TY - JOUR
T1 - Missing and Mis-in Concept Images of Parallelograms
T2 - the Case of Tal
AU - Tirosh, Dina
AU - Tsamir, Pessia
N1 - Publisher Copyright:
© 2021, Ministry of Science and Technology, Taiwan.
PY - 2022/6
Y1 - 2022/6
N2 - In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students’ concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition–concept image as reported by Tall and Vinner (Educational Studies in Mathematics 12:151–169, 1981), a theory that is widely used in mathematics education. The occurrences during our interviews with one of the first students that we interviewed led us to identify a need to extend this theory. This manuscript suggests to add two new constructs to the theory of concept definition–concept image: missing concept images and mis-in concept images. Missing concept image defines a situation in which an example of a concept is erroneously categorized as a non-example of the concept. Mis-in concept image is the somewhat complementary case, in which a non-example of the concept is mis(takenly) in(cluded) in the set of examples of the concept and consequently this non-example is erroneously identified as an example of the concept. In this manuscript, we introduce these two constructs. We also describe two possible sources of students’ decisions regarding their ways of sorting figures into examples and non-examples of parallelograms that were detected during the interviews. To the best of our knowledge, these sources were not reported in the related literature.
AB - In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students’ concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition–concept image as reported by Tall and Vinner (Educational Studies in Mathematics 12:151–169, 1981), a theory that is widely used in mathematics education. The occurrences during our interviews with one of the first students that we interviewed led us to identify a need to extend this theory. This manuscript suggests to add two new constructs to the theory of concept definition–concept image: missing concept images and mis-in concept images. Missing concept image defines a situation in which an example of a concept is erroneously categorized as a non-example of the concept. Mis-in concept image is the somewhat complementary case, in which a non-example of the concept is mis(takenly) in(cluded) in the set of examples of the concept and consequently this non-example is erroneously identified as an example of the concept. In this manuscript, we introduce these two constructs. We also describe two possible sources of students’ decisions regarding their ways of sorting figures into examples and non-examples of parallelograms that were detected during the interviews. To the best of our knowledge, these sources were not reported in the related literature.
KW - Concept definition
KW - Concept image
KW - Mis-in concept images
KW - Missing concept images
KW - Parallelograms
UR - http://www.scopus.com/inward/record.url?scp=85104103490&partnerID=8YFLogxK
U2 - 10.1007/s10763-021-10175-0
DO - 10.1007/s10763-021-10175-0
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85104103490
SN - 1571-0068
VL - 20
SP - 981
EP - 997
JO - International Journal of Science and Mathematics Education
JF - International Journal of Science and Mathematics Education
IS - 5
ER -