Information Age Education Blog
The Changing Face of Math Education
I was recently corresponding with one of my long-time math education friends, and I decided to formulate a math education question that I thought would be fun to discuss. This IAE Blog entry is based on the question I asked my friend:
When you look back over your long career in math education, what changes have you seen in math education that you feel have been particularly successful (good) and particularly unsuccessful (not-good)? (Moursund, 2018b).
A similar question can be asked about each of the other subjects taught in our schools. This is a very challenging question that each discipline of study needs to address.
The question reminded me of when I was still regularly teaching preservice and inservice teachers before I retired. I liked to pose hard questions, provide time for small group discussion, and then listen to some of the answers my students came up with.
When I posed such a question to my students, I typically had not given much thought as to possible answers. Rather, I thought about possible answers as I listened to their small group discussions and the whole-class answers. While listening, I gained insight into what my students knew and were interested in, and I formulated my answers that I would use to summarize the students’ insights. This proved to be a useful teaching technique. (I still think of this as being somewhat sneaky.)
Changing Goals of Math Education
My first response to talking about possible changes in the goals of math education is to summarize what I believe are a good set of goals. Thus:
I think that the goals of math education are to help students understand and solve problems that are mathematical in nature, that are relevant to their current lives, and are likely to be relevant to their futures. I want my students to learn to use their minds and currently widely available tools to understand and solve such math-related problems (Moursund, 2018c; Moursund, 2018d).
That is a rather sophisticated answer. Suppose that I am a math teacher. First, what does it mean for a problem to be mathematical in nature? How much math does a student have to know to decide whether a problem is mathematical in nature? Perhaps math education should spend more time helping students to learn recognize such problems.
What can a person learn about the extent to which a problem is mathematical in nature without knowing about the math needed to solve the problem? Right now, we tend to assume that a good way to build this math understanding is to learn to solve the underlying math problems by hand. Hmm. What about a math problem that an inexpensive handheld calculator can solve? Today’s students do not learn to calculate square roots by hand. Moreover, I never did understand what learning to calculate square roots by hand had to do with understanding square roots. Even with my doctorate in mathematics, it took me quite a bit of effort to figure out why the “by hand” method I had memorized while in secondary school actually worked.
Second, what math is relevant to the current lives of my particular students? A little thinking about this question is likely to lead you to the conclusion that this varies widely with the students, even if they are all at the same grade level and/or if they have all had the prescribed prerequisite math instruction. This makes it quite difficult for me, the teacher, to design and implement math instruction for a group of students.
Third, what about the future of these students? What math will be relevant to their various needs in the future? It seems to me that these needs will be at least as varied as the current math-related aspects of their current lives. Moreover, how can I talk about their future needs when computer technology and artificial intelligence are making such rapid progress?
A Specific, Personal Example
I have very poor spatial sense. Indeed, I have sometimes found myself lost after wandering out of a hotel, walking around the block that contains the hotel, and trying to find my way back to the lobby. Embarrassing, to say the least. (Perhaps especially embarrassing since I am a mathematician.)
Now consider this same inability when I am trying to drive a car to some specified location. I am very poor at finding my way from one location to another. But wait! I now have a GPS in my Smartphone, and I use it to give me driving directions. The GPS solves a complex math problem for me. I am still amazed by GPS capabilities, although I have read enough to have a little bit of understanding about how it works.
My point is that I have a math-related problem of location that my brain and education do not effectively cope with. It takes little knowledge of math to understand the problem. A modest amount of practice in inputting addresses into my GPS and following the oral directions it provides can solve this problem for me. When I was a young student, the problem was not relevant to me. As an adult car driver, the problem is very relevant. A Smartphone equipped with GPS capabilities solves the problem for me. And, of course, computers can solve a very wide range of other math-related problems. How should this affect math education?
