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What is Mathematics?

Major Unifying Themes in This Document


Foundational Information

Learning Theories

Mind and Body Tools

Science of Teaching & Learning

Project-Based Learning

Computational Mathematics

The Future




 Website Author
"Dr. Dave" Moursund

Foundational History and Background Information

This page is a "work in progress" that has a long way to go. It provides some background information in Brain Science, ICT, and Mathematics Education.

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This Website integrates Brain Science, ICT, and Mathematics Education. Each of these three fields has its own history. Some background information in each of these fields is helpful in understanding modern interactions among the three fields.

Brain Science

Brief Summary: This field is just emerging from its infancy and is in a period of very rapid growth. Current knowledge in the field is beginning to contribute to improving our education system

Information and Communications Technology

Brief Summary: This field is being driven by a continuing exponential rate of improvement in the capabilities of computer hardware and telecommunications systems. ICT provides powerful (and, steadily increasingly powerful) aids to the human mind and body.

Mathematics and Mathematics Education

Brief Summary: Mathematics as a "language" and the formal study of mathematics is as old as writing and the teaching of reading and writing (approximately 5,000 years). Contemporary mathematics education standards, as well as the math needs in many career field, are outstripping the teaching and learning capabilities in our math education system.

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Mathematics and Mathematics Education


The Sumerians began to develop clay tokens about 9000 BC, which was about 11,000 years ago.

Accessed 7/17/01:

These are samples of the clay counters used in the Near East from about 9,000 B.C. (calibrated) to 1500 B.C. There were about 500 distinct types, although not in all times and places. Tokens start to be found at widely separated sites as of 8,000 B.C. (C-14), such as Level III of Tell Mureybet in Syria and Level E of Ganj Dareh in western Iran. Tokens were used at sites throughout the Near East, from Israel to Syria, Turkey, Iraq, and Iran, with the exception of Central Anatolia. The farthest extent of their use was from Khartoum in the Sudan to the pre-Harappan site of Mehrgahr in Pakistan.

Regarding the cultural significance of this system, their primary researcher says, "The tokens were an entirely new medium for conveying information. Compared to the previous tallies, the conceptual leap was to endow each token shape, such as the cone, sphere, or disk, with a specific meaning." "The token system was, in fact, the first code -- the earliest system of signs used for transmitting information." Denise Schmandt-Besserat, Before Writing, Volume 1, From Counting to Cuneiform (University of Texas Press, Austin: 1992), p. 161.


The Agricultural Age began about 10,000 years ago.

Over a period of about 5,000 years the number of different clay tokens grew to at least 192. (Need to check the reference. It indicates that tokens started before the start of agriculture, and that evidently this system continued after the development of writing. leading to about 500 different tokens.

The human-created "languages" we call writing and mathematics were invented by the Sumerians a little over 5,000 years ago.

It led to greatly increased population, large cities, bureaucracies, bigger businesses.

The record keeping and calculating systems of the time were gradually overwhelmed. By about 5000 years ago this led to the development of writing and mathematics by the Sumerians.

A formal education system (schooling) that could help a very limited number of people learn the 3 Rs.

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