One of the ways in which I would like to create and maintain a positive classroom environment is through designing and implementing mathematical experiences that stimulate students’ interests and intellect. I believe that digital tools, especially GeoGebra, can be exploited to pursue interactive classroom activities and engaging mathematical investigations. For instance, instead of starting a unit on differentiation with a sheet of formula that may appeal to only fervent students, I would begin by using suitable GeoGebra applets to challenge students to extend their knowledge through visualization of what a derivative at a point or derivative of a function means. Visualization of mathematical concepts and ideas is an intermediate process. It is a process in which students use their prior knowledge and experiences (slope, secant line, limits, continuity, etc.) to actively form their own representation of knowledge. These applets will act as in-class demonstrations and/or student explorations to motivate new situations or content.
I like presenting new content through GeoGebra applets, partly because teaching and learning becomes more active, curious, and imaginative. When presenting new concepts and ideas through interactive tools, I find that students get more involved in the process, which is a big first step in creating a positive learning environment. Instead of the teacher constantly posing questions, students take ownership of their learning and start posing questions to the teacher and to each other. When students start asking questions, take ownership of their learning, and connect classroom to real world applications of mathematics, that’s when the role of the teacher in the classrooms changes from an expert to a facilitator of knowledge creation and generation. As a facilitator, I believe that a teacher would float around the classroom to observe students’ interactions and conversations for gaining a better of sense of where students are, in terms of their understanding of the content. These formal or informal observations will offer important insights for designing future classroom experiences.
I believe that a caring and safe learning environment will influence the mathematics that is taught and experienced by the students. Experiencing mathematical problem-solving through inquiry-based projects will enable students to be the most active mathematical participants in the classrooms, instead of being spectators. For example, in an inquiry project related to an optimization problem centered around designing natural gas pipelines between three cities in BC, finding reasonable solutions would require thinking differently, unconventionally, and from new perspectives. Solutions to real world mathematical problems are considered to be reasonable when a solution is a good approximation or estimate to the original problem. Students would be expected to work in small groups and think of themselves as a team of engineers or professionals to design and determine backup pipeline routes to existing pipeline. In such a project, students will carry out independent research and utilize previously learnt geometrical concepts and ideas, such as reflecting a point across a line, properties of isosceles triangles, constructing triangle centers (incenter, centroid, orthocenter), and solving mini-problems involving angles and triangles (acute, right, obtuse). The intention of this project is for students to be able to incorporate relevant mathematical details and socio-economic issues when determining their pipeline routes. And so solving this problem would involve considering First Nations communities and interests, infrastructure needs, overarching regulations, emergency and disaster responses, climate, etc. The expectation of the inquiry project is that this project will provide students with the confidence and competence to actively investigate problems and find solutions. This project is designed to develop skills necessary to critically analyze information, make logical guesses, and apply problem solving strategies to solve increasingly complex problems. Students will carry out research by considering environmental issues, safety of nearby communities, and economic necessities from multiple perspectives to build a convincing argument on pipelines construction. When students are proposing an optimal design (reasonable solution) for their backup pipeline routes, it is expected that they have used mathematical reasoning and thinking to go from concrete context to abstract concepts.