What kind of skills do children develop when adults ask them questions like "What if" or "How could we solve this..."?
I wholeheartedly concur with all of the comments of the previous posts and would add that these kinds of questions lead to the next level of questioning. When we ask "What if...?" the child responds. Then we get to push them to the next step and ask a few more questions, or even better, teach the students to ask themselves those questions. The students start to apply a reasoning process to their thoughts. They could then formulate more cause/effect relationships and/or consider how to test their theories, or elaborate their proof of their positions.
Critical thinking skills are crucial to developing the abilities needed to solve problems in the future. If children learn to be inventive at a young age, and learn how to do things for themselves, they will learn how to solve problems. There are many problems we as a society have yet to solve. Our schools are focusing more and more on rote skills. Until we regain our prowess in ingenuity, these problems will have no solutions.
Just to back up #7, Bloom's Taxonomy is a very important teaching tool for all educators as it presents us with six different analytical stages ranging from simple recall to complex analysis and justification of arguments and facts. Questioning techniques can greatly help children and adults develop their critical thinking skills, making them more at ease in displaying some of the higher levels of Bloom's Taxonomy.
To be more specific than critical thinking or problem solving, which are kind of catch all terms, we could also say comprehension skills, analytical skills and synthesis skills are also developed when questions such as these are used. (Depending on how they are worded) Bloom's Taxonomy details the use of language and skill level in different forms of education questioning.
I would agree with most of the previous posts that not defining the question really clearly helps kids themselves come up with the right question or just a question they think is important. "Being less helpful" is what some folks have begun to call this, but if you define everything and kids just plug in certain numbers to get the answer, students do not have the opportunity to really develop all the skills that people have mentioned here.
Critical thinking and reasoning! "What if...?" encourages children to think hypothetically and abstractly instead of always looking for the direct answer. Acknowledging possibilities is an important skill for later in life, because you need to be able to predict possble outcomes before embarking on any decision. "What if..." also aids with planning skills.
I think posing these questions also builds creativity, which seems to be lacking as much as critical thinking now days. Thankfully, I get to see this process of critical thinking and creativity quite often with my toddler, but not too much interaction at the secondary level when asking these questions. Not only are these types of questions great for occupying little minds (and big ones), but they can come up with some pretty good ideas. These questions provide an avenue for students to think outside the box without the threat of being wrong, most of the time. Unfortunately, it is difficult to access responses to these questions, and we do not typically spend much time engaging our students at this level. Of course, some subjects better lend themselves to this type of discussion. In math, the "what if's" and the "How's" tend to create confusion for the struggling student.
Asking these types of questions helps children develop abstract thinking skills. Again, as pohnpei said, it is critical thinking. Instead of just recalling information they have to take the information they have and apply it to a new situation. This is very important in young children because the jump from concrete to abstract thinking is a big one that will only develop fully if cultivated. Even if children are still too young and can only think literally, asking these questions starts the building blocks of this kind of abstract thinking, which develops in stages.
I would say that the skills that children develop when asked questions like these are critical thinking skills. When children are asked a question like this, they have to think about the subject rather than simply coming up with information.
If you look at this on Bloom's taxonomy, I would say that these questions could be used to elicit thinking on the levels of analysis and synthesis. These kinds of questions ask kids to look at an issue, break it down into its parts, and (perhaps) put the parts back together in new ways. These questions are not likely to reach the evaluation level of the taxonomy.
Children learn to ask questions, think for themselves, explain processes, and to justify their answers. All of these skills are HOTS- Higher Order Thinking Skills. So many children today are exposed to the majority of their education being in the form of memorizing facts, vocabulary, skills, etc... We need to teach children how to think for themselves. I don't want my students to just learn what I'm teaching. I want them to be able to perform it and explain it to someone else. This also helps instill more confidence in them as learners and leaders.