Solving problems in mathematics and physics with 3D Geoboard

By Elitsa Tsoneva,Teacher in Technolgy, 25/04/2022


Many people have trouble imagining three-dimensional figures and solving problems related to geometry and physics. In information technology classes, students often find it difficult to create projects by drawing geometric objects. The ability to visualize things is especially important for engineering sciences. Many studies show that in the period between 12-13 years Bulgarian students begin to lose motivation to study science, and this affects their further choice of profession. In addition, online learning has led to a decline in the desire to learn and to some gaps in the understanding of complex learning material.
In order to achieve higher knowledge and motivation of students aged 11 to 13, on 26.04.2022 New Bulgaria Association conducted a multidisciplinary training at the Thomas Edison Private Primary School (Sofia, Bulgaria). The training “3D Geoboard workshop” was completed using an innovative STEM learning tool. 3D Open Geoboard tool is a mathematical learning tool that builds on the familiar geoboard with the ability to create geometric shapes in 3D space. Working with it, students encounter some physical phenomena. The device was created by engineer Nikola Chernev. A team of scientists and teachers works on the methodology of its use and implementation in the learning process. Maria Brauhle is a member of the team. She is a scientist at the Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences.

The lesson was conducted under the guidance of Nikola Chernev and Maria Brauhle, and on behalf of the school coordinator Elitsa Tsoneva – a teacher of Information Technology and a representative of the non-profit company New Bulgaria. The training was fully consistent with what the students were learning at school:
The curriculum of students in grades 6-7 in mathematics, physics and information technology at school includes:
• Drawing 2D geometric shapes according to given dimensions
• Orientation in a coordinate system
• Calculation of geometric figures parameters
• Math calculations
• Physical process of friction of materials and resistance of materials
• In information technology: Drawing 2d and 3d geometric figures with different technological software tools
The resources used for the activities are:
• 3D Open Geoboard set for each child – it includes a wooden board with two coordinate systems and elements for building shapes
• Working templates with Cartesian coordinate system
• Measuring instruments (ruler, protractor)
• Presentation shared on an interactive whiteboard

Student work
The students worked in groups of 2, completing 3 consecutive tasks:
• research independent task
• team performance task
• task – game in pairs
The research task involved creating a complex geometric figure of your choice, using the 3D Open Geoboard kit and measuring instruments. The aim of the task was for the children to learn to build figures with the help of the elements in the set, orienting themselves in the two parallel coordinate systems on the board.

With this Cartesian coordinate workflow template, participants measured the position and dimensions of the figures, and the position of each added element could be calculated with accuracy in the relevant quadrant.

The other challenge was to look at and calculate and balance the resistance that the elastics that support them put on the figures.

Their second task was to create a specific three-dimensional figure on a model, in which participants had to calculate the size, position and height of the object. The example shown on the spot was the creation of an inverted pyramid in a cube.

The final task in pairs was to create figures / architectural forms, with the first participant inventing and constructing the three-dimensional object, and the second having to create its symmetrical figure using central symmetry or an axis of symmetry. For this purpose, the second participant had to measure the position of the object and imagine the projection of its mirror image.

To practice working with a coordinate system, students have an assignment to work in a class on computer technology – making a project with programming figures in a coordinate system. This last task can also be done online, using the open learning coding platform for students:
and the shared project “Geometry puzzle” :

Nikola Chernev presented in front of the students a presentation about the profession of engineer; about how the idea for 3D Open Geoboard came about; what challenges he encountered in the process of its creation and how he solved them using mathematics. 3D Open Geoboard is an excellent visual example of how a tool for solving mathematical problems is created with the help of mathematics.
The students worked with great desire on the project. Thepractical STEM lessons help them to better understand and draw / construct three-dimensional figures, as well as in the overall understanding of mathematics and some laws of physics. Thanks to the story of engineer Chernev, their interest in future similar activities and STEM professions has increased.