Abstract
In history, geometry was founded more as a practical endeavor than a theoretical one. Early developments of the branch portray philosophers' attempts to make sense of their surroundings, including the measurement of distances on earth and in space. Such a link between earth and space sciences and geometry motivated us to develop and implement a multidisciplinary lesson focusing on the conceptual understanding of the law of cosines in the context of astronomy. In our content specific STEAM lesson, the authors aimed to facilitate an understanding of the law of cosines in ninth grade students, and then apply the law in a star map task to find approximate distances between stars. The second part of the lesson also included the use of an instructional technology to support students' work with the star map task. In the conclusion, the authors discuss possible ways to improve the quality of their STEAM education efforts for the given context.
TopContent Information
The lesson we present in this chapter aims to address many content and practice standards active in the U.S. education system. The following Common Core State Standards for Mathematical Practice have been targeted within the lesson: MP1. Make sense of problems and persevere in solving them; MP2. Reason abstractly and quantitatively; MP4. Model with mathematics; MP5. Use appropriate tools strategically; and MP7. Look for and make use of structure (Common Core State Standards Initiative [CCSSI], 2010). In addition, two Common Core Content Standards shaped the mathematical tasks for our lesson:
Key Terms in this Chapter
Dynamic Geometry Software: Instructional technology commonly used for the geometry content. The affordances of this technology enables users to construct various geometrical figures, develop conjectures and assess the validity of these conjectures. GeoGebra is an example of the dynamic geometry software.
Angular Distance: The measurement of the angle between two objects based on the use of optical instruments by an observer. While angle on a 2D plane can be measured using protractor, identifying the angular distance between two objects in 3D space requires the use of angular distance by an observer.
Algebraic Identities: Set of equalities that are held valid for any group of variables. The standard algebraic product identity can be established using the Binomial Theorem. A subset of these equalities can also be used to find the factors for given formulas.
Trigonometric Ratios: Trigonometric relationships in any right triangle. There are 3 basic trigonometric ratios: sine, cosine, and tangent. This list can be expanded with the following additional trigonometric ratios: cotangent, secant, and cosecant.
Law of Cosines: This is the equation used to find one unknown side of any triangle when the lengths of the other two vertices and the angle between these two vertices are given.
Information Communication Technologies: This is the broader term used for infrastructure and devices used for communication, application, collection and analysis of data.
Pythagorean Theorem: This theorem describes the numerical relationship among three vertices of any right triangle.