Number Sense and Mental Computation

The topic of our workshop today was number sense and mental computation. A whole bag of mixed emotions is the metaphor I would ascribe to my own school experiences of performing number operations and mental computation. I remember that as a child, I enjoyed numbers and by grade two or three I had a good conceptual understanding of what the operations meant. I had rote-learnt the basic number facts before moving to Australia at the age of eight, and since I could not speak English when I first arrived, number facts were in fact a source of comfort for me at school as they were pretty much the only thing I knew how to do.

However, by about grade 4 or 5, even though I learnt my time tables, playing games such as around the world and buzz in front of the whole class always scared me. If I got to stand next to someone who I knew did not know their facts well, I confidently shouted it out, but if I knew that the child next to me was also good at number facts, I would freeze in anticipation of not getting it right quick enough. I remember the boost of confidence when I get it right, and the utter humiliation of getting it wrong, or coming off second best. I wonder how many children these days experience highs and lows when they play those games like I did.

I remember feeling satisfied when I get 100% on the Friday morning quizzes, and my friends saying how much they hated maths when they could not remember 6-times, 7-times and 8-times tables. Then again, my favourite experiences with mental computation is was around grade 5 when my dad (who believed that I was not getting taught enough maths at school) and I would lie on the carpet next to each other, stare at the ceiling and performing mental calculations with two or three digit numbers and comparing strategies. Today’s workshop reminded me of these experiences.

I found comparing strategies of how we did it to be the most enjoyable part. Being given a chance to justify how you got your answer meant you had to have a thorough understanding of what you actually did is satisfying and listening to other people justifying their answers was also interesting. Giving children opportunities to do the same in the classroom would give them a chance to listen to how each other think, compare strategies and choose more efficient strategies. It also gives us, as teachers, insight into the children’s ability to think mathematically and conceptual understanding of the operations which is important in order for them to make connections and transfer mathematical knowledge from one context to another. Discussing strategies take the focus off of getting the right answer, by emphasising the process that justifies one’s answer. This assists students to develop number sense – which is the ability to understand and appreciate how numbers work, what the operations mean conceptually, and how they relate to each other (Bobis, Mulligan & Lowrie, 2004).

Furthermore as a verbal learner, I found strategies such as empty number line and hundred charts useful because it gave me insight as to possible resources and strategies that will help visual learners in my classroom. My prac experiences indicate that there are many of them, and I often struggled to think how they would, and communicate effectively with such children.
I learnt that also exposing children to different strategies is a great thing, presenting each strategy e.g. hundred-chart/ninety-nine chart, empty number line, as units of work is not the best way to teach children. Firstly, it is not unauthentic, as opposed to just presenting the number problem and asking children to suggest ways of solving it.

Secondly, I believe it does not assist students to understand that different strategies can be used to achieve the same outcome, that sometimes strategies can be used interchangeably, and that some strategies are more efficient in one context, but less efficient in another.

Thirdly, it limits children’s ability to choose strategies and identify preferences for themselves which I believe discourages children from taking responsibility for their own learning. As Bobis, Mulligan and Lowrie (2004) highlight, many teachers often spend time and effort imposing procedures at the expense of children actually making meaningfulness of those procedures. I take that to mean, for example, the children are more concerned with remembering to write “the magic one” on top of “the tens column” than understanding what that “magic one” actually means. Or another example, they perform the full algorithm rather than use more efficient strategies of calculating the problem – e.g. adding 100 to 181 (281) and taking away one (280) when calculating 181 + 99 rather than add 9 to 1, write the zero, carry the ten, then add 90 to 90, write down the 80, then carrying the 100, adding it to the other 100, and writing down two hundred (281).

References:
Bobbis, J., Mulligan, J., Lowrie, T. (2004). Mathematics for children: challenging children to think mathematically. Frenchs Forest: Pearson Education Australia.