From Conjecture to Proof is about learning proof and acquiring skills of constructing proof. It is a book for teachers and teachers in training, which revisits the ideas of mathematical proof in a way that encourages students to learn by 'doing'.
A conjecture is formed when a person notes a pattern in mathematics. The conjecture is made based on what the person observes or already knows about mathematics. This conjecture can be either proven to be true or false. To prove that the conjecture is false, a counterexample must be found.