Taekwondo is something I have loved since a young age. Throughout my 17 years of doing this sport I have had to face many challenges however it wasn’t until our recent workshop that I started to think about the mathematics that are involved.

One of the most obvious concepts of mathematics is the scoring system that is used. In ITF taekwondo the scoring system is pretty straight forward. If you score a punch to anywhere in the body, then you gain one point. If you manage to land a kick to the body, then you gain two points and if you are lucky enough to score a head kick then you gain three points. As well as gaining points you can also receive warnings and lose points. If you hit the back of your opponent, then you get a warning. Stepping two feet out of the ring, falling down or using excessive contact can also warrant a warning. In taekwondo if you receive three warnings then you lose a point.

Here is a video explaining how it all works out.

(https://www.youtube.com/watch?v=uXrSEDmHonA)

During our workshop we were asked to develop a sport and change the rules to identify the mathematical concepts that would change the outcome. One of the main changes that we decided to change was the size of the ring. In ITF competitions, a standard ring is 9 metres by 9 metres however we decided to change this. As a group we decided to decrease the size of the ring in each round so that the fighters would have less chance to run around and avoid the fight.

We also decided that we should change the scoring system. In doing this, we changed the variables that points could be awarded. We decided to give one point for a punch to the body and two points for a punch to the head. This difference was introduced as we believed that a punch to the head was more difficult to score than a punch to the body. We then continued with a kick to the body worth three points and a kick to the head worth four points.

We also decided to change the times of the fights. We decided to make it a shorter time for each match as this would stop the running around with no contact. We believed that if we reduced the time for the fight then the fighters would give it their all for the full time in order to score as many points as possible. As a result, this would make it more exciting for spectators.

Another change that was decided was making the fights a match of doubles! This would mean that there would be 2 vs. 2 in the match which would completely change how the fighters would fight. We also spoke about the importance for other rules to be introduced to ensure that fighters did not just attack the same person for the duration of the fight. This idea is similar to the WWE tag-team wrestling matches.

This links to Liping Ma’s (2010) theory as she believes that maths cannot just be looked in one way and that it should be explored in as many ways as possible. This example of changing a sport can also be seen to represent multiple perspectives from Ma’s profound understanding of fundamental mathematics. We had to decided what rules we wanted to change and evaluate the impact of that on the outcome of the sport.

References

Bellos, Alex (2010) Alex’s Adventures in Numberland London: Bloomsbury

Ma, L (2010). Knowing and Teaching Elementary Mathematics. Oxon: Routledge. p120-125.

When I was first asked to describe what profound understanding of fundamental mathematics (PUFM) meant, the panic and fear immediately set in. To me this was something that seemed really complicated and confusing however upon further research and reading I have discovered this is not the case.

Liping Ma believes that there are four different properties in both teaching and learning which highlight a teacher’s profound understanding of fundamental mathematics that can be displayed within the classroom. These four properties include interconnectedness, multiple perspectives, basic ideas and longitudinal coherence. Therefore, Ma means that if a teacher can show these four properties successfully then they have a profound understanding of fundamental mathematics.

Interconnectedness is the idea that mathematic topics depend on one another. Ma (2010) describes a teacher with PUFM has making a great effort to show the connections between different mathematical concepts and procedures. She believes that when this is applied within a classroom then the pupil’s learning will not become fragmented and instead of being separate individual lessons, it will become one unified body of knowledge.

Multiple perspectives can be described as the ability to approach mathematical problems in many ways. This can be highlighted within maths as there are many different ways to reach the same answer and all of those different ways can be correct. Liping Ma (2010) says that teachers who have achieved PUFM are able to appreciate different ideas and approaches to a problem, taking into account the advantages and disadvantages. Also on top of this, teachers within a classroom should be able to explain the different mathematical concepts to a problem. By doing this, the teacher allows their pupils to develop a flexible understanding of mathematics and how it works.

The basic ideas within mathematics refer to the basic principles such as place value and ordering. Ma (2010) states that those with PUFM will show an awareness for these basic principles and appreciate their importance. These teachers will often revisit and reinforce these basic ideas and principles. This then means that pupils are not only encouraged to approach problems, but they are guided to carry out proper mathematical activity.

Longitudinal coherence can be explained as the way that one basic idea can build on another idea. Liping Ma (2010) believes that in order for a teacher to achieve PUFM then they should have a holistic view of the curriculum. These teachers are not just limited to the knowledge required for their stage as they have an understanding of the whole curriculum. Within a classroom, a teacher with PUFM is ready to take every opportunity to review crucial concepts and ideas that the pupils have covered previously. Longitudinal coherence can also be displayed within a classroom as the teacher will know what mathematical concepts that the class is going to cover in the future. They will prepare the pupils effectively by laying the proper foundations ahead of time.

These four properties are crucial to my understanding of mathematics and how to teach the subject. When I have my own class one day I will ensure I am a teacher that shows connectedness, highlights multiple approaches to problems, revisits and reinforces basic ideas and lays the proper foundations for future teaching.

Ma, L (2010). Knowing and Teaching Elementary Mathematics. Oxon: Routledge. p120-125.