- Why do a project?
- The Netflix Prize
- Is life really that complex?
- The Mathematics of War
- Running the numbers - Chris Jordan
- Hans Rosling - Gapminder world
- Data Visualisation - David McCandless
- The Happy Planet Index
- Fermats last theorem
- Exponential growth
- Guardian Datablogger
The idea of a Mathematical project or investigation is something that always really excites a lot of Maths teachers, but often Maths Studies students need a little bit more persuasion to get excited. There are a number of things that can be done to in this attempt to persuade. Some are inspiring and others simply pragmatic but all are worth sharing in the hope that some will do the job. It is really important to show students the relevance of Mathematical investigation by showing them some examples of it being done and demonstrating by use of different media how often it is always being done, particularly with reference to statistical investigation. Equally there are some fascinating stories about Mathematicians through history who have spent their lives investigating and moved Mathematics forward in doing so. The ideas on this page are not necessarily intended as possible projects but more as inspiration and justification for the idea of Mathematical investigations. There is a brief section at the bottom for the pragmatists as well!
This was a great example of the role of data analysis in popular society and of opportunities in the connected world! Netflix offered an open competition and prize of 1 million USD to anyone who could come up with an algorithm to predict user ratings for movies so that their recommendations would be more effective. Read more about it here .Netflix is a household name in many parts of the world and it is wonderful to think that anyone had the opportunity to help them!
This is a good movie that tells the story about how Oakland A's coach, Billy Beane transformed the team's fortunes on a meager budget by devising and using a statistical analysis system know as 'Sabermetrics' It is a really nice example of how statistics has been used in context. The film doesn't' concentrate too much on the mathematics, but the sentiment is there and that makes it good for inspiration. You can read more about 'Sabermetrics' at this link. Find a moment to watch a bit of the film or certainly get a copy join the department for students to borrow.
At the same time, you might refer to this article from Maths Journalist John Allen Paulos - in particular, this quote is related.....
Example from baseball - An example cited in the American Statistician from 2001 provides a good counterexample from baseball. Examining the batting records of the New York Yankees with more than 300 at bats-in the previous year, the authors (Langford, Schwertman, and Owens) found that the number of triples hit by a player correlated positively with the number of base hits he had, which in turn correlated positively with the number of home runs he hit. Yet the number of triples a player hit correlated negatively with the number of home runs he hit.
Stated differently, players who got a lot of triples generally got a lot of hits of all kinds, and players who got a lot of hits also tended to hit a lot of home runs.
The reason triples and home runs were nevertheless negatively correlated is that players who hit a lot of triples were usually lithe and fast, traits that do not lend themselves to home run hitting, and players who hit homerun a lot were generally big and slow, traits that do not lend themselves to hitting a lot of triples.
In general, even if a quantity X correlates positively with another quantity Y, and Y correlates positively with a third quantity Z, we can't conclude that X correlates positively with Z. Transitivity may not hold.
This is a great 10 minute video from Hannah Fry based on how mathematics might be able to help us answer the question above. She starts by giving us examples of why things might seem so hopelessly complex that we are never likely to get any understanding of them and then cleverly shows us some other examples of how maybe we might. There is a nice useable example in there about the last London riots and the distances the rioters lived from the places they rioted. Equally there is some more complex mathematics about how 'Burglary hotspots' resemble the patterns of leopard spots - and an understandable explanation for why!
In this 7 minute clip from a TED talk, Sean Gourley gives a fascinating overview of a project to investigate the Mathematics of war. By looking for common elements and patterns in different conflicts, they suggest a predictability and the notion that if the Mathematical pattern could be broken then the conflict could be be resolved. Its a wild notion, but fascinating to consider, even more so in the knowledge that there is a group of Mathematicians busy working on it! It is also an interesting example of how the data was collected since it all came from news reports rather than official sources.
This is 11 minutes well spent as Chris Jordan shows us numbers as we have never seen them before. He makes art installations that represent huge, relevant numbers. For me, the most shocking stat is about the fact that breast augmentation is fast becoming the most popular graduation gift for girls in the US. His image for this figure is brilliant. This video inspired a student of mine to do some research on trends in plastic surgery that turned in to an excellent project. Here is Chris Jordan's website for Running the numbers.
Hans Rosling is becoming increasingly well known for his great ability to present statistics. He has done a huge amount of work for getting data in to the public domain and has lead the Gapminder.org project that makes all this data available both as raw data and through his fantastic dynamic scatter graphs - Gapminder World. He has done so many great videos that it is actually hard to pick just one. You can see all of his videos, including the hour long documentary 'The Joy of Stats' here on Gapminder Videos. I have included a short clip below that gives you an idea of the dynamic scattergraphs. I seriously recommend putting some time aside to watch the rest of his videos too though!
I have been a big fan of Informations is beautiful from the beginning. I love the whole idea behind infographics. As teachers, they give us plenty of material because of the number of them that are hopelessly inaccurate and their ability to distort numbers. Equally, infographics have played a role in making statistics more approachable. I actually think it should be a part of the stats curriculum now to help students be conversant in the language, and critical of infographics. One of the items I like in this video is the work he has done by collecting facebook status updates! This is very relevant and reminds us all the data is facebook's business. It has inspired more than one if my students to do their project on facebook. I also like his take that 'data is the new oil' or 'soil' to make us think! I also recommend the book for your classrooms.
An organisation whose work it is to produce a statistical index about how happy a country is. It is perfect for a project and people are really doing it. What information do they collect? How do they process it? Have a look at the website Happy planet index and watch the video below.
I don't need to say too much about this well known story, but I do think that it is worth telling as part of demonstrating to students more about how real mathematical investigation is. I recommend the Fermat's last theorem documentary from horizon. It is often used in ToK so perhaps there is an opportunity to dovetail here!
I have made reference to this amusing titled video 'The most important video you will ever see' in other places on this site. It is very relevant in the teaching of exponential modelling. I don't feel the need to show the whole 50 minutes, but do find that students like it. 'The single biggest failing of the human race is our inability to understand the exponential function'. Any data that can be modelled with an exponential is bound to make an interesting project because of the counter intuitive nature of these feunctions!
The Guardian Datablog is a truly fabulous source of interesting and relevant data. It is also prolific with near daily updates. They always include raw data and I would guess most students could find something interesting to work with from this site.
Inspired or not by any of the ideas above it is worth pausing to think about the value of the project to the overall subject grade! At 20% of the grade a good project can really help students take control of their progress. Pragmatically, the criteria are not actually that difficult to meet and anyone that is prepared to give some time and take advice should be able to get a 12 or better without too much trouble. As I said above, the real challenge is to do this in the pursuit of something really interesting!