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14 minutes reading time (2872 words)

Grand Challenges in Math Education

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Thanks

Dave Moursund

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“We cannot hope that many children will learn mathematics unless we find a way to share our enjoyment and show them its beauty as well as its utility.” (Mary Beth Ruskai; American mathematics and quantum physics researcher; 1944-.)

“The point is to make math intrinsically interesting to children. We should not have to sell mathematics by pointing to its usefulness in other subject areas, which, of course, is real. Love for math will not come about by trying to convince a child that it happens to be a handy tool for life; it grows when a good teacher can draw out a child's curiosity about how numbers and mathematical principles work. The very high percentage of adults who are unashamed to say that they are bad with math is a good indication of how maligned the subject is and how very little we were taught in school about the enchantment of numbers.” (Alfred S. Posamentier; American math educator; 1942-.)

This IAE Blog entry is about Grand Challenges in Math Education. It is prompted by the following email message I recently received from the National Council of Teachers of Mathematics Research Council:

The National Council of Teachers of Mathematics (NCTM) Research Committee has begun the process of identifying the grand challenges for the field of mathematics education. As a first step, your responses to our brief survey will help us better frame our understanding of the grand challenges in mathematics education.

A number of national and international organizations have compiled lists of grand challenges in their fields. For example, see Omenn's (2006) discussion of great challenges in Science.

For the purposes of this survey, grand challenges—

(1) are extremely hard to do, yet are doable;

(2) produce outcomes potentially affecting millions, if not hundreds of millions, of people;

(3) require multiple research projects across many subdisciplines to be satisfactorily addressed;

(4) consist of well-defined metrics [measures of progress and success] so that, through creativity and commitment, they can realistically be met, and one knows when the end has been reached; and

(5) capture the popular imagination, and thus garner political support. (Gould, 2010)

The end of their message, which I received on June 13th, said:

Use this link to complete the survey: https://www.surveymonkey.com/s/NCTMGreatChal by June 30, 2014.

The SurveyMonkey response form provided two boxes for open-ended responses:

Box 1: What revisions would you suggest to the characteristics of grand challenges listed above?

Box 2: What would you propose as grand challenges that mathematics educators need to solve?

My first reaction was to wonder why the NCTM had provided such a short time for ideas from the NCTM membership.

My second reaction was to think about what they—the NCTM organization—can do versus what you and I can do. Lots of organizations pose Grand Challenges. Some of these come from government organizations and are backed by the possibilities that the best suggestions will lead to multi-million dollar grants or contracts. Others have the backing of large organizations such as the NCTM.

Grand Challenges

I have long been interested in Grand Challenges, so I decided to spend some time exploring both the general topic of Grand Challenges and the specific math education Grand Challenge from the NCTM Research Council. This is the first of two IAE Blog entries resulting from my exploration. It focuses specifically on the NCTM Grand Challenge. The second IAE Blog entry will focus on Grand Challenges in Education and in various science and technology areas.

First, however, is a preview example of material that will be in the second IAE Blog entry:

The driverless motor vehicles came from a federally funded Grand Challenge Grand Challenge. In 2004 Congress authorized the Defense Advanced Research Projects Agency (DARPA) to award cash prizes to further DARPA's mission to sponsor revolutionary, high-payoff research that bridges the gap between fundamental discoveries and military use. The initial DARPA Grand Challenge was created to spur the development of technologies needed to create the first fully autonomous ground vehicles capable of completing a substantial off-road course within a limited time.

Quoting from the Wikipedia:

The Google Self-Driving Car is a project by Google that involves developing technology for autonomous cars. … The project is currently being led by Google engineer Sebastian Thrun, former director of the Stanford Artificial Intelligence Laboratory and co-inventor of Google Street View. Thrun's team at Stanford created the robotic vehicle Stanley which won the 2005 DARPA Grand Challenge and its US$2 million prize from the United States Department of Defense. [Bold added for emphasis.]

Now, less than ten years later, the technology has been developed and extensively field-tested. I find that rate of progress to be truly amazing! That success illustrates what Grand Challenges are all about.

Improving Math Education

Both in the United States and in many other countries there is agreement that math education is not as successful as many people would like. But, what is the meaning of “not as successful as many people would like”?

One answer is to look at scores on international math tests. The United States spends far more on education per K-12 student per year than most other countries (Ryan, 12/3/2013). But, its students score less well in math than those in many other countries that spend far less per student. Why aren’t we #1?

Math is a beautiful, enjoyable, broad, and deep discipline of study. Reread the two quotes at the beginning of this IAE Blog entry. They each represent a particular Grand Challenge of what is needed to improve math education. What is there about the ways in which we teach math that leads so many students to claim, “I can’t do math” and “I hate math”? How can we change math education so that it doesn’t turn off so many students?

Of course, there are many other possible goals for math education and ways to work toward achieving these goals. Differences in opinion led to the “Math Education Wars” in the 1990s. The question of proper roles of calculators and computers in math education has a still longer and more contentious history.

