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Improving Math Education

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Dave Moursund


I have just finished a considerable revision and updating effort on my IAE-pedia entry Improving Math Education. The document is mainly intended for preservice and inservice teachers of math at the K-12 level—and teachers of these teachers. I wrote the first version of this document in 2008. Since then it has been revised, updated, and expanded a number of times. It has had more than 104,000 “hits.”

This IAE Blog entry provides a little of my background in math education and then summarizes a few key ideas from the updated Improving Math Education.

About David Moursund

I became involved in math education well before I started college. My parents had both taught math at the precollege level and were teaching math at the University of Oregon. My precollege experiences included math tutoring and helping my parents grade Math Correspondence Courses.

My teaching career began to develop after I finished my doctorate at the University of Wisconsin. I had opportunities such as helping to teach a summer computer course for talented and gifted high school students and then teaching a numerical analysis (computer math) course for secondary school teachers. The latter experience led to my receiving funding to run National Science Foundation summer institute programs for secondary school math teachers beginning in 1966.

My University of Oregon career included teaching a very large number of preservice and inservice teachers in the areas of math education and computers in education. It also included serving as major professor or co-major professor for 82 doctoral students—76 in the field of Computers in Education and six in Mathematics. I founded the International Society for Technology in Education (ISTE), and was CEO for 19 years and also editor of its journals and books. I wrote a great many books and articles about math education and computers in education, many now available free at the IAE websites.

As I neared retirement, I wanted to continue to do much of the work I was doing—except no more grading papers or dealing with administrivia. I started the Oregon non-profit company Information Age Education (IAE) in 2007 to serve as an outlet for my writing interests.

My first IAE activity was the IAE-pedia, followed by the IAE Blog and the IAE Newsletter. One of the first IAE-pedia entries was Improving Math Education.

The Improving Math Education IAE-pedia Entry

There are six unifying themes in this document:

1.  Problem solving and higher-order thinking.

2.  Math maturity (math knowledge and understanding that can serve a student for a lifetime).

3.  Computers and math education. (Two brains are better than one.) Making effective use of Information and Communication Technology both as an aid to doing math and as an aid to learning math.

4.  Communication in the language of mathematics. This includes thinking, reading, writing, speaking, and listening in the language of math.

5.  Developing math “habits of mind” that help make learning and using math a lifelong endeavor that cuts across all areas of interest of students. Here are two examples of habits of mind quoted from the link given above.

Persisting. Stick to it through task completion. Remain focused—keep your eye on the ball. Try alternative approaches when you are stuck.Don’t give up easily.

Questioning and problem posing. Effective problem solvers know how to ask questions to fill in the gaps between what they know and what they don't know.

6.  Change. We live in a time of great change and a number of problems people label as Global Challenges. How is our math education system coping with these changes?

Reflection and Discussion

On of the features of Improving Math Education is the inclusion of many short sections titled For Reflection and Discussion (also found in most of the IAE-pedia entries). These are designed to engage readers individually, in small group discussions, and in whole class discussion and thinking. Here are two examples from the “What Is Math?” section.

For Reflection and Discussion. Select some age group of students, such as fifth grade. Ask what they think math is. Then, do the same thing for "typical" adults. What insights does this activity give you into the current success of our math education system?

For Reflection and Discussion. Think back over your own studies of math. Where did you receive explicit instruction on the topic "math modeling?" If you asked various students and adults what they think math modeling is, what kinds of answers do you expect you would receive?

For Reflection and Discussion. Just for the fun of it, think about some area (such as food, clothing, music, art, and so on) in which you have strong personal opinions. What caused you to develop a good attitude or a bad attitude toward specific food, clothing, music, art, and so on? Is there anything particularly wrong about having a bad attitude toward certain forms of food, clothing, music, art, and so on? Now, do some reflective thinking to compare and contrast between these situations and the bad attitudes that many adults have toward math.


Improving Math Education includes a number of quotes from my extensive collection of math education quotes. These “tidbits” help to capture a tiny bit of the history of math education and provide food for thought. Here are a few examples:

"The reason most kids don't like school is not that the work is too hard, but that it is utterly boring." (Seymour Papert; South African/American mathematician, computer scientist, and educator; 1928-.)

