What If Not Problem Posing

The What-If-Not Method is something that it seems has been used a lot before in our math studies, but making it more conscious to ourselves can definitely improve our abilities to becoming thought provoking teachers. The method firstly allows the teacher to make sure they posses a good knowledge of the subject and also prepares the teacher for possible questions arising from students’ curiosity. By posing these questions beforehand, a teacher will be able to be more prepared in class discussions rather than possibly being blindsided by a student’s question. But more importantly the teacher allows the student to not only understand the taught subject, but deepen the student’s understanding of it. From the example given in the book, a student not only learn about Pythagoras’ theorem of right angled triangles, but it also makes the student think of why only right angles? It broadens the students’ understanding of that subject and doesn’t just focus on one aspect of it, like just memorizing the theorem. This way when given geometrical problems, the student will also be more aware that if it’s not a right angled triangle, then the Pythagorean Theorem does not apply and they have to find another way to find its sides.
At the same time it seems like the WIN Method they discussed in the book do take it too far in questioning. It’s great that the student is challenged and engaged when they’re learning topics, but sometimes the questions go beyond the topic and sometimes becomes irrelevant to the learned topic. With regards to the Pythagorean Theorem, once we get into the cycling phase, it starts talking about a2 + b2 < c, and it seem to become more number theory rather than the theorem students are taught to relate to triangles.
But putting it to practical use, such as introducing sines and cosines for teaching, it is a great way to make the students think about the ratios of the triangle’s side lengths when it’s not a right angled triangle. In this manner they can be more cautious as to when to use sin and cos.