Abstract:

Research has shown that students have difficulty understanding the angle as a mathematical object, due to both the semiotic representations used to teach it and epistemological obstacles (Brousseau, 1983). The multiple definitions of angle, each focused on different aspects of it, represent a further challenge.

Hence, Angolandia, a two-part simulation game for primary students on the concept of angle, was designed, implemented, and validated to explore whether combining the conventional "grammar" of simulation games with selected educational theory and methods facilitated children’s comprehension of the concept of angle.

The teaching-learning model in Angolandia presents angle in different perceptual situations, while immersing children in solving problem scenarios of incremental difficulty by following the rules of the game. Learning is by discovery. The game is informed by a semiotic perspective on maths learning that recognizes the role of interaction with objects and people in constructing key concepts and the use of multiple semiotic signs for the same concept (Duval, 2006). It represents angle both statically and dynamically, using simple materials, and based on standard primary school definitions (Henderson, D.W. and Taimina, D., 2005).

The first episode of Angolandia was piloted with 31 fourth-graders. Outcomes were assessed via a written interview with the children on their understanding of angle, both pre- and post- the teaching-learning intervention; the processes that unfolded during the game were also observed, while teachers were interviewed at the end of the intervention. The game’s overall structure, component activities, and materials prompted the students to identify key regularities, enabling them to construct their own representations of angle, including an elementary notion of unlimitedness. The second episode was designed on the same theoretical-methodological bases as the first, to consolidate students’ understanding of angle and to explicitly explore unlimitedness, which was only implicitly grasped during the first episode.

The second episode was piloted, along with the first, with a class of fifth-graders. The impact on children’s understanding of angle was assessed by administering a written test and oral interview to the students both before and after the intervention; again, the processes that unfolded during the game were observed, and the teachers were interviewed at the end of the project. The research data, particularly the children’s representations of angle, suggested that the two-part game had produced key learning outcomes, such as: noting the division of the plane into two regions, representing extensions of line segments, and verbalizing aspects of unlimitedness. The observational data suggested the need for a supplementary activity on extensions. The pilot tests also led the researchers to refine the debriefing discussion guides for each of the two episodes.

References:
[1] Brousseau, G., (1983). Les obstacles épistémologiques et les problèmes en mathematiques. Recherches en didactique des mathématiques. 4(3), 165-198.
[2] Duval, R., (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1), 103-131.
[3] Henderson, D.W. and Taimina, D., (2005). Experiencing geometry. Euclidean and non-Euclidean with history. New York: Cornell University.

Keywords:

Learning angles, primary school, simulation games, teaching geometry, research.