Thursday, 31 July 2014

Angle Hunt with iPads

We've had our iPads for 6 months now and confidence was high. Time to let the little angels run free and see what they could produce...

The Angle Hunt

Our activity was to use our iPads to photograph different types of angles that we could find in the playground


to put the picture together in some form of presentation. This bit was left open-ended - I knew the kids were familiar with a variety of different aps such as Explain Everything and Educreation. I wanted to see what they would come up with.

The aim was not so much the identifying angles part - this had been covered last year in Year 4 - it was more about the application of technology.

So they paired up and headed out the door...

What We Produced

Here are a few examples of what we did:

Only found 3 examples but they were correctly identified

Here we can name the angles and give the degrees

And this one nicely represents the angles

All of these used the Explain Everything ap. Nice work and clearly presented. 

One other was done as a movie using Educreation:


 Nicely done!

So my curiosity was satisfied - yes, the kids can use their iPads to record their learning and - yes, they can identify some angles.


Mission accomplished. 


Wednesday, 30 July 2014

Maths in Dance - In Conclusion

So, that was a great experience. 

I was a bit disappointed that I only got 7 dancers or choreographers to participate


the quality of the responses was extraordinary.

Here are a few things that really stood out for me:

  • the dancers who responded were so enthusiastic in their support of the project and gave very generously of their time to write their answers, which they had obviously given considerable thought. I was totally overwhelmed by their openness and honesty. 

  • so many of the dancers had really positive experiences of maths at school - and many of them had pursued maths to a very high level. This is not what I had anticipated. Perhaps that was my preconceived ideas about dancers in general. Thank you for changing my opinion on this one.

  • the dancers demonstrated deep vision and awareness of ideas that I had never considered. Elena Grinenko's explanation of fractions in the rhythm of different dance styles was a revelation to me. 

  • the awareness of space and position was something that I had anticipated would be critical in dance. I even learnt a new word - proprioception - that was used by several of the dancers to describe this awareness of body position and movement. 

  • many of the dancers, especially Michael Apuzzo and Linda Gamblin, described the specific and directed use of maths and physics in their training and preparation for performance, in choreography and in the performance itself. 

So once again, a huge thank you to the participating dancers who were part of the "Maths in Dance" project - I am forever in your debt.

Let me finish with a few quotes that have stuck in my mind, thoughts that I hope will resonate with you as well:

Understanding one's own body mathematically is imperative for a heightened sense of spacial awareness and proprioception.

- Linda Gamblin

Math seemed both academic and artistic to me even at a young age.
- Michael Apuzzo

As dancers we are also very aware of the space around us and the shapes and dimensions we form and create within the space.
- Corey Herbert

"It's not how much you practice, it's how smart you practice" plays a huge roll in your improvements. I can put 10 000 hours into practising something wrong then it will be impossible to fix it.
- Elena Grinenko

It is impossible to get away from math in everything that we do. It is like the inevitability of is involved in all of our thinking and doing, and the way we behave.
- Alonzo King

So that wraps up the "Maths in Dance" project.

Future plans include a "Maths in Science" project for October and the big one I am really excited about - "Maths in Music" coming this way in January!

So, does anyone have Elton's e-mail address?

Wednesday, 23 July 2014

Maths in Dance - Linda Gamblin

An Interview with Linda Gamblin

Linda Gamblin trained with the Royal Ballet School in London and has performed in a number of principal roles whilst working with The Australian Ballet, Royal Ballet London, National Ballet of Portugal and Sydney Dance Company. She has worked with choreographers such as Michael Clarke, Meryl Tankard and Graeme Murphy and has performed works by Jiri Kylian, Maurice Bejart and Jerome Robbins. 

Linda is a passionate dance educator and has a keen interest in understanding the workings of the body. She attained her Level 3 Diploma in Anatomy and Physiology whilst teaching Pilates, and has continued to develop her education on the muscular and skeletal systems and biomechanics. This knowledge has become an integral part of her teaching practice.

Linda is excited to ... challenge and inspire (students) through the exploration of what dance practice is as well as what it can be. Linda is passionate about embracing a dancers’ individuality and uniqueness and working with them to reach their ultimate potential.

Linda very kindly accepted the invitation to participate in the "Maths in Dance" project and answer a few questions for me. I am, once again, overwhelmed by the thoughtfulness and generosity of professional dancers who have given up their time to write. 

The Questions and the Answers

1. Describe what maths lessons were like for you at school. 

I loved maths at school as I was able to link it directly to my dance training. I had a very musical dance teacher and feel this is linked to my understand of timing, space and outcome. With my own children, who are 14 and 10 years, I often relate their maths homework back to every day movement soccer, tap dancing, surfing or eating pizza when it comes to fractions….

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

Strangely I link a lot of my life to equations.

3. Do you divide dances or movements into parts or sections that might be expressed as mathematical fractions? 

Absolutely there's no question about it.

4. How aware are you of angles in dancing technique – angle of body, angle of arms and legs, angle of movements? 

I am very interested  in somatic practices and biomechanics of the body. We speak angles every day. I get my students to visit the physiotherapist to confirm the degree of external and internal rotation they have in their hip joints and whether limitations come from structural weakness. We would then discuss and work with the angles to create optimal physical ability.

5. When dancers are moving in a performance, how much is “mathematical thinking and calculating where the space is” and how much is “feel for the space”? 

We look at spacial awareness, proprioceptive self image, space and time every day. Understanding one's own body mathematically is imperative for a heightened sense of spacial awareness and proprioception.

