Objects

 

Objects are very important tools in the field of maths education for braille pupils. They help to make maths less abstract and deepen the spatial insight of the braille pupil. They strengthen the experience of geometric figures. Especially during the learning phase, it's necessary to use them, whether or not in combination with tactile drawings. Once the braille pupil knows and understands these concepts, s/he will be able to interpret oral explanations or drawings by means of a reference to the objects. Some objects can be bought premade. But you can also make some of them yourself, or use objects you find at home.

 

1) FRACTIONS & RATIO

The objects shown below are used to explain fractions and ratio to braille pupils.

Plastic discs and partitions

Plastic discs and partitions.

 

Plastic foldable strips

Plastic foldable strips.

 

Home-made wooden disc, divided into ten equal pieces. Home-made wooden disc, divided into ten equal pieces opened

Homemade wooden disc, divided into ten equal pieces.

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Wooden cube consisting of smaller cubes, made by Emanuela Ughi.

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Wooden and plastic cubes consisting of smaller components.
These can also be used to teach about geometry and volume.

 

 

2) COMBINATORICS

Homemade tactile objects can be used to teach about combinatorics.

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Wooden domino pieces with fragments of different
tactile materials (rubber, felt,...) pasted on, made by
Annemiek van Leendert.

 


3) GEOMETRIC SHAPES

The 2D geometric shapes shown below have relief lines on them, depicting radius, diameter, chord, altitude, diagonal, ... They are made by INJA Paris. As a result of the Comenius project, INJA brought them into production. You can order them on their website.

Plastic flat geometric shapes

2Dfigures

Plastic flat geometric shapes (trial version), made by INJA.

 

In most schools you can find solid geometric 3D objects like the wooden ones shown below. Use them for your braille pupil! Be creative. You can find objects in your kitchen or bathroom cupboard: storage cans, corks, different types of boxes,... It's quite easy to cut and paste cubes, pyramids,... out of cardboard.

Wooden geometric objects

Wooden geometric objects.

Cardboard to fold into geometric objects

Cardboard to fold into geometric objects.

 

Unfoldable 3D objects are very useful when teaching a braille pupil about volume, surface, perimeter,... and even the Pythagorean theorem. You can make them yourself out of cardboard or, if you're very handy, out of metal. Several companies sell educational materials in plastic

Homemade unfoldable pyramid in metal

Homemade unfoldable pyramid in metal, made by Huseby Resource Center.

Homemade foldouts of pyramids and Phytagorean theorem

Homemade foldouts of pyramids and Phytagorean theorem.

'Polydron' building toys

'Polydron' building toys.

Folding Geometric Shapes' building toys, by Learning Resources

'Folding Geometric Shapes' building toys, by Learning Resources.

'Clics' construction toys

'Clics' construction toys.

'Lokon' construction toys

'Lokon' construction toys.

 

Building toys like Kugeli, K'Nex and Geomag are perfect to build all possible geometric shapes.

'Kugeli' building toys.

'Kugeli' building toys.

'K'nex' building toys

'K'nex' building toys.

Building toys

Building toys.

'Geomag' building toys

'Geomag' building toys.

 

More complex 3D objects, demonstrating altitude, space diagonals,... are shown below.

 Plastic educational figures

 Plastic educational figures.

Homemade wireframe pyramid

 Homemade wireframe pyramid, made by Huseby Resource Center.

 

Because the principles of intersection are difficult to grasp for braille users, it's a good idea to introduce some solid objects which are cut through. The figures shown below are home-made.

Wooden objects made by Emanuela Ughi

 Wooden objects made by Emanuela Ughi.

Plastic objects made by Emanuela Ughi

 Plastic objects made by Emanuela Ughi.

 

Mirror symmetry can be explained using tactile objects like the homemade ones shown below. You could ask the braille pupil to complete an unfinished shape.

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Wooden pieces with tactile figures in felt, made by
Annemiek van Leendert


 

4) GRAPHS

Create alterable graphs using tactile boards. 

Homemade wooden board encarved with axes and grid

Homemade wooden board engraved with axes and grid,
made by Johann-August-Zeune Schule.

geo graph

Plastic board with tactile axes and grid.

 

5) TRIGINOMETRY

Explain trigonometry using tactile boards. These allow you to work alterably and to create different angles.

 Homemade wooden board encarved with goniometric circle

 Homemade wooden board engraved with goniometric circle,
made by Johann-August-Zeune Schule.

geo trigono

 Plastic board with goniometric circle.