In ancient times, the sun and moon were used as measurement devices because of the scientific understanding of the physical world at that time. This lesson sequence occurred during a summer camp attended by students who had an interest in science. The purpose of the week-long camp was to offer explorations in science, mathematics, and computer programming.
LESSON 1: LUNAR PHASES
To engage in the lessons, students needed to understand the lunar phases. Having a conceptual awareness that moonlight is reflected sunlight, rather than light generated by the moon, was a crucial entry point in understanding lunar phases. To address these misconceptions, we produced a set of carefully painted spheres. 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. Students described the appear-ance of the moon as seen from Earth by coloring the eight moon phases. These visual models helped students become aware of the reasons behind the changing appearance of the moon during differ-ent phases in the lunar cycle. By describing the appearance of the moon in this way, we were able to name all the phases and label the spheres with their corresponding names In small groups, the students sorted the months in order, using only the indicated moon phase images displayed on each day of each month
LESSON 2: STANDARD UNITS
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). Before proceeding, we wanted to help students develop shared language of these five measurement concepts: Iteration, Coverage, Same-size units, Zero indicator, Infinite divisibility. For our lessons, students needed to be able to identify conceptual difficul-ties with measuring time using lunar cycles. Students were given a blank calendar activity sheet, asked to find the approximate locations of the 8 moon phases, and answer the follow-ing four questions: How long is a lunar cycle? How long is a year? How many days are in 12 lunar cycles? How many days are in 13 lunar cycles? 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). 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.
LESSON 3: THE HOPI
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.
Background of the Significance of the Hopi Moon
ancient astronomers measured time using both the sun and the moon to plan associated celebrations. introduce our students to 13 Hopi moon names, which were compiled from a variety of references (Secakuku 1995; Wright and Roat 1965; Ellis 1975; James 2000; Sharp 2015). We opened the discussion by asking, “How did the Hopi connect moons to their calendar and plan for correct timing of celebrations?” Students discussed the apparent contradiction between their determi-nation that a moon could not serve as a standard unit and the Hopi’s suc-cessful use of the moon. One promising result was the general agreement that the moon was a dependable constant, longer than a day and shorter than a season.
LESSON 4: DESCRIBING TIME
The last lesson opened with this ques-tion, “Why would a culture choose to measure time with a moon?” Answers included that “It’s always there”; “It’s shorter than a year”; and “They didn’t have clocks or calendars.” Lively discussion among students erupted from the questions that followed: How do different cultures measure time? Describe two ways in which time can or has been measured by various cultures. In ancient times, why do you think many cultures measured time by the seasons rather than by the clock?
This discussion reinforced students’ understandings that the text validated how a moon was used to mark time for the Hopi.
We closed the four lessons with a final assessment that required critical think-ing as well as calculations to demon-strate students’ understandings of time measurement.
INTEGRATING SCIENCE, MATH, AND LITERACY
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.
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