The volume of the Sphere

Introduction

The best movies have an interesting topic, appealing to many of us, humans. Moreover, the best movies are based on a good script. Let us not forget about the modern 3D movies or the actors featuring in the movies.

Staring off from cinematography I have dared to compare the film with a lesson, which could become a small step in the development of the pupils’ geospatial thinking and can however become “one giant leap for mankind”. I have decided the topic of the lesson to be “the volume of the sphere”, which is of interest to the pupils (at least for the fact that the soccer ball of tennis ball are globular or because the topic is included in the curriculum and the examination topics for the final middle school examination). Moreover, I consider that a good lesson is a lesson that follows a logical teaching scenario, efficient for approaching a concrete teaching – learning – assessment situation and last but not least, a complex script since it involves both the actors of the educational process and the conditions to achieve it as well as the set methods and objectives. As most movie scripts, the teaching scenario must contain the dialog, in my opinion. Although communication is not only achieved by way of words, the dialog must be kept up during the entire class on several levels, at least pupil to pupil, pupil to teacher, teacher to teacher. I compare a modern lesson to a 3D movie in the sense that the pupils must overcome the barriers of the notions / knowledge in the lesson and “see in space”, be able to translate in practice what they have learnt and act constructively in everyday life. 

The main actors in this teaching scenario are the pupils. They become the active participants to their own training, active knowledge seekers. Similarly to the movie-making industry several where takes are shot for a scene to be perfect, mistakes are also allowed for the learning activity in this lesson to be successful. If each pupil learns from his/her mistakes he/she makes in class, does not give up, sticks to it and succeeds in their undertaking, the lesson is considered very good. Just as one would like to see a good movie again, the same way the pupils will want to apply what they have learnt in a good lesson whenever they can. And let us not forget that the pupils have a major influence on the aspects related to what they are to study about and the manner in which it shall occur. The pupils’ freedom to participate in their own training by their very own abilities involves the responsibility for their own learning progress.

My role as a teacher in this teaching scenario is secondary but still allows me to take up several characters: a counselor, mediating the pupils’ relation to the learning sources and methods; a communication mediator, encouraging the pupils’ active attitude by ideas; a partner, cooperating with the pupils and with every pupil separately in order to succeed in the learning and educational undertaking; a mentor, teaching the pupil how to learn and become a role model myself; a guide, leading the pupils throughout the class and not only. Thus, in this teaching scenario my attention as a teacher shall focus on the pupils’ interest for innovation, stimulating creativity as well as ensuring the development of geospatial thinking.

 In this teaching scenario, the topic “The volume of the sphere” is approached from the perspective of the concept of geospatial thinking. Thus from an ordinary lesson in the 8th grade mathematics syllabus, “The volume of the sphere” becomes an efficient way to pursue, an innovative and concrete model in the teaching of pupils.

Argument

I have started off in drafting this teaching scenario being aware of the ever so important place of geospatial thinking in the learning-teaching-assessment process as well as the role of geospatial thinking in pupils’ training.

Scope

The aim of this document is to underline once more the importance of geospatial thinking in the development of the pupils’ skills, which would turn them into individuals with an enhanced spatial intelligence, capable to act in new circumstances, take decisions and take up major roles in a society of knowledge and a world of permanent change.

Title of the lesson

The volume of the Sphere

Educational objectives

Cognitive

  • Calculate the volume a of sphere with a given radius,

  • Demonstrate the calculation formula for the volume of the sphere,

  • Identify round bodies in daily life,

  • Apply the calculation formula for the volume of a tennis ball and the volume of the Earth,

  • Collect data from various sources,

  • Analyze and compare data,

  • Select the necessary data in order to achieve the set objectives,

  • Convert from a volume unit of measurement into another,

  • Present the products of the lesson activity in English.

Affective

  • Actively participate by involvement and  co-work,

  • Word and communicate ideas,

  • Work together with their fellows,

  • Use English in a presentation,

  • Listen to and respect the others’ opinions,

  • Bring arguments in the support of their opinions,

  • Contribute to the creation of a stimulating (for thinking and creativity) and relaxing (open to free expression) environment

Psychomotor

  • Use ITC means,

  • Use geometrical tools for the construction of bodies,

  • Select the necessary sources for the suggested topic,

  • Create the materials necessary for the topic,

  • Make the experiment and advance their own conclusions,

  • Develop mobility skills in catching the tennis ball.

Concepts

  • three dimensional figures, polyhedrons, prism, cube, pyramid, pyramidal frustum, cylinder, cone, conical frustum, sphere, hemisphere, cubic meters, cubic yards, cubic inches, cubic feets, cubic kilometers, cubic centimeters, cubic miles, length, width, heigth, volume, bases, faces, verticies, edges, area of the large base, area of the small base, irrational number, circles, discs, radius, distance, center point, experiment, spheriod, formula.

Interdisciplinarity

  • Mathematics, Physics, Geography, ITC, English, Civic Culture, Drawing, Music, Physical Education.

Target group

  • 8th grade pupils

Duration 2 hours

Location

The class takes place in the ITC laboratory where the pupils have access to computers with Internet connection, a printer, a beamer, interactive whiteboard,  GeoGebra software, speakers. Besides the equipment in the ITC laboratory, the pupils shall have access to other materials, too: A4 paper, cardboard,  flipchart, writing tools, geometry tools, watercolors and paint brushes, Romanian-English dictionary, textbooks (Mathematics, Geography, Physics), world atlas and, for each group of pupils, hemisphere, cylinder, cone and a packet of corn flour.