
06426603
j
2015c.00716
Yigit, Melike
An examination of preservice secondary mathematics teachers' conceptions of angles.
Math. Enthus. 11, No. 3, 707736 (2014).
2014
Information Age Publishing (IAP), Charlotte, NC; University of Montana, Department of Mathematical Sciences, Missoula, MT
EN
G49
C39
B53
research
interviews
preservice teacher characteristics
subject content knowledge
mental constructions
elementary geometry
angles
concepts
APOS learning theory
right triangles
learning
cognitive science
http://www.math.umt.edu/tmme/vol11no3/Yilgit_12.pdf
Summary: The concept of angles is one of the foundational concepts to develop of geometric knowledge, but it remains a difficult concept for students and teachers to grasp. Exiting studies claimed that students' difficulties in learning of the concept of angles are based on learning of the multiple definitions of an angle, describing angles measuring the size of angles, and conceiving different types of angles such as 0line angles, 1line angles, and 2line angles. This study was designed to gain better insight into preservice secondary mathematics teachers' (PSMTs) mental constructions of the concept of angles from the perspective of ActionProcessObjectSchema (APOS) learning theory. The study also explains what kind of mental constructions of angles is needed in the righttriangle context. The four PSMTs were chosen from two courses at a large public university in the Midwest United States. Using Clements' clinical interview methodology, this study utilized three explanatory interviews to gather evidence of PSMTs' mental constructions of angles and angle measurement. All of the interview data was analyzed using the APOS framework. Consistent with the existing studies, it was found that all PSMTs had a schema for 2line angles and angle measurement. PSMTs were also less flexible on constructions of 1line and 0line angles and angle measurement as it applied to these angles. Additionally, it was also found that although PSMTs do not have a full schema regarding 0line and 1line angles and angle measurement, their mental constructions of 1line and 0line angles and angle measurement were not required in right triangles, and the schema level for 2line angles was sufficient for constructions of right triangle context.