Category Archives: 2.1 Curriculum

Tennis and Mathematics

The obvious mathematical concept involved in tennis would be counting. The scoring system in tennis is unusual as it doesn’t go up in units of one, or even units of the same amount. the follow picture depicts the different scoring options that could take place during one tennis game. As you can see, the first two scores (if won by the same person) go up in units of 15 (15-0, 30-0). However if the same person won the next point, one would presume it would be 45-0, however, due to the unusual scoring system, the new score would be 40-0.

http://mycodehere.blogspot.co.uk/2011_02_01_archive.html

http://mycodehere.blogspot.co.uk/2011_02_01_archive.html

Are there any deeper mathematical concepts embedded in the game of tennis?

Analysing statistics is a vital aspect for anybody involved in professional sport. Statistics can help players identify individual strengths and weaknesses and also the weaknesses of their opponents, which might inform their strategy and tactics for future matches. Percentages are the usual way of comparing players. In tennis, the typical statistics you see after each set include: first-serve percentage, service games won, break points saved, second-serve return points won, break points converted, unforced errors, forehand winners and so on.

 

 

MURRAY

http://www.changeovertennis.com/wp-content/uploads/2013/01/matchstatsmurraydjok.png

 

Before Andy Murray takes to the court to play a big semi-final against Djockovic, members of his training team will have analysed Djockovic’s match statistics from that specific tournament so see if they can identify any trends, likely predictions of play and any areas which are particularly weak so that Murray is stepping onto the court with informed information. This may not alter how Murray chooses to play, however if the match is not going as he would like, it would make sense that he would draw on the information he had been given to try and change up his tactics and play more aggressively to his opponents current weaknesses.

What about geometry?

Could tennis just be a problem of geometry? When playing a game of tennis, your aim is to win by the point by hitting the ball hard over the net, with spin, to a position where you opponent cannot return the ball. Is geometry involved in this process? In the path of the ball? The position of the player? The spin on the ball? It has been said by many commentators and some of the greats of the game that tennis is about controlling the middle of the court, cutting of angles and geometrical concepts support players in achieving this.

www.google.co.uk/tennisangles

www.google.co.uk/tennisangles

An attacking shot in tennis why relies on the play having a knowledge of angles is the angled approach shot. Hitting a short angled ball over the net forces your opponent forward, scooping up their return which should theoretically leave you with an easy volley to put away. You create a greater number of steeper angles when you step into the court and this forces your opponent to move around playing less confident and challenging returns. The following article discusses some of the geometric concepts in tennis further and provides some interesting food for thought for the next time you step out onto the tennis court.

Geometry and the Art of Tennis

What about the impact of top spin?

www.google.com/tennisbounce

www.google.com/tennisbounce

The ball bounce can greatly affect how an opponent returns your shot. Two properties which are involved in this process are Coefficient of restitution and Coefficient of kinetic friction. These two elements involve mathematical concepts such as ration, speed, distance and angles. The above diagram shows the bounce of a flat shot with no spin. The angle of incidence is approximately equal to the angle of reflection. This means the angle at which the balls impacts the ground and which the ball leaves the ground are almost the same. The ball slows down after it bounces due to the impact when hitting the surface.

www.google.co.uk/tennisbouncespin

www.google.co.uk/tennisbouncespin

The diagram above shows that when a ball is hit with top spin the angle of reflection is lower than the angle of incidence. The ball is not affected by the friction when impacting the surface of the court and the forward spin pushes the ball forward with greater speed after it bounces.

The following link is great for describing the effect different spins have on the ball bounce and how the different spins change the velocity, speed and direction of the ball.

The Physics of tennis 

 

Modern Languages – Isolated or integrated approach?

If I am honest, I have always felt more comfortable with the thought of a specialist language teacher delivering the modern language curriculum to my class. My justification for this was that these teachers have specialist knowledge and understanding of the language which would allow them to teach the language more effectively than I could. The children would then get an informed and specialist educated professional delivering the lessons and their learning experiences would be greater than what I could offer. I think this train of thought is encouraged by my lack of confidence in modern languages and the fear that I would teach something incorrectly.

After leaving my first Modern Languages tutorial, I was surprised at how much French I could actually remember from school and I was happy that I could follow most of the discussions. This tutorial gave us some brilliant teaching strategies for a beginners language class and the emphasis on ‘why these strategies were effective’ was really valuable. Some of these strategies were: repetition, voice modulation, clear and precise dictation (providing a good speech model), mime, gestures, facial expressions, eye contact and games. It’s all good and well choosing a teaching strategy, but if you don’t know ‘why’ and ‘how’ it is going to help pupils learn and develop, then you will not be able to deliver your lesson effectively.

