Proof?

    I believe Geogebra is a good visualizing tool that students can explore to convince themselves of geometric theorems. However, I still do not think that it provides valid proofs. Similarly, students can use sine law and cosine law etc to explore trigonometric identities, yet it is the process of justifying, not presenting proofs. 

    In secondary school class today, the main goal of teaching traditional proofs is to promote deductive thinking. The introduction of proofs in math is in a scaffolding form. Students start from conjectures and inductive reasoning first and then explore counterexamples to disprove some conjectures. When discussing the topic of valid proof, here is one question I used to show to my students:

        Choose a number. Add 3. Multiply by 2. Add 4. Divide by 2. Subtract the number you started with. What is the result? Prove why it works.

    Students were always amazed by the result when choosing different numbers. After several tries, they turned to generalize and tried to do the proof by using algebra. Although this practice of proving is kind of easy, it is actually in a high degree of rigour. I believe in this way, students develop a stronger sense of proof and thus, develop more on deductive thinking.