In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his "Key to Arithmetic", a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life…

To improve on the classic school trip to the museum and the traditional distinctions between formal and informal learning, every year we run a project where the schools (first the teachers and then the pupils) are actively involved right from the very first stages of planning. The various projects realised so far involve schools with children of…

I present a novel way to introduce the lunar orbital eccentricity in introductory astronomy courses. The Moon is perhaps the clearest illustration of the general orbital elements such as inclination, ascending node, eccentricity, perigee, and so on. Furthermore, I like the students to discover astronomical phenomena for themselves, by means of a…

The question examined in this "Science 101" column was inspired by "Find Your School's Analemma" (in this issue). What causes the Sun's apparent position in the sky to trace a figure-eight pattern throughout one year? The analemma, or figure eight pattern that the Sun makes throughout the year, is due to two major…

Humans have always had the vision to one day live on other planets. This vision existed even before the first person was put into orbit. Since the early space missions of putting humans into orbit around Earth, many advances have been made in space technology. We have now sent many space probes deep into the Solar system to explore the planets and…

Is moonlight "silver" or "cold"? In this paper we discuss the interesting combination of factors that contribute to the common descriptions of moonlight. Sunlight is reflected from the lunar surface and red-shifted. When traversing the atmosphere, moonlight is further depleted of short wavelength content by Rayleigh scattering.…

The changing altitude of the Sun (either over the course of a day or longer periods) is a phenomenon that students do not normally appreciate. However, the altitude of the Sun affects many topics in disciplines as diverse as astronomy, meteorology, navigation, or horology, such as the basis for seasons, determination of latitude and longitude, or…

William Herschel (Fig. 1) is rightfully known as one of the greatest astronomers of all time. Born in Hanover (in modern Germany) in 1738, Herschel immigrated to England in 1757 and began a successful career as a professional musician. Later in life Herschel developed a strong interest in astronomy. He began making his own reflecting telescopes in…

The 5000-year-old remains of Stonehenge, in England, testify to humankind's reverence for the stars. Humans hauled four-ton stones from as far away as 240 km to make these monuments. They are the remains of a larger structure used for religious purposes and to predict astronomical events such as solstices, equinoxes, and perhaps even eclipses, an…

Educators at all levels and in all settings are getting questions these days about the approaching "end of the world" catastrophes supposedly coming in December 2012. This resource guide provides a selection of useful resources for responding to student and public questions in this arena. The latest internet myth to gain traction is the notion…

The clarity of the argument, and the detail in the mathematics, make this a real piece of "mathematics in context". However, while this might be not described as "mathematics for the faint hearted", there are classroom implications for application, interest, and motivation. "All things solar" have seen a rise in popularity through the serious…

Immersive environments hold promise to provide unique and heightened sensory experiences that focus a learner's attention, and thus may be useful learning platforms. In particular, portable planetariums may be useful in advancing conceptual knowledge about the night sky, because they afford learners with Earth-based views of celestial motions,…

Literature in "Physics Education" has shown that students encounter many difficulties in understanding wave propagation. Such difficulties lead to misconceptions also in understanding sound, often used as context to teach wave propagation. To address these issues, we present in this paper a module in which the students are engaged in…

This study aims to assess primary school teachers' knowledge of basic astronomy concepts, such as the sizes and shapes of, and the distances between, the Sun, the Earth, and the Moon, lunar and solar eclipses, and the motions of the Moon and the Earth. Out of a total of 1,533 teachers, 398 (26%) were reached and asked to take a knowledge test. On…

Modeling is an important approach in the teaching and learning of science. In this study, we attempt to bring modeling within the reach of young children by creating the SimSketch modeling system, which is based on freehand drawings that can be turned into simulations. This system was used by 247 children (ages ranging from 7 to 15) to create a…