Efforts have been underway since 1973 to determine if there are elements of Navajo culture that potentially impact upon a Navajo student's attainment of mathematics concepts. Extensive reading and discussion with Navajo students and educational leaders on the Navajo reservation show that basic concepts and objectives of Navajo philosophy (a quest for unity, harmony, order, and beauty) appear to be entirely consistent with views of the greatest contributors to the development of mathematics. However, there are no words for "multiply" and "divide" in Navajo, and no agreed upon word for "if," and difficulties arise when Navajo students handle situations calling for use of those functions or syllogistic reasoning. While Anglo folklore has many references to numbers (e.g., the three little pigs), Navajo folklore is more personal. Sentence word order (nouns in particular), the role of imaging in problem solving, clan characteristics, and cultural views of geometry pose additional hazards. Navajo culture has traditionally been transmitted orally, and it is possible that the students' facility for memorization has not been fully appreciated. The teacher should have visual classroom models of certain basic mathematical entities, and should make every effort to close the gap between the hypothesis form of teaching and the real world of the Navajo. (BRR)