I work at an OSHC. In my experience working with children in primary school, chance and data is often a dreaded strand of maths, notoriously well-known for useless worksheets such as the one I witnessed this afternoon when discussing with the children what they have been learning in maths:
After reading through this worksheet, I discussed its contents with the girl, a grade 4 student, who had completed it for homework just a few days ago. When I asked if she enjoyed doing this worksheet, she answered, “No, not particularly, it was easy, but it was boring. But then again maths is boring, so yeah. ” Then I asked her is there anything about it that she liked, and she optimistically pointed out that at least she got to make a choice about whether to colour the bars in colour or not, and she chose not to.
It was not just the lack of authentic context that annoyed me about the worksheet, but that fact that its design did not really highlight the usefulness of graphs. If you look at the worksheet in detail, it asks the student to graph the table of information provided at the top of the page, then use the graph to answer the following questions: Which was the city with the highest recorded temperature? Which was the city recorded the same temperature? How much hotter was Darwin than Hobart? Much of this information would have been just as easy to answer without constructing the graph, let alone the last question which would have been easier to calculate without the graph. I was astonished and annoyed by how chance and data, a topic which lends itself so easily to authentic investigations based on real-life contexts or other hands-on learning experiences, could be treated in this way. In the same afternoon at work, while playing connect four with another child in grade 1, an authentic context arose for her to record some real data, and she did so on her own accord.
This grade 1 girl started to tally the number of wins each of us achieved as a result of playing a series of games of Connect Four. In actual fact, we did not play as many games as was shown on this piece of paper. The score started off as:
She accurately recorded the results and made statements about them, “You’ve won four games and I’ve only won one”. “If you win one more game then I’ll put an across mark and you would have won five games.”
After playing four more games the score table read:
She said, “If I win one more game we’ll be tied.” We talked about where she got the idea of doing up a table from. She said that she picked it up from watching other girls keep score when they play Connect Four.
Then the call for afternoon tea was announced and she quickly scribbled in the remaining tally-marks. When I asked her what she was doing she said, “I’m just mucking around, look we both won lots of games”.
If we had more time, we could have explored different ways of graphically representing the information she collected or made up with post-its, bundle sticks, stickers and so forth. I am confident that she would have enjoyed that experience and gained a lot more from it than the girl in grade 4 seemed to have from completing her homework. This led me to think deeper. I wonder, what does actually constitute an authentic context for learning chance and data? Furthermore, is having an authentic context the crucial deciding factor in determining if this strand of maths is taught well or not?
Nisbet, Langrall and Mooney (2007) conducted a study which raised the research question "How do students knowledge of real-life contexts affected their ability to analyse some data provided to them?" The result of the study suggest that when primary-aged students were given sets of data related to a topic area which they had special knowledge and interest in, they used their understandings of the real-life context to "rationalise their data or their interpretations, in taking a critical stance towards the data, and in ways that were not necessarily productive or pertinent in addressing the task at hand." (p.16) According to Nisbet, Langrall and Mooney (2007), providing opportunities for learners to integrate contexual knowledge and statistical information through investigating real-life data is important. However, teachers need to be aware that learners can be just as easily distracted by their contextual knowledge, which can lead them to disengage with the mathematical problem or task. This hypothesis seems to be supported by English and Watters (2005) who found in their study that children who were participants in their study used their informal knowledge to relate to and identify important problem information, but at times became "absorbed in applying their informal knowledge" (p.72).
Therefore it is clear that providing data which is taken from real-life contexts or may be of interest to children is not enough. As teachers we need to crtically reflect on our lesson designs so as to assist students to use their informal knowledge to critically evaluate data where it is appropritate, as well as develop statictical literacy in considering the data itself and how it applies to the problem (English & Watters, 2005). Perhaps activities where students take part in collecting the data, as well as manipulating it to solve problems which they pose for themselves would be appropriate (see fishing game blog-post).
References:
English, L. D. & Watters, J. J. (2005). Mathematical modelling in the early school years. Mathematical Education Research Journal. 16(3), 58-79.
Nisbet, S. Langrall, C., & Mooney, E. (2007). The role of context in students' analysis of data. Australian Primary Mathematics Classroom, 12(1), 16-22.
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