ReMSTEP Maths – Fractals

This video is one is a series of 3 that were developed as part of  the REMSTEP Project (http://remstep.org.au/). The videos were produced through collaboration between staff in the Faculties of Education and Science at Monash University. The videos are aimed at pre-service teachers but are just as relevant to practicing teachers of secondary school mathematics. The purpose of the videos is to inspire pre-service teachers to think of mathematics as a beautiful, creative and relevant discipline. We aim to challenge preconceived ideas about what maths is, and isn’t and for the beauty of maths to be appreciated, understood and shared with learners of maths. For further information see the Mathematical Association of Victoria’s publication – Common Denominator, Term3, 2017, pg15.

A key objective is for the video to provide inspiration for classroom activities that deal with the underpinning concepts, rather than the technical and computational aspects, of mathematics.

Acknowledgements
These videos were produced as part of the ReMSTEP Project. We are grateful to the following people who made these videos possible; Norman Do, Rebecca Cooper, Jo Burke, Magnolia Lowe Film Communications, Owen Kazula, Chris Nagy, Greg Lancaster and the pre-service and in-service teachers who provided us with feedback.

 

Dr Norman Do is a self-proclaimed mathematics geek, and lecturer at Monash University. He loves to study and teach mathematics and aspires to engage people in study mathematics and to appreciate the diverse and varied jobs that exist for mathematicians. His main research interests lie in geometry and topology, including knot theory.
Norman believes “We need to encourage people to take on challenges, do hard things and gain a sense of self-worth from learning,” he adds “We need to celebrate our mathematical heroes like Terry Tao and we need to understand that if you’re a mathematician you can work behind the scenes in jobs as varied as biochemistry, animation and finance.” View Dr Do’s profile.

There are place markers in the video labelled ‘Stop & Think’. This gives the viewer opportunities to pause the video and to complete some related activities. These are accessed using the Tabs across the bottom of the video. They are designed to assist pre-service teachers to appreciate the concepts, attitudes and contexts of contemporary mathematics and their relevance to classroom teaching.

Before Viewing the video

1) Consider –

  • What do you consider to be Mathematics?
  • Why is it important to teach it?
  • What is the purpose of Maths in the lives of your students?
  • How might Maths influence what happens in the real world?
  • How do you justify the inclusion of Mathematics in the school curriculum?
  • Can you think of examples of doing Maths which don’t involve numbers?

2) Which of the choices below do you consider to be the best metaphor and why? Can you think of a better one?

How is an excellent teacher of mathematics like a …?

  • Social Worker
  • gardener
  • orchestra conductor
  • actor
  • doctor
  • librarian
  • missionary
  • sculptor
  • games show host

Stop & Think (1)

1. Where do fractals arise?

2. How many other fractals are there?

3. Are fractals just the play things for people with too much time on their hands OR are there real world applications of fractals?

4. Would you use or have you used aspects of this topic in your maths lessons? Why? Why not?

5. If you have, then where, when, why and how did you refer to this topic?

6. How did your students react? Or, how do you think your students’ would react to the ideas introduced in this video?

Stop & Think (2)

1. What are the underpinning maths questions here?

2. What could a learner hope to take from watching this video?

3. Does this topic have any explicit or implicit links to the curriculum?

4. How and why/why wouldn’t you use this video in your maths class?

 

Stop & Think (3)

1. How did these images of fractals make you feel about mathematics?

2. Is there a place for this in maths education? Explain.

Stop & Think (4)

1. What are the actual maths questions here?

2. What could a learner take from this?

3. Does this link to the curriculum?

4. How and why would/wouldn’t you use this in your maths class?

After viewing the videos consider;

1. Each video contains a story of human endeavour in mathematics. Whilst watching the series, consider how this might be a useful perspective to adopt in mathematics education.

2. This video series is presented by a Mathematics lecturer and researcher, Dr Norman Do – does his specialist knowledge and expert understanding make a difference when you are watching the video? Do you think it would make a difference to your students?

3. Considering everything that has been presented about fractals:

–  Are these ideas useful to maths teacher education? Why/why not?

–  Do you think your students would see these ideas as a useful and relevant approach to learning about maths?

4. Complete each of the sentences below…

  • I used to think that a mathematician was … now I think a mathematician is …
  • I used to think a maths teacher was … now I think a maths teacher is …
  • I used to think a maths learner was … now I think a maths learner is …

Links

Listed below are a number of links that could be used to further explore the topic and context of Fractals.

Articles

Davis, B., & Sumara, D. J. (2000). Curriculum forms: On the assumed shapes of knowing and knowledge. Curriculum Studies, 32, 821-845.

Gluchoff, A. (2006). Hands-on fractals and the unexpected in mathematics. NCTM: The Mathematics Teacher, 99, 570-575.

Jarry-Shore, M. (2013). An exploration of per cents and fractions through a study of fractals. Delta-k, 50, 34-38.

Padula, J. (2005). Fractal music: The mathematics behind ‘techno’ music. The Australian Mathematics Teacher, 47, 4-8.

Padula, J. (2009). More about how to teach fractal geometry with music. The Australian Mathematics Teacher, 65, 37-40.