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 -