Jones_eurologo.pdf (115.38 kB)
A logo-based task for arithmetical activity
Young children attend to answer-getting readings of arithmetical notation. This is evidenced by
many children’s exclusive acceptance of a + b = c syntaxes that lend themselves to
computational readings (e.g. Behr et al., 1976; Carpenter and Levi, 2000; Knuth et al. 2006).
Even those children who do accept a wider variety of syntaxes, such as and
, adhere to a computational view involving getting answers to both sides of the equals
sign and checking they are the same (Jones, 2006).
a + b = b + a
c = a + b
I report here on the trialling of a Logo-based task (see screenshot below) designed to foster
meaningful engagement with the structural properties of arithmetical equality statements. The
design rationale is that of diagrammatic reasoning where arithmetic inscriptions onscreen are
observed and manipulated according to precise operational rules. The dual functionality of
selecting equality statements and substituting terms is intended to afford the specific
diagrammatic activities of iconic matching and transformation making towards the construction of
purposeful meanings for differing statement syntaxes. The data show that the children’s readings of arithmetic notation were broadened from
computation to iconic matching during trialling. This pattern-based observation of notation
combined with the activity of transformation making resulted in commutative and partitional
meaning-making for a + b = b + a and c = a + b syntaxes respectively. The data also suggest
that various factors impacted on the diagrammatic strategies developed by the children to
complete the task. These factors included blind experimentation, systematic testing, existing
computational readings, and emergent commutative and partitional readings.
History
School
- Science
Department
- Mathematics Education Centre
Citation
JONES, I., 2007. A logo-based task for arithmetical activity. IN: Kalas, I. (ed.). Proceedings of the 11th European Logo Conference, EuroLogo 2007, Bratislava, Slovakia, 19th-24th August.Publisher
Department of Informtics Education, Comenius UniversityVersion
- VoR (Version of Record)
Publication date
2007Notes
This is a conference paper.ISBN
9788089186204Publisher version
Language
- en
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