Can we change how Maths is perceived?
Maths is currently perceived by a lot of people to be a subject that is a waste of their time. It seems to lack the creativity of other subjects and work wise is considered to be solitary by nature. It seems to lack any application to peoples day to day lives, combine that with people who are proud to be bad at maths and the upshot is a subject that does not seem to offer much to people who don’t wish to pursue a career requiring maths. Much of this is due to the way maths has been taught, although some is perhaps due to people’s attitudes to school.
By looking at different possibilities of how we could teach maths I hope to arrive at a potential way in which to improve its perception within the student body. To do so I will begin by looking at how group work may be integrated in to the maths classroom, as well as looking at whether maths is inherently a solitary subject. I will also look at how maths can be shown to be more real life and how it is not just a bunch of topics thrown together. This should allow Maths to be seen as more relevant and more coherent.
The renowned Mathematician from the 1930’s Nicolas Bourbaki produced work at an unparalleled rate and left many stunned at how he was able to output such a quantity of work at such a high rate. Ultimately this powerhouse of a man turned out to be a group of French mathematicians attempting to create what amounted to an encyclopaedia of Maths using an entirely axiomatic method. There are many other times where maths relies on groups working together, from ancient Greece to the use of supercomputers in modern times.
Group work has a role in jobs later in life and as such several people believe that we should be integrating it into our curriculum. Both Jo Boaler and Ken Robinson appear to be of this opinion, they suggest that by working as a group students are able to help each other and gain more perspective on the work they are doing. Certainly this is something that is true in future life, we wouldn’t expect someone to not be allowed to ask for help in a work place. Why should this happen within a school environment?
The idea of progress being made through group work is echoed outside of academic circles too and Steven Kutler discusses how a group dynamic, aiding in obtaining a flow state, has pushed extreme sports to progress over the past two decades.
However, while I can see that group work does have its advantages and allows students to learn these skills now in my experience it can also be the cause of undue friction. A group is only as strong as its weakest member and with inadequate support the strongest students may well end up doing all the work. This might eventually lead to the stronger students not making as much of an effort as they see no benefit to themselves. Equally the tiresome nature of doing anything too much may appear with the overuse of group work. Sometimes it is just easier to do things yourself.
It should also be noted that there are several critics of both Boaler and Robinson regarding the information they have presented. The fact that Boalers critics are colleagues from the same University suggests that the accusations are fairly serious. However one of her critics was the part of a committee that drafted the State Standards for education that Boaler is critical of. Perhaps this suggests we need to be wary of fully accepting Boalers work until more research has been done.
It would strike me that while there is perhaps something to be said for group work embracing it as a sole method of teaching would be limiting and would almost certainly be counter-productive. However, using it to encourage students to help one another and perhaps even to undertake some enquiry as part of a group could make maths more appealing to students. There almost certainly requires some balance between group work and individual work to cater to the needs of the students who also prefer to work alone.
Hopefully use of group work within the classroom and perhaps a little more information regarding how certain maths work was originally discovered could break the illusion of maths as a subject for individuals. This may well allow for students who struggle to not feel so intimidated by maths and therefore encourage a greater appreciation for the subject.
The next issue to address is how we can make maths more applicable to most people’s lives. Most people seem to use little more than basic calculations in their lives and much of that can be done with a calculator, so although estimation is useful as is basic arithmetic higher maths seems to lack relevance to people in general.
Dan Meyer has suggested several ways to make maths more relevant to students by attempting to remove a lot of the information that is presented to students. This allows the students to begin by asking their own questions and also allows for them to develop their estimation skills. This to me seems like an interesting idea and certainly he has a lot of support for his ideas. However, it is impossible to teach all areas of maths in this way. It would make teaching things such as surface area and volume more complex, perhaps his methods could be used to introduce the topics which might increase interest in the topic but is this another case of a novel approach that will be all too boring with repetition.
In another video Meyer also discusses how we can create real life maths within the classroom. He alludes to the idea of how “Mathsy” a classroom is, and that to encourage and build a discussion around Maths we need to lower the amount of Maths that is presented initially and as the session continues it is possible to increase the “Mathsy-ness” of the classroom. I found this interesting as currently maths classrooms are filled with numbers, number lines for example, and I have certainly seen how they can be useful. Perhaps he does not suggest we do away with these entirely, yet I do feel that these must contribute to the “Mathsy-ness” of a classroom. While I can appreciate the idea of “Mathsy-ness” as it stands the curriculum is already full and students are going to be expected to face an exam which is going to be “Mathsy-ness” set full on. Perhaps with a change in curriculum and a change in style of exams this method could be implemented but I do feel that if a solution requires a wholesale change within the curriculum is it really a solution. Although the outcomes from such a change might be positive due to the increased understanding that maths isn’t just sums.
