The profound understanding of fundamental mathematics can be expanded through the four key properties that teaching and learning need. According to Ma (2011, p.122), these four key properties are connectedness; multiple perspectives; basic ideas and longitudinal coherence. All of these properties are interconnected and relate to one another in fundamental mathematics.

Firstly in my opinion, I believe that connectedness is how all mathematical concepts and ideas are related. An example of connectedness in wider society could be the idea of numbers and the importance they play in our lives. These appropriative contextual ideas could consist of number lines; temperatures and thermometers; page numbers in books and novels; and lastly travelling up and down lifts in hotels and department stores (Haylock and Cockburn, 2013, p.35-36).

From Ma’s definition of multiple perspectives, I believe it as the understanding of mathematics through many strategies and methods and from this, solving problems in different ways. Multiple perspectives in real life situations could be most likely farmers and gardeners planting and organising crops and food types by using array representation (Barmby, Bilsborough, Harries and Higgins, 2010, p.50-51). Farmers and gardeners would use the components of multiplication and division in a grid situation. They would decide how many crops or food types would be planted in one particular area and how much that space would be needed between the items to allow them to grow.

From my understanding, I have interrupted that basic ideas are simply the starting blocks of mathematics and the beginning of primary knowledge. Basic ideas in real life contexts would include the idea of addition and subtraction by using money when shopping for food, clothes or socialising. Also the idea of time would be included in basic ideas as people use watches and clocks to tell the time and use time to function their lives.

Lastly, Ma’s final property, longitudinal coherence, I believe that longitudinal coherence is building on basic ideas with new concepts over a long period of time, e.g. months or years. An example of longitudinal coherence would consist to the property of basic ideas in regards to addition and subtraction and then linking these topics to percentages, fractions and decimals from previous knowledge that was stored and learnt.

References

Barmby, P., Bilsborough, L., Harries, T. and Higgins, S. (2010) Primary Mathematics: Teaching for Understanding. Maidenhead: Open University Press.

Haylock, D. and Cockburn, A. (2013) Understanding Mathematics for Young Children (4^th ed.). London: SAGE.

Ma, L. (2010) Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States – Anniversary Edition. Oxon: Routledge.

Mathematics is very apparent in wider society and in real life situations because as humans, we use mathematics in many different capacities whether it functions our lives or is essential in our careers.

Football is one of the most popular sports in the world with millions of people watching and playing the sport on a weekly basis. The rise of television coverage has had a big impact of the popularity with over 212 territories over the world watching the Barclays Premier League meaning over 4.7 billion people are watching live football weekly (Premier League, 2016). Furthermore, millions of youngsters are idolising all these talented footballers for playing the sport but many people do not realise how mathematical driven the sport is and how mathematics is used all the time in football.

Firstly, the size of an everyday eleven-a-side football pitch has themes of measurement and geometry by the sizes of the six-yard and eighteen-yard boxes, centre circle in the middle of the pitch and the quarter-circles in the corners of the pitch. This demonstrates that football uses metres, yards and inches to measure out the pitches correctly. As well the pitch uses shapes such as rectangles and circles to identify important parts on the pitch. Lastly a football goal also has aspects of geometry as the frame of the goal is rectangular and the tessellation of squares are used to make up the goal netting (SportsKnowHow, no date).

In addition to that, all footballs are made of leather or from a similar material with the shape always being spherical. In a regular eleven-a-side game, it consists eleven players against eleven players with substitutes taken place at different points of a ninety minute game (2×45 minutes). All the players on the pitch will have different shirt or jersey numbers which represents different numbers, for example, 1 for goalkeeper, 9 for centre forward and 11 for left midfielder. To end, data analysis is used to gesture scores and goals to create league tables which have meaning in the long term, for example, winning the league or relegated to the league below.

References

Premier League. (2016) The world’s most watched league. Available at: http://www.premierleague.com/en-gb/about/the-worlds-most-watched-league.html [Accessed on 27th March 2016].

SportsKnowHow. (no date) Soccer dimensions. Available at: http://www.sportsknowhow.com/soccer/dimensions/soccer-dimensions.html [Accessed on 27th March 2016].

The link between mathematics and music may not be apparent, however these two subjects are very much interconnected. There are several aspects in mathematics that support musical development. To understand music, on a very basic level, you must first understand beats which inevitably involves counting. In the early years of nursery, this can be demonstrated through nursery rhymes and teaching young children how to count. This is highly significant in the importance of music in supporting and enabling memory recall.

One aspect that supports the relationship between mathematics and music is the physics of sound. This can be shown through using musical instruments that creates sounds which produce either high or low sounds and are dependent on the type of instrument as well.

Finally, the interconnection continues with mathematics and music as they are both used for patterns. People are constantly using patterns and routines to complete a task and understand a concept and that no different when working with mathematics and music. In regards to mathematical patterns, children find it difficult to understand the idea and that is where the teacher gets involved to help and support the children. Patterns in life can be ideas such as pictures, fabrics and events which are helpful for children’s understanding in concepts like repeating, increasing and decreasing.

Reference

Pound, L. and Lee, T. (2015) Teaching Mathematics Creatively (2^nd edn.). Oxon: Routledge.

As adults we take numbers for granted we all use numbers on a daily basis without really thinking. Examples of using numbers are telephone numbers, addresses and door numbers. In addition to that, numbers are used constantly in sport whether it is scoring games and matches or adding points together for a table or league format.

So where do numbers come from?

Firstly, a number can be represented as a symbol as numbers can be mean something different as it has many principles and properties. Also numbers can be used in many contextual ideas whether it is in a classroom teaching multiplication or pricing food and drink products. Furthermore, it is stated that there are a variety of different types of numbers – natural numbers; whole numbers or integers; rational numbers or fractions; real numbers and lastly imaginary and complex numbers.

Number systems have been prevalent in society for thousands of years. Examples of number systems include the Egyptian number system; the Mayan number system; the Babylonian number system and the ancient Chinese number system. Each number system is unique as the symbols and numbers represent different meanings and ideas. In this instance, the Egyptian number system can be described by having many symbols to represent numbers from one up to ten thousand. These symbols consist of lines for the unit numbers and shapes and symbols explaining the numbers ten to ten thousand.

Today, people use the base-10 system to understand and represent numbers in everyday life. The base-10 system originated from and has been developed from the Hindi-Arabic system. In the base-10 system, it uses symbols for the numbers one to nine and then uses a place value system with a place holder of zero takes care of the representation of larger numbers. Finally the base-10 system is effective in the way it uses numbers and brings the numbers together through the place value system.

Reference

Barmby, P., Bilsborough, L., Harries, T. and Higgins, S. (2010) Primary Mathematics: Teaching for Understanding. Maidenhead: Open University Press.

Mathematics has played a big part in the way that my practice has developed. It is increasingly apparent the role that mathematics plays not only in the teaching and learning sense but indeed in everyday life.

Having had the opportunity to teach children from four to twelve years through various placements, both in college and in university, I have seen that the way in which mathematics is approached and taught for the various ages differs. From my experiences, I have seen teachers teach mathematics in many simple strategies by explaining the very basic methods to using contextual examples to allow the children to understand the particular topic. Recently during my MA1 placement I had the responsibility of taking a small maths group on a regular basis as well as the whole class. The lesson plans for those differing situations varied but the conceptual understanding of basic concepts remained the same.

My personal experiences of mathematics have thus far been very positive and on the most part enjoyable throughout childhood. At primary school, I thoroughly enjoyed mathematics as I felt that I understood what the teachers were discussing in many of the topics. I was consistently placed in the middle to higher groups throughout my schooling and I felt that this, at times, challenged me and most likely set the context for my future relationship with mathematics.

I never had many issues during schooling and the only criticism that I have would be that I would have liked to have covered some of the topics in greater depth instead of just touching upon them.

My decision to undertake the elective module, Discovering Mathematics, was purely down to the fact that mathematics is an area that I feel confident in and I felt that I would like to build upon my prior knowledge and develop that into teaching practice.