Before reading on, think about what you would recommend to the NCTM. From your point of view, what are some major problem areas in math education that can and should be addressed by our math education system?

My Comments on the NCTM Research Committee Grand Challenge

This section repeats the five items in the NCTM Grand Challenge listed earlier, with some comments that occurred to me as I read the list. First of all, I noted that there was no presentation or discussion of what constitutes the problems that are to be solved (Moursund, 2012). What are the major faults in our current math education system? How have these been determined, and how important are they? What are the goals to be achieved? If the Grand Challenge is to figure out and implement ways to achieve the goals, then we must first identify and agree upon the goals to be achieved.

Now, here is the initial NCTM communication with some of my comments:

For the purposes of this survey, grand challenges—

(1) are extremely hard to do, yet are doable;

Comment: I suppose the assumption is that, if a solution were easy to find and implement, we would already have done it. This seems to me to be a rather strange assumption. Maybe there is a good solution that is easy to do. For example, consider the addition of iodine to table salt to prevent goiters. Here we have a worldwide medical problem that was solved by a quite simple remedy. But, it took many years of research to identify the problem and a solution.

(2) produce outcomes potentially affecting millions, if not hundreds of millions, of people;

Comment: This statement suggests that the NCTM Research Committee believes that math education is an important worldwide problem. Different countries have different goals for their educational systems. A solution that meets the needs of the U.S. might be—or might not be—a good solution for other countries, or vice versa.

Research in math education has not yet produced a “magic bullet” (such as iodine to prevent goiters). The computer, along with progress in educational cognitive neuroscience, eventually may produce a magic bullet of worldwide value. Progress is definitely occurring!

But, we need to think carefully about what math education problem(s) we want to solve. Here is a proposal that would likely substantially decrease the adult syndrome, “I hate math.” It is a proposal that I have heard from several people.

Change the math education requirements so that students are not required to take any math beyond the pre-algebra level. In this case, both higher levels of math and math related to specific disciplines that students study in high school would be available as electives. The teachers in each non-math discipline would assume more responsibility for helping their students learn what math classes they need to take for success within their discipline, and also to select the math classes they will need to take if they are seeking higher education and/or a career in that discipline.

Of course, this proposal would likely prove unacceptable to those who want the United States to score #1 in math in the world comparisons of students nearing graduation from high school.

(3) require multiple research projects across many subdisciplines to be satisfactorily addressed;

Comment: Math is useful in essentially every academic discipline of study. Transfer of learning from math classes to other classes and to outside of school is very difficult for many students. If the amount of math that students are required to take is decreased (see # 2 above) those students who need more math for a particular career or other goal need to have the opportunity to take courses that will provide the needed instruction. It may well be that this math instruction could/should be integrated thoroughly into a variety of non-math courses in the non-math discipline being studied.

Each discipline area where math is used falls into the “subdisciplines” that need to be addressed. In addition, there are broad-based problems such as poverty (Moursund, 6/1/2014).

(4) consist of well-defined metrics so that, through creativity and commitment, they can realistically be met, and one knows when the end has been reached; and

Comment: “Aye, there's the rub.” For example, you find you can't get a job unless you have experience. And there's the rub—how do you get experience if you can't get a job?

Specifically, the rub in this instance is deciding who is to define these metrics and establish criteria for determining when they have been met. How do we know “the end has been reached” when we haven’t yet defined the end? As you think about this topic, take note of the huge difference between education in Finland and in the U.S. Finland has moved in the direction of less high-stakes testing and less requirements, and at the same time has substantially improved its educational system as rated in international comparisons.

See my comment for (2) above. Getting agreement about our goal(s) and developing ways to measure progress and eventual success toward reaching the goal(s) is a challenge all by itself.

(5) capture the popular imagination, and thus garner political support (Gould, 2010).

Comment: This is an acknowledgement of the challenge of top-down versus bottom-up in efforts to improve our educational system. The controversies and difficulties surrounding the current Common Core State Standards in Mathematics give an indication of the magnitude of that challenge.

My Personal Answers to the Math Education Grand Challenge Question

For more than two decades I have believed that we should provide all students with the computer capabilities of a modern laptop or tablet computer and with good connectivity to the Internet. My goal is to substantially improve students’ quality of math content education and math maturity education for life in our current and future Information Age. Within the discipline of math, course materials and other resources should include:

1.  Excellent quality Highly Interactive Intelligent Computer-assisted Learning (HIICAL) math materials for both students and teachers that cover the K-14 math curriculum and other math content that students might want to explore on their own.

2.  A substantial library of math-oriented books and other learning resources, including math problem-solving software. The collection of materials would include books, articles, videos, guided access to appropriate websites, and so on, designed to help students learn about roles of math in each of the disciplines they are required to study and/or might be interested in studying. Students need good opportunities to learn about what math they will need if they want to pursue various disciplines and careers after they finish high school.

3.  Very good self-assessment materials that include diagnostic tests with links to appropriate remediation and to more advanced and challenging work.

