Classroom - Indian Academy of Sciences

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[email protected] Keywords. Summer solstice. Imagine a world without facts. No hard truths whatsoever. It's difficult because in the world we're used ...

Classroom

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. “Classroom” is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. Vishwesha Guttal Centre for Ecological Sciences, Indian Institute of Science

Discovering Facts Finding the Longest Day with School Children

Bengaluru 560 012, India. [email protected]

Imagine a world without facts. No hard truths whatsoever. It’s difficult because in the world we’re used to, facts are a way of life. They are handed down to us from our elders, teachers, books, the television – the list is endless. Especially in school, we’re told to memorize a number of facts and we are rarely encouraged to question them. But, how do we discover facts if there is no one to tell us about them? In a delightful set of interactions with school children, I had an opportunity to discuss how they know that the longest day in the year, the summer solstice, falls on June 21st. While I was teaching children of 5th standard, all aged around 11–12 years, I made my own surprise discovery with their help! It is delightful to talk to children, especially when it is about science. Having no constraints about the syllabus makes the experience even better. In 2012, I was invited to interact with the children of a primary school – Purnapramati [1]. The idea was to involve children from Class 5, all aged about 10–12 years, in a short-term, hands-on project.

Keywords Summer solstice.

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The school imposed no restriction on the choice of the topic I wanted to discuss with the students. I thought a lot about what

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could be a feasible, short-term, yet interesting project that these kids could do. As I continued to contemplate, I was already in the class and began my interaction by exchanging greetings. But the project subject remained elusive until our interactions gained momentum. I realized that the first day of my interaction happened to be the 21st of June 2012. I asked the students, "Is there anything special about today"? The answer came almost immediately when one student said, "Yes, today is the summer solstice."

It is delightful to talk to children, especially when it is about science. Having no constraints about the syllabus makes the experience even better.

I then said, "I have never heard of that. What does that mean"? One student, with a grin, said, "Don't you know? It is the longest day of the year." "May be. But how do you know it’s the summer solstice"? I asked. "We learnt in the class. Our teacher told us", the response came from one corner. "How did your teacher know about that"? I continued my questions. "From her teacher," was one answer, while another student said, "From our textbook." "How did your teacher's teacher or even the textbook writer know that 21st June is the longest day in the year"? I heard the answer, "From their teachers," from some students. However, it was already clear to many of them that I was going to ask, "And how did that teacher come to know about this fact"? After teasing their minds for a bit, I got the answer I was waiting to hear when one student said, "Someone must have measured the length of each day throughout the year and found the longest of all days". I continued, “What if your teacher had never told you that June 21st is the summer solstice? If your challenge is to find it out yourself, how will you do it” ?

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I got to hear a lot of creative and courageous solutions. Several students said that they will wake up and note down the sunrise and sunset time every day. I told them that there were two challenges associated with that. One was that they would need to wake up early in the morning, and to my surprise this didn’t seem to be a problem to them. So, I pointed out the second challenge, which was to know the precise time of sunrise or sunset. For most of us, living in cities with buildings all around, seeing the sunrise or sunset is next to impossible. Some students were willing to go to mountains and deserts so that they could see horizon to horizon. Some, clearly showing an orientation towards technology, even thought of setting up devices that will record sunrise and sunset times automatically.

Since an hour has 60 minutes, and time switches to 1 pm after 12:59 am, the students first had to learn that merely subtracting the sunrise time from the sunset time would not give them the length of the day! This, by itself, was an important mathematics concept to master during the course of the project.

