European Research in Mathematics Education I - Fakultät für ...

European Research in Mathematics Education I: Group 2 192
3. Analysis
We use the term formalising to encapsulate three categories of activity which we
observed as contributing to the construction of meaning for formal notation:
connecting a pattern based on the data with the experiment,
connecting a pattern based on the data with a rule, and
connecting a rule based on the data with a formula.
Our use of the word ‘pattern’ here is deliberately a little ambiguous, referring
sometimes to an obvious numerical pattern, and sometimes to a fixed relationship
between numbers. We will exemplify formalising by providing extracts from the data
before discussing links with other themes in the research.
4. Connecting a pattern based on the data with the experiment
In both activities, the formula for the area was introduced in the beginning with the help
of the teacher, so the notion of such a formula was familiar to the children. In Display
Area the children began by working with a 75 cm length of ribbon, and pinning out
rectangles on a display board. This naturally led to some inaccuracies as ‘imperfect’
rectangles were produced, although the children were not initially aware of this. Later
the children went through a period of growing realisation that the length and the width
are somehow interrelated. Consider this incident from work on Display Area . (Note: all
boxed items are extracts from the data. The first person refers to the researcher.
Numerical inaccuracies in these extracts are due to difficulties in making
measurements, or to hasty calculations.)
I ask Laura and Daniel whether their measurements have become more accurate. I observe how
they are doing it and notice they are fixing the length. I ask them whether they can find out the
width given the length. Daniel does the 23-length case: he doubles 23 and then the pair notice that
their measurement of 16 cm for the width makes the perimeter 76 cm. They measure the 23 cm
sides and the other comes out as 15.5 cm, so they record 15.5 cm as the width. (ACT II: session 1)
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