After some reading and research into the strategies used to develop a modern language (ML), I have been able to identify some criticisms of my initial ‘Isolated-approach’ method delivered by a specialist. As a result of a ML being taught by a language specialist, there is very little room for embedding modern languages into the curriculum as teachers wouldn’t have the knowledge or skills to provide cross-curricular learning experiences. There is also limited opportunity for children to learn the target language in meaningful contexts as all language learning would be restricted to small slot in the timetable.

“Pupils need to encounter, process and use new language in different, meaningful contexts in order for it to be embedded in their minds.” (McLachlan and Jones 2009)

As my understanding in this field has grown, I now consider a whole-school approach as being vital to the success and effective delivery of ML.  By this, I mean that class teachers have the support of their management team and other members of staff in promoting Modern Languages around the school and embedding it within daily routines. For example, this could be ML display boards in the school reception promoting welcoming phrases and increasing the status of languages for parents and visitors. Simple classroom routines such as the register, instructions, behaviour management and timetabling could be introduced in the target language. Welcome and introductions in assemblies could be done in the target language which would create a positive whole-school attitude towards ML.

“A clear and shared vision for the whole school’s present and future language provision will considerably enhance the initial classroom teaching.” (Hood and Tobutt, 2009)

This approach could be hindered by teacher’s lack of confidence in Modern Languages. Being able to provide cross-curricular learning experiences in the target language can be challenging and a daunting experience for members of staff and this could work against the integrated approach which schools are aiming for. A way in which schools could tackle this issue would be promoting professional development opportunities in Modern Languages. Schools need to give teachers the opportunity to develop their own knowledge and understanding of the languages being taught which would increase their confidence and would take a step in the right direction for embedding language in the whole curriculum. Another option would be to work with a Language Specialist, or another teacher who is particular competent in languages, to plan cross-curicular learning experiences and work through some lesson plans to ensure the class teacher felt secure in delivering them. Collaborating with other professionals is a valuable experience and one that allows you to share good practice, come up with new ideas and benefit from each other’s strengths.

An important point to consider when teaching a new language is, should my lessons be delivered only in the target language? Or, should I be using the english language to teach the new language? Teachers have differing views on this issue. Some say that the english helps to establish meaning in the target language and will prevent students from getting lost and de-motivated during lessons. Others say it doesn’t make sense to learn a new language by speaking your native tongue language. I fall in-between these two statements with a slight tendency to lean towards the latter. I do believe that children should be immersed in the target language and be able to develop the four language skills through this immersion. However, I agree that in the early stages of learning language, it is appropriate and often necessary to return to english to establish meaning, to cover tricky grammar rules and instructions and to check for your pupils’ understanding.

The video below is an interview with an experienced language teachers and she discusses her views on using the target language when teaching ML.

 

For my 2CM6 assignment, I am going to do further research into the use of singing, rhymes, games and story-telling to develop the target language. I want to develop my understanding of why and how teachers are slowing moving away from rote learning in ML acquisition to strategies which introduce Knowledge about language, language exploration and language comparisons.

References

Hood,P. and Tobutt, K. (2009) Modern languages in the primary school. London: SAGE Publications

McLachlan, A. and Jones, J. (2009) Primary languages in practice: a guide to teaching and learning. Maidenhead: Open University Press

My Educational Philosophy

I value education as it has the opportunity to support and guide children through their learning and development with the aim of producing confident, independent individuals who are able to contribute effectively to society and the economy.

Many people have differing views on the purpose of education. My belief is that its primary role is to provide an equal and active learning experience for all children and young people regardless of gender, race, religion or social classification. It is important that schools adopt an ethos which encourages pupils to have a sense of belonging to a community; with children feeling united and part of something great. Through achieving this, schools and education will be able to combine academic learning experiences and the transmission of morals and values with the intention of creating a fair and more egalitarian society.

It is absolutely critical that children are at the heart of the education process. They deserve to have a voice and play an active role in their learning. This differs from the idea that education is consumed and that it involves the creation of accepting minds rather than creative individuals. Having looked at practices such as Montessori schooling, I can see the benefits of children having the freedom to engage in activities which interest them and how this can support their development. I also like how the focus is on the process of learning and not the end result. Children are rewarded on effort and not by test results or grades. I believe that this approach is a crucial aspect of intrinsic motivation and one that will result in confident, independent thinkers who are not afraid of facing challenges.

In summary, education plays a vital role in creating  ethical, independent  and  successful individuals. It is a teachers role to provide an engaging and stimulating learning environment which allows children to grow and explore through social and environmental interactions. It is absolutely critical that this opportunity is provided to all children and young people.