
06034606
j
2012c.00414
Tillema, Erik
Hackenberg, Amy
Developing systems of notation as a trace of reasoning.
Learn. Math. 31, No. 3, 2935 (2011).
2011
FLM Publishing Association, c/o University of New Brunswick, Faculty of Education, Fredericton, NB; Canadian mathematics education study group  CMESG (Groupe Canadien d'\'etude en didactique des math\'ematiques  GCEDM), [s. l.]
EN
E43
C33
F43
educational research
experiments
learning
teaching methods
mathematics instruction
identification
critical thinking
cognitive processes
science activities
http://flmjournal.org/index.php?do=details&lang=en&vol=31&num=3&pages=2935
Summary: In this paper, we engage in a thought experiment about how students might notate their reasoning for composing fractions multiplicatively (taking a fraction of a fraction and determining its size in relation to the whole). In the thought experiment we differentiate between two levels of a fraction composition scheme, which have been identified in prior research, and discuss differences in systems of notation that students might produce, depending on the level of their scheme. We situate this discussion within a framework for learning in order to articulate how developing systems of notation with students can contribute to their learning. (ERIC)