Each discipline of study can be defined by the nature of the problems and tasks it addresses, the tools it uses, and the education it takes to become proficient in recognizing, understanding, and solving the problems and accomplishing the tasks using the available tools. New tools are being developed as aids to solving the problems and accomplishing the tasks. New knowledge is being gained about the human brain and about the teaching/learning processes (Moursund, 2018a). Each student is unique, and their interests and needs at a particular age or grade level change over time. All of this combines to make “the education problem” very complex and constantly changing.
Our current educational systems were not designed to adequately address this problem. Personally, I see no simple solutions. My particular set of suggestions is based on placing much more emphasis on converting education-related research progress in computer capabilities (including artificial intelligence) into the routine, everyday education of all students in our schools. We must redesign our educational systems to function well in this rapidly changing environment. For years, Robert Branson has argued that our current educational systems are stuck in a rut, and will not significantly improve until we learn to make effective use of computers in education (Moursund, 01/16/2016).,
My particular current interest is in the full integration of Information and Communication Technology (ICT) throughout all grade levels and curriculum areas. ICT is a major change agent in curriculum content, instructional processes, and assessment. My newly revised and free book, The Fourth R (Second Edition), summarizes my current thoughts about some of the needed changes (Moursund, August, 2018).
What You Can Do
As I have said many times, each of us is both a lifelong teacher and a lifelong student. Examine your current ongoing education—what you are learning in your everyday life. Strive to keep up and to keep involved in our changing world. Support our schools as they work to adjust to the changes they must make in order to provide our students with a good education.
References and Resources
Moursund, D. (2018a). Brain science. IAE-pedia. Retrieved 8/8/2018 from http://iae-pedia.org/Brain_Science.
Moursund, D. (2018b) Improving math education. IAE-pedia. Retrieved 8/8/2018 from http://iae-pedia.org/Improving_Math_Education.
Moursund, D. (2018c). What is mathematics? IAE-pedia. Retrieved 8/8/2018 from http://iae-pedia.org/What_is_Mathematics.
Moursund, D.( 2018d). What the future is bringing us. IAE-pedia. Retrieved 8/8/2018 from http://iae-pedia.org/What_the_Future_is_Bringing_Us.
Moursund, D. (August, 2018). The Fourth R (Second Edition). Available online at http://iae-pedia.org/The_Fourth_R_(Second_Edition). Download the Microsoft Word file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/307-the-fourth-r-second-edition.html. . Download the PDF file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/308-the-fourth-r-second-edition-1.html.
Moursund, D. (10/16/2016). Robert Branson’s upper limit hypothesis. IAE Newsletter. Retrieved 8/8/2018 from http://i-a-e.org/newsletters/IAE-Newsletter-2016-195.html.
The core message of Dave Moursund’s blog post is that any individual or institution hoping to thrive in the future must think continuously and deeply about goals, resources, and methods and must always be open to change. The institution of K-12 education in the United States is not notable for its willingness to engage in thoughtful reflection on its objectives and practices or to implement fundamental change in longstanding traditions. In fact, persistent public criticisms of education most often end with loud calls to ‘get back to basics’ of some presumably idyllic past era. Nonetheless, there have been a number of slow but certain improvements in the practice of school mathematics curriculum and teaching over the past 50 years.
For example, research on early mathematics learning, such as the Cognitively Guided Instruction work led by Tom Carpenter, has almost certainly transformed standard practice in teaching of elementary arithmetic to a focus on meaningful development of arithmetic concepts and skills. At the middle and high school levels there has been slow but steady movement to more student-active classrooms, inclusion of substantial statistics/data analysis content, and increased attention to teaching mathematics through problem solving in realistic contexts. Though still clearly a work in progress, the prominent attention of NCTM and other groups to equity in school mathematics is an admirable theme in work of the field.
At the same time, the verdict is still out on effects of recent innovations like national common core curriculum standards and associated high stakes tests. It also seems fair to say that mathematics curricula and teaching in K-12 schools have only begun to reflect the astonishing resources of almost universally available technologies like graphing calculators, computer algebra systems, and dynamic geometry tools. The potential impact of those information and communication technologies is enormous. Much deep thought and experimental work is still ahead. But that’s what makes mathematics education such an exciting and challenging field!