Mathematics is elegant and fascinating, but is too often daunting for students, who may have been put off from math at an early age. I believe if students enjoy mathematics, and have the ambition and ability to study mathematics, then they can accomplish more than they can learn in a single class. Therefore, my priority as a teacher is to create a learning environment that fosters to these attributes.
First, in order to foster to both ambition and ability, I employ active learning. To achieve this, I try to follow the following learning style. Exploration. First, I introduce the idea, through cross-curricular links, historical perspectives, and real life applications, and allow students to explore the content of the lesson, by using guided research. By learning the history behind the mathematics and how it may relate to other fields and life, students gain an
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Conjecture. Next, I get students to make conjectures about the content, by noticing patterns in the guided research. Once students come up with a conjecture, I guide students to think about and test their conjecture, with guided questions. By finding and proposing their own conjecture, students improve upon their ability to think critically, notice patterns, and remember the content. Proof. Once the student is satisfied with their conjecture, their next goal is to prove it, or if necessary, explain clearly, why it works. By successfully proving their conjecture, students will gain a great sense of accomplishment, allowing them to enjoy mathematics more. In addition, by proving the conjecture, students will be able to know exactly why the conjecture is true, and not only rely on someone telling them it is true.