TY - JOUR
T1 - Cultural relevance of validation during mathematical modeling and word problem-solving
T2 - Reconceptualizing validation as an integration of possible fictional worlds
AU - Ishibashi, Ippo
AU - Uegatani, Yusuke
N1 - Funding Information:
This work was partially supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number 20K22188 , 18K13162 , and 21K13587 .
Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/6
Y1 - 2022/6
N2 - This study proposes a theoretical view for bridging mathematical modeling and word problem-solving activities. We introduce and elaborate on two theoretical ideas of the fictionality of word problems and the creation of possible fictional worlds. A world described by a word problem exists only fictionally (or potentially). A fictional world includes any imaginable world, any model for the real world, and any mathematical model. We developed a semi-open problem based on these theoretical ideas and observed Japanese eighth-grade students’ activity when solving it in an experimental lesson. Consequently, we identified a theoretically overlooked type of validation: considering the cultural relevance of solutions. The most important implication we draw from our observation is that the current definition of validation as a comparison between two stages in modeling should be extended to consider the integration of a target into a base possible fictional world.
AB - This study proposes a theoretical view for bridging mathematical modeling and word problem-solving activities. We introduce and elaborate on two theoretical ideas of the fictionality of word problems and the creation of possible fictional worlds. A world described by a word problem exists only fictionally (or potentially). A fictional world includes any imaginable world, any model for the real world, and any mathematical model. We developed a semi-open problem based on these theoretical ideas and observed Japanese eighth-grade students’ activity when solving it in an experimental lesson. Consequently, we identified a theoretically overlooked type of validation: considering the cultural relevance of solutions. The most important implication we draw from our observation is that the current definition of validation as a comparison between two stages in modeling should be extended to consider the integration of a target into a base possible fictional world.
KW - Creation of possible fictional worlds
KW - Fictionality of word problems
KW - Mathematical modeling
KW - Mathematical word problem-solving
KW - Validation
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U2 - 10.1016/j.jmathb.2022.100934
DO - 10.1016/j.jmathb.2022.100934
M3 - Article
AN - SCOPUS:85124246928
VL - 66
JO - Journal of Mathematical Behavior
JF - Journal of Mathematical Behavior
SN - 0732-3123
M1 - 100934
ER -