Zeno of Elea

Zeno of Elea was a pre-Socratic Greek philosopher of Southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best know for his paradoxes, which Bertrand Russell has described as "immeasurably subtle and profound". (Source and for more information - wikipedia) 

Further information can be found on the MacTutor History of Mathematics.

Collection of Youtube videos on Zeno's Paradoxes

Numberphile

Math Bites with Danica McKeller

Math Bites on the Nerdist Youtube Channel - a quirky and light-hearted set of youtube videos on Mathematics, starring Danica McKeller

McKella studied at UCLA and earned a Bachelor of Science with honours (summa cum laude) in 1998. As an undergraduate, she coauthored a scientific paper with Professro Lincoln Chayes and fellow student Brandy Winn entitled "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on ". Their results are termed the 'Chayes-McKeller-Winn theorem'. Referring to the mathematical abilities of his student coauthors, Chayes was quoted in The New York Times as saying, "I thought that the two were really, really first-rate." McKellar's Erdos Number is four and her Erdos-Bacon number is 6. (source: wikipedia)

1. The Pi Episode - Join Danica McKeller as she explains the joys and mysteries of the wonderful world of Pi!

 

2. Math Head: DO MATH IN YOUR HEAD!

3. Binary Numbers. Danica McKeller demystifies the 1's and 0's of binary numbers

4. Percents: explains percents and the value they have in everyday life

5. World Math - Mathematical concepts may be universal, but the mathematics around the world varies.

6. Dance of the Sugar Pi Fairies - it's pi like you've never seen before! Look out for Simon Pegg...

McKellar has written a number of books on mathematics, mainly designed to pass on her love of mathematics to girls. Titles include: "Girls Get Curves: Geometry takes Shape", "Math Doesn't Suck", "Kiss my Math" and "Hot X: Algebra Exposed"

Book Review - The Simpsons and Their Mathematical Secrets by Simon Singh

This is a superb book for anyone who loves Mathematics and is a fan of The Simpsons. I found it fascinating discovering the mathematical expertise of the writers of The Simpson and how they sneakily embed mathematical concepts into episodes. Simon Singh writes from a fans point of view. He obviously enjoys The Simpsons and his love of mathematics is clearly evident. This book is a joy to read.

Talks at Google, Simon Singh, "The Simpsons and Their Mathematical Secrets".

Pi and Four Fingers - Numberphile

Follow Simon Singh on Twitter @SLSingh

Why is x the unknown?

Terry Moore's Ted Talk about why 'x' is used to represent the unknown.

Terry Moore directs the Radius Foundation in New York, which, as its website says, "seeks new ways of exploring and understanding dissimilar conceptual systems or paradigms - scientific, religious, philosophical, and aesthetic - with the aim to find a world view of more complete insight and innovation."

Book Review - Adapt by Tim Harford

A review of Adapt by Tim Harford and how it can be "adapted" for the world of education. (Inspired to read and reflect about this book after it was recommended by John Tomsett at NTEN ResearchED York).

Tim Harford composes a clear and structured argument on the importance of adapting, not just from an ecological point of view but as individuals, companies and other organisations. Mistakes are commonplace and inevitable. Harford uses a number of case studies from the development of the Spitfire, changing tactics in Iraq, the Credit Crunch to modern companies such as Google to explain and demonstrate the importance of adapting and the problems that emerge when this doesn't take place.

Harford draws deeply on the three Peter Palchinsky Principles:

1. Seek out new ideas and try new things
2. When trying out new things, do it on a scale that is survivable
3. Seek out feedback and learn from your mistakes

What is intriguing about this book is how Harford unravels the mystery of adaption by highlighting the traps and promoting the benefits of adapting.

Barriers to learning from mistakes include: bundling losses up with gains, reinterpreting failures as successes, denial and loss chasing. To counteract this, Harford perscribes working by the Palchinsky Principles. We need to listen, whether this is as a company to whistleblowers or as individuals to what is described as the "validation squad" of trusted individuals who will give us their honest opinions. Change needs to be completed on a scale that promotes reflection and honesty.

Why adapt? 

"The process of correcting the mistakes can be more liberating than the mistakes themselves are crushing, even though at the time we so often feel the reverse is true". Mistakes in life are inevitable. However, "a single experiment that succeeds can transform our lives for the better in a way that a failed experiment will not transform them for the worse - as long as we don't engage in denial or chase our losses".

