Problem Solving: Posing and Answering Questions





Introduction
Problem solving is a fundamental component of every academic discipline. There are many different types of problem-solving situations. The following is not intended to be all inclusive, but serves to indicate the breadth of what I include:


 * Question situations: recognizing, posing, clarifying, and answering questions.
 * Problem situations: recognizing, posing, clarifying, and then solving problems.
 * Task situations: recognizing, posing, clarifying, and accomplishing tasks.
 * Decision situations: recognizing, posing, clarifying, and making good decisions.
 * All situations: using higher-order critical, creative, wise, and foresightful thinking to do all of the above. Often the results are shared, demonstrated, or used as a product, performance, or presentation.

Here is a definition of problem that I have found useful in my teaching and writing:

You (personally) have a problem if the following four conditions are satisfied:


 * 1) You have a clearly defined given initial situation.
 * 2) You have a clearly defined goal (a desired end situation). Some writers talk about having multiple goals in a problem. However, such a multiple goal situation can be broken down into a number of single-goal problems.
 * 3) You have a clearly defined set of resources that may be applicable in helping you move from the given initial situation to the desired goal situation. These typically include some of your time, knowledge, and skills. Resources might include money, the Web, and the telecommunication system. There may be specified limitations on resources, such as rules, regulations, guidelines, and time-lines for what you are allowed to do in attempting to solve a particular problem.
 * 4) You have some ownership—you are committed to using some of your own resources, such as your knowledge, skills, time, and energy, to achieve the desired final goal.

In many problem-solving situations, Information and Communication Technology and computerized tools are resources of the type mentioned in the third part of the definition. These resources have grown more powerful over the years. That is one reason why it is so important to integrate the use of computers in problem solving across the curriculum.

The fourth part of the definition of a problem is particularly important. Unless you have ownership—through an appropriate combination of intrinsic and extrinsic motivation—you (personally) do not have a problem.

This document focuses mainly on the educational topic of asking questions and seeking answers to question asked by yourself and others.

Some Relevant Quotes
Here are some quotes that give important insights into question asking:


 * "He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever." (Confucius; Chinese thinker and social philosopher, whose teachings and philosophy have deeply influenced Chinese, Korean, Japanese, Taiwanese and Vietnamese thought and life; 551 BC–479 BC.)


 * “If I had an hour to solve a problem and my life depended on the solution, I would spend the first 55 minutes determining the proper question to ask, for once I know the proper question, I could solve the problem in less than five minutes.” (Albert Einstein; German-born theoretical physicist and 1921 Nobel Prize winner; 1879–1955.)


 * "Once you have learned how to ask relevant and appropriate questions, you have learned how to learn and no one can keep you from learning whatever you want or need to know." (Neil Postman and Charles Weingartner. Teaching as a Subversive Activity.)


 * “The 'silly question' is the first intimation of some totally new development."(Alfred North Whitehead; English mathematician and philosopher; 1861–1947.)

That's A Researchable Question
The following is quoted from the article:


 * Moursund, D. (11/22/2011). That's a Researchable Question. Retrieved 10/24/2012 from http://i-a-e.org/component/content/article/55-improving-education/245.html.


 * A great many years ago I served on an Advisory Panel that helped the Educational Testing Service in its efforts to develop a Computer Literacy Assessment Instrument.


 * Educational Testing Service (ETS), founded in 1947, is the world's largest private nonprofit educational testing and assessment organization. It is presently headquartered near Princeton, New Jersey. (Wikipedia)


 * My three deep remembrances of this activity are:


 * 1. I was amazed (indeed, somewhat overwhelmed) by the breadth and depth of the knowledge and skills of the panel members. It was a pleasure to rub shoulders with such well-qualified computer educators.
 * 2. By that time in history, a number of people had written about possible meanings of Computer Literacy. See the Web page Computer Literacy in 1972 at http://iae-pedia.org/Computer_Literacy_in_1972. The term “Computer Literacy” has been with us since 1972. Art Luehrmann, the author of a seminal 1972 article about computer literacy, "Should the computer teach the student, or vice-versa?" He was one of the panel members, and a link to his original paper is included in the Website mentioned above.
 * 3. A woman from ETS served as our leader. (I apologize for not remembering her name.) From her I learned the this statement over and over again as we struggled with our quite difficult task and asked questions of each other.


 * Computer literacy has had its ups and downs during the past 39 years. Also, a variety of definitions have been proposed. From my point of view, whatever its definition, most students then and now have a relatively low level of computer literacy.


 * Researchable Question


 * “That’s a researchable question” is as important a statement now as it was long before the development of electronic digital computers. What has changed is our tools that help us to find answers to researchable questions.


 * One way to try to find an answer to a researchable question is to search the literature.  Computers are now a routine tool in this endeavor. In my opinion, all students should be gaining a high level of skill and experience in doing literature searches for possible answers to researchable questions.


