Promoting Risk Taking in Mathematics Classrooms: The importance of Creating a Safe Learning Environment

Do the one thing you think you cannot do. Fail at it. Try again. Do better the second time. The only people who never tumble are those who never mount the high wire. This is your moment. Own it.-Oprah WinfreyRisk abounds in our everyday life and workplace. Risk can delight, annoy and engage us. As the above quote suggests people need to be aware of the importance of risk taking. Notions of risk appear in various messages that we encounter such as when receiving forecasts of medical, financial or environmental risks from media research reports and public officials. In such situations, we have to make decisions in the presence of conflicting goals and constraints (Schlottmann & Wilkening, 2011; Shapira, Nattinger, & McHomey, 2001). In recent times, risk taking and risk-aversion has drawn increased attention of educators and researchers for a range of reasons (Anthony & Walshaw, 2007; Fesser, Martignon, Engel & Kuntze, 2010; Martignon & Kurz-Milcke, 2006; Till, 2014). These include recognition of its importance for solving differences and reaching consensus, as well as its central role in thinking and making infonned decisions (Gaissmaier & Gigerenzer, 2008; Galesic & Garcia-Retamero, 2010; Martignon & Krauss, 2009; Schlottmann & Wilkening, 2011). Indeed, to learn and grow people must take risks, but most people will not take risks in an emotionally unsafe environment.Moreover, there has been significant shifts in the way teaching and learning of mathematics is conceptualised internationally. The American policy document, Principles and Standards for School Mathematics states that if students are to learn to "construct mathematical arguments and respond to others" arguments, then creating an environment that fosters these kinds of activities is essential (National Council of Teachers of Mathematics, 2000, p. 18). This reform teaching aligns with vision promoted by NCTM's Professional Teaching Standards (National Governor's Association for Best Practices and Council of Chief State School Officers. 2010) that encourages students to communicate mathematical ideas and nurtures intellectual risk-taking by students. However, reasoning at complex cognitive levels and risk taking through mathematical discourse is not something many students are able to achieve easily without adult mediation (Anthony & Walshaw, 2007; Cobb & McClain, 2004; French, 2009; Hunter, 2010).While there has been ample discussion of students at risk (Clark, 2001; Franco, Sztajn, & Ortigao, 2007; Lubienski, 2007; Winsor, 2007), mathematics education at risk, and nations at risk (Center for the Study of Mathematics Curriculum, 2005; Nasir,, Hand, & Taylor, 2008; Wagner, 2008), risk assessment (Gigerenzer, 2002; Gigerenzer, Gaissmaier, Kurz-Milcke, Schwartz, & Woloshin, 2009; Martignon & Krauss, 2009), there has been limited discussion of students' willingness to take risks in mathematics classrooms where they are asked to solve open-ended tasks (Lubienski, 2007; Sullivan, Mousley, & Zevenbergen, 2006). Individuals who have different perceptions of risk are more or less likely to do well in these environments (Clifford, 1991; Hills, Stroup, & Wilensky, 2005). It follows that learning environments must take into account individual student's and teachers' risk-taking or risk-averse behaviours. There is very little research on students' mind-sets and motivation for risk tolerance in mathematics education. In 2010, for the first time, risk was included in a session of the ICOTS, as a topic for instruction in school in connection with statistics education (Fesser et al., 2010).This paper describes some research-based ideas for promoting risk taking behaviours in a mathematics classroom. It presents interactional pedagogical strategies from a design collaborative research (Sharma et al., 2011) conducted at one secondary school. As part of the learning activities, students critically evaluated statistical investigations undertaken by others (Ministry of Education, 2007). …