Maths in Sport - Holly Crawford

An interview with... Holly Crawford

Holly Crawford is an Australian snowboarder who was World Champion for half-pipe at the 2011 World Championships, as well as coming second in 2009 and 2013. She is representing Australia at the Sochi 2014 Winter Olympics, her third Olympic games. 

Holly took some time to reflect on how mathematics relates to her sport. 

The questions and answers:

Describe what mathematics lessons were like for you at school. 

Early on in my education I was very good at maths, the simplicity of right or wrong answers really appealed to me, as I got older and spent more time snowboarding and less time at school I found it more difficult to keep up. I discovered that with english you could fluff it out, make it up, and there often wasn’t a wrong or right answer as long as you could prove your point or come to a conclusion you couldn’t really be wrong!

When you left school, did you expect to be using any of the mathematics that you were taught ever again?

Of course, maths is a part of every day life and without it I would be at a significant disadvantage in my day to day life.

How good do you need to be at mental arithmetic to do calculations in your head when you are training or competing?

In all honesty we don’t use it very often. Calculating the scores on the leader board or how many people are competing vs. how many will go through to the final would be the only instances I can think of that we might use it. The simple rules of addition, subtraction or division that I learnt early in my mathematical education are all that are needed for such calculations.

How aware are you of angles when snowboarding  – such as angle of approach into and out of jumps, angle of slope, angle of body etc?
Snowboarding is all about angles. The angle of your body to the hill, the angle of your board to the hill, the angle of your board to your body, the angle at which you leave and enter the Halfpipe or jumps, the angle of all of the above when you are in the air!

When you are in a competition, how much is “mathematical thinking and calculating” and how much is “feel”?
There is not a lot of what you would really ‘recognise' as 'mathematical thinking and calculating’ in extreme sports. 

You are obviously 'thinking and calculating' all the time - am I going fast enough, is my board at the right angle, why am I upside-down all of a sudden… But mostly it is feel. You know how these things feel from doing them time and time again and you know how to correct them through that knowledge of feeling and repitition, much like one knows how to calculate mathematically from having done it time and time again!

Is estimation good enough or do you prefer to measure distances and spaces accurately?
There is obviously a wright or wrong answer. For example, not going far enough to make a landing can be disastrous but it is always an estimation, a guess, regardless of how educated that guess may be you will never take off at exactly the same spot, at exactly the same speed, in exactly the same weather conditions.

When you are competing, do you keep an eye on the scoreboard and mentally calculate how many points you need to win?
I have a tendency to not look at the score board until after I’ve competed as I don’t like it to get into my head and change what I am doing. After competition I often have a look but until then I leave it up to my coach to worry about calculations and placings and just let me know if I need to do more or less!

Have your coaches ever used mathematics and physics to explain your style?
'You have to finish your tricks in order to land them' could be considered putting 2 + 2 together which in essence is mathematics. And physics is 'the branch of science concerned with the nature and properties of matter and energy’, both of which I am made of so yes, if I were to break it down both mathematics and physics are used to explain my style but not in a colloquial fashion.

Do you look at statistics much to analyse your training and performance?

Not so much with ‘On-snow' training as with ‘Dry-land’ training. Our fitness testing results are analysed by our ’Sports science’ division who then use the statistics to give us feed back.

Do you have any other insights to offer into how you use mathematics when snowboarding?

As a by product of being an Australian and Snowboarding for a living we are forced (for obvious reasons) to spend the majority of our time traveling overseas. 

With this in mind we are often having to calculate different travel times and time zones and convert different currencies, all of which I would be unable to do if I hadn’t learned mathematics!

In relation to the activity of snowboarding mental calculations together with the general physics of the action occur every second. Regardless of the fact I’m sure I am doing mathematics in my head all day long you don’t realise this as it becomes second nature like breathing, you don’t think about doing it you just do!
Of course, you use mathematics when snowboarding that there are the degrees of rotation (tricks), 180’s, 360’s, 540’s, 720’s and so on!

Thank you Holly for being part of "Maths in Sport". Good luck with the current season and preparations for the Sochi 2014 Winter Olympics!

