Statistics resources

Statistics are fun.  I'm not even kidding - it is the most fun of all the mathematical domains.  I was asked to put together five resources that taught statistics.  Unfortunately, I was unable to present the fun stuff, because we needed to provide content - rather than activities. Anyway, here is an example clips that presented the concept of chance.  Keep in mind, they are designed for learners with no experience at all of statistics.

The editing is a little clunky, but I've managed to sort this out now, so the newer versions have smoother transitions, better filming and placement of me, and better graphics.

Learning curves

This year I have been adding to my skill-set the 'art' of making video clips.  It requires know-how, technical skills, editing skills, patience, cunning and content.  Anyway, here is a sample of some of the content.  The process is very long, but the hardest part by far is generating and sequencing content so that the audience is engaged and able to learn from the clip.  It's a new medium for me but I see huge potential.

I think we are heading in the right direction, but lots of room for improvement.  The clips were designed for tutors of learners with low literacy skills, and covered a variety of topics.  This one addresses writing 'personal profiles'.  

This one here is about the basics of conversations.  You may think it is rather simple, but believe me, it is needed.

Mathematics and Moral Courage

I have been preparing a paper for a conference in Hamburg Germany with the support of my supervisors - Professor Diana Coben and Assoc Professor Jenny Young-Loveridge.  The paper is pulled from data I collected as part of the PhD but has not made it into the thesis.  The data set is a full audio recording of a vocational mathematics class which included Youth Guarantee learners and older adult learners.  

The paper contrasts three engagement patterns found within the class.  There are actually as many engagement patterns as there are learners but when limited to 8 pages it is not possible to include more.  I called the three: resistant, defensive and engaged. 

What I found is that some learners are very hesitant, or resistant to engage with mathematics because it presents danger to their social-selves.  They are even more resistant to engaging in a discussion because of the social aspect. Some are defensive, in fact they are aggressive about their non-engagement.  Obviously, this is going to have an impact on the class dynamic, and it certainly has a constraining effect on the others.

Finally, there are those that engage fully, and make new understandings.  Quite amazing to watch.   In summary, in a class of 15 learners, five engaged at a meaningful level, and of these five, two made new meanings out of the content presented.

Many mathematics researchers insist that discussing mathematics is the only way to learn.  Some even suggest that you are only doing mathematics when you are arguing about it (Lakatos for example).  Polya argues that doing mathematics requires moral courage above all else.  You must be able to generate an idea that might be wrong, share it with others, and then work toward a better idea. Your idea will likely be wrong, but you have to be brave enough to do it anyway - that's the courage part.  You have to accept that it might be wrong, and be graceful when others point that out, and then move forward - that is the moral part.

This raises real challenges for the Tertiary sector.  How do we better engage and support learners who have had poor school experiences?  Or those who begin to feel small when they make mistakes with maths? Or those who are terrified their friends will think they are dumb? How do we get learners to take risks and engage - how do we cultivate moral courage?

I'll be very interested to see what the international community makes of it all.  Not sure whether the paper has been accepted but will find out over Christmas.

Reading and the mind

Reading quantity may be related to IQ.  That is, the more you read, the smarter you get.  The relationship is somewhat complicated, and not the least bit controversial, but there is some evidence. For a good, although somewhat dated summary, check out this article.

I personally think that the quality of the reading material (aside from vocabulary level) is also important, and hence why the map below interested me.  It is far harder to find evidence to support this, but generally the books that have more 'life on the page' as Ray Bradbury would say, have more themes - and themes give you more to think about.  Being introduced to new themes makes you a better informed, deeper and more reflective person.

The map below shows the most read book by High School seniors in the USA.  Firstly, great!  Young people are reading!  Second, they are reading some good material.  
























Now, there are good books, bad books and ugly books.  The graph above adds an extra category - recently advertised books (i.e huge publicity push, usually with movie).  I see some absolutely life changing books on the chart.  Namely: Night, Animal Farm, Macbeth, and maybe Frankenstein (barely, but with great themes).  It would be enlightening to see the top five most read books.  It may be that those who read the Fault in our Stars also read all the others, but who knows.

The Fault in our Stars is neither ugly nor is it bad.  One way to look at it is, does it play on the emotions of teenagers, or in contrast, expand their paradigms of human experience?  In my opinion it definitely does the first, and perhaps the second a little.  It's an okay book (IMHO), but clearly the teenagers love it.  And why wouldn't they?  It's carefully designed to appeal to them.    

'Night' on the other hand is not.  'Night' is a recount by Elie Wiesel who was sent to the concentration camps in Nazi Germany when he was 14.  You cannot read that book and not be changed.  And yet, it is not designed for anyone, no market research went into it, it is simply a chunk of real life.  If you read 'Fault in our Stars' you will 'feel' (loss, pain, anger, love) but you may not be changed.

Anyway, its great to see young people reading - and not all of them are falling for the commercialization of books and are reading material that is old but powerful, rather than new, glossy and popular.  How much of these are required reading for school we don't know either.  I suspect all the older ones are.  However, any young person who gets through Animal Farm or Night is going to be an educated and interesting person.    

Long live the book.

My STAR WARS - How it all started.

Yip, I was the kid that played Star Wars out on the farm by myself.  The big old Macrocarpa tree was the Millennium Falcon, and Chewie and I use to fly from planet to planet smuggling goods.  I made a blaster, strapped it to my leg in a home sown holster and hit the skies.  Times were never so good.

I got given a Star Wars colouring book - on one page it had a picture of Luke in an X-wing fighter and on the screen it had a code.  Oh boy, Star Wars language!  Turns out it was the code 'pig pen', which doesn't sound that great but is actually a pretty cool code and - STAR WARS!

It got me interested in codes and then ciphers.  Its great for kids to use, and it's also great for parents to use to send messages to them.  The idea is to cultivate an interest in alternative message systems.

The real fun, and learning, occurs when you begin to change the relationship between the two codes.  For example, the most common structure is that below.

However, you can change the letter relationship to create a challenge for the reader.  Just be sure the letter placement is not random and the reader will be able to use a letter frequency strategy to solve the puzzle.  In other words, because 'e' is usually the most common letter, by identifying the most common symbol, it can be solved pretty quickly.  For example, in the code below, if you did not have the key, you could identify the most common symbol (an 'L' looking shape) and determine that it represents an 'e'.  From here you could deduce the position of the other letters.

I might write another post on this - called 'Code busting - turning your kids into analytical code breaking machines - and how this will help them conquer the world'.

Anyway, I've included a variation of the code below.  This version is used in Assassins Creed.  It's a little more complex, but still fun.  Good luck.

A bit rough - but you get the idea.

Pythagoras theorem puzzles

A friend of mine was talking to me about how boring maths is to teach.  He is working on trigonometry and reviewing the Pythagoras theorem.  There are so many great ways to make both of these topics fun, interesting and engaging.

Anyway, fresh from the NCLANA here are a couple of ideas that can be adapted.  The main idea is to use problem situations to engage learners and to get them thinking mathematically, before giving them a procedural solution.

 


One more: