Understanding. It's more than knowing the facts. It's more than being able to apply the Pythagorean theorem upon demand. Understanding is the ability to take the knowledge given and recognize it as a tool, not an answer. Educators are supposed to be supplying our students with the knowledge that the world is open for dissection. Teachers supply our students with recognition that the lessons we teach them will help them pick apart the world for themselves.
    If that is our goal, why are so many students coming out of high school and into college struggling with open ended questions? Why, when prompted by the teacher that there is no specific answer, do students wrack their brains for "the obviously correct answer" to the question? Why are they afraid to answer?
    It is because they have been trained with nonessential questions. It is because they have been introduced to new material in the wrong manner. Look at the 'Brainology' Approach of the September 11, 2013 Edweek article: "Growth Mindset Gaining Traction as School Improvement Strategy." (I have provided a link at the bottom of this post.) Students in the classroom often maintain one of two mindsets: fixed or growth. Students of a fixed mindset will believe their intelligence is ingrained in their DNA, that's it is fixed and incapable of significantly improving. But students of growth mindset will approach knowledge as something they can easily obtain with effort. These mindsets are introduced and entertained by how teachers question their students. When asked questions such as, "In what ways did the pilgrims mistreat the Native Americans?"--students are being trained to answer questions with facts found in their book. What is not being taught are deeper connections between the past and present. In the same sense, teachers introducing new material under the impression, "This is an easy question to begin our lesson," are leading students who struggle with the easy question to negatively view the lesson and, more importantly, their own intelligence. If something that is supposed to "be easy" leaves a student struggling for the answer, how are students supposed to be encouraged to challenge their knowledge and trust their understanding as a useful tool for harder questions.
    Let's go back to the pilgrims and Native Americans and try broadening the question: "How might one culture be affected by the introduction of a new and different culture?" Stop and think how the students might approach this question. They are still able to use the example of the pilgrims moving in on the Native Americans to develop their answers, but this question also allows them to argue their own opinions and dig deeper into the mixing of cultures, what changes might occur (good or bad), what biases might be made, and how differences can be overcome or reinforced. Such a question may have stemmed from the subject being taught, but it is essential in the basis that the students can make connections between what they are learning and how it applies personally in their own lives. That is understanding. Being able to take the information beyond "the right answer" and using it as a tool to answer "my life question."
   How teachers phrase the question or introduce new material can affect students' learning and should be monitored. Remember that "easy question" introducing the new lesson? By reintroducing that question as "This one might take a few tries" students who struggle are not as discouraged as those who struggled with the "easy question." Instead they are approaching the same question with a growth mindset: "I can figure this out if I try hard enough and learn from my mistakes."
    Teachers must keep in mind the importance of wording and application. Questions should be more than test material; they should encourage the students to strive for knowledge. Questions should reveal to students important skills and provide a deeper understanding in which students can take said skills, apply them effectively in situations outside of the classroom, and do so without explicit directions on how to solve problems.
http://www.edweek.org/ew/articles/2013/09/11/03mindset_ep.h33.html?tkn=OMMFBUpoZuQwY4qvMMvS1tu%2BEpDD9iqQZV0U&cmp=ENL-EU-NEWS1