Maths in Sport - Ellie Cole

An interview with... Ellie Cole

How good would it be to go into an international competition, compete against your childhood hero and come away with a gold medal? In 2012, Australian swimmer Ellie Cole went to the London Paralympic Games and came away with 4 gold medals and 2 bronze, broke Australian and World records and beat her childhood inspiration Natalie du Toit of South Africa. Ellie's events include 50m freestyle, 100m freestyle, 400m freestyle, 4 x 100m freestyle relay and 4 x 100m medley relay.

Ellie visited our school in 2012 to talk about her personal history and her battle with cancer. An inspiration to all who heard her, Ellie told of us how she had been diagnosed with a sarcoma when she was very young and had to have her leg amputated at the age of 3. 

Ellie is an amazing and accomplished young woman who very kindly agreed to participate in the "Maths in Sport" project and share her experiences with us all. You can read more about Ellie and the "Kick Sarcoma" organisation that she is patron of via the link at the bottom of this post.

The questions and answers:

Describe what maths lessons were like for you at school.

Honestly, maths was not my strong suit at school. I always struggled at maths and dreaded walking through the doors and sitting through a few hours of something that didn't come naturally to me. My dad is an engineer and uses maths in his everyday life so he always just assumed I would be a natural at maths like he was. I was forever being tutored by him.

When you left school, did you expect to be using any of the maths that you were taught ever again?

I always remember sitting in maths class and learning things that I never thought I would use. I am doing Exercise Science at school and all I study now is maths and physics. I am now enjoying it more because it is being applied to something that I have a passion for. 

How good do you need to be at mental arithmetic to do calculations in your head as you go up and down the pool?
To be honest it's all done for you by your coaches! They tell you what your stroke count needs to be and what times you have to swim each lap in. Over time, you learn what that feels like in the water and adapt to it. I think swimming is executed by how it feels. Subconsciously, your body calculates it naturally. 

How aware are you of angles in your technique ­ angle of a dive, angle of arms, angle of hands etc?
While swimming at the Australian Institute of Sport, I was fortunate enough to have access to world-class biomechanists who devoted hours of time to analyse my technique. Everything was about angles in swimming, particularly the catch in your freestyle. I work as a High Performance Swim Coach in Sydney now and am forever explaining to my athletes the importance of angles in swimming. 

When you are racing, how much is "mathematical thinking and calculating" and how much is "swim as fast as you can"?
If you are in the right mind-set for a race it all comes down to something I like to call 'auto-pilot'. The reason we train 6 hours a day is so that your race plan becomes second nature and your body can execute it without your mind having to think. Usually, when you ask an elite swimmer what they think about when they race they will not be able to remember. The mathematical calculations are done months beforehand. For example, in a 100m Freestyle race the first 50m should be done approximately 2 seconds faster than the second lap. The second lap is obviously slower because you don't have the dive and you factor in fatigue. Your race plans are also dependant on stroke rate, distance per stroke and effort.

In a race like 50m freestyle, do you count the strokes for the lap and do you know where you should be for each stroke? 
Usually, you should know your stroke rate like the back of your hand. Sometimes, while swimming at 5am I like to swim with my eyes closed and I usually know when to turn because of my stroke count and feel for the distance. In a 50m freestyle I don't usually focus on my stroke count. My attention usually goes towards stroke efficiency and power.

Do you keep an eye on the clock as you go up and down the pool in training and in races?
Absolutely. The clock is always something that will give you instant feed-back.  In races, you try not to but sometimes you might have a sneaky peek and regret it when you realise that you just ruined your body position in the water. 

Have your coaches ever used maths and physics to explain your stroke?
That usually comes down to biomechanists. Unfortunately, not all athletes have a biomechanist on their team. Junior and development swimmers usually rely on their coaches to improve their technique. It can sometimes be difficult to assess a stroke from pool-deck however a coach can still explain the importance of angles from the deck. 

Do you look at statistics much to analyse your training and races?
I am a big statistics fan when it comes to racing! After every race I am issued with a race report that displays a graph with time, stroke rate and distance per stroke. It also displays every other number you can think of. You can then assess where the weak part of your race is and make changes to it for the final. Its such a great tool to perfect your race plan. 

