When reading this article I was struck by a topic that, to be honest, I had never really put to much thought into. I had always known tidbits about mathematics history but had never really considered how I learnt it nor how I may incorporate it into my teaching practices. I found it interesting that Tzanakis and Arcavi bring up possible objections to the incorporation of the history of mathematics into curriculum so early on in their article. I am assuming this is to address any skeptics that may be engaging in the article. I found it powerful that they decided to state both "philosophical and practical" objections because by mentioning them, they are able to validate that they have been considered in the decision making process.
Tzanakis and Arcavi raise "five main areas in which mathematics teaching may be supported, enriched, and improved through the history of mathematics into the educational process:
a) the learning of mathematics;
b) the development of views on the nature of mathematics and mathematical activity;
c) the didactical background of teachers and their pedagogical repertoire;
d) the affective predisposition towards mathematics; and
e) the appreciation of mathematics as a cultural-human endeavour.
I found many relevant points that support the teaching of the history of mathematics. You are able to emphasize the imperfect nature of the discipline, and that many failures or attempts were made before formulas or proofs were achieved. This will hopefully lead your students to taking more risks and realizing that they do not always need to get the right answer right away. You are also able to make clear interdisciplinary links that have been around for centuries and are sometimes lost when getting stuck in formulas. You can include information about past notations and methods for doing calculations.
The article went on to give many examples of application; however, I was discouraged that many of the ideas were focused on high school and university level classes. I believe the teaching of the history of mathematics is valuable at all age levels. As mentioned in the article, it is all about making sure the teachers have the knowledge and resources in order to properly incorporate it into their practices. Currently the teacher's lack resources and it is not taught in the pre-service programs. In my opinion, I think we have a long way to go in this regard. I also think that the skeptics that worry about not having enough time to teach everything will definitely continue to worry about this and not see this inclusion as a feasible option.
Philippa,
ReplyDeleteYour article sounds like a good read! I might have to take a look at it myself.
The math education reading group in the math department had a discussion today that I think kind of relates to much of what you are saying. We were discussing the recently announced curriculum changes in Finland. They are doing away with "subjects" and teaching "by phenomena". The integration of history into mathematics learning would be particularly intriguing under this "phenomena" model. As you mention though, having the knowledge and resources (as a teacher) to do such a thing is not a trivial matter! I was lamenting during the seminar that I really think there should be more subject specific offerings for pre-service teachers. I suppose it's a goal of mine (at some point in my life) to work between an education department and math department to get such an initiative going!
For me, the most attractive aspect of teaching mathematics in a historical context, is showing to students that mathematics has been a human endeavour. Often, I think that students believe mathematics "happened" just as fast as it "happened" in class. For students to see that the development of mathematics is not an instantaneous event could help in a number of ways, as you mention. Moreover, the historical aspect might help students realize that not all math is "done". That is, it is an ever growing field and people (real people!) are making discoveries every day. In fact, it might be nice to have mention within primary and secondary schools of what "real mathematicians" are doing now. The knowledge needed for this, particularly if you want to put it in simple terms, is very high; I would probably struggle with such a task. Regardless, it would be a pretty cool thing to do!
Thanks for the blog post Philippa.
ReplyDeleteI terms of having elementary school teachers acquaint themselves with the history of mathematics, I wonder how easy that would be given how many subjects they usually teach.
Much like you and Vanessa, I agree that one of the benefits of teaching the history of mathematics is that it portrays it as a human endeavour. It allows students to see that many of the struggles they are going through were also historical struggles. in terms of making math a more human endeavour and taking a historical perspective, I wonder how this would be done in such a way as to not portray math as an exclusively male dominated subject.