Information Age Education
   Issue Number 218
September 30, 2017   

This free Information Age Education Newsletter is edited by Dave Moursund and produced by Ken Loge. The newsletter is one component of the Information Age Education (IAE) publications.

All back issues of the newsletter and subscription information are available online. In addition, six free books based on the newsletters are available: Joy of Learning; Validity and Credibility of Information; Education for Students’ Futures; Understanding and Mastering Complexity; Consciousness and Morality: Recent Research Developments; Creating an Appropriate 21st Century Education; and Common Core State Standards for Education in America.

Improving Math and Other Education

David Moursund
Professor Emeritus, College of Education
University of Oregon

The Math Learning Center is a non-profit corporation that grew out of a project funded by the National Science Foundation and carried out in Oregon during 1971-1976 (MLC, 2017a). I have served on its Board of Directors since the MLC began in 1977. The MLC stresses problem solving, use of math manipulatives, and mathematical thinking in its K-5 curriculum, workshops, and supportive materials. During my 40 years on the Board, I have emphasized use of computers (including calculators and computerized math manipulatives) as an aid to learning, doing, and using math.

Full disclosure. I funded the MLC’s initial development of a few computerized math manipulatives. The collection has grown considerably and has had wwell over 2 million downloads. See the complete 10-item collection that the MLC makes available free online at (MLC, 2017b).

Shortly before the MLC Board meeting on 9/16/2017, I prepared and distributed the document given in the next section of this IAE Newsletter. I have slightly edited and added references to the version distributed to the Board. The following sections then summarize some of the key ideas presented that came up in the hour-length discussion of my document.
 
My Challenge to the MLC Board


The Board has given considerable thought to the issues of the future of the MLC and of math education. I would like us to spend some time on Saturday getting input from each of us on these three questions:
  1. If precollege math education in the US and other parts of the world where the MLC has some interest and influence continues on its current path, what will math education look like in 10 to 20 or so years?
  2. What is your personal opinion of what math education should look like 10 to 20 or so years from now? (I wonder if we have some consensus on this. Are we working together to move the MLC is a direction that we generally agree on?)
  3. Assuming we have a reasonable level of agreement about where we think math education should be headed—and that it is significantly different from what we believe will happen (from Q1)—what can the MLC do to move math education in the direction(s) we collectively believe would be better?
Of course, we do not have enough time at Saturday’s (9/16/2017) meeting to delve deeply into our individual and collective opinions. However, perhaps each of us could give a short and pithy answer that will provide us with a starting point for a more protracted discussion. As an example, here is my short response.


 
My Answers to the Questions

Any non-profit company Board of Directors can formulate and discuss a similar set of questions to fit their own particular situation. These same types of questions are applicable to all curriculum areas currently taught in our schools.

For me, problem solving and mathematical thinking are at the core of good math education. I want students to have to made significant progress in learning to effectively deal with the types of math-related problems they are encountering and are apt to encounter in their lives—both in school and outside of school. To me, this includes having a personal level of math knowledge/skill to be able to communicate with self and others about math-related problems and tasks, and to gain some proficiency in learning math. I guess I would call this being life ready as well as informal and formal education ready. Another way of stating this is in terms of achieving a level of math maturity that meets an appropriate balance between meeting one’s own needs and meeting the needs specified by the “powers that be” (Moursund, 2016).

Now, my three answers:
  1. I strongly believe that our current math education system is moving far too slowly in helping students to make effective use of Information and Communications Technology (ICT) aids to both learning and doing math. The worldwide pace of research and development in improvement of computerized aids to learning and doing math is far out-pacing our math education pace of change in incorporating such research and development into our PreK-12 education system. It seems quite likely to me that we will continue to steadily fall further and further behind over the next couple of decades.

  2. The computer field has adopted the ideas and vocabulary of computational thinking. I believe that math education should adopt and fully integrate the ideas of computational thinking as they apply to learning and using math. Quoting Jeannette Wing (10/28/2008):
Computational thinking is taking an approach to solving problems, designing systems and understanding human behavior that draws on concepts fundamental to computing.

