Mhairi (Vi) Maeers and Rick Seaman

Faculty of Education

University of Regina

"Pattern is all around us" and "the world is composed
of many intricate patterns" are expressions we
sometimes hear from students and colleagues. Pattern
is certainly very much a part of our everyday lives,
but it is the recognition and application of pattern
which enables us to survive more than the fact that
pattern 'exists'. One may even wonder if pattern does
exist outside our personal interpretation,
understanding and application of it. In this
introduction to the latest issue of Ideas and Resources
for Teachers of Mathematics we would like to
introduce the concept of pattern through some ideas
from the literature and through a recent personal
'pattern' experience.
Mathematicians have been described as makers of
patterns of ideas (Billstein, Libeskind & Lott, 1993, p.
4) and mathematics has been considered the
classification and study of all possible patterns
(Sawyer, 1963, in Orton, 1993, p. 8). Patterns
created by one mathematician may well lay the
groundwork for another (Polya has stated that Rene
Descartes' ideas helped him with his work on problem
solving). Searching for and identifying patterns has
long been considered a very important problem
solving heuristic. Determining patterns is crucial to
police investigation, to household plumbing problems,
to young children's daily routines. Anything 'out of
the pattern,' for example taking a nap before lunch
instead of after lunch can throw a young child's day
askew. We tend to live by personally 'inflicted'
patterns in order to survive the stress of daily life.
Once something becomes a commonly accepted
pattern, then it no longer needs to be calculated; one
has established order out of what may appear chaotic--but we know now that chaos has an implied order of
its own.
The National Council of Teachers of Mathematics
[NCTM] (1989) in
http://www.enc.org/reform/journals/ENC2280/nf_28060s13.htm Standard 8 at the grades 5-8 level (Pattern and Functions) informs us that "the mathematics curriculum should include explorations of patterns and functions so that students can
http://www.enc.org/reform/journals/ENC2280/nf_28098s8.htm
There is no specific http://www.enc.org/reform/journals/ENC2280/nf_280dtoc1.htm
From 1991-93 the NCTM published two Addenda Series
documents which concentrated on Pattern Websites Meteorology--Does Weather Happen Randomly: Penrose Tilings and the Golden Mean: 3-D Modeling, Fabrication and Illustration: Tessellations Project (and links to other tessellation sites): Puzzles Involving the Fibonacci Series: You can view many more pattern sites at the Math Forum--> Steve's Dump at http://forum.swarthmore.edu/~steve/. Simply click on "Quick Search" and enter the word pattern. The sites listed above are ones that we visited and found useful as a result of this search. At our own Math Central, there are a number of resources that focus on pattern. They can be found in the Resource Room/Keyword/Pattern.
Pattern can be interpreted through all disciplines and
can connect all disciplines, an idea similar to the last
sentence in the above quote by Pengelly. Just recently
a group of five elementary education professors
worked with 60 third year students on a semester-long
curriculum integration project. The focus of study
was PATTERN and our task was to: (1) determine
how pattern could be represented and interpreted
through each discipline [mathematics (Vi Maeers and
Liz Cooper), language arts (Carol Fulton), social
studies (Kathryn McNaughton), and the arts (Nancy
Browne)], (2) demonstrate to our students our
collective perspectives on pattern (through a
Hyperstudio presentation), (3) take our students
through a variety of pattern-focused activities within
each subject area, and (4) work with groups of
children in a local elementary school to help them
understand different ways of thinking about pattern.
Ideas and Resources for Teachers of
Mathematics you will find suggestions for
activities at different grade levels that enable both
you and your students to explore both the
process and product of pattern.
References
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