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 (4th 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.
