Metaphors for Mathematics

In the week 2 workshop we explored different conceptualisations of what learning maths is like.

The following metaphors are useful images to articulate how I picture mathematics learning and teaching...



From our discussions, the useful analogy of a brick wall was mentioned. I find this a useful way of conceptualising mathematics learning as learners must build up their "wall of mathematics knowledge" sequentially, that is, basic or foundational concepts need to be well understood before more difficult concepts can be learnt or taught.

The second metaphor is that of a language. If children truly understand mathematical concepts, they should be able to transfer their knowledge from one context to another, so that their mathematics learning should become a way of thinking. Therefore mathematical learning experiences ought assist children develop their ability to use mathematics as Irons (1999) suggests, to reason and problem solve with, rather than to use the prescribed strategy to obtain the correct answer in classroom mundane activities which often consists of filling in worksheets.

After some further research, I discovered that I was not the first to think of maths in this way. Sterenberg (2008) suggests that the metaphor of mathematics as a language "encouraged a consideration of the humanistic dimensions of mathematics" (p.89. Sterenberg (2008) stated that "language can be described as a systematic method of communicating through oral and written words" (p.96) and just like language, "the purpose of mathematics is to communicate" (p.97). In fact, mathematics is often been described by mathematicians and philosophers such as Galileo, as the universal language. Sterenberg (2008) argues that it is more accurate to consider the ideas of mathematics, rather than the language of mathematics, as being universal because like human languages, mathematics is human creation, which is niehter static nor unchanging.

Other metaphors for mathematics that emerged from the participants' discussion in the study include images of "a battle", "a mountain" and "a bridge".

For the pre-service teacher participants in the study, mathematics is a battle because it was linked to experiences of fear, struggle and even survival. It is also a mountain because it is looming and sometimes menacing, and although they wanted to form a relationship with it, like they want to climb Mount Everest, they find even the thought of it challenging and unnerving. Furthermore, mathematics is a bridge, because it is difficult to build, it must be constructed over a somewhat long period of time, and its construction means overcoming obstacles such as mechanical failure of machinery, and unavailability of raw materials, just like at times the tools and strategies used by teachers to teach mathematics is not appropriate and inhibits learners from constructing mathematical knowledge and understanding.


Sterenberg (2008) argues that investigations of metaphors of mathematics helps to create a "shared communicative space" (p.89) and can be helpful for aiding already-held perceptions about maths learning of teachers and pre-service teachesr alike. I also believe that reflecting on their personal images of mathematics is very important because our beliefs about what we teach not only affects how we teach but how students learn. Additionally, discussing metaphors of mathematics with students is important as it can give teachers valuable insight into how students feel towards mathematics learning. Students' dispositions towards mathematics will no doubt be affected by how they conceptualise mathematics, which will in turn also affect their learning in mathematics.


References:

Irons, R. R. (1999). Numeracy in Early Childhood. Educating Young Children: Learning and Teaching in Early Childhood. 5(3), 26-32

Sterenberg, G. (2008). Investigating teahcers' images of mathematics. Journal of mathematics Teacher Education, 11(2), 89-105