Category Archives: 3.1 Teaching & Learning

Liping Ma

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By choosing the Discovery Mathematics elective I hope to gain a better understanding of what fundamental mathematics entails and further still how to develop my ideas on this to incorporate in to my practice.

I believe the fundamental aspects of mathematics are the basic concepts in which a learner needs to understand in order to progress to more complex mathematic problems and processes. These are used as the building blocks or the foundation in which all other understanding and learning can take place from. Liping Ma (2010) suggests that we need to develop a ‘profound understanding of fundamental mathematics’ in order to teach and promote effective mathematical learning. This suggests that you need to have a more coherent knowledge of the conceptual structures included in mathematics and how they are used for higher order thinking. According to Liping Ma (2010) there are four key elements that contribute to a persons profound understanding of fundamental mathematics, the four elements are:

Connectedness: ability to relate topics to one another so that you can build on prior knowledge to work through new processes and ideas.

Multiple Perspectives: ability to use a variety approaches to solve mathematical problems. the ability to see things in different ways and become flexible in your approach

Basic Ideas: ability to identify the basic mathematical ideas which are prominent throughout maths topics and use these ideas to inform future processes.

Longitudinal Coherence: what we learn from the start of our mathematical journey influences our current mathematical status regardless of how fragmented our previous knowledge may be.

In order to become a teacher with a profound understanding of fundamental mathematics, I need to ensure that I am able to interlink mathematically concepts and ideas together with other concepts and processes, this will also allow me to fully understand how the topics involved in mathematics interlink and are connected. I need to explore different methods of calculating sums, equations and problems this will allow me to model different solutions to my learners which will hopefully allow for their understanding to develop and progress easier, this will also allow my learners to gain a more flexible view on mathematical problems. I think it is crucial to ensure that basic ideas are always revisited to reinforce learning and to build a solid understanding of mathematics. I hope that my understanding of this elective will allow me to develop and create a positive mathematical classroom environment.

References:

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. Abingdon, Oxon: Routledge

Instrumental Understanding V Relational Understanding?

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When it comes to thinking about how people may start to understand new ideas and concepts the best theorist to look at is Skemp. Skemp (1989) believed that there are two types of understanding when it comes to mathematics: Instrumental and Relational. Through this module and professional reading I have attempted to try and understand the two approaches.

Instrumental understanding is when you are able to use the mathematical rule or concept but do not really have the knowledge behind the concept/rule to apply it in other situations, the method is more a “habit” understanding whereas relational understanding is when you are able to use, apply and manipulate the rule or concept and you know why you use the particular method. Relational understanding allows people to have a more reflective attitude to learning and allows for more exploration to occur.

From this, I can see that relational understanding is a deeper, more complex understanding of instrumental understanding.  Although it is important to highlight that a person who lacks confidence in mathematics can benefit from having an instrumental understanding as it allows for immediate satisfaction and can boost self esteem, however it is equally important that as teachers you try to promote a more relational understanding as this will allow for a more concrete understanding of mathematics.

Maths – Creative and Beautiful?

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Throughout the Discovering Mathematics module, there has been a lot of discussion between the creativity and beauty that mathematics can offer. Before this module I would not have given this much thought, I have never looked into the way in which buildings are created or the way in which an artist’s masterpiece is formed. I have always been in the mindset that people are creative and you either have the creative flare or not, I am now considering the fact that maybe people have been clever by using a mathematically concept to produce aesthetically pleasing objects.

Fibonacci is probably the first name that springs to mind when talking about mathematics holding some form of beauty and creativity.  It was Fibonacci that devised a set of numbers after studying the mating habits of rabbits!!!! These numbers have been used across the world for centuries to create aesthetically pleasing buildings, statues, artwork, logos and so much more. Not only this but mathematics can be found inbuilt in nature, the spiral of a pine cone or the amount of petals on a flower all follow the Fibonacci sequence.

The Golden ratio was devised by dividing the Fibonacci number by themselves in sequence – the answer is 1.618 – or PHI. By using this ratio, people are able to select appropriate proportions which allows people to produce attractive looking and appealing products, objects or artwork. In one or our recent inputs we were given the opportunity to measure the lengths of various different parts of our bodies and use the measurements to assess how aesthetically pleasing we appear according to the Golden Ratio. It’s safe to say I’m lucky to have found my Mr. Right already as my measurements would not have satisfied Mr Fibonacci!!!!

Image result for fibonacci sequence

By looking into the work of Fibonacci and the Golden Ratio it is clear to see that mathematics surrounds us and our daily lives, it has been instilled within nature for such a long time that it suggests to me that Mathematics may have been formed from studying nature all those years ago and mathematics has been used as a tool to understand the world we live in. I believe that so many of us walk around today totally oblivious to how much mathematics has contributed to our world. I wonder is mathematics such a huge part of our life that we subconsciously forget that we are using mathematically concepts on an everyday basis?