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9 minutes reading time (1875 words)

Moursund’s 1987 Futuristic Visions of Math Education

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Thanks

Dave Moursund

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“Those who cannot remember the past are condemned to repeat it.” (George Santayana; Spanish citizen raised and educated in the United States, generally considered an American man of letters; 1863–1952.)

“What goes around comes around.” (Ancient adage.)

During the period 1986-1987, I was involved with the Mathematical Sciences Education Board and their work on national planning for the future of math education in the U.S. I recently “dug out” a key section from a book I wrote that included a discussion of this project. See Effective Inservice for Integrating Computer-as-Tool into the Curriculum (Moursund, 1989). The book includes my1987 forecasts and and is available online. An excerpt from the book is available in the IAE-pedia as Three 1987 Math Education Scenarios (Moursund, 1987, 2014).

We are currently in the throes of implementing the Common Core State Standards Math Education Initiative. Yet consider the fact that, more than 25 years ago, the math education leadership in this country was already seriously working on ways to improve our math education system. Indeed, our math education system was “recovering” from the New Math of the 1960s. During 1986-87 I happened to be at the right place and time to contribute my insights on what computers could (and, I hoped, would) bring to math education in the future.

You may be amused as you read this article to discover the “far out” thinking on this topic from 1987. As they sometimes say when playing poker, “Read ‘em and weep.” We have made some progress, but the very disappointingly slow rate of this progress brings tears to my eyes.

Mathematical Sciences Education Board

In the fall of 1985 the National Research Council created a Mathematical Sciences Education Board (MSEB). Its initial task was to make recommendations on precollege mathematics education for 10-15 years in the future. I was asked to submit a position paper discussing possible roles of computers in such a mathematics education system. Quoting from (Moursund, 1987, 2014):

The MSEB held a working session of 20 mathematics educators during August 10-14, 1987 at the Xerox Training Center in Leesburg, Virginia. The five-person working group I was in focused on possible roles of technology in mathematics education in the year 2000 and beyond. Other members of my working group were Richard Anderson (Louisiana), Gail Burrill (Wisconsin), Margaret Kasten (Ohio), and Robert Reys (Missouri). I used my modified position paper as the starting point for the writing I did during that session. After a number of major additions and revisions, it doubled in length and began to reflect quite a bit of the thinking of our group, as well as some of the ideas of the MSEB. Since that working session I have revised and expanded the paper quite a bit more.

Purpose of the 1987 Paper

In the remainder of this IAE Blog, I will refer to the docuent (Moursund, 1987, 2014) as the 1987 paper. The purpose of the 1987 paper was to provide a suggested framework for planning major curriculum content and pedagogy changes designed to improve our mathematics education system.

Here are five major factors presented and discussed in 1987 that suggested changes were necessary and improvements were possible in our mathematics education system. They are presented here as written in 1987. As you read this list, ponder on what has changed during the past 27 years. To me, some of these “old” statements still seem quite fresh and relevant.

Quoted from the 1987 Paper

1.   The nature of the intended audience of our mathematics education system has changed quite a bit in the past couple of decades. For example, kids in high school now have spent about as much time watching TV as time in school. They have spent their entire lives in the Information Age, while our school system was designed to fit the needs of an Industrial Age society. (According to John Naisbitt, the Information Age officially began in the US in 1956.) This analysis suggests that mathematics education might be improved by moving it more towards the needs of people living in an Information Age society.

One key component of the Information Age is rapidly increasing access to more and more information. A common estimate is that the total accumulated knowledge in mathematics is doubling every ten years. This suggests that information retrieval skills are of increasing value and that math-oriented information retrieval be given increased emphasis in the curriculum.

2.  Over the past couple of decades there has been substantial progress in our understanding of teaching theory, learning theory, and cognitive science. Our educational system tends to be slow in translating such theory and research results into practice. While progress is occurring, much remains to be done. Research is continuing at a rapid pace.

Research into cooperative learning and cooperative problem solving strongly supports their potential in education. This suggests that cooperative learning and cooperative problem solving should be given increased emphasis in the mathematics curriculum.

3.  Calculators and computers can be used to help students learn mathematics topics. (One of the topics might be to learn to use a calculator or computer to help solve math problems.) The research literature on computer-assisted learning (CAL) is extensive and quite supportive of increased use of CAL. While much of the research in the use of CAL in mathematics focuses on basic skills, the body of literature on uses to improve higher-order skills is growing. There is quite a bit of software designed to enhance higher-order skills.

CAL can make available instruction in individual topics or entire courses that might not otherwise be available to students. It can incorporate pedagogy (for example, sophisticated simulations and motion graphics) that is not readily duplicated without the use of a computer.

4.  Computers can be a substantial aid to classroom management and to testing, especially as one works to meet the diverse needs of individual students. Computers can help increase the amount of individualization of instruction in our math classrooms.

 Computers also can be an aid to teachers in whole-class presentations and activities. Most math teachers already know how to use an overhead projector. There are now relatively inexpensive devices (about $1,000) that allow the output from a computer to be projected using an overhead projector. Many math teachers will eventually find such a system to be quite valuable in their teaching. The cost of these devices will likely decrease substantially in the next few years.

