?”, and so on.
Few of his discoveries come as complete surprises, yet many are genuinely enlightening. For instance, the best teachers “have an unusually keen sense of the histories of their disciplines, including the controversies that have swirled within them, and that understanding seems to help them reflect deeply on the nature of thinking within their fields”.
Many of the insights within this book derive from the removal of extraneous and superficial aspects of education. How do good teachers speak to their students? Obviously, there are countless possible answers. But what do these approaches have in common? “Perhaps the most significant skill the teachers in our study displayed in the classroom… was the ability to communicate orally in ways that stimulated thought.”
The author often allows his educators to speak for themselves, and as one might expect, they are a thoughtful and frequently amusing group. Thus we read the Harvard political theorist Michael Sandel opining that teaching is “above all… about commanding attention and holding it… Our task… is not unlike that of a commercial for a soft drink”. On the other hand, Jeanette Norden, professor of cell biology at Vanderbilt University, “told us that before she begins the first class in any semester, she thinks about the awe and excitement she felt the first time anyone explained the brain to her, and she considers how she can help her students achieve that same feeling.”
The teachers analysed come from a wide range of Colleges and academic disciplines; some teach only elite students, others specialise in assisting strugglers; while several are eminent researchers, a few have no research publications at all; they deploy a variety of educational techniques. Among this diversity, the conclusions that Bain avoids are as interesting as those he draws. “[P]ersonality played little or no role in successful teaching. We encountered both the bashful and the bold, the restrained and the histrionic…. We found no pattern in instructors’ sartorial habits, or in what students and professors called each other. In some classrooms first names were common; in others, only titles and surnames prevailed.”
All the same, some common traits are apparent. “Exceptional teachers treat their lectures… and other elements of teaching as serious intellectual endeavors, as intellectually demanding and important as their research and scholarship.”
Particularly important, Bain argues, is the fostering of a “natural critical learning environment”. This is the closest the book ever comes to jargon, but that judgement would be unfair: “‘natural’ because students encounter the skills, habits, attitudes, and information they are trying to learn embedded in questions and tasks they find fascinating… ‘critical’ because students learn to… reason from evidence, to examine the quality of their reasoning… and to ask probing and insightful questions about the thinking of other people”.
At this stage, the reader might worry that this catalogue of heroic deeds could be dispiriting to the rest of us. Not so. Whilst Bain is full of admiration for his teachers, he by no means deifies them. “Even the best teachers have bad days… they are not immune to frustrations, lapses in judgement, worry, or failure.” On the contrary, their ability to confront their own shortcomings is one thing which sets the best teachers apart from those others who “never saw any problems with their own teaching, or they believed they could do little to correct deficiencies”. Good teachers show humility and willingness to improve.
In comparison, the teachers identified as the “worst” by their students often appear to carry the attitude, as one of Bain’s subjects puts it, that only “smart men can possibly comprehend this material and that if you can’t understand what I’m saying, that must mean I’m a lot smarter than you are”. As the biologist Craig Nelson says “The trouble with most of us… is that we teach like we were god.” Contrast this to the view of Dudley Herrschbach, another of the teachers in the study (as well as being a Nobel Prize-winning Chemist) that “You have to be confused… before you can reach a new level of understanding anything.”
In summary, this short book is far more readable and entertaining than a text on educational theory has any right to be. It offers every Higher Education teacher an invaluable opportunity: to learn from the best.
Ken Bain, What the Best College Teachers Do, Harvard University Press, 2004. ISBN-10: 0674013255. ISBN-13: 978-0674013254.
It seems that this problem, already well-known to many our colleagues, has started to go mainstream:
Students Are Not Asking Questions: A Working Conference to Address a Fundamental Problem in Education
A Conference to Address a Fundamental Problem in Education on July 13 and 14, 2015. 9:00 AM – 4:00 PM at Park Plaza Hotel, Boston, Massachusetts
University Mathematics in Perspective
29th Residential Course for Sixth Form Students
Wednesday 24 – Friday 26 June 2015
University of Leeds, Devonshire Hall
Sample lectures include:
A few posts from Dominic Cumming’s Blog touching on issues of mathematics education policy.
A random quote from Bureaucratic cancer …
Some have asked ‘how much confidence did you have in ALCAB doing a good job?’ Answer? Initially not much. They are all under huge pressure to say everything is fine. Initially for example, despite physics departments across the country complaining about the removal of calculus from Physics A Level (complaints that practically none of them will repeat publicly because of fear of their VC office), it did not look like ALCAB would be much use and they rejected calls from various professors I know on this subject. There is massive political pressure to focus exclusively on the numbers taking an A Level rather than the quality of the A Level.
But my hope was that by creating something that would be seen as the ‘voice of the university subject experts’, they would have to listen and adapt in order to maintain credibility and avoid embarrassing challenges. There are more and more enraged academics fed up of VC offices lying to the media and misrepresenting academics’ opinions. I thought that creating something would push the debate in increasingly sensible directions where the emphasis would be on the skills needed on arrival at university. Now, everything to do with A Levels is dominated by political not educational concerns about the numbers doing them and ‘access’. This has helped corrupt the exam system. If we had professors of physics, French, music etc every year publicly humiliating exam boards for errors, this would soon improve things from a low base and make it much harder for MPs and Whitehall to keep corrupting public exams.
Report from Sir Andrew Carter, chair of the independent review of the quality and effectiveness of initial teacher training (ITT) courses. [pdf] The report sets out how the ITT system is performing and highlights examples of good practice as well as areas for improvement. The government’s response to the review is also available.
Some recommendations of the report relevant to mathematics departments in universities:
- Recommendation 1a: Subject knowledge development should be part of a future framework for ITT content.
- Recommendation 1b: Issues in subject-specific pedagogy, such as pupil misconceptions, phases of progression in the subject as well as practical work, should be part of a framework for ITT content.
- Recommendation 3: Schools should include subject knowledge as an essential element of professional development.
- Recommendation 4: DfE should make funded in-service subject knowledge enhancement courses available for new primary teachers to access as professional development.
- Recommendation 5: Universities should explore offering “bridge to ITT” modules in the final years of their subject degrees for students who are considering ITT programmes.
- Recommendation 8: There are many universities that are home to world-leading research and assessment organisations – yet in our experience it can be the case that these organisations are either not involved in ITT or are involved in a superficial way. ITT partnerships should make more systematic use of wider expertise outside university departments of education.
- Recommendation 13: All schools should, whenever practically possible, seek out and participate in robust local partnership arrangements. In a school-led system, this recommendation is naturally the responsibility of schools.
The Government response to the Carter review of initial teacher training (ITT) is difficult to interpret. Department for Education has no control over universities (the only serious providers of “subject knowledge”), and is therefore is unable to formulate a coherent policy of improvement of teachers’ subject knowledge. The deliberate attempt to shift ITT away from universities – towards a school-based, apprentice training model is a very recent and peculiarly English idea, whose (real and potential) flaws do not seem to be recognised in either the report or the government response.
Disclaimer: writing for this blog, I act in my personal capacity; the views expressed here are my own and do not necessarily represent position of my employer, or the London Mathematical Society, or any other organisation or institution.