Reflection: Modeling Proving the Medians in a Triangle Meet at a Point - Section 3: Proving the General Case


With the advent of the Common Core, I think one misconception is that everything should be student-centered and constructivist. Math is still an esoteric discipline and in many cases students are uninitiated to the techniques that they will need to complete a given task. 

In these instances, I have found that it is much more efficient and more effective to use worked examples. So what led me to decide that this would proof would best be taught through a worked example? For one, the sheer number of variables involved in the problems makes the algebra very intimidating for students who are not accustomed to dealing with these kinds of problems. There will come a time when they will actually see these problems as simpler problems since they require no computation, but at this point they are just plain intimidating. Secondly, there are algebraic moves that streamline the proof and I suspect that the overwhelming majority of students would not ever discover these moves on their own. Using the worked example allows me to give students experience with these types of problems so that they will not see them as so intimidating, and it also allows me to model and explain the expert algebraic moves that were made in the proof so that they understand why they were made and why they were better than other moves that could have been made.

Basically, it was clear to me that the expertise required to write this proof was not something that students would magically discover or arrive at. I needed to take them through an apprenticeship in order for them to begin acquiring this expertise. Hence my decision to employ the worked example. Then in the next section, students get to put what they have seen in the worked example into practice.


  Knowing when to use the worked example
  Modeling: Knowing when to use the worked example
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Proving the Medians in a Triangle Meet at a Point

Unit 9: Analytic Geometry
Lesson 5 of 7

Objective: SWBAT use analytic geometry to prove that the medians of a triangle must be concurrent.

Big Idea: Alphabet soup anyone? Students will really need to master the abc's of algebra and be on their p's and q's to digest what's on the menu in this lesson.

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