5.   Calculators, computers, and other related technology have become more and more available as aids to productivity and problem solving in our society. Our current mathematics curriculum largely ignores possible impacts of computer-related technology on content. Perhaps the classical examples are the use of quite inexpensive calculators to do arithmetic calculations and the use of computers (or, more sophisticated calculators) to graph data and functions. Widespread implementation of even just these two types of aids to problem solving would have a significant impact on the mathematics curriculum.

Remember, the above five statements were written in 1987!

Two Additional Tidbits from the 1987 Document

Goals in Math Education

The 1987 document lists and discusses nine goal areas for math education.

1.   Reasoning.

2.   Mental mathematics.

3.   Valuing.

4.   Problem solving.

5.   Communication.

6.   Study and learning skills.

7.   Technology.

8.   Producing mathematics leaders.

9.    Teachers’ role.

This list has served me well over the years. Think about what you would add to the list in light of changes in the world and in education during the past 27 years. For example, there is no mention of Brain Science (cognitive neuroscience) in the list (Moursund, 2014). The Web did not exist at that time. Tim Berne-Lee published a proposal for the development of the Web on March 12, 1989. Although Howard Gardner's first book on Multiple Intelligences was published in 1983, the topic of Multiple Intelligences was not mentioned in my 1987 document.

Mathematics Education Computer System (MECS)

Quoting from my1987 document:

People doing long-range planning for mathematics education should not dwell unduly on inadequacies of current computer capabilities and student access to these systems. Rather, they should assume that eventually every student will have easy access to a very powerful computer system. The time frame necessary for making significant changes in our mathematics education system is sufficiently long so that during the same time frame computers will become readily available to all students (and others, such as workers and people in their homes) who have need to use them.

People doing very long-range planning (10 -15 years) for computers in mathematics education might want to assume that something like today's Macintosh 2, IBM PS/2 Model 70, or NeXT computers will be readily available to students. Let's call this a Mathematics Education Computer System (MECS). The needed software and courseware for MECS has four main components. While much of this software and courseware already exists in discrete components, it has not been drawn together in a unified manner. Thus, we should assume that the software and courseware facilities available for the MECS will continue to improve rapidly with time.

The NeXT computer initially became available in 1988. It was a very fast microcomputer at that time. Current microcomputers are several hundred times as fast and much less expensive.

The 1987 document then lists four components of the (hypothetical) MECS. These are much like I describe in my recent IAE Blog entry, Grand Challenges in Math Education (Moursund, 6/16/2014).

What You Can Do

Read Grand Challenges in Math Education mentioned above. It may give you fresh insights into how slowly our math education system has been changing in its attempts to deal with the very rapid changes in Information and Communication Technology (ICT).

Think about the future potentials of ICT, not only in math education but in all of education. Select a specific piece of this future that seems particularly important to you and (quoting Captain Jean-Luc Picard in Star Trek) work to “Make it so.”

References

Moursund, D. (6/16/2014). Grand Challenges in math education. IAE Blog. Retrieved 4/21/2014 from http://i-a-e.org/iae-blog/entry/grand-challenges-in-math-education.html.

Moursund, D. (2014). Brain science. IAE-pedia. Retrieved 6/21/2014 from http://iae-pedia.org/Brain_Science.

Moursund, D. (1989). Effective inservice for integrating computer-as-tool into the curriculum. Eugene, OR: Information Age Education. Available free in PDF from http://i-a-e.org/downloads/doc_download/25-effective-inservice-for-integrating-computer-as-tool-into-the-curriculum.html. Available free in Microsoft Word from http://i-a-e.org/downloads/doc_checkout/26-effective-inservice-for-integrating-computer-as-tool-into-the-curriculum.html.

Moursund, D. (1987, 2014). Three 1987 math education scenarios. IAE-pedia. Retrieved 6/21/2014 from http://iae-pedia.org/Three_1987_Math_Education_Scenarios.

IAE Resources

Moursund, D. (2014). Improving math education. IAE-pedia. Retrieved 6/21/2014 from http://iae-pedia.org/Improving_Math_Education.

Moursund, D. (2014). Substantially improving education. IAE-pedia. Retrieved 6/21/2014 from http://iae-pedia.org/Substantially_Improving_Education.

Moursund, D. (2013). Communicating in the language of mathematics. IAE-pedia. Retrieved 6/21/2014 from http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics.

Moursund, D. (2013). Good math lesson plans. IAE-pedia. Retrieved 6/21/2014 from http://iae-pedia.org/Good_Math_Lesson_Plans.

Moursund, D. (2013). Math maturity. IAE-pedia. Retrieved 6/21/2014 from http://iae-pedia.org/Math_Maturity.

Moursund, D. (2010-2014). What the future is bringing us. IAE-pedia. Retrieved 6//21/2014 from http://iae-pedia.org/What_the_Future_is_Bringing_Us.

Moursund, D. (2009). Computational thinking. IAE-pedia. Retrieved 6/27/2014 from http://iae-pedia.org/Computational_Thinking.

Moursund, D. (2008-2013). Two brains ae better than one. IAE-pedia. Retrieved 6/21/2014 fro. http://iae-pedia.org/Two_Brains_Are_Better_Than_One.

 

Improving Math Education
Grand Challenges in Math Education
 

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