Reflections on Readings - Chapter Two

          "Doing mathematics begins with posing worthwhile tasks and then creating an environment where students take risks and share and defend mathematical ideas." (Van De Walle, Karp, Bay-Williams, 2013, p. 14). As a teacher I find this to be an important statement. I  need to create an environment that stimulates children's learning and provides challenges for them. An environment in which they can be actively thinking mathematical ideas while trying to solve the problems. A place where they can be engaged in sharing their ideas and reflecting on their mistakes as well as make connections between different strategies in solving a problem.
          In the learning process, both the Constructivist and Sociocultural theories should be applied to enhance the learning journey as both these theories emphasize the learner using their own knowledge and experience to solve problems through social interactions and reflections (Van De Walle, Karp, Bay-Williams, 2013, p. 29). As a teacher, I need to know the prior knowledge of my students in order to provide them with appropriate challenges in making the connections and bringing them to the next level. I need to apply the following strategies when considering practices that maximize learning:

• Build new knowledge from prior knowledge - through inquiry based approach.
• Provide opportunities for talk about Mathematics - through interaction with peers and teacher.
• Build in opportunities for reflective thought - by engaging students in interesting problems in which they use their prior knowledge to search for solutions and create new ideas.
• Encourage multiple approaches - by sharing ideas.
• Engage students in productive struggle - not by showing them but by asking probing questions until they reach a solution.
• Treat errors as opportunities for learning - by addressing student misconception.
• Scaffold new content - by giving more structure, and 
• Honour diversity - by including student's ideas for classroom discussion