Connectedness and basic ideas
Haylock states teachers should move away from the “notion of teaching recipes and more towards development of understanding” (Haylock, 2006, pg. 7). I believe this applies to both, student and teacher.
When learning multiplication for example it could mean that multiplication in its simplest form is repeated addition. Although most teachers would know this, the purpose of explaining these strategies in the first instance may take away any anxieties students may have when they see multiplication for the first time. So then connecting the basic ideas that multiplication is repeated addition, which they can do with ease, then moving to long multiplication will seem less fragmented. This is where teachers need to be careful in how they frame “rules” within mathematics (Devlin, 2008). Basic multiplication e.g. 4×4=16 is like repeated addition – 4+4+4+4=16. Therefore, is useful in the introduction of simple multiplication, however, moving on to multiplication of fractions, the “repeated addition” statement no longer makes sense (Devlin, 2008). This also corresponds with Haylock states about learning recipes. This also evident when introducing multiplication of negative numbers where the “repeated addition” no longer applies. Rote learning although may help with consolidating processes of how to do a particular concept, the meaning of why must also be in the mind of the teacher.
BODMAS
I think it is hard to connect something like BODMAS to the wider world. It’s almost like grammar, where there are rules that help you make sense to read and write something and that is it. This doesn’t agree with Haylock’s statement above, of moving away from teaching recipes because that is what BODMAS really is. There is a way to do something and it has to be in that order for it to be correct. However, when moving looking at concepts within BODMAS and multiplication in brackets which is a topic which I taught during my placement there is opportunity for making connections. Explaining to the children that the mathematics they were doing was not something new but it was the way (order) they were to do it in I think made the children feel at ease. I think it is very important that teachers not how know the connections but show positive attitudes when connecting topics.
Forcing connections
Ma’s view of connectedness is a teacher making and demonstrating connections between topics within mathematics. This is possible in a topic such as BODMAS however, making connections to the wider world is harder to make. I think children do need to see the connections between concepts and topics however certain areas, as proven with BODMAS, there cannot be a connection to the wider world so why force it?
Some teachers may feel under pressure to make connections with everything after reading Ma’s definitions of Profound Understand of Fundamental Mathematics (PUFM). I feel as long as they can see themselves and show the connections where possible and where necessary, without confusion the children. Making connections with every possible topic does not show PUFM. Making the decision when and where to show the connections shows the “profound” in my opinion.
References
Devlin, K. (2008). ‘It ain’t no repeated addition’ Available at: https://www.maa.org/external_archive/devlin/devlin_06_08.html (Accessed: 14th November 2016)
Ma, L. (2010) Knowing and Teaching Elementary Mathematics. London: Routledge.
