the other way we try and make the work relevant is by linking the work to their interests using things such as sport to calculate statistics and optimal angles, but due to many students dislike of mathematics quite often what comes back is "why are you trying to ruin football for me my making it into a maths lesson". They enjoy the sport and playing it, but don't want to know about the maths involved.
The argument about relevance also becomes about who it is relevant to. If you make the lesson about football, then it is not personally relevant to anyone who does not like that sport, this could easily be more than half of your class.
The idea of relevance can be used very successfully for engagement, there have been some highly relevant lessons that I have taught, that students have also found highly engaging. But I have also had some highly relevant lesson fail miserably. Over the last few years I have found that embracing the idea of presenting students with ridiculous problems has increased student engagement more than anything else.
So how do I define an ridiculous problem
Some of the questions of this type I have had success with in the past are as follows
All of these questions immediately gained the students interest, the looked at me like I was insane, but also had that look of "I want to know the answer to this". As can be seen they are all very much related to something they have seen before, money, burgers, post-it's nuggets but it takes how they have thought about these things far outside the realm of what we consider "normal". It is this deviation from the normal that students find really interesting and the work they have produced on these sort of tasks has been quite stunning. In my observations of students working on these type of tasks it is clear that they are discussing the work more with others, coming up with stronger, well reasoned responses and also add value to the task for looking at ways they can extend it such as looking at how many calories in the 100 x 100 burger or the cost of a 1000 x 1000 burger. In particular the chicken nuggets question still continued to have students talking about it 8 weeks after the task had finished, students even went to McDonalds and tried to order that number of nuggets to see what they would say.
I think that most of the time it is not the highly positive praise that drives you to be better, it is the highly negative criticism that drives that growth, especially if it is criticism regarding something you really care about.
For me this moment came as a pre-service teacher in one of my teaching practicums. In my final report for the teaching prac one of my supervising teachers described me as "dispassionate about teaching". To be honest at the time I was devastated with this comment, however I also thought the comment was unfair as given the teacher I was working with I know the comment was one somewhat based on me having a very different teaching style to them. I have always loved to teach, I taught my brothers from a young age and have known I want to be maths/science teacher since year 8. My passion for this profession started at a young age which is why the comment was so soul destroying to me.
However, in some ways, even though I still hold a great deal of anger towards this teacher, I have to also thank her. It is a comment I think about regularly and in many ways it always keeps me honest, and it keeps me improving. With everything I do in my classroom and in my job, I think about whether it is showing enough passion, is it my best work, is it working for my students, how can I make it better next time, what went well and what didn't.
The thing about praise is that it gives no incentive for change if you go about your job day to day and get praised for what you are doing, then it gives the impression that what you are doing is enough, or even more than enough. So if what you are doing is enough, why would you try harder, there is no indication that there is anything that needs to change. Criticism on the other hand has the opposite effect, by definition it suggests that there is something that needs to happen, some change that needs to be made. Criticism demands you to grow as a person or grow as an employee if you do not want to continue to be seen in that light.
If I was currently thought of as a dispassionate teacher by students or colleagues I would be quite horrified as I don't believe it was me all the way back then, and I do not believe that is me now. However if I am to be sure that I am thought of as a person with a passion for teaching I need to set myself on a path of continuous improvement. Central to do that is to constantly seek feedback from my students and colleagues and to focus predominantly on the negative feedback. But it also requires me to be very self-reflective in my practice. By working to continuously fill the gaps in my own practice it will ensure that i will not become complacent in what is a very important job.
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.