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

Dancers have to estimate. We can't rely on accurate measurements. We are human. We are not a computer or calculator. The ability to estimate distances and time to a near perfect result is what we practice every day. There is a great game we play call triangles. I'm not sure where it comes from but a lot a choreographers use it to warm up with. It hightens the group's sense of spacial awareness and communication. Each  dancer choses 2 other dancers to make a triangle with. You don't tell anyone else who you choose and every dancer chooses someone different. So you can imagine it's difficult to stay in a triangle with 2 moving people but a lot of fun. There was only once in my lifetime that we all found 'stillness'  in our respective triangles as a group after about 10 minutes. Felt like a miracle! We are often asked in an improvisation 'you have one minute to find stillness'. This is timed and when we get it exact it is very rewarding. However it takes some time of practice to be precise more than once.

7. How aware are you of timing and beat in dance? 

Yes again every day. And it's not just the ability to count to 8!! Some times to be truly present in dance we count in 'ones'. Then it's a call and response with the music especially if its a very difficult piece of classical music. I guess that's why an orchestra will have a conductor…  to let the players know what part of that one beat they should play. This is very similar to dance however we don't have a conductor. We have to be aware of what part or fraction of the beat we are all looking for and eventually without counting being precise with the movement and music.

8. Have you ever used maths and physics to explain your technique, movement or choreography? 

I really wish I had of concentrated more in my physics classes. Yes it is so related to movement technique and choreography how could it not. Every day I use concepts such as energy and force, potential energy, centripetal force and often quote Newton's Laws.

9. Do you look at statistics much to analyse your art? 

I guess we should. I'd love to be more scientific about it. I know dance is really heading that way in the contemporary art form and hear of much research going on and linking with science units at well known universities.

For more information about Linda and the Evolve Dance visit:

Monday, 21 July 2014

Maths in Dance - Michael Apuzzo

An Interview with Michael Apuzzo

Michael grew up in North Haven, Connecticut and graduated Yale University, Magna Cum Laude, in 2005 having studied Economics and Theater. Michael began acting at age 6 and has not stopped since. His work ranges from classical theater to contemporary and on camera, and his credits include work on all the New York City based soap operas, feature work in several award-winning independent films, credit working on the HBO pilot "Bored To Death" and a feature performing on "Live! with Regis & Kelly". He began his dance training while in college, performing and choreographing in undergraduate organizations, and then debuted professionally performing at the Yale Repertory Theatre. 

Michael has performed in numerous musicals and at equity theaters across the country, and recently finished performing on the national tour of Twyla Tharp’s Broadway show, Movin’ Out. A former NYC math teacher, Abercrombie&Fitch model, 2nd Degree Black Belt, and active AEA and AFTRA member, Michael was overjoyed to join the Paul Taylor Dance Company in the Fall of 2008 and has been performing with the company full time since. Michael is also the author of the recently published young adult book "Flying Through Yellow".


from Live with Regis & Kelly

Obviously he is a really busy person so I was particularly impressed when Michael agreed to answer some questions about mathematics in dance.

The Questions and Answers

1. Describe what math lessons were like for you at school.

Most people would tell you that they hated math growing up. I on the other hand really (really) loved math growing up. I always liked the concept that there was always one right answer, especially in algebra. But then I came to love geometry because of the creative shapes and the concept of graphing through space. Math seemed both academic and artistic to me even at a young age. Also, lessons were exciting and manageable because I would always figure out a solution to every problem.

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

Of course. Post school I was a full time math teacher for one year, teaching in the Bronx. I also used it to budget my spending and manage my finances. Living as an artist in NYC can be / is demanding and challenging.

3. Do you divide dances or movements into parts or sections that might be expressed as mathematical fractions?

To a degree- I usually divide each dance by musical sections (mathematical fractions). I count almost every step in each dance. Rhythm and time signature are a few variables that can mathematically alter or divide the dances as well.

4. How aware are you of angles in your technique – angle of body, angle of arms and legs, angle of movements?

Very aware! A dancer is always trained and critiqued for their lines which ultimately are measured in the angles of their body positions. This would include the degree of turn out (or angle) of their legs and feet. Even the angle of your head relative to the rest of your body is important for making shapes in movement.

5. When you are moving in a performance, how much is “mathematical thinking and calculating where the space is” and how much is “feel for the space”?

A smart dancer always has strong spatial awareness. I try to be as aware as possible, including my spatial relationship to other dancers and to the marks on the stage. As I perform I rely on my feel for the space around me.

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

The marks on the stage are accurate including center and quarter marks.  I rely heavily on those.

7. How aware are you of timing and beat when you are dancing?

Extremely aware. Every step has a choreographed position in the music, and especially in an ensemble, your timing for movement and musicality must be accurate.

8. Have your teachers or choreographers ever used math and physics to explain your technique?

More and more. Some teachers use anatomy charts to show what body parts are being used or overworked by certain movements. Choreographers generally originate movement through body positions and musical interpretation, and don't rely as much on math during creation.

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

Marginally. Perhaps when analyzing what movements or techniques lead to injury and when calculating injury prevention. But performance is a live art, and unlike solutions to math problems, they are not meant to be perfect.

10. Do you have any other insights to offer into how you use mathematics in dance?

Dancing is a calculated art form. Often you have to calculate when you should stretch your foot to jump and land safely and with ease. You have to be aware of the degree of contraction in your back, the alignment of your hips over your shoulders, and the spacing of your head relative to the rest of your body. Making dance shapes is similar to making geometric shapes, and proper ones have certain angles in order to make them correctly. As much as I love the Mathematics in dance as movement, dance is also an art form. At the end of the day, you have to let go and live in the moment that is live theater. My greatest challenge and biggest thrill is enjoying the moments when I am dancing, whether they are right or wrong, and believing in the live art I'm creating as it happens.

Thank you so much Michael for this amazing insight into the relationship between dance and mathematics. Your ideas have really made me stop and think - I hope there are a few teachers and students out there who have been provoked in the same way!