 * A second approach is to communicate with people who might know an answer or where to find an answer. The Internet is now a routine aid to such communication. Students need to become skilled in finding answers from humans.
 * A third area of understanding and skill I believe students should be learning is roles of computer technology in actually carrying out empirical (as distinguished from library-based) research. Quoting from the Wikipedia:


 * Empirical research is a way of gaining knowledge by means of direct and indirect observation or experience. Empirical evidence (the record of one's direct observations or experiences) can be analyzed quantitatively or qualitatively. Through quantifying the evidence or making sense of it in qualitative form, a researcher can answer empirical questions, which should be clearly defined and answerable with the evidence collected (usually called data). Research design varies by field and by the question being investigated. Many researchers combine qualitative and quantitative forms of analysis to better answer questions which cannot be studied in laboratory settings, particularly in the social sciences and in education.


 * Computer technology and computerized instrumentation are routine tools of empirical researchers. Their use in the sciences has become so common place that Computer Modeling is now a routine aid to research in these disciplines. See http://iae-pedia.org/Computational_Thinking.


 * A key aspect of understanding modern research is to understand capabilities and limitations of computers as an aid in all three of the methodologies mentioned above.


 * What is a Researchable Question?


 * “What is a researchable question?” Surely students should be exploring this question in each of the disciplines they study in school. In a specific discipline, what did we know in the past and what do we know now? What are very difficult and quite challenging questions that we have a chance of answering in the near and long term future?


 * Finally, what are examples of questions that are not researchable? How can one tell a researchable from a non-researchable question? What do we want students to learn about dealing with questions that are well beyond current research capabilities an/or that may never be answered by empirical research? I find it interesting to listen to discussions of this topic among top notch science researchers and religious scholars and leaders.


 * What You Can Do


 * Begin to experiment with the topic, "That's a researchable question" in your teaching. In whatever you teach, help your students learn to ask and try to answer researchable questions. One approach is to pose questions to your students, and help them to explore whether the questions are researchable within their current level of knowledge and understanding.

Asking the "Right" Researchable Questions
This section is based on the article:


 * Moursund, D. (10/22/2012). In Math Education and Other Disciplines: Asking the “Right” Researchable Questions. Retrieved 10/24/2012 from http://i-a-e.org/iae-blog/in-math-education-and-other-disciplines-asking-the-right-researchable-questions.html. Quoting this IAE Blog entry:


 * My IAE Blog entry, That’s a Researchable Question, emphasizes the value of students learning to pose—and then trying to answer—researchable questions (Moursund, 11/22/2011). I find it quite easy to ask a question that I would like to have answered, but that my brain cannot immediately answer. I often go to my computer and access the Web to help me answer the question.


 * If you have helped to raise young children, you have encountered a never-ending stream of child-posed questions. Young children seek answers to whatever questions occur to them. They may ask the same question or nearly the same question repeatedly. Their knowledge base is small, but is growing rapidly. This question asking and answering process helps to build their knowledge base.


 * Informal and formal education, coupled with a child’s growing brainpower, allows children to answer an increasing number of their own questions. In addition, children gradually learn that being asked too many questions annoys adults. Unfortunately, the teaching methodologies of many teachers help to discourage students from asking questions.


 * Goals of Education


 * There are many goals of education. My brief summary of these goals is:


 * 1. We want students to learn a large number of “facts” and basic skills such as reading, writing, and arithmetic.


 * 2. We want students to learn to represent and solve problems. We want them to use logical thinking and problem-solving processes, their memorized facts, their learned skills, their growing experience base, information that they can retrieve from outside their own brains as needed, and new skills that they can learn as needed.


 * 3. As students gain increased mental maturity and education, we want them to learn to pose questions on topics that interest them, and we want them to learn to understand and deal with problems posed by others. We want them to learn to make reasonably good distinctions among questions that:


 * a. Are quite possibly answerable using their personal and growing research capabilities, knowledge, and skills.
 * b. Are likely beyond their current research capabilities, knowledge, and skills, but may well be within their future capabilities.
 * c. Are likely to be at the frontiers of or beyond the frontiers of current human research.
 * d. Are not researchable questions.


 * Think about the first of these two goals. If many of the so-called facts that a student learns are incorrect, this leads to serious difficulties in achieving the second goal. Reasoning from incorrect and perhaps contradictory information is not a very useful approach to solving problems and accomplishing tasks. This type of analysis supports the third goal.


 * What Questions Are Researchable But Still Are Not Worth Researching?


 * In my everyday life, I read about research projects that other people and groups are undertaking, the questions they are trying to answer, and the progress they are making. Occasionally I encounter a research question that I feel is misguided. It may be researchable, but probably is not worth researching.


