Megan Barnett

EMAT 4680-Tu/TH

Assignment #4

Dr. Olive

The Role and Function of Proof with Sketchpad

  1. Verification/Conviction- An example of when the student could understand proof as a means of verification/conviction is teaching a problem over and over again with examples. Sooner or later, the student is convinced that the problem works (distance formula).
  2. Explanation-A good example of the need for explanation in the mathematics environment would be the Pythagorean theorem. It is used for right triangles for where the hypotenuse-squared is equal to the sum of the other two sides-squared. Once a teacher has explained this concept, the student can use it for all other right triangles.
  3. Discovery- Here, I will use system of equations as an example. When the students are learning about system of equations, they discover that when given two equations, they can find the point of intersection. Furthermore, students discover that when they plug the point of intersection back into the two equations of the line, the points of intersection works out for both equations…

    4. Given: X + Y= 5 and 2X — 3Y= -5 at (2,3)

    When you plug the points of intersection into the equations of the line, they both WORK OUT!

  4. Systematization- A facilitator can use systematization in the classroom when

    5. something is not specifically stated (where the student can not comprehend because it does not give exact instructions on what or how to do something). Say Susie simply can’t understand the concept of 3-4-5 triangles when discussed in class. The teacher can then explain the definition of Pythagorean theorem and do examples of a2 + b2 = c2 to prove 3-4-5 triangles.

  5. Communication-When explaining proofs, a teacher is trying to communicate to

    6. her/his students. At any point and time, a teacher needs to be able to communicate with their students. I believe that communication is the key to education and a classroom lacking such communication is one of a poor learning environment. If a teacher/student can’t communicate back and forth, there will be no progression. That is why communication is SO important.

  6. Intellectual Challenge-A student needs proofs as a means of intellectual challenge

to encourage themselves and to feel good about themselves and all they have

achieved. This will allow progression because if a student is confident in oneself,

they will have no fear to move ahead towards the future. This is also an important

role proofs can portray in the mathematical environment.