Using the Socratic Method
The Socratic Method (also known as Socratic teaching or questioning) is probably the most ancient of all teaching methodologies. In its original form, the master tutor questioned the student until the student actually became confused about what he knew regarding a particular subject. Then slowly the master tutor asked open-ended questions that not only reintroduced subject knowledge to the student, but also raised the student's level of thinking to a higher level of synthesis and creativity.
This is a dialogue I had with a GED Mathematics student using The Socratic Method...
1 What are triangles?
A triangle is a plane (flat figure) with three sides.
2 Could you elaborate further? Could you give me an example?
Has three angles that the sum equal to 180 degrees, example is a triangle with angles of 90 degrees, 30 degrees and 60 degrees. Each of the three points is called a vertax (sp.).
3 How can we determine if that is true? How can we verify your statements?
I don't know.
You could reference the book...
4 Could you be more specific? Could you provide more details?
I don't know.
The angles of a triangle are easy to understand if you start with a square.
5 What are the different types of triangles?
Scalene Triangle/Equilateral Triangle/Isosceles Triangle/Right Triangle
6 What are some of the complexities of this question? What factors need to be considered?
One complexity is that the third side of an isosceles triangle maybe longer or shorter than either of the two equal sides. You have to consider how many equal sides, how many equal angles, if there is a 90 degree angle.
7 What is a vertex?
Each of the three points where the sides of a triangle meet is called a vertex.
8 Compare and Contrast similarity and congruence.
In Geometry, similar figures has the same shape but different sizes. Congruent has the same shape and same size.
9 Define corresponding.
Corresponding refers to matching sides of similar figures, corresponding sides can be written as a proportion.
10 How can we tell if triangles are congruent?
Triangles are congruent if they meet any one of the three conditions; Angle Side Angle,Side Angle Side, Side Side Side.