Thanks Ellie for being a part of "Maths in Sport" - you are a legend and a great Australian athlete. 

Website - http://www.kicksarcoma.org.au
Twitter - @EllieVCole
Facebook - Ellie-Cole

Maths in Sport - David Florence

An interview with... David Florence

 

David Florence won silver medals at the 2008 Beijing and the 2012 London Olympic games in C1 - individual canoe slalom. He won the C1 World Cup title in 2009. He was ranked #1 in the world in C1 in 2012 and has won 12 World Cup medals, including 4 gold medals. David also competes in the C2 canoe slalom for pairs and won an incredible double gold medal for C1 and C2 at the 2013 World Championships in Prague, a feat that has not happened for 60 years.

David also studied mathematical physics at the University of Nottigham.

David kindly agreed to participate in the Maths in Sport project by answering 10 questions about how maths applies to his sport. Here is what he had to say:

The questions and answers:

Describe what maths lessons were like for you at school.
I was fairly good at maths and generally enjoyed the subject. 

When you left school, did you expect to be using any of the maths that you were taught ever again?
Yes, I use basic maths every day.

How good do you need to be at mental arithmetic to do calculations in your head as you race?
I don't do any actual mathematical calculations whilst I race, though I do after the race use maths in comparing my own times and my times with other competitors.

How aware are you of angles in your technique – angle of approach into a corner, angles in the course, angle of arms, angle of body etc?
It's important to get the angles right in lots of senses in my sport. We often talk about the angle of boat lean or approach angle to gate.

When you are racing, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?
There isn't any mathematical thinking or calculating as such, but it's useful to be analytically minded.

Is estimation good enough or do you rely on accurate measurement of distances and times?
I use both estimation and accurate measurement for different aspects of racing and training.

Do you keep an eye on the clock as you go around a course in training and in races?
No, it's not really possible in my sport.

Have your coaches ever used mathematics and physics to explain your style and movement?
Not in such terms, but physics and maths are a part of what we are often discussing.

Do you look at statistics much to analyse your training and races?
Yes, we use statistics all the time.

Do you have any other insights to offer into how you use mathematics in racing?
We use percentages often to measure performance and in planning training we look at the mathematics of it. How many minutes work we do per session/per week, how many sessions we are averaging a week, how many runs are we doing, how many gates, etc.

Thank you David for taking time out of your busy training schedule to answer these questions and be a part of Authentic Inquiry Maths.

Website - http://www.davidflorence.co.uk
Twitter - @David_Florence

Maths in Sport - Caroline Buchanan

An interview with... Caroline Buchanan

Caroline Buchanan is a world champion in BMX (2013) and Mountain Biking (2008, 2009 and 2012). She has been Australian BMX champion 11 times and Australian Sportsperson of the Year in 2013. She is also from Canberra, which is a pretty nice place to live...

Caroline took some time out of her training schedule to answer the 10 questions below. 

 

The questions and answers:

Describe what maths lessons were like for you at school. 
Actually I was better at maths than english and so I enjoyed it more. I must admit I did struggle with maths later on in high school as maths was the only subject that was not easy to catch up with after I had been away travelling.

When you left school, did you expect to be using any of the maths that you were taught ever again?

Only in a direct sense, like buying something in bulk cheaper than buying individual packets!

How good do you need to be at mental arithmetic to do calculations in your head as you train for and participate in a race?

It’s not really a matter for me to be consciously doing that at a race but in training it is something I do automatically now. Whilst I may not have been very good at specific questions in maths I definitely understand what affects my bike and my racing! With time I have been able to feel the speed coming into a jump and judge off feel if I have enough speed to clear the jump.

How aware are you of angles in your technique – angle of a slope, angle of body on the bike, angle of a corner etc?

Definitely angles come into our from especially with the gate start the angle of our back, foot position, angle and position of crank height when applying force to get maximal power generated. The angle that we enter the corners to have maximum exit speed as well as the points on the jumps that we need to hit and redirect our force to get over the jumps as fast as possible and most bio mechanically and aerodynamically efficient.

