The question of the best possible way to teach mathematics, or any subject for that matter, is a quite an ambiguous and controversial one. In mathematics education the inclusion of elements such as theoretical concepts and history in curricula is generally not as valued as the applications of mathematics. In the discussion today we spoke of the benefits both of these components can provide to a student's understanding, but there was no consensus on the best way of engaging students with the material nor was there a clear agreement on how these elements should even be introduced into the classroom.
One of the final things brought up in the discussion was the idea that a teacher can only ever teach what they are. I think this theory points out how variable the inclusion of non-traditional components of a subject is based on the educator. An instructor has the responsibility of designing lesson plans that allow them to naturally progress through the subject matter according to their own understanding. In the context of mathematics education in order for a teacher to meaningfully integrate theoretical and historical content into their lesson plans that content itself should be a part of how the instructor comes to understand the material being presented. If we do agree with the opening statement, that you can only ever teach what you are, in order to improve the depth in which an instructor is able to communicate their subject matter they themselves must try to expand and deepen their own understandings through the relevant components. I certainly agree that all teachers ought to try and expose themselves to media and materials that could allow for them to have a better understanding of their subject matter through non-traditional means.
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