Lifelong Learning Programme

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Title of the Experience
Stereometry - cube cuts
Name of the teacher
Katarína Javorová
Country where it took place
School typology
Lower Secondary School
Thematic Area
Experience typology
Teaching in class
Type of contact
Description of the Experience
The topic of Stereometry, specifically the cube cuts a good imagination is needed. 3D bodies are plotted on a blackboard in 2D, which creates the problem for some students. The imagination of 3rd grade students of high schools is very weak. They can not often imagine the front, rear, and the top sides of the cube. It does not even help them when I highlight the cube image with colored chalks. It happens that pupils know the rules of stereometry, but as the pupils say by themselves "they do not see anything there ... where you draw it there? There are only lines there … it does not make sense to me! ... "And so they can not cope with the curriculum. They do not like it and have no willingness to address the practicing examples of the dice cuts.
It was proved to me that at the beginning of learning the new topics we first repeated with the students what bodies we knew already and what terms we will use (node, edge, wall, grid body shell, body height, footprint, side view, and parallel lines, vertical...). Then we made a net of some bodies such as cube, cuboid, prism, cone, and cylinder. We cut out the net and glued the network models together. During the lesson we usually manage to complete only the bodies of cube and cuboid. Other bodies pupils complete as their homework. For this they can earn bonus points. We have introduced a competition for The Best Body when the pupils cut paint their body models freely marked as they wanted. For the next class, the pupils brought with them play dough and wooden sticks and created by themselves a teaching tool - a cube (cube edge 10 cm). With this model they will use during the next classes. Instead of a play dough, we sometimes used construction kits for building models. These cube models are stronger and more durable. When we have the topic of sections the pupils work with their own dice models. As a further tool serves a string, as well as cube walls made of cardboard. Then they pull the string as a teacher makes incisions on the board (or using the programme Geogebra). At the beginning we make simple sections. Students compare what they have created with what is drawn on the board. The pupils work on the cube section tasks on pre-prepared worksheet. Here are some "clean" cubes, empty cube images. Here on these examples they learn the basics of stereometry (parallel lines, center parties, vertical, etc.). Then are the class tasks followed a simple exercise task of sections (Fig. 1).

Fig. 1 sample of simple tasks of cube sections
I write from my own experience that the majority of pupils do not need their teaching tool anymore after two lessons. They no longer need it or use it only without the string to confirm their solutions.
We used to sometimes make the first cut of the cube by free hand as an estimation of what the cut might have looked like and only then we approached the drawing.
Great help in drafting bodies allows the Geogebra program in which the body can be moved or rotated. I greatly appreciate the opportunity to work with Geogebra, as in it you can create Java applets step by step drawings and during the lesson I can spend more time on the interpretation of the topic and individual pupils when they have problems. Individual design steps can be repeated several times so I do not have to erase the chalkboard and draw again the whole cube. However, not always I have at my disposal technical equipment such as a computer or a data projector.

Comments on this Teachers Experience

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Date: 2014.11.09

Posted by Viera Kolbaska (Slovakia)

This experience is significant when teaching cube cuts. The author tried to stimulate students' spatial imagination through manual activities - students learn about bodies through constructing – through their own activities. Students can see their creation, they can link a picture made by them at the E3 with an illustrative sketch of E2 and then learns about the bodies’ cuts through their own manual activities.
• Does this experience explain the causes of students’ low motivation to learn science subjects?
This experience approximates Math teachers the causes of low motivation to learn science subjects – subjects lack teaching students through their own observation and their own activities.
• Does this experience offer possible solution to overcome this low motivation?
Yes, this experience shows the way how to solve the problem with low motivation of teaching science subjects. Procedure: I show – you watch – see – think - create your idea - construct.
• Do you have a similar experience?
I have a similar experience; we were constructing bodies by using toothpicks and gummy bears. Thus, through the construction we were creating the ideas, with which we later worked.


Dissemination Seminar in Florence

31 October 2015 The seminar has been held in ITIS “A. Meucci” one of the schools involved within Goerudio project activities. Its main aim was to promote the results of the project toward a broad sample of stakeholders even overcrossing the number of people directly involved in the production of project outcomes. This purpose has been totally achieved especially thanks to the participation of students and teachers coming from different schools or from other classes instead of those ones directly involved within the project activities.