When you are racing, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?

During races it is mostly on auto pilot going as fast as possible, however there is a lot of visualisation and mathematical thinking of cornering angles, landing perfectly on the back of jumps to gain maximum speed and “if this…. then that” scenarios which in a lot of cases is maths I guess and problem solving.

Is estimation good enough or do you rely on accurate measurement of distances and times?

In BMX, estimation is never good enough, we do special timing sessions with lights to the .001 of a second. Reaction time, timing and precision is key.

Do you keep an eye on the times of other competitors as you prepare for a race in competitions?

For time trials yes, in race competitions not really as every race is so variable interacting with seven other riders. We used to have to be aware of race times as the fastest qualifier got the first gate pick in following race/s but that is changing now with random gate draws being used more.

Have your coaches ever used maths and physics to explain your technique?

Not in a school teacher kind of way, using specific terms, but the inference is there, pumping to increase speed, manualling in certain ways will increase speed and in other circumstances it will decrease it. Thinking about it now, yes, it is something used in the sport a lot. My mum often says I am talking to the ‘lowest common denominator’ when trying to explain some things to her!

Do you look at statistics much to analyse your training and races?

Absolutely, all the time. You need figures to have a benchmark and to have goals to train towards. Some things that we look at is my power to weight ratio and monitor that, my max power, relative power, acceletation, velocity, revolutions per minute and speed etc. I am glad that I finished my schooling thats for sure.

Do you have any other insights to offer into how you use mathematics in your sport?

Probably gearing is the main set of equations important to the sport of BMX and least understood by many riders. There is a chain ring at the front with a number of teeth on it, and a sprocket at the back wheel also with teeth on it. The combination of these numbers in conjunction with tyre type affects the circumference of the wheel which gives a gear ratio. Changing say a chain ring by one tooth can make peddling harder or easier for certain tracks and will affect how far the bike will travel for each crank revolution.

I change gear ratios depending on the steepness of a start hill, how strong I am feeling and by the type of jumps on the track. After almost twenty years of riding this is almost a subconscious decision but we do work out the benefits of say a 1cm gain in travel with every crank revolution on a track especially when the first straight of racing is absolutely critical and when there may be few passing opportunities on the rest of the track.

That’s pretty mind bending stuff – let’s just say my favourite numbers are 1 (first) and 68 (my racing number) !

Thanks Caroline for being a part of the "Maths in Sport" project at Authentic Inquiry Maths!

Good luck for 2014!

Website - http://www.carolinebuchanan.com/caroline-buchanan/index.asp
Twitter - @CBuchanan68
Facebook - CBuchanan68

Maths in Sport - Marcel Hirscher

An Interview with... Marcel Hirscher

Marcel Hirscher is an Austrian alpine skier who was born in 1989. His achievements include World Cup Giant Slalom Champion for the 2012 season, World Cup Slalom Champion in 2013 and overall World Cup Champion in 2012 and 2013. In 2012 he was awarded the Skieur d'Or by the International Association of Ski Journalists. 


Marcel kindly took some time out of his busy schedule, including World Cup events that are currently underway and WInter Olympic preparations, to answer some questions for me about how mathematics relates to his sport.
  

Marcel with the slalom and overall World Cup trophies in early 2013

The questions and answers:

Describe what mathematics lessons were like for you at school. 

I’m surely more talented in the creative part. As a matter of fact languages were my preferred business. But of course I passed all my math-units as well.

When you left school, did you expect to be using any of the mathematics that you were taught ever again?

Not really, no. But I’ve learned my lessons and it didn’t harm neither me nor anybody to keep body and mind in training so far. Furthermore I think math is a good way to keep the brain in shape, even if you're mathematically not that privileged.

How good do you need to be at mental arithmetic to do calculations in your head when you are training or racing?

The calculations in my job are not that much linked with the ability for mental arithmetic. It’s quite simple, I don‘t see my real position before the first sight on the timetables. That applies for training as well as for every race.

How aware are you of angles when skiing – such as angle of approach into corners, angle of slope, angle of body etc?