Computational thinking is a kind of analytical thinking. It shares with mathematical thinking in the general ways in which we might approach solving a problem. It shares with engineering thinking in the general ways in which we might approach designing and evaluating a large, complex system that operates within the constraints of the real world. It shares with scientific thinking in the general ways in which we might approach understanding computability, intelligence, the mind and human behavior.
  1. There is both substantial and ongoing research on the effectiveness of human brains and computer brains working together to solve problems and accomplish tasks. In a steadily increasing number of examples, the two together outperform either alone. I strongly believe that this dual-brain approach is highly desirable both teaching, learning, and doing/using math. My opinion is that the MLC should move much more strongly in this direction.
Summary of Key Ideas from the Board Discussion

The Board agreed that the activity I had proposed was quite relevant and the members willingly participated in a protracted and heartfelt discussion. Here are some of key ideas that came up in the discussion.
  • The MLC’s K-5 curriculum meets the standards set by the Common Core State Mathematics Initiative (Common Core, n.d.). That is essential to being able to successfully market our materials to today’s schools in the United States. The Board is proud of this achievement.

  • Mathematics is a very important, useful, and beautiful human endeavor. We are all born with some innate capabilities to learn, use, and appreciate this human endeavor. It is inexcusable that our math education system makes so many students feel mathematically inept. Indications of our failures are things like students making statements such as: “I hate math” and “I just can’t do math.”

  • The group as a whole agreed that our current math education system is seriously flawed and the steps currently being taken to improve this situation will not produce the needed improvement in a timely fashion. One of the flaws is that we are in a rut. Our precollege math education system is what it is. Perspective teachers graduating from this system enter teacher education programs in college, and end up becoming teachers who are good at replicating the current system. The new ideas they have been exposed to in their teacher education program of study are lost as they struggle to survive and gain tenure in the current (old) system that is so highly resistant to change. “Teaching to the Test” continues to dominate.

  • There was general acknowledgement that computers are in no sense “the” answer, but that they are an indispensable part of good answers. Used poorly, they have the potential to decrease the overall quality of our math education system. Good use of computer technology is occurring in some schools and school districts. Pockets of excellence are emerging. Unfortunately, poor uses are becoming well-entrenched in many schools and school districts. Examples include still more emphasis on rote memory, “drill and kill,” and computerized versions of traditional paper-and-pencil worksheets. MLC Board members believe that using computers to still better implement a considerably flawed math education system is a great folly.

  • Humans have developed an oral and written language of mathematics that facilitates precise communication within the discipline. Learning to communicate in this language is part of learning math. But, math is more than this. It is a discipline requiring and using logical thinking and proof. A major goal in math education is to help students to understand and develop skills in mathematical thinking, logical reasoning, and evidence-based arguments and proofs in their everyday lives (Moursund & Sylwester, 10/3/2015).

  • Good teachers know and love the students they teach as well as the discipline areas and content they teach. Good math teachers understand the challenges students face as they encounter both the depth and breadth of the discipline of mathematics. Those of us who strongly support the use of ICT as an aid to learning math need to think carefully about current serious limitations of computer systems in terms of computer-assisted instruction systems’ understanding of children, what it means to be a human being, and the challenges students face as they work to learn mathematics.

  • At all levels of PreK-12 math teaching, there are some teachers who know a lot of math, are good at helping children to learn math, and who are good at helping their fellow teachers improve both their math content and their math teaching knowledge and skills. While it would be highly desirable if every student had such math teachers, we are a very long way from achieving this goal. Thus, we need to make more effective use of such excellent math teachers in areas such as: designing curriculum, pedagogy, and assessment; teaching both math teachers and teachers in other disciplines where math is an important and useful aspect of their discipline; and providing leadership in their schools.
Final Remarks

I like to think and write about the idea of a tool being both an aid to accomplishing some task and an aid to learning to accomplish the task. Now that we have computers, we are able to develop tools that have a type of artificial intelligence. We also are able to build into many of these tools the aids needed to learn to use the tools effectively (Moursund, September, 2014).

