Summary
The article examines two major arguments - history as a goal and history as a tool. The former is linked with meta-issues which allow one to see math history from a holistic view in terms of its evolution, individual contributions, cultural influences, and social fabric. In contrast, the latter treats math history as an inspirational source to increase students' perseverance and interest in the learning of math related to inner issues which cover concepts, theories, methods and so on.
Jankvist presents three approaches to teaching math history: illumination (integration of historical events), module (lessons dedicated to history) and history-based (sequencing topics in line with chronological order). He also considers two genetic principles for teaching and learning math.
(1) The historical-genetic principle is intended to help students progress in their learning from the lowest to the highest level of complexity as in the historical development of math.
(2) The psychological-genetic principle is based on active learning through discovery.
Reflections
In my opinion, teaching students math history related to meta-issues does not offer students any concrete help in improving their math understanding since historical events give only factual information. When I tutor students, I notice that they pay no attention to the pages about history and go straight to the examples and exercises. These pages seem to serve no purposes for them. On the other hand, in-issues supported by history-as-a-tool arguments are more applicable to the aims of mainstream math curricula which focus on math relationships and structures. How one plans a current lesson, connects it with the prerequisites from past lessons, and guides students from this lesson to the next are generally influenced by the in-issues.
Jankvist suggests that teacher tell struggling students stories about how historical mathematicians stumbled over the course of their learning and remained determined for years to resolve their difficulties. These stories may be inspiring, but I am not sure if they would have any affective effects on struggling students. I believe that struggling students may need direct support from their parents and teachers whom they can trust.
Lastly, the psychological-genetic principle seems to offer math education its current direction. This direction gives students opportunities to explore, discover and invent math concepts using their own strategies. This may also give the teacher opportunities to present historical approaches briefly relevant to the concepts the students investigate. So, the historical approaches may broaden the students' understanding of the math concepts.
I see your point about students skipping straight to the math questions, and ignoring the historical references. We see that all the time. I even find that the majority of my class will skip the examples in the textbook and try the questions. Then they will ask me how to do a question without even doing the pre-reading. I think that in order for a historical approach to work effectively, the teacher would have to take the initiative and be one who discusses it, rather than having hoping that the students will read it. Unless of course a historical reading is assigned and will be assessed. That might fit into the module-based approach which I am not a big fan of.
ReplyDeletePerhaps an assignment could be designed where the students have to pick a theorem to analyze it's historical origins and create a cartoon depicting how the theorem came to fruition.
I agree with you that snippets of historical data in mathematics textbooks are nothing more than mathematics trivia. I am not surprised when students skip pages to go directly into the problem sets. I did this too. When I was learning mathematics or science, the focus was to learn or memorize texts that were inserted in coloured boxes. The knowledge that was worth more were in boxes. I think that problems will arise as long as there are discriminations between which and what knowledge is most worth. We make this decision everyday in our lives: if something is not worth investing our time, then we ignore it. Our students do the same.
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