What if not?

The applications of the "what if not" (WIN) strategy are many when it comes to math education. One thing that I have always advocated (although not really had the chance to practice yet) is the value of allowing kids the opportunity to feel like they're discovering something for themselves. WIN type questions allow for this to happen. By carefully posing your initial question or problem you can allow students to lead themselves to desired learning outcomes via exploration of the possibilities of the original question. As shown in the text, even a "simple" theorem can lead to an endless rabbit hole of new inquiries in to diverse and sophisticated branches of mathematics. Sure, some of the topics may not be valuable to a grade 8 student, but recognizing the relationships between the legs of the triangle and the hypotenuse (ie, what does a^2 + b^2 < c^2 mean?) is really useful. And, who's to say that explorations of Number Theory or Abstract Algebra would not be interesting to some learners. In our Education Education, there has been plenty of talk about asking the right type of questions when teaching class, WIN questions help to give us a path to some of these questions.

Strengths:
-Revealing the depth of even simple math problems.
-Self exploration of the subject.
-Interesting discussions could abound.
-Room for learning from "failure."

Weaknesses:
-A topic could be lost in the sea of questions.
-Student's/My mind could be blown/melted by ensuing puzzles.
-It is more difficult to ask WIN questions than it is to not.