Universal Journal of Educational Research Vol. 9(8), pp. 1511 - 1520
DOI: 10.13189/ujer.2021.090803
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Conceptual Misunderstanding: On the Interplay of Understanding and Misunderstanding in Geometry

Anass Bayaga ^1,*, Michael J. Bossé ², John Sevier ^2
1 Senior Secondary Education, Faculty of Education, Nelson Mandela University, Port Elizabeth, South Africa
² Mathematical Sciences, Appalachian State University, USA

ABSTRACT

Analyzing the communication and work of high school geometry students through error-prone topics such as transformations, constructions and employing various thinking processes such as factual and procedural knowledge could reveal insight to students understanding of Geometry. Such a body of work [1, 4, 5], could reveal suitable or unsuitable considerations of a topic combined with suitable or unsuitable uses of a thinking process thereby producing suitable or unsuitable conclusions. Directed by the objective of the study, three high school geometry students' interpretations were analyzed in order to explore: (1) connections among topics and thinking processes; (2) relationships among suitable and unsuitable uses of the topic and thinking processes; and (3) whether unsuitable uses of topics and unsuitable thinking processes can yet lead to suitable understanding. The results revealed no definitive association among some topics and some thinking processes, whether suitable or unsuitable in either realm. Unsuitable applications of factual, procedural, and conceptual knowledge were not associated simply with the lack of these thinking processes, at times. However unsuitable thinking processes were present, deliberate, purposive, and not absent. By implication, there is a need for more studies regarding student use and misuse of thinking processes regarding other mathematical subjects.

KEYWORDS
Misunderstanding, Geometry, Factual Knowledge, Conceptual Knowledge and Procedural Knowledge

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Anass Bayaga , Michael J. Bossé , John Sevier , "Conceptual Misunderstanding: On the Interplay of Understanding and Misunderstanding in Geometry," Universal Journal of Educational Research, Vol. 9, No. 8, pp. 1511 - 1520, 2021. DOI: 10.13189/ujer.2021.090803.

(b). APA Format:
Anass Bayaga , Michael J. Bossé , John Sevier (2021). Conceptual Misunderstanding: On the Interplay of Understanding and Misunderstanding in Geometry. Universal Journal of Educational Research, 9(8), 1511 - 1520. DOI: 10.13189/ujer.2021.090803.