When I first started my university teaching, I thought teaching was easy. As a math teacher, I had a book selected by departmental experts and written by an expert. The department provided me with a syllabus for frequently taught courses. I was expected to selected the book and developed my own syllabus for courses in my specialty area.

The content I presented was mainly an explanation of what was in the book, but included an orientation of how I understood the material and how I thought it would best fit the needs and current understanding of the students. Students who did well on tests and homework got good grades. Those who did less well got lower grades. Some students failed mainly through lack of effort or through having an inadequate preparation for the new material being presented.

Over time, two things happened. First, I began teaching courses that (from my point of view) did not have satisfactory books. I took care of that by writing my own books. This habit started me on a path of writing more than 50 books. About 25 of these are available free on the Web at http://iae-pedia.org/David_Moursund_Books.

Second, I began to understand that teaching and learning are very complex activities. It is not easy to be a good teacher and it is not easy to be a good student.

Thus, for me the Scholarship of Teaching and Learning (SoTL) began to seem chaotic. The more I learned, the less I felt like I knew. For more about SoTL see http://i-a-e.org/iae-blog/expanding-the-science-and-technology-learning-experiences-of-children.html,   http://i-a-e.org/iae-blog/the-math-brain-keith-devlins-chapter-in-the-book-mind-brain-and-education.html, and  http://darkwing.uoregon.edu/~moursund/Math/sotl.htm.

Now, in my retirement years, I look back over what I have done and I continue to do new things. From time to time an idea pops into my head that seems relevant to teaching and learning. Here is an example of an idea that occurred to me earlier today:

1. An academic discipline can seem chaotic. Each discipline is a huge, growing, and changing collection of data, information, knowledge, wisdom, and foresight. From a novice learner’s point of view, this collection is both overwhelming and chaotic.
2. Bringing order out of chaos. Many courses that are routinely taught attempt to bring order out of chaos. The order is usually provided by a “tried and true” book, lecture notes, syllabus, and assessments. The students gain basic knowledge and skills, and practice them on the types of somewhat traditional and widely used problems and questions provided by the book and instructor. Note that if the discipline is changing rapidly, the course content is apt to be somewhat out of date.
3. Creating more chaos.  Once a student begins to learn a discipline, the student’s learning focus can begin to move toward problem posing in that discipline and in interdisciplinary applications of that discipline. See http://iae-pedia.org/Math_Education.

In some sense, problem posing creates chaos out of order. We want students to creatively apply their growing knowledge and skills to new situations and to new ways of looking at old problems. We want them to challenge the traditional content and the ways of teaching and learning the content. We want them to think about interdisciplinary applications of what they are learning, and we want them to integrate their new knowledge with what they are learning in other courses and what they are learning on their own. As an example, think in terms of Computational Thinking and the general discipline of Information and Communication Technology. Both areas are applicable in every discipline, are changing rapidly, and are routine tools for students pursuing their own interests. For other examples, look at cognitive neuroscience and genomics.

To me, this is an interesting way to view education. I am especially interested in students who can recognize how chaotic a problem area is and who can pose problems and ask questions that help make clear that the accumulated knowledge in the discipline is chaotic. This requires insightful, creative, higher-order thinking. This thinking can draw on knowledge and skills in one discipline or in multiple disciplines. It leads to progress in solving the newly posed problems, answering the newly asked questions, and then integrating these new results into the broadly taught courses.

My conclusion is that at all levels, teaching needs to include a strong emphasis on students gaining increased skill in problem posing and question asking—and then working to solve the problems and answer the questions.

What You Can Do

 Put yourself in the mind of a listener or student who is attempting to learn from you. What does this person already know about your topic? What does the person want to learn, what do you want the person to learn, and how do these differ?

Is the person's knowledge and skills in your topic area confused, chaotic, and undisciplined? What specifically do you do to bring order out of this chaos?

Now, apply these same questions to yourself and to your own learning.

Suggested Readings from IAE and Other Publications

You can use Google to search all of the IAE publications. Click here to begin. Then click in the IAE Search box that is provided, insert your search terms, and click on the Search button.

Click here to search the entire collection of IAE Blog entries.

Here are some examples of publications that might interest you.

Breaking the “telling” parts of teaching into short pieces. See http://i-a-e.org/iae-blog/breaking-the-telling-parts-of-teaching-into-short-pieces.html.

High school graduation rates are only one measure of educational success. See http://i-a-e.org/iae-blog/high-school-graduation-rates-are-only-one-measure-of-educational-success.html.

Purposes of education. See http://i-a-e.org/iae-blog/purposes-of-education.html.

School reform. See http://i-a-e.org/iae-blog/school-reform.html.

The future of IBM's Watson computer system. See http://i-a-e.org/iae-blog/the-future-of-ibms-watson-computer-system.html.

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