in looking at all of the aspects of maths that are expected to be covered over the course of a year I feel that statistics offers some really great opportunities. It allows a really authentic way for students to get into some real maths with data that matters to them and to others. It is not that there is not authentic ways to engage with the other aspects of the course and get into some real maths, it just sometimes seems like it doesn't seem like an authentic situation for them, there is not the emotional buy in. With statistics you have the opportunity to introduce some very provocative data sets or ones that directly speak about them. You can have some really great discussions about how statistics are used to make decisions, how others use them to make decisions that effect you, to look at how you or other people can use them to build convincing arguments (even if the stats are quite deceiving).
I am at the very start of my unit on statistics, but I wanted to start it with them having a discussion about some data, their own diagnostic testing data. I chose to use this data for a because sometimes I feel they don't see the use of doing the testing, they don't always treat it properly and that skews our data. I also chose it as I feel that they do not always understand the results of the data, I wanted them to have much more awareness of what the data tells them and of how we use the data as eduators.
The last person to talk picks the next person to talk (from those with a counter out) by throwing them a ball or similar, only the one with the ball can talk. Once a person has used all of their counters they then cannot contribute any more to the discussion, they can sit and listen, but that is it. The teacher in this process is a facilitator, but tries to stay out of the discussion as much as possible. They provide the provocation to start off with, they pick the first person to talk and they will ask questions to stimulate the discussion if it dies off completely. In this role you need to avoid jumping in to help with that I tend to give myself the same number of talking stones that everyone else gets, if they only have three opportunities to add to the discussion then I only have three to stimulate it, it forces me to be strategic as well. This is hard when you completely disagree with what is being said, but you need to let students be the ones to respond them and to challenge that thinking.
I gave them two prompts to start their contribution with they could start with
It is always a little nice when I still find some of the answers I get for questions I give to students surprising. It is not that the answers are unexpected, it is more that sometimes I get excited by the solutions.
A local supermarket chain on and off for the last few years has been running a bit of a promotion. The promotion involves a series of 108 animal cards. For every $20 spent at their store you get a pack of 4 animal cards. I have a three year old daughter who loves these cards. She loves collecting them and seeing which ones we have missing. I know that over the course of the promotion we have collected a lot of cards and have got a lot of doubles, it got me wondering how many cards I would need to collect (doubles and all) to collect the full set of 108.
and sometimes less gaps, but the 20 represents the average number of cards missing. At 400 cards the average missing drops to about 2, a substantial gain in cards. However at this point you have spent $2000 dollars at their store. In running the multiple simulations of the 400 cards there was only one or two occasions out of the dozens of times tested that I managed to get a full set of 108 out of the 400 cards.
Raising this again to 600 cards there is still a gap. about a third of the time there was a full set cards, but in two thirds of cases there was an average of one card missing, it was only when taking the number of cards to 800 that we began to consistently got a full set of cards. At 800 cards you have spent $4000 in their stores.
Having to spend $4000 to in a sense guarantee a full set of cards that probably cost them less than $5 to produce is not necessarily something that sits well with me. Part of the money generated is being used to support a few zoo's, so it is not so bad. In reality people will swap cards with other people to fill the gaps, and they are likely to spend this money any way, they are not doing more shopping just to get cards. However if the parents of these children used to shop at another supermarket chain, then the introduction of these cards. if only for a short time, has no doubt swung quite a bit of business their way. These were the sort of discussions that were so valuable in conducting this task with the class.
Ok, before I get too many hateful thoughts from people who may read this, I don't have anything against literacy, I think it is an incredibly important skill that all people must develop and it is an incredibly important part of being able to talk about mathematics. My issue is not with literacy itself, but more with the way the word literacy is being used, particularly in relation to terms such as statistical literacy and financial literacy. In trying to make my point I have taken the following definitions for statistical and financial literacy from Wikipedia
Statistical literacy is the ability to understand statistics. Statistical literacy is necessary for citizens to understand material presented in publications such as newspapers, television, and the Internet. Numeracy is a prerequisite to being statistically literate. Being statistically literate is sometimes taken to include having both the ability to critically evaluate statistical material and to appreciate the relevance of statistically-based approaches to all aspects of life in general (http://en.wikipedia.org/wiki/Statistical_literacy)
Financial literacy is the ability to understand how money works in the world: how someone manages to earn or make it, how that person manages it, how he/she invests it (turn it into more) and how that person donates it to help others. More specifically, it refers to the set of skills and knowledge that allows an individual to make informed and effective decisions with all of their financial resources. (http://en.wikipedia.org/wiki/Financial_literacy)
In looking at those definitions it should be clear that these are not only very important, but it should also be clear that these are not literacy skills, they are numeracy skills. For many it would be "so what, it is just a label" but it is much more than that. As it is, numeracy is not a term that is respected as much as it should by the general public, and people cannot generally identify the aspects of their lives that deal with numeracy. By taking two very large aspects of numeracy and labeling them with a literacy tag, people start to associate them less with numeracy and more with literacy.
It seems like the term literacy is being associated with every aspect of learning considered an essential life skill. Apart from the ones already mentioned there are terms such as technological or computer literacy, emotional literacy and physical literacy, this was just with a quick Google search. Although not necessarily numeracy skills, they are also not literacy skills, just terms given the literacy tag again to hopefully gain support for their importance.
It is interesting that people are starting to believe that these things are really literacy skills, and not numeracy skills. Having spoken to some teachers from other schools, teachers who work in English faculties, they believe skills such as reading and constructing graphs are truly literacy skills, but I also doubt that these skills have ever been taught in an English class, but they are taught every year in Mathematics classrooms. Just because there is a fact, figure, graph or table as part of a written text, it doesn't make it a literacy skill, simply it is just a part of the text that needs some numeracy to fully comprehend it.
The argument has been made for years that you can't be numerate without being literate, and with that I do agree, at least to some degree. Many mathematical problems require the comprehension and decoding of written texts or problems and being able to transcribe them into a mathematical construct. However I would also argue the reverse is true, that you can't been literate without also being numerate, it is a reciprocal relationship not a one way relationship. Often texts include numbers that students may not recognize the size of, graphs and tables that they find it difficult to interpret and map, flowcharts and other diagrams requiring spatial reasoning that they may not be able to fully interpret
If we are to have any significant impact on both numeracy and literacy levels in students we need to acknowledge that they are separate skill sets that are connected by the idea that you cannot fully have one without the other. Central to doing this is acknowledging the numeracy that is present and not forcing the literacy tag onto everything.
Senior Leader of Pedagogical Innovation and Mathematics Coordinator in Regional South Australia.
Opinions in this blog are my own and do not necessarily represent the views of my employer.