In the same video he also discusses what real life maths actually might look like and to me this is his most important point, yet I feel he hasn’t implemented it to its fullest extent. He suggests doing away with questions like “How many meatballs can I fit in this saucepan that has x amount of sauce in it already?” even if this style of question is made more relevant to the students. His idea of real life maths is being able to ask questions of a problem and make estimations of it. This is certainly an extremely deep idea that does seem to touch on the skills that most people will need in their real life. By teaching estimation and questioning we are encouraging students to be creative and approach a situation from their own angle. However, the step that he doesn’t seem to highlight is just how important problem solving is. I do feel he seems to have not fully grasped this and his primary desire appears to increase questioning from students. This is not a problem in and of itself yet it seems to let this cloud what could be an incredible method for demonstrating the importance of problem solving.
The final issue that is to be remedied is this idea of maths being made up of lots of separate topics that are going to have to be learnt individually. This seems to be a hang up from when Maths was taught as Geometry, Trigonometry, and Arithmetic. Although topics tend to fall in to these categories they are extremely related to one another and as such learning something in one area may well lead to a greater understanding of another area. Richard Skemp was the proponent of this and he called it Relational Learning, this was to counter the methods that had been traditionally used which he called Instrumental learning.
If we are to consider these two approaches we must understand what is meant by both of these. Instrumental learning amounts to a set of directions from one place to another, whilst relational learning is understanding the whole map. My favourite description of this was done by David Wees, it says that in essence relational learning lets you understand where you are and how you can create a short-cut from one place to another whilst still understanding how you got there, whilst Instrumental means if you stray off the path you may very well be lost and have to start again. My appreciation for relational learning has increased drastically over the past year and I love the idea that Maths is all interconnected. However, I feel that instrumental learning has its place within maths. Should a teacher be encouraged to teach entirely relationally when a students is clearly not capable of fully understanding it? Clearly not. If a student has an exam in two weeks the clear winner is instrumental learning. What about if we already understand something an instrumental approach still has its merits in the form of an algorithm to get from one place to another. I yet again feel that a balance here is needed. Whilst relational learning clearly allows for a deeper understanding the use of instrumental understanding has its place within the curriculum.
The problem with Maths being real life is that most of maths in real life isn’t explicit, and what is explicit can be done using a calculator. So while I feel using some of Dan Meyers ideas to encourage problem solving and develop peoples implicit use of maths I am not sure I buy in to his philosophy whole heartedly. In much the same way I believe that relational learning is certainly a style of learning I would intend to use as much as possible it cannot be used entirely on its own. How Meyers ideas fit with Skemps I am not entirely sure and I feel that Meyers ideas might well be relegated to special sessions to test students understanding of a topic and develop their problem solving skills. Again the issue seems to be that will both will help and Meyers approach improves skills for daily life there is a requirement that students pass exams and little of what Meyer teaches will fulfil that requirement.
In an ideal world I believe that there is another approach that might take suggestions from both Meyer and Skemp. The solution is not to ask what makes maths interesting to students as a whole but what would make maths more interesting to each student as it is completely dependent on that student. If statistics could be taught through the context of history or geography would it make it more interesting to students? Personally I feel that this is what school should be trying to show, not just for maths but for all subjects. More cross curricular studies to learn that one subject is never really entirely separated from another.
So, how can we change people’s perceptions of maths? A lot seems to be related to how people themselves were taught and as such it can create a loop of negativity around the subject. Certainly by countering the stereotypes of Maths being an individualistic subject by using group work it may go a long way to changing this perception. Just as important is the way we teach maths and the ideas we saw from Meyer and Skemp should definitely be embraced in some way, both would hopefully allow for a more enjoyable learning environment. As well as facilitating learning through the use of relational understanding. To me these are merely a way to patch what seems to be a flawed education system. Everyone is offering different ideas and solutions and the truth is that compromise is never going to suit everyone.