A Mathematics Lesson from the Mayan Civilization
Lara-Alecio, Rafael, Irby, Beverly J., Morales-Aldana, Leonel, Teaching Children Mathematics
Mayan mathematics, a significant part of the great civilization of the ancient people, is of true interest to all who admire the monuments, architecture, and art of the great Mayan cities. Among the Maya's multiple accomplishments involving mathematical skills were -
* building ancient cities, such as Copan, Chichen Itza, Tikal, Tayasol, Quirigua, Tulum, and Palenque;
* supporting the employment of thousands of construction workers;
* collecting taxes and developing commerce in a vast geographical area;
* calculating an accurate calendar with the cycles of the Sun and Moon and of Venus and other planets;
* developing the astronomical alignments of temples, pyramids, and stelae;
* inventing the technology of cement and concrete; and
* creating the geometry used in construction and works of art.
Such major attainments by the Mayan civilization rest in the development of an efficient system of computation. Although many Mayan artifacts that may have provided proof of these accomplishments were burned during the Spanish conquest and colonization (Landa 1938), still remaining is evidence found in inscriptions in stone; in a few surviving Mayan books, such as The Popol Vuh (Recinos, Goetz, and Moreley 1950) and The Book of the Chilam Balam of Chumayel (Mediz 1941); and in ancient customs and traditions that survive among the millions of Maya today.
Mayan Culture and Real-Life Mathematics
Teachers can infuse culture into the curriculum and develop students' competence and confidence by using ethnomathematics (D'Ambrosio 1987; Massey 1989; Stigler and Baranes 1988). Ethnomathematics calls for a reconstruction of the mathematics curriculum to achieve cultural compatibility (Moll and Diaz 1987; Trueba 1988). In this reconstruction, students' cultural and background experiences and vocabulary are used to frame mathematics problems in the classroom (Henderson and Landesman 1992). When the materials and problems being used originate from the students' daily-life experiences or cultural heritage, we find real-world problem solving at work. In this situation, the problem-solving activity can motivate the students to create mathematical models that may, in reality, become the real object of study (Bohan, Irby, and Vogel 1995).
Kamii (1992) motivates elementary students to rediscover arithmetic with objects of daily life, including material originally designed for game purposes. Research conducted by Doyle (1988), Resnick (1980), Schoenfeld (1985), Wilttrock (1974), and Hiebert and Carpenter (1992) supports reality-based mathematics teaching. This research advocates the need for problems to be taken from real life and brought into the classroom. Real-life problems involving concrete, as well as semiconcrete, materials can be taken from many of today's students' historical or cultural milieus.
One such cultural and historical event took place more than 5000 years ago in a region named Mesoamerica, where the Maya developed a numerical written system that dealt ingeniously with the relationship between numeral and number (Morales-Aldana 1994). According to Otto Neugebauer, a science historian, the Mayan numeration system with positionality and place value was "one of the most fertile inventions of humanity, comparable in a way with the invention of the alphabet" (Coe 1966, 156).
Mayan mathematics was characterized by a positional numerical system that had as a base the number 20. The Maya created a symbol for the 0, which had a use similar to that in any other positional numerical system. Furthermore, in addition to their mathematical advances, compared with other civilizations, their system of teaching mathematics was based on the use of concrete, semiconcrete, and representational materials. Probably, that characteristic expanded the dominant structure's potential to develop numerical computations and also allowed the priests, the academicians, and the religious class of that time to carry out the great astronomical and scientific advances that are still impressive today. …