What are the implications for teaching?

In teaching, there is a constant need to adapt and change. In the classroom, what works one moment can fail disastrously the next. Teenagers can sometimes be a little volatile. However, how do we know we are doing the right thing and not just bumbling along? One of the most important principles mentioned is listening - whether this is to a trusted colleague or a sensible student. 

Education is bombarded with new ideas and the hunt for the pot of gold at the end of the rainbow. The difficulty is sifting and finding the sensible ideas - the ones which benefit students and make the lives of teachers easier. Harford promotes the importance of trying out new ideas. However, this needs to be done in a controlled way and not gun-ho, devil-may-care and by the seat of the pants. Adaption needs to be on a scale where success can be measured. Allowing ourselves times to reflect and most importantly, to listen to the opinions of those we trust. By investing on a modest scale, the traps of chasing losses and denial are more likely to be avoided. 

The Palchinsky Principles should be above the door of every staffroom.

For Students:

Students need to be encouraged to try new things and to accept mistakes as a part of life. This links to a previous blog by me, Developing Grit and a Growth Mindset.

I really enjoyed this book. It has made me reflect on the implications adaption has on my life and the wider world around me.

Book Review - "Taming the Infinite" by Prof Ian Stewart

This is a fascinating book on the history of Mathematics. Stewart goes way back to over 4000 years ago and the early days of recording the number system using tallies etc to an in depth look at the most important topics of the 20th and 21st century, such as Chaos Theory. Along the way, Stewart provides interesting insight into the lives of the brilliant mathematicians who have contributed significantly to the subject. He looks at how mathematics has develop and its most important advances. He considers the effects of mathematics on other areas of study and how mathematics affects our daily lives.

This is a must read for any student of maths (including teachers!). I love this book and look forward to reading it again.

Book Review - "The Hidden Lives of Learners" by Graham Nuthall

I bought this book after hearing a number of very positive comments about it at NTEN ResearchED York.

Graham Nuthall's book "The Hidden Lives of Learners" is a study of learning from a student's point of view. It focuses on the highly influential world of peers, and the student's own private world and experiences. Nuthall has used a comprehensive array of research tools and collected data over forty years, bring this all together in this one book. What becomes clear is that just because a teaching, does not mean students are learning.

"Learning requires motivation, but motivation does not necessarily lead to learning."

Nuthall's book provides a simple check list to effective teaching. The book discusses memory in detail. He slams learning styles (e.g. VAK) and states to build memory, students need to make connections with new knowledge and known concepts. For knowledge to be retained students need "several different interactions with relevant content for that content to be processed int their working memory and integrated into their long-term memory in such a way that it becomes part of their knowledge and beliefs."

Assessment is a tricky topic. He sees the best strategy for assessment is for it to be "conducted individual by individual, and embedded in a programme that fully considers individual preferences." This has obvious difficulties from a time management point of view, but one that we as educators need to consider and think carefully about.

The one area I was not completely convinced by was his idea of "becoming involved in peer culture" and in fairness, Nuthall too was reserved about this idea. I understand the advantages of knowing your students, but I also consider it to be healthy for their to be a little professional distance in the teacher/student relationship (especially in the age category I teach 11-18).

For me personally, I like to strive for the optimum seating arrangements in my class to develop co-operative learning. I think about peer groups but the driving force is finding which individual students work well with who.  I try to create pods of 3 or 4 students (preferably of varying ability and other factors). Most importantly, I look at my assessment results and if I believe a pod is not working effectively, I look to change it.

I prefer the "alternative culture" within the classroom by creating a "learning community". A complex idea but, in my opinion, this should be at the heart of any school and run through it like a river.

I was particularly interested in the strong evidence shown for the effects of students managing their own learning. This ideas seem to run alongside ideas of a Growth Mindset, grit and determination, and developing independent learning. I try hard in my teaching of mathematics to open this door, by using Mymaths,  Hegarty Maths, or BBC Bitesize. I also like to stretch their knowledge and understanding by looking at advanced material e.g. Numberphile or Vi Hart.

For more information, visit The Graham Nuthall Classroom Research Trust website.