"God created the natural numbers; all the rest is the work of man." (Leopold Kronecker; German mathematician; 1823-1891.)

“Mathematics consists of content and know-how. What is know-how in mathematics? The ability to solve problems.” (George Polya; Hungarian and American mathematician; 1887-1985.)

Change—Including the Teaching of Arithmetick:

Charles Darwin is known for his insights into evolutionary change:

"It is not the strongest of the species that survive, nor the most intelligent, but the one most responsive to change." (Charles Darwin; British scientist and developer of the theory of evolution; 1809-1882.)

Here is a story I find to be quite interesting. In 1778 Thomas Jefferson brought before the Virginia Legislature A Bill for the More General Diffusion of Knowledge. His bill (quoted below) was not approved! In some sense, it was too far out—too big a change—for the Virginia Legislature to accept.

At every one of these schools shall be taught reading, writing, and common arithmetick, and the books which shall be used therein for instructing the children to read shall be such as will at the same time make them acquainted with Graecian, Roman, English, and American history. At these schools all the free children, male and female, resident within the respective hundred, shall be intitled to receive tuition gratis, for the term of three years, and as much longer, at their private expence, as their parents, guardians or friends, shall think proper. See

Final Remarks

Improving Math Education in the IAE-pedia is not in any sense a “finished document.” We all know that as math education is a large and very challenging discipline, and growing/changing human endeavor. Rather than being finished, the document is a vehicle I use to explore and share my current thinking about ways to improve math education. As you think about and discuss these ideas, please consider sharing any of your suggestions that might be added to this document by sending them to me This email address is being protected from spambots. You need JavaScript enabled to view it.. I welcome your feedback.

What You Can Do

Consider the sample Reflection and Discussion questions above and the many others throughout Improving Math Education in the IAE-pedia. I hope you will develop the “habit of mind” of raising and pondering such challenging questions in math education and in other areas of study. Raise some of these issues with your students and also share the issues with the teachers, preservice teachers, and others you know who are working to improve our math education system.

IAE Resources

Moursund, D. (2014). Exploring the college math placement testing process. IAE-pedia. Retrieved 6/26/2014 from

Moursund, D. (2014). Improving math education. IAE-pedia. Retrieved 6/26/2014 from

Moursund, D. (6/21/2014). Moursund’s 1987 futuristic view of math education. IAE Blog. Retrieved 6/26/2014 from

Moursund, D. (6/16/2014). Grand challenges in math education. IAE Blog. Retrieved 6/26/2014 from

Moursund, D. (6/9/2014). An introduction to college math placement testing. IAE Blog. Retrieved 6/15/2014 from

Moursund, D. (2013). Empowering learners and teachers. IAE-pedia. Retrieved 6/26/2014 from

Moursund, D. (2013). Good math lesson plans. IAE-pedia. Retrieved 6/26/2014 from

Moursund, D. (2013). Math education digital filing cabinet. IAE-pedia. Retrieved 6/26/2014 from

Moursund, D. (12/21/2013). Education for the future. IAE Blog. Retrieved 6/26/2014 from

Moursund, D. (10/31/2013). Transfer of learning. IAE Blog. Retrieved 6/26/2014 from

Moursund, D. (2010). Syllabus: Increasing the math maturity of K-8 students and their teachers. A course developed by David Moursund. Eugene, OR: Information Age Education. Retrieved 6/26/2014 from

Moursund, D., & Albrecht, R. (2011). Becoming a better math tutor. Eugene, OR: Information Age Education. The PDF file is available at The Microsoft Word file is available at

Moursund, D., & Sylwester, R., eds. (March, 2013). Common Core State Standards for K-12 education in America. Eugene, OR: Information Age Education. The book is available free. See for the Microsoft Word document and for the PDF.

Sylwester, R., & Moursund, D., eds. (August, 2012). Creating an appropriate 21st century education. Eugene, OR: Information Age Education. Download the PDF file from and the Microsoft Word file from

Adequacy of Teacher Preparation
Moursund’s 1987 Futuristic Visions of Math Educati...


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Wednesday, 12 August 2020

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