 * Recently I received a very interesting question that may well fit this description. Many of us have read about the “fact” that a number of countries are surpassing the U.S. in math education. The question I received questioned this fact and provided several arguments that perhaps the fact is indeed incorrect, or rather it is an assertion that may very well be incorrect. My first thoughts to myself were quite defensive. I thought to myself:


 * "I don't really know that other countries are more successful in math education than is the U.S. We all read the same literature/arguments that the U.S. is not doing as well as some other countries, and some of the papers are written by people whose work and insights I respect. It seems to be somewhat insulting to question these authorities."


 * Then I thought some more. What next occurred to me was that maybe people are asking and exploring a question that is not particularly useful. Maybe they are asking the wrong question.


 * This led me to posing several other questions that are related to the original question, but are much more interesting to me.


 * 1. What evidence do we have that the math education results achieved by students in the U.S are inadequate to our students’ needs and to the needs of our country? (I enjoy reading, and usually agreeing with, articles suggesting that algebra for all—along with still more algebra for all—is not the right way to be going. This quite specific component of our math curriculum is important for many students, but is a major mistake for many others.


 * 2. Do we know cost effective, student time effective, and readily replicable ways to improve math education? As an aside, I love math—but there are many other disciplines that also are very important. Are we perhaps going overboard in our emphasis on math? I firmly believe that we are making a major educational error by taking time away from some so-called less important areas such as music and the fine and performing arts in order to devote more time to the areas being assessed on national and/or international tests. What if the subject areas being assessed internationally were music and the fine and performing arts? Would we decide that our educational system should be changed in these areas in order for us to out-perform other countries?


 * 3. Do our goals in math education appropriately and adequately reflect the steadily improving computer aids to representing and solving math problems, both directly within the math discipline/curriculum area and in applications of math in the other disciplines/curriculum areas? The same question can be asked about our rapid progress in cognitive neuroscience.


 * I could pose other questions. What I am suggesting is that we probably are asking the wrong question—or stating the wrong problem on which to focus our attention—when we place such an emphasis on how well U.S. students are doing in international comparisons of performance on math tests.


 * Final Remarks


 * The popular media—as well as a huge number of people who communicate face-to-face, via social media, via blogs, and so on—raise innumerable questions. It is easy to accept these questions at face value and to be troubled by the facts that their writers state as answers. In many cases the facts that support the importance of their questions and their opinions of “correct” answers to the questions may be skewed by any number of factors.


 * In this IAE Blog entry I picked a frequently asked question, one with answers usually based on asserted facts. I suggest that I don’t really know the facts for sure. But, more importantly, I suggest that perhaps I don’t really care about the question or the facts used to answer it. My concern is whether or not the question is important to the improvement of our own educational system here in the U.S.


 * What You Can Do


 * Pick some aspect of education that really concerns you. Pick a standard question or frequently repeated assertion about this aspect of our educational system. Then pose one or more new questions that you believe may be more relevant and productive.


 * For example, you might pick the assertion that our colleges of education are doing a poor job of preparing teachers or that alternate paths to teacher certification might be better. Each is a broad, sweeping assertion. Could you develop a researchable question to investigate either of these assertions?


 * More importantly, would your question be worth researching? Think of other somewhat related productive and useful researchable questions you would like to have answered. For example, your thinking might lead to questions about the quality of the mentoring system for new teachers or the ongoing staff development for teachers.

Final Remarks to This IAE-pedia Entry
Informal education, formal education, and lots of practice helps build skill in asking "relevant" question of oneself and others, and seeking answers to these questions. The strategies for question asking and answering vary from discipline to discipline. Thus, a person who is highly skilled in asking and answering math questions (that is, solving math problems) may not be so skilled at asking and answering art or music questions, and vice versa.

Question asking and question answering lend themselves to small group and paired learning in classroom setting. In a paired learning setting, each member of a pair gets to pose and answer questions. Each person learns about his or her partner's insights into posing and answering questions. Each gets a chance to help analyze the relevance and/or importance of the questions being asked. In a paired or small group setting that includes a networked computer or other device that accesses the Web, all can participate in formulating search strategies and interpreting the results the computer produces.

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.

Computer Technology Is Only One of Many Technologies. See http://i-a-e.org/iae-blog/computer-technology-is-only-one-of-many-technologies.html.

Deep Insights into Problems with Our Educational System. See http://i-a-e.org/iae-blog/deep-insights-into-problems-with-our-educational-system.html.

National Academic Standards Versus Inequities in Funding Schools. See http://i-a-e.org/iae-blog/national-academic-standards-versus-inequities-in-funding-schools.html.

Personalizing Educational Content and Delivery. See http://i-a-e.org/iae-blog/personalizing-educational-content-and-delivery.html.

Requiring Online Education in Virginia. See http://i-a-e.org/iae-blog/requiring-online-education-in-virginia.html.

Some Grand Global Challenges. See http://i-a-e.org/iae-blog/some-grand-global-challenges.html.

Author or Authors
The original version of this entry was written by David Moursund.