4.   An overall math curriculum of study that thoroughly integrates the resources and content from items 1-3 above into the content, formative assessment, and summative assessment of the required math courses.

5.   Math teachers who are skilled in working in this 1-4 type of a highly individualized math education environment. See http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics#Native_Natural_Language_Speakers_and_Native_Math_Language_Speakers.

What You Can Do vs. What They Can Do

Large organizations have the resources to approach Grand Challenge problems in a top-down manner. Individuals and small organizations can approach such problems in a bottom-up manner. As an individual, you daily interact with a number of other people. This gives you the opportunity to practice communicating your ideas and possibly to enlist the people you communicate with in achieving goals that you believe to be worthy.

Teachers are in an especially powerful position. In their classrooms they are free to experiment (within reason) with new ideas and approaches designed to improve the education of their students.

Suppose, for example, you believe that all students should become skilled in making use of the Web within the disciplines that you teach. This includes helping students learn to critically evaluate online information for accuracy, timeliness, and lack of undisclosed bias in order to “separate the wheat from the chaff.” They need to learn to integrate Web-based information into their own current knowledge, skills, and insights, and also be able to “learn to learn” effectively from Web-based materials. You believe that this can and should be part of every course in every discipline starting as soon as it is deemed appropriate for children to make use of the Web.

Thus, any person who teaches math could take the position that all students should learn to read, write, and speak math with understanding—that is, learn to effectively communicate in the language of math. Whatever Web access resources are available to a math teacher’s students could/should be fully integrated into an ongoing study of effective communication in math. If you are a math teacher, this could be one of your personal math education Grand Challenges.

In this bottom-up approach you can keep detailed records of what you are doing and how well it works. This is a type of Action Research. The knowledge and experience you gain can be shared with your fellow teachers and spread throughout your school. Aha! You now have a larger group working on the goal(s) you have set. From the school, your goal(s) can spread to other schools and then to the entire school district. That is the power of a bottom-up approach.

References

Gould, M. (2010). How can research and technology in this field address big-picture problems? ArcUser, 64-65. Retrieved 6/15/2014 from http://www.esri.com/news/arcuser/1010/geochallenges.html.

Moursund, D. (6/1/2014). Hungry children—America’s shame. IAE Blog. Retrieved 6/15/2014 from http://i-a-e.org/iae-blog/entry/hungry-children-america-s-shame.html.

Moursund, D. (2012). Problem solving: Posing and answering questions. IAE-pedia. Retrieved 6/16/2014 from http://iae-pedia.org/Problem_Solving:_Posing_and_Answering_Questions.

NCTM (June, 2014). Mathematics Research Council survey. Retrieved 6/15/2014 from https://www.magnetmail.net/actions/email_web_version.cfm?recipient_id=1107346865&message_id=4862599&user_id=NCTM1&group_id=1299975&jobid=19424053.

Ryan, J. (12/3/2013). American schools vs. the world: Expensive, unequal, bad at math. The Atlantic. Retrieved 6/16/2014 from http://www.theatlantic.com/education/archive/2013/12/american-schools-vs-the-world-expensive-unequal-bad-at-math/281983/.

The White House (4/13/2013). 21st Century Grand Challenges. Office of Science and Technology Policy. Retrieved 6/15/2014 from http://www.whitehouse.gov/administration/eop/ostp/grand-challenges.

IAE Resources

Moursund, D. (6/9/2014). An introduction to College Math Placement Testing. IAE Blog. Retrieved 6/15/2014 from http://i-a-e.org/iae-blog/entry/an-introduction-to-college-math-placement-testing.html.

Moursund, D. ( 2013). Empowering learners and teachers‏‎. IAE-pedia. Retrieved 6/16/2014 from http://iae-pedia.org/Empowering_Learners_and_Teachers.

Moursund, D. (12/21/2013.) Education for the future. IAE Blog. Retrieved 6/15/2014 from http://i-a-e.org/iae-blog/entry/education-for-the-future.html.

Moursund, D. (10/31/2013). Transfer of learning. IAE Blog. Retrieved 6/15/2014 from http://i-a-e.org/iae-blog/entry/education-for-the-future.html.

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 12/16/2011 from http://i-a-e.org/downloads/doc_download/201-extended-syllabusfor-prism-course.html.

Moursund, D. (2008-2014). Improving math education. IAE-pedia. Retrieved 6/15/2014 from http://iae-pedia.org/Improving_Math_Education.

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 http://i-a-e.org/downloads/doc_download/249-common-core-state-standards-for-k-12-education-in-america.html for the Microsoft Word document and http://i-a-e.org/downloads/doc_download/248-common-core-state-standards-for-k-12-education-in-america.html 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 http://i-a-e.org/downloads/doc_download/243-creating-an-appropriate-21st-century-education.html and the Microsoft Word file from http://i-a-e.org/downloads/doc_download/242-creating-an-appropriate-21st-century-education.html.

Moursund’s 1987 Futuristic Visions of Math Educati...
An Introduction to College Math Placement Testing
 

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