TY - CONF
AB - In this paper, we first outline a Hypothetical Learning Trajectory (HLT), which aims at a formal understanding of the rules for manipulating integers. The HLT is based on task formats, which promote algebraic thinking in terms of generalizing rules from the analysis of patterns and should be familiar to students from their mathematics education experiences in elementary school. Second, we analyze two students' actual learning process based on Peircean semiotics. The analysis shows that the actual learning process diverges from the hypothesized learning process in that the students do not relate the different levels of the diagrams in a way that allows them to extrapolate the rule for the subtraction of negative numbers. Based on this finding, we point out consequences for the design of the tasks.
AU - Schumacher, Jan
AU - Rezat, Sebastian
ED - Jankvist, Uffe Thomas
ED - Van den Heuvel-Panhuizen, Marja
ED - Veldhuis, Michiel
ID - 13107
KW - diagrammatic reasoning
KW - hypothetical learning trajectory
KW - induction extrapolatory method
KW - integers
KW - negative numbers
KW - permanence principle
KW - semiotics
T2 - Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (CERME11, February 6 – 10, 2019)
TI - A Hypothetical Learning Trajectory for the Learning of the Rules for Manipulating Integers
ER -