Information Age Education Blog
In Math Education and Other Disciplines: Asking the “Right” Researchable Questions
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.
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.
So, here is a third goal.
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.
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 factis indeed incorrect, or rather it is an assertion that may very well be incorrect. My first thoughts to myself were quite defensive:
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.
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.
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.
Moursund, D. (11/22/2011).That’s a Researchable Question. IAE Blog. Retrieved 8/16/2014 from http://i-a-e.org/component/easyblog/entry/that-s-a-researchable-question.html?Itemid=58.
Written by davem, October 22, 2012 .
I think the most important idea covered in this IAE Blog entry is helping students learn to pose good questions and then answer their own questions. With good education and growing mental maturity, students should make steady progress in this endeavor. The skills they develop will serve them throughout their lives.
Here is a quote that I enjoyed:
"By framing one’s work around priority questions, we make it far more likely that learning remains focused, coherent, and less stressful when the unexpected happens.”
—Grant Wiggins and Jay McTighe