I wouldn’t use the term ‘aware’. I work hard on strength and balance in my workouts. But physically and not mathematically. To become aware of the angle of a slope I’m doing the course tour. As a result I’m dealing quite well with all the upcoming angles.

When you are in a race, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?

It’s always “go as fast as you can”. But of course I have to do my homework to beat time. As already mentioned there’s no mathematical thinking needed in this context.

Is estimation good enough or do you prefer to measure distances and times accurately?

I think estimation does not fit in the life of a professional racer. So accurate measurements are indispensable.

When you are racing, do you keep an eye on the time clock?

It’s not really a clock. When I crossed the finish line I keep my eyes on the time display.

Have your coaches ever used mathematics and physics to explain your style?

I’ve often been told that my size has a positive effect on my agility. So maybe it’s about angles again.

Do you look at statistics much to analyse your training and races?

Yes I do, especially concerning lactate values, my weight, muscle mass and every other indicators which are important for my profession.

Do you have any other insights to offer into how you use mathematics when skiing?

Keep calculations down, count on your team and yourself - more mathematic isn’t necessary when skiing.

Thank you Marcel and good luck for the season. Hope you do well at the Winter Olympics.

Website - http://www.marcelhirscher.at/
Twitter - @MarcelHirscher
Facebook - hirschermarcel

Maths in Sport - Cesar Cielo

An Interview with... Cesar Cielo

Cesar Cielo is a Brazilian swimming world champion. He is the world record holder for 50m freestyle and 100m freestyle. He has been world champion 6 times. He won the gold medal for 50m freestyle and bronze in the 100m freestyle at the 2008 Olympics as well as bronze in the 50m freestyle at the 2012 Olympics when all 8 finalists finished within 0.68 seconds of the winner. 

No doubt he is looking forward to the 2016 Olympics being hosted in Brazil. 

Cesar is the first interview subject for my "Maths in Sport" series, partly because of my personal history as Senior Men's Champion at Ulladulla Swimming Club (2004-5) and partly because he is such a champion in his sport.

The questions and answers: 

1.  Describe what maths lessons were like for you at school. (Please be honest – not all of us loved maths at school)

I have never had a problem with math. Honestly, I was not in love with it but at the same time it was not a class I hated studying.

2. When you left school, did you expect to be using any of the maths that you were taught ever again?

I knew that a lot of what I have learned was going to be useful. I'm constantly making calculations because of swimming. Its not as complex as it used to be in school but sometimes it gets pretty hard.

For an example, finding the standard deviation for a specific set and compare that to previous times I have done that set.

3. How good do you need to be at mental arithmetic to do calculations in your head as you go up and down the pool?

You don't need to be an expert =) Most of the times I'm counting strokes and calculating intervals on the clock. I think when it comes to the work out in the pool physics also has a great role as we are constantly thinking about the resistance our body creates in the water.

4. How aware are you of angles in your technique – angle of a dive, angle of arms, angle of hands etc?

That's something really important in swimming. From the angle of entry in your dive to the position you want your body be while you are swimming. We are always looking for ways to reduce the drag our body creates and how we can minimize it.

5. When you are racing, how much is “mathematical thinking and calculating” and how much is “swim as fast as you can”?

Racing is more about the feeling and management of your energy and "breath". 

6. In a 50m freestyle race, do you count the strokes for the lap and do you know where you should be for each stroke?

Yes, in my 50's I take around 32 to 34 strokes. Depending on how long I go underwater after the start, I could take one more or one less stroke.

7. Do you keep an eye on the clock as you go up and down the pool in training and in races?
Between the efforts yes, while swimming I'm looking to the bottom of the pool and counting my strokes and thinking about my technique and intensity. 

8. Have your coaches ever used maths and physics to explain your stroke?
Many times. Physics has a huge role in swimming. The details like starts and turns are easier to see how much physics change the speed you can achieve. 

9. Do you look at statistics much to analyse your training and races?
Yes. It's more often in training since you are trying to compare yourself to past seasons and sets that you have done before. In competitions it is more about comparing the races and the technique to see what it could have been done better.

