id: 06664681
dt: j
an: 2016f.01031
au: Turner, Paul
ti: Making connections.
so: Aust. Sr. Math. J. 29, No. 2, 51-61 (2015).
py: 2015
pu: Australian Association of Mathematics Teachers (AAMT), Adelaide, SA
la: EN
cc: G40 A30
ut: geometric concepts; mutually tangent circles
ci:
li:
ab: Summary: This article aims to illustrate a process of making connections,
not between mathematics and other activities, but within mathematics
itself ‒ between diverse parts of the subject. Novel connections are
still possible in previously explored mathematics when the material
happens to be unfamiliar, as may be the case for a learner at any
career stage. The geometrical configuration explored in this paper, now
known as “Ford circles” after Lester R. Ford, Sr. (1886‒1967), is
related to ideas about mutually tangent circles that were studied by,
among others, Apollonius of Perga in the third century BC and by René
Descartes in the 17th century. This exposition is intended to conjure
the thoughts of a hypothetical mathematician attempting to find and
explain some connections, in the process exploring some lines that turn
out to be unproductive, and making observations that are really non
sequiturs, before eventually achieving some success. The author
suggests that seemingly innocent mathematical fragments can have
connections to many related ideas. If a teacher is in possession of a
broad subject knowledge, then the likelihood seems high that it is
possible to draw out useful connections in the classroom or in
well-designed projects and assignments. For this reason, the author
claims that an ever-widening subject knowledge is of utmost importance
in a teacher’s program of professional development. (ERIC)
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