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Finally, we all agreed to take a shortcut given the difficulties of going out of home to a desert or even that of devising a technology to note the precise times. The shortcut, which was also suggested by students, was to look at the newspaper everyday and note down sunrise and sunset times. Once the concept for the project was ready – which took just about an hour of intensive and very interesting discussions outlined above – it was time for implementation. The project took nearly three to four months, working at a frequency of twice a month. The entire implementation was very well supported by their enthusiastic teacher, Indumathi. The class had 12 students, an ideal number for our task involving calculation of daylengths over 12 months! Each student was assigned a specific month and was asked to collect data – to note down sunrise–sunset times in Bengaluru from newspapers at home (many of them also used sources from the Internet). They then calculated the duration of the daytime based on the timings they had recorded (Figures 1 a, b). Since an hour has 60 minutes, and time switches to 1 pm after 12:59 am, the students first had to learn that merely subtracting the sunrise time from the sunset time would not give them the length of the day! This, by itself, was an important mathematics

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Figure 1. Sunrise, sunset and length of the day calculated from data from Bangalore for the year 2012 [3].

concept to master during the course of the project. Another new concept that they learnt was plotting data on graph sheets; this was initially learnt in a simple intuitive manner with different examples such as plotting heights and weights of students in the class. With all necessary concepts and tools at their hand, each student plotted the duration of the day versus the date for all 30 days of the month assigned to him or her. When they finally put together all these graphs from January to December, next to one another, we were all extremely fascinated to see the oscillating pattern of duration of the day (Figure 1c). The students immediately went back to the original aim of our project, and from their own analysis, found that the duration of the day was maximum for

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Figure 2. The longest and shortest days are 21st of June and 21st of Dec respectively, if we plot day length up to an accuracy of one second.

about 10 days in the last two weeks of June (Figure 1c). So, it was not one day when it was maximum, but for 10 days! Similarly, the shortest day was around the 20th December of the year. All the students, by now, were wondering why everyone considered June 21st as the longest day, when there were actually 10 days that were of roughly the same duration. In fact, this was something I was not expecting at all and was an interesting new observation for me! In the meantime, students also discovered the reason for finding 10 long days instead of a single day by discussing among themselves: they said that they had the data of sunrise–sunset only to an accuracy of minutes. To find which day among those 10 days was longest, they would need even more accurate data of sunrise-sunset times – down to seconds, not just minutes! In fact, when we plot the length of the day to an accuracy of seconds for those 10 days, we do indeed find that June 21st is the longest day of the year (Figure 2a). The difference in the length of the day between June 21st, the longest day, and the two neighboring days, June 19th and 22nd, is only one second! Likewise, we also find that Dec 21st is the shortest day of the year (Figure 2b).

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Some Questions for Curious Readers We obtained the length of the day from sunrise and sunset times. Why do sunrise and sunset times vary over the year? Do we notice any interesting patterns in them? For example, on which day does the sun rise earliest (and latest?) Intuitively, you would expect that the sun would rise earliest on the summer solstice and latest on winter solstice. Is that actually true? Figure 1 shows plots of sunrise and sunset times for Bengaluru. As is clear from these plots, the earliest sunrise occurs during May and not on June 21st! Likewise, the day on which the sunrise occurs latest is not on the winter solstice (December 21st), but it’s on a day in November.

The students had no issues with learning about sunrise and sunset together with plotting and related mathematical concepts needed for the project. This made the learning truly interdisciplinary and not compartmentalized.

Another interesting pattern to note is that the sunrise occurs nearly at the same time (around 6:09 am) for the entire month of September. Why do you think these patterns occur? If you were to take data for sunrise and sunset from other parts of India, such as Bhopal and Delhi in the North and Kanyakumari in the South India, and Bhuj in Gujarat and eastern parts of India such as Arunachal or the Andaman & Nicobar islands, would you expect to see a difference in their patterns? While it is clear what students learnt from this exercise, from my point of view, it was extremely interesting to interact with students and answer their amusing and intelligent questions. The students had no issues with learning about sunrise and sunset together with plotting and related mathematical concepts needed for the project. This made the learning truly interdisciplinary and not compartmentalized. It was also revealing to me to learn the finer details and facts about which I myself was unaware of until I worked on this simple teaching project! Acknowledgements I thank Sandhya Sekar for comments on the article and Elsa Mini Jos for the help in producing the figure.

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