Cultures need to accurately record
dates and times for various societal purposes, ranging from knowing when to
plant crops to planning travel. In ancient times, the sun and moon were used as
measurement devices because of the scientific understanding of the physical
world at that time. Ancient timekeepers monitored celestial events and either
used or discarded them, depending on whether or not they were useful as
standard units. Our sixth-grade students’ under-standing of time was enriched
by a four-lesson sequence that integrated science (the constantly progressing
lunar cycle), mathematics (what makes a “good” standard unit), and literacy
(cultural events dependent ). phases. Having a conceptual aware-ness that
moonlight is reflected sunlight, rather than light generated by the moon, was a
crucial entry point in understanding lunar phases. To gather information about
the students’ knowledge of the lunar cycle, we opened the morning with this
question, “Why does the shape of the
moon change?” Responses included, “Earth is rotating, and we can only see part
of it” and “The sun is eclipsing it.” We
modeled the moon phases with eight spheres that were painted one-half black and
one-half white, to represent the dark and light sides of the moon. These
movable models showed relative locations of the sun, the moon, and Earth.
Manipulating these materials demonstrated that sunlight was reflected and
allowed the lesson to segue into a representation of the cyclic patterns of
lunar phases as reflected sunlight
Appropriately measuring time
re-quires a conceptual awareness of char-acteristics that a time-based standard
unit must possess. Knowing about standard units, making comparisons between
standard units, and using a standard unit to record the size of an object are critical
bits of information when learning to measure (Lehrer
et al. 1999). the lunar cycle was a
convenient unit of measure because it iterates, covers, and remains the same
size. Each phase length is predictably 29.5 days (same size), there is always
one set of moon phases after another (iteration), and there is no time during
which the moon stops progressing through phases (coverage). Although the 2 days
of a “new moon” caused a brief discussion about “covering,” the students agreed
that the moon was there, progressing toward the begin-ning of the next phase,
the lunar cycle cannot be picked up partway through a phase (infinitely
divisible) and moved to the winter solstice, for example, and forced to begin a
new phase (zero indicator). The moon moves through its phases, independent of
when the winter solstice occurs. As a standard unit, the lunar cycle would not
work well for measuring an Earth year. Students found that there were either 12
or 13 moons in a calendar year. We connected our lesson to the Hopi society
because of the impressive manner with which Hopi astronomers demonstrated
scientific and math-ematical dexterity in marking the passage of time. They
understood rhythms of the moon and Earth and used science, mathematics, and
literacy to inform their people. The ancient Hopi had a name for each lunar
cycle, or moon, and related it to a particular cultural activity, such as corn
planting (Ellis 1975). They communicated the yearly calendar to the people with
outstanding accuracy. Understanding the Hopi use of the moon provided students
with a solid foundation for understanding mea-surement ideas. Of critical
importance to the Hopi culture were two events: the timing of the Sparrow-Hawk
moon, mark-ing the emergence of Katsinas from the mountains, and the winter
solstice ceremony, marking the preplanting season (James 2000). Either event
quickly coupled the Sparrow-Hawk moon with the wrong time of the solar year. If
this happened, the people would not be appropriately prepared for the winter
solstice, and the criti-cal appearance of the Katsinas would occur at the wrong
time
The lessons described in this article illustrate how a
measurement lesson can benefit from substantive connec-tions among science,
mathematics, and literacy and how those disciplines are revealed in a culture’s
way of measur-ing time. Knowing that the lunar cycle will not divide a
calen-dar year, they recognized and named
a 13th moon and inserted it whenever
it was needed. Studying lunar cycles, culture, and literature allowed our sixth-grade
students to grow in their understanding of standard units.