10. Do you have any other insights to offer into how you use mathematics when swimming?
We often use the stop watch to get the "stroke frequency" or the tempo of the stroke to see how fast your stroke cycles are. That's data that only works if you combine this info with some other factors, like technique and stroke length. 
For an example, if you take very quick cycles naturally you will have a very high tempo / frequency, but that doesn't mean you are going faster as you have to keep the efficiency through the sprint. We use this data to see if the swimmer is just "spinning" his arms and increasing the tempo and "slipping" water.



Thanks to Cesar for being a contributor to "Maths in Sport". I wish him all the best for 2014 and his future in swimming.

Website - http://www.cesarcielo.com.br/home/
Twitter - @CesarCielo
Facebook - Cesar Cielo

Photographs courtesy of Osvaldo

Maths in Sport - An Overview

When I had the idea for "Maths in Sport", it was already the last week in November. Time was ticking. My plan was to get interviews with famous sportspeople and post their responses here in January. I realised I had to move quick.

So I made a "Wish list" of all the big names in sport that I thought might be interesting to hear from. I also got the kids in my class to list who they thought were the most famous sportspeople in the world. From this list, I started tracking down contacts, websites, PR companies and business managers in the sport industry.

In the end I had 65 names on my list. I aimed at world champions, people at the elite level of their chosen sports. I was able to find some sort of e-mail contact for 57 of these and so I send out a "feeler" e-mail to see if they might be interested in participating.

Of the 20 who replied, 15 have agreed to answer 10 questions about how they use maths in their sport. Only 5 declined the offer. 37 didn't reply at all. I'm sure they are all busy people so I was really impressed with my strike rate - over 25%.

For the 15 who have agreed to answer questions, I needed to work out a set of 10 questions that would be:

a) interesting

b) reveal some insight into maths in sport

c) have some sort of commonality so that I could attempt to draw some common threads from each "conversation".

So here's what I came up with:

The 10 Questions:

Question 1 - Describe what maths lessons were like for you at school. (Please be honest – not all of us loved maths at school)

This was a general question that I gave to everyone to see how they felt about maths at school. 


Question 2 - When you left school, did you expect to be using any of the maths that you were taught ever again?

This is something I am keen to learn about - does what we do at school actually prepare us for anything in the real world? And specifically in sport, do we really need maths?


Question 3 - How good do you need to be at mental arithmetic to do calculations in your head as you race/shoot/play/compete etc?

This one was modified slightly for each sport but the focus was on the need to do quick mental calculations whilst competing at an elite level. Would this ability be an advantage?


Question 4 - How aware are you of angles in your technique – angle of approach into a corner, angles in the course, angle of arms, angle of body etc?

This one was modified also for each sport but the focus was on angles and how an awareness of them improved performance.


Question 5 - When you are racing, how much is “mathematical thinking and calculating” and how much is “go as fast as you can”?

Again, modified to be sport-specific but looking at how much is based on thinking and how much is on feel.


Question 6 - Is estimation good enough or do you rely on accurate measurement of distances and times?

We do a lot of work in class with estimation. Why? Does a professional sportsperson estimate or measure accurately? How does this change between sports?


Question 7 - Do you keep an eye on the clock as you go around a course in training and in races?

Keeping an eye on time measurement - is this important to success in sport? 


Question 8 - Have your coaches ever used mathematics and physics to explain your style and movement?

Sports science is a huge industry. How do these scientists communicate with their athletes? What do they say? What maths do they use?


Question 9 - Do you look at statistics much to analyse your training and races?

Data analysis - another growth industry in the world of sport. How do athletes use this to improve their performance?


Question 10 - Do you have any other insights to offer into how you use mathematics in racing?

Just on the off-chance that I had over-lloed something really obvious, I provided this last question to see if there are other ways that maths comes into sport.


So, there you have the questions I have asked. Over the month of January I will be posting responses that I have received. Of the 15 who accepted questions, I have only got 6  completed replies so far, but we have had Christmas etc in the interim so I am sure the other answers will be sent soon. I will do some follow-up on those that haven't come back to me yet.

In the meantime, I hope you enjoy the answers that I will start posting soon.

Happy New Year!

Fireworks over Canberra last night