id: 06546559
dt: j
an: 2016b.00039
au: Ernest, Paul
ti: The history of mathematics in the classroom.
so: Math. Sch. (Leicester) 40, No. 4, 14-20 (2011).
py: 2011
pu: Mathematical Association (MA), Leicester
la: EN
cc: A30 U63 D43
ut: history of mathematics; worksheets; lower secondary; student activities;
genetic method; discovery learning; group work; justifying; proving;
time; solving equations; graph theory; induction; infinity; Egyptian
fractions; unit fractions; Greek mathematics; Egyptian mathematics;
Indian mathematics; Hindu mathematics; partitions of integers; Rangoli
patterns; symmetry; Pascal’s triangle; binomial expansion; nondecimal
systems; ancient number systems; Euler’s polyhedron formula; Euler
characteristic; music; strings; frequencies; Chinese mathematics; magic
squares; Roman mosaics; patterns; rotational symmetry; reflectional
symmetry
ci: ME 1999f.03647; ME 2015c.00402; Zbl 0061.00616
li:
ab: Summary: This article was previously published in [the author, Math. Sch.
(Leicester) 27, No. 4, 25‒31 (1998; ME 1999f.03647)], and has been
chosen to be republished. From the text: Problems and problem solving
are central to both the history of mathematics and the learning of
mathematics. In both areas they stimulate knowledge growth. Historical
problems, such as the Königsberg Bridge Problem which stimulated Euler
to create Topology, can introduce students to network theory in
today’s classroom. Mathematicians in history struggled to create
mathematical processes and strategies which are still valuable in
learning and doing mathematics. Descartes (1628) offered a wonderful
set of ‘rules for the direction of the mind’ which are as valuable
today as when he first used them. {\it G. Pólya}’s [How to solve it.
A new aspect of mathematical method. Princeton, N. J.: Princeton
University Press (1945; ME 2015c.00402; Zbl 0061.00616)] heuristics
have long been in use in mathematical classrooms. In the following
worksheets a number of historical problems are posed as classroom
tasks. As a mathematics teacher educator I get my student teachers to
design classroom worksheets drawing on the history of mathematics as a
way to open their eyes to its value. The following are a few examples
of what they have produced.
rv: