"The sum of two sides of a triangle is always greater than the third side."
She proceeds to prove the theorem and tells students to learn the theorem by rote.
The teacher is happy, she has "finished" the theorem.
Students understand the proof, then do a worksheet where they measure the lengths of the sides of triangles and veryify the theorem.
Students are happier than in the First Way, they have participated in the learning process.
The strips are of different lengths and each student picks up three sticks randomly.
Students are asked to make triangles out of their strips.
Some students succeed, some don't.
Those who don't are questioned why. They reply, the strips aren't long enough.
Through Socratic questioning, the teacher finally elicits the answer: the longest strip must be shorter than the sum of the other two strips!
The teacher summarizes the discovery, giving due credit to the students and then proves the theorem!
Students feel a sense of achievement, it is after all their theorem!
They have Become Mathematicians and they have Done Mathematics!
The teacher points to the first student and asks her to read the first paragraph from the textbook.
With a lot of hesitation and wrong pronunciation (which the teacher does not bother to correct) the student manages to read one paragraph.
Another student is then asked to read the next paragraph.
In this way, the lesson is read. The teacher then reads out the questions, makes the students mark the answers.
The lesson is over!
She has many teaching aids on her table, which she uses to demonstrate her points.
Students try their hands at forming shadows and playing with the teaching aids.
The class is lively and students look forward to the class.
As soon as the teacher enters the classroom, students look eagerly at what she is carrying!
For example, she switches on the light and asks students to create monster shadows of themselves.
She hands over a common object (e.g., a pen) and asks students to study the shadows formed by the pen.
Students form small groups and solve the problems; at the end, they present their findings to the teacher.
She writes the main findings on the board and summarises them properly, using the correct words to describe what the students have discovered.
The class is noisy, with students eager to tell the teacher what they have discovered, but the noise is due to exuberance, not due to mischievousness.
However, there is a fundamental difference: in modern classrooms, students verify what they have been taught; in Third Way classrooms, they discover knowledge themselves.
In the second approach, students are trained to follow instructions—good for work that involves meticulous work and execution of plans.
In the Third Way, students develop curiosity, critical thinking, and problem-solving skills—qualities that define innovators and leaders.
In addition, the intangible outcomes would also be a sense of achievement and confidence among these learners.
Do we want a generation that merely follows directions, or do we want thinkers, creators, and changemakers?
The answer lies in embracing The Third Way.