
06649811
j
2016f.01012
Katz, Sara
Stupel, Moshe
Segal, Ruth
Proofs without words with geometric representations: a trigger to selfefficacy and mathematical argumentation.
Far East J. Math. Educ. 16, No. 1, 2156 (2016).
2016
Pushpa Publishing House, Allahabad, Uttar Pradesh, India
EN
G40
E50
proofs without words
argumentation
selfefficacy
deductivereasoning
divergentthinking
higherorder thinking
creativity
http://www.pphmj.com/abstract/9637.htm
Summary: Proofs without words (PWWs) are visual representations that provide the observer with clues to stimulate mathematical thought. There is an increasing consensus among researchers that visual representations can potentially contribute to mathematics learning processes and better understanding of problems. In schools, PWWs are less common than logical proofs. Evidence from many metaanalyses of more than two decades of study shows that efficacy beliefs contribute significantly to level of motivation and learning, sociocognitive functioning, emotional wellbeing, and performance accomplishments. Therefore, efficacy beliefs are crucial for educating young people. Efficacy beliefs provide students with a sense of agency to motivate their learning through use of selfregulatory processes. We performed a qualitative exploration of how PWWs activity contributed to efficacy beliefs and performance in mathematics. Two groups of mathematics studentteachers and teachers ($n=50$) aged 2027 participated in the study. Research tools were semistructured reflections (50), nonparticipant observations (3), and field notes (10). The PWWs activity was presented in the methodology courses as a pedagogical device that the participants had to experience for future use in their classes. Data were analyzed using a constantcomparative method and grounded theory techniques. PWWs (a) enhanced participants' selfefficacy to make argumentations, (b) contributed to making mathematical argumentation, divergent thinking, creativity, and (c) fostered selfregulation. Difficulties with PWWs among some participants also emerged. The contribution of this study is threefold: strengthening this ``oldnew'' genre as a pedagogical thinking tool to foster future mathematics thinking; engaging students in activities that make them realize the beauty and elegance of mathematics, thus enhancing their selfefficacy to learn mathematics, and enhancing thinking performances. Providing students with PWWs opportunities is recommended.