This is especially true in math and the other STEM (science, technology, engineering) disciplines. Math education has long made use of paper, pencil, protractor, ruler, and compass–both as tools and as aids to learning and doing math. Computerization of these tools, along with the development of computer systems that can accomplish the “mechanical” aspects of essentially all of the PreK-12 math content, can and should be leading to major changes in math content, pedagogy, and assessment (Moursund, 12/23/2016; 2016).

But, success in this endeavor depends on a substantial increase and improvement in both preservice and inservice education of (human) PreK-12 math teachers so they have the needed ICT-in-education knowledge and skills, as well as educating parents with children in school and the general population.

References and Resources

Common Core (n.d.). Common Core State Mathematics Initiative. Retrieved 9/17/2017 from http://www.corestandards.org/Math/Practice/.

MLC (2017a). Math Learning Center free computer applications. Retrieved 9/20/2017 from https://www.mathlearningcenter.org/resources/apps.

MLC (2017b). Math Learning Center general information. Retrieved 9/20/2017 from https://catalog.mathlearningcenter.org/.

Moursund D. (2017). Computational thinking. IAE-pedia. Retrieved 9/17 2017 from http://iae-pedia.org/Computational_Thinking.

Moursund, D. (12/23/2016). The fourth R. Eugene, OR: Information Age Education. Download the Microsoft Word file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/289-the-fourth-r/file.html. Download the PDF file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/290-the-fourth-r-1/file.html. Access the book online at http://iae-pedia.org/The_Fourth_R.

Moursund, D. (2016), Math maturity. IAE-pedia. Retrieved 9/17/2017 from http://iae-pedia.org/Math_Maturity.

Moursund, D., & Sylwester, R. (10/3/2015). Validity and credibility of information. Eugene, OR: Information Age Education. Download the Microsoft Word file from http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/275-validity-and-credibility-of-information/file.html. Download the PDF file from  http://i-a-e.org/downloads/free-ebooks-by-dave-moursund/277-validity-and-credibility-of-information-2/file.html.

Moursund, D. (September, 2014). The teaching machine is both tool and teacher. IAE Newsletter. Retrieved 9/18/2017 from http://i-a-e.org/newsletters/IAE-Newsletter-2014-146.html.

Wing, J. (10/28/2008). Computational thinking and thinking about computing. Philosophical Transactions A. Retrieved 9/14/2017 from: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2696102/.

Free Educational Resources from IAE
Author

David Moursund is an Emeritus Professor of Education at the University of Oregon, and editor of the IAE Newsletter. His professional career includes founding the International Society for Technology in Education (ISTE) in 1979, serving as ISTE’s executive officer for 19 years, and establishing ISTE’s flagship publication, Learning and Leading with Technology. He was the major professor or co-major professor for 82 doctoral students. He has presented hundreds of professional talks and workshops. He has authored or coauthored more than 60 academic books and hundreds of articles. Many of these books are available free online. See http://iaepedia.org/David_Moursund_Books.

In 2007, Moursund founded Information Age Education (IAE). IAE provides free online educational materials via its IAE-pedia, IAE Newsletter, IAE Blog, and books. See http://iaepedia.org/Main_Page#IAE_in_a_Nutshell. Information Age Education is now fully integrated into the 501(C)(3) non-profit corporation, Advancement of Globally Appropriate Technology and Education (AGATE) that was established in 2016. David Moursund is the Chief Executuve Officer of AGATE.

Email: moursund@uoregon.edu.

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Information Age Education is a non-profit organization dedicated to improving education for learners of all ages throughout the world. Current IAE activities and free materials include the IAE-pedia at http://iae-pedia.org, a Website containing free books and articles at http://i-a-e.org/, a Blog at http://i-a-e.org/iae-blog.html, and the free newsletter you are now reading. See all back issues of the Blog at http://iae-pedia.org/IAE_Blog and all back issues of the Newsletter at http://i-a-e.org/iae-newsletter.html.