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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:
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?
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?)
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:
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.
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.
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.
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.
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