Exploring high-achieving sixth grade students’ erroneous answers and misconceptions on the angle concept

Abstract

The aim of this research was to investigate high achievers' erroneous answers and misconceptions on the angle concept. The participants consisted of 233 grade 6 students drawn from eight classes in two well-established elementary schools of Trabzon, Turkey. All participants were considered to be current achievers in mathematics, graded 4 or 5 out of 5, and selected via a purposive sampling method. Data were collected through six questions reflecting the learning competencies set out in the grade 6 curriculum in Turkey and the findings of previous studies that aimed to identify students' misconceptions of the angle concept. This questionnaire was then applied over a 40 minute period in each class. The findings were analyzed by two researchers whose inter-rater agreement was computed as 0.97, or almost perfect. Thereafter, coding discrepancies were resolved, and consensus was established. We found that although the participants in this study were high achievers, they still held several misconceptions on the angle concept such as recognizing a straight angle or a right angle in different orientations. We also show how some of these misconceptions could have arisen due to the definitions or representations used in the textbook, and offer suggestions concerning their content in the future.

Sixth Grade Students’ Some Difficulties and Misconceptions on Angle Concept

“…In this study, when the students were asked to draw an angle, it was seen that they mostly chose to draw the acute angle and right angle. The tendency to draw right angles as a prototype in angle drawings has been emphasized in the literature (Baldy et al, 2005;Butuner & Filiz, 2017;Devichi & Munier, 2013;Doyuran, 2014). For example, in the study by Baldy et al (2005), when students were asked to draw any angle, they generally drew right angles and tended not to accept obtuse angle as an angle.…”

“…) Doyuran (2014) Related to Angle Measure:  It depends on the size of the shaded interior region,  Depends on the length of the arc (or radius of the arc) pointing to the angle,  It depends on the length of the edges and there may be a right-angle effect in this misconception,  Congruent angles with different orientation or edge lengths are different angles. Butuner & Filiz (2017), Devichi & Munier (2013) Keiser (2004, Mitchelmore (1998).…”

“… The tendency of positioning the perpendicular to be drawn from a point not on a line parallel to the long side of the paper,  A perpendicular cannot be drawn from a point on a line. Butuner & Filiz (2017).…”

“…The existence of various definitions of the concepts in the literature is shown as one of the most important reasons for students' difficulties (Butuner & Filiz, 2017;Henderson & Taimina, 2005;Keiser, 2004). Definitions as the building blocks of mathematical thoughts undertake a fundamental task in forming a concept and distinguishing it from other concepts (Cakiroglu, 2015).…”

“…It has been stated that a right angle can be a significant learning barrier, in particular for the tasks asked to focus on the edge length and angle (Devichi & Munier, 2013). On the other hand, Butuner and Filiz (2017) showed that most high-achieving sixth-grade students have misconceptions and have difficulties understanding the conceptual meaning of angle concept.…”