Classroom Stories: Establishing a Common Vocabulary
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Classroom Stories: Calendars, Leap Years, and Graphs

By Stacy Palen.

Discussing the calendar can bring a “science and society” learning objective into the astronomy classroom.

Lunar Calendars

Islam, for example, uses a lunar calendar. The resulting gradual drift of holidays and festivals such as Ramadan through the seasons opens discussion not only to the use of calendars, but also to the earliest observed crescent phase that marks the beginning and end of the fasting month.

Asking students to imagine, and then explain, how Ramadan differs when it is celebrated in different seasons, can give students a better appreciation for why seasons and calendars matter. When we discuss the lunar calendar, Muslim students often raise their hands to add stories of Ramadan, such as waiting for the first observation of the crescent moon that signifies the end of the fasting period.

A few years ago, a Muslim student, Kimi, would come to intro astronomy class wearing traditional attire and veil. Kimi was quiet until we reached this discussion of the calendar. She stepped in to talk about the meaning and practice of Ramadan. This talk, in turn, transformed the views of other students, and they welcomed hearing about her experience.

Later in the year, Kimi had some problems in her neighborhood. Her car was broken into, and her door was vandalized. Kimi stayed after class to explain that this was why she was late that day. Three other students waited to walk with her across campus and offer moral support. We do teach more than astronomy in the astronomy classroom.

The Gregorian Calendar

Students find it surprising that the date of a long-ago event does not tell you precisely how many days ago it happened. This is due to the number of days in a year (365.25) not being an integer. A random error occurs because early calendars did not take the fraction of a day into account, so they needed adjusting once in a while. Students are often surprised to hear this.

For example, in 1582, when the calendar changed from Julian to Gregorian, 10 days were deleted: Thursday, October 4 was followed by Friday, October 15! The Gregorian calendar was invented to correct the systematic errors, so that the random adjustments were no longer necessary.

Explaining the Gregorian calendar is cumbersome: every fourth year is a leap year, except if it's a centennial. The only exception to this is if the centennial is divisible by 400. The effect can be difficult to visualize.

800px-Gregoriancalendarleap_solstice.svg

Image created by Wikipedia user BasZoetekouw using Astrolabe data and used under Creative Commons Attribution 3.0 Unported license.

This graphical representation shows how the date of the summer solstice changes over the course of 400 years. This graph shows that the summer solstice moves 1/4 day later each year, until the fourth year, when it resets to, almost, the original date. As time passes, those almost errors accumulate, until they add up to just about one day after 100 years.

That “just about” error accumulates until it adds up to a full day after 400 years. And then the leap day is skipped.

Asking students to visualize how far the blue line would rise without the leap-year reset helps them understand that the date of the summer solstice would change significantly, by nearly a month, over the course of just one human lifetime. A visual representation of the effect helps students grasp a difficult concept with ease.

Image retrieved from: https://commons.wikimedia.org/wiki/File:Gregoriancalendarleap_solstice.svg

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