One tool to help further thinking through questioning is Wiederhold's Question Matrix. This matrix can help channel questions from more closed to open. If you look at the red quadrant above you will notice that the questions are more factual. The yellow and green quadrants may overlap between factual and debatable. The blue quadrant is more solidly conceptual in the types of questions produced. These four quadrants were originally proposed by Wiederhold, and I would say he was off to a good start. However, in discussing this matrix with a few other MYP educators (Thanks Kim and Ashish!), we realized that there was no real debatable starters.
I would propose that we add an extra level on the vertical axis to enrich each of the columns. By introducing 'should' we give questions the option for value judgement, which allows exploration of more than one side of an issue.
Overall, we might consider factual questions to be questions with a single, or narrow range, of right answers, such as "what is an atom?". There are more than one atomic models, but the answers are all within a narrow range. Conceptual questions on the other hand have multiple possible answers, each being equally possible. A question of this sort might be "how has our understanding of the atom changed the world?". There are many ways the atom has changed the world, from nanotechnology and material sciences to nuclear reactions and energy. Each may be explored in depth and all have equal footing. To shift to a debatable question requires the addition of a value judgement. So our question about atoms might become "what is the most important change that has arisen from our understanding of the atom?", or if we use the chart above to form the question we might ask "who should decide how we use our knowledge of atomic energy?". These additions of a value statement shift from multiple correct answers, and requires the inquirer to make a decision and justify it. This relates closely with the DP's Theory of Knowledge course's knowledge claims. Personally, I like to tell my students to "get off the fence" and make a choice.
Hopefully this might help you shape inquiry questions for your own classes. Or, even better, use it with your students to start off your inquiry and refine it along the way.