Pure mathematics is, in its way, the poetry of logical ideas ~ Albert Einstein

Saturday, 30 March 2013

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

Reflections on Readings - Chapter One

          In this chapter, I have come to understand the different principles and standards for the instruction of Mathematics in schools. This comes to show that Mathematics is definitely an essential aspect of education. All these frameworks have one thing in common. They all focus on the need to make it possible for all students to have the opportunity and the support necessary to learn significant mathematics with depth and understanding. It is evident that the long-term goal is for all students to develop lifelong problem solving skills. Mathematics ability is not inherited as anyone can learn mathematics.
          Mathematics was never my forte as a student, so I was a little apprehensive when I read that I would need to have a profound, flexible, and adaptive knowledge of mathematics content to be a teacher of Mathematics. I realized the important role a teacher plays in the teaching of Mathematics. The fact that student's learning of Mathematics may come only from the teacher, puts an enormous responsibility on the teacher. I totally agree that a teacher has to demonstrate persistence, have a positive attitude towards mathematics, be prepared for change, and always make time to be self-conscious and reflective (Van De Walle, Karp, Bay-Williams, 2013, p. 10).
          I need to change my attitude towards mathematics and be receptive to the joy that can be found in solving mathematical problems. This is important to me not only as an individual but more so as a teacher so that I can be a positive role model to my students. Only then can I nurture in my students a positive attitude and a life-long passion for mathematics.