Tactile drawings

 

For sighted people, a drawing visualizes information and offers a quick overview.  Not so for blind pupils. They need to explore the drawing, which is time-consuming. Therefore you should always consider if the drawing is a surplus for the braille pupil. It is unnecessary to transform every single drawing in the original maths book into a tactile drawing.

 

1) Is it useful for the braille pupil to learn about the given mathematical subject using a drawing?

2) Is it better to explain it verbally, or with an object, or through a combination of drawings and objects?

3) Is it necessary to make a (quite expensive) swell drawing or tactile drawing, or is a cursory drawing on plastic foil sufficient? (These have to be made in mirror view!)

4) How to adjust the original drawing?


 

CHARACTERISTICS OF GOOD DRAWINGS


A uniform and predictable lay-out would shorten the exploration phase. We have some suggestions for more standardised drawings.

1) GENERAL CHARACTERISTICS

- Put the title in the upper left corner of the drawing. This way, the pupil knows how to place the drawing: in landscape or portrait position.

- Enlargen and simplify the drawing. When the original drawing is very 'full' and confusing, it's better to split it up into two drawings.

- Don't put too much information in braille in the drawing itself. Write it underneath the title for a 'clean' drawing.

- When there are several figures in a drawing refering to the same title or exercise, mark this after the title using #.
Eg. #4 can mean there are 4 polygons on the page which are related to one exercise.

- When there are several drawings related to the same head title or subject, put short subtitles above every one and name them.
Eg. 1) Rotations - 1a) Rotation of a point - 1b) Rotation of a line segment - 1c) ... 

- When several related drawings take more than one page, number the pages.
Eg. 1/3 - 2/3 - 3/3

congruence test for triangle congruence test for triangle

 

 

2) DIAGRAMS

- Reading diagrams is time-consuming for a braille user. Therefore we advise to write the data in a table for a quick transfer of information. But, we do believe it's important for a braille user to know the principle of a diagram. So tactile diagrams are useful when the focus lies on learning how to read diagrams.

- Pie charts shouldn't be larger than handsize. Use different patterns for each piece. If there are small pieces involved, it's a good idea to draw the pieces apart: leave some blank space between each piece.

Pie chart

- For bar charts, we suggest to stretch out the horizontal scaling in thin dotted lines. Fill up the vertical bars and leave some blank space between them, so the dotted lines can be felt in between them. Name each bar underneath, or use different kinds of filling. Put an index underneath the title.

bar charts

- An alternative way to draw bar charts, is to present them horizontally in the text document using the = symbol. Group them by five.
Eg. The following bar chart contains four data, with values 6, 3, 1 and 8:
===== =
===
=
===== ===

 

 

3) GEOMETRY

- Distinguish important (thick) from less important (thin) lines. Use different types of lines: guide lines are dotted, grid lines are thin and dotted.

- Points which are named and thus identified, are marked with a dot.

 2 crossing lines

- If three or more lines are intersecting, surround the dot with some blank space.

 3 crossing lines

But:

 bisector

- Names of lines are written on their left and above them whenever possible:

 straight lines

- Mark perpendicular angles with a little square:

 perpendicular

- The difference between interior and exterior angles is marked with a bow:

 interior and exterior angles

- Angles of the same size are marked with a bow and one (or several) crossing lines:

 angles same size

- An orientated angle is marked with a bow and arrow:

orientated angle

- Name the angles of intersecting lines with a combination of a letter and a number. In the visual drawing, the angles are marked with a number and the letter is written somewhere near. But, when other intersection points are nearby, this could get confusing for the braille user.

crossing lines angles

- Mark line segments of the same length with one or several short perpendicular lines:

 lines same size

- The indication of the length of line segments can be confusing. A number written in between two points, applies to the length of that part of the line segment. The total length of the line segment, eg. the side of a figure, is written below or aside. The line segment is duplicated and marked out with two perpendicular lines at each far end.

line size indication

 

 

4) GEOMETRY: REFLECTIONS - TRANSLATIONS - ROTATIONS

- Some braille users have more spatial visualization skills than others. Their insight in this aspect of geometry depends partially on their ability to build a mental image. Braille pupils who still have some vision left, or visual memories, can be more capable of doing this. Do not expect the same insight or result of all braille pupils.

- It's important to take some time for the learning phase, and use objects to support the drawings. Use a pre-made flat figure, or cut one out of cardboard. Place it on the table, a pinboard or the drawing and let the braille pupil feel what happens.

- Make a clear distinction between the various types of lines. Draw the reflected / translated / rotated figures in thick, full lines. Axes in thinner full lines. Guide lines are dotted thin lines.

reflection of parallel straight line
a translation of a circle shift and angle

- Drawings of rotations can get quite complex. Therefore it is better to make two drawings: one indicating the rotation angle and the starting position of the figure, and one with the implementation and the result. 

rotation of a quadrangle rotation of a quadrangle

 

 

5) GEOMETRY: PERSPECTIVE DRAWINGS

- We don't believe perspective drawings are very useful for braille users. It is almost unpossible for them to read solid figures in a flat representation. Replace these drawings with an object, or a drawing of the unfolded faces of the figure, or a drawing of the different views of the figure, or a combination of these.

Drawing of the different views and foldout of surface area of a cuboid

Drawing of the different views and foldout of surface area of a cuboid.

'Folding Geometric Shapes' can be used to replace perspective drawings.
'Folding Geometric Shapes' can be used to replace perspective drawings.

 

 

6) GRAPHS

- Draw the axes in full thin lines, the grid in dotted thin lines. Leave the gridlines out when they're not necessary.

basic raster

- Surround the function with some blank space where it is intersecting with the axes and grid. This way it is easier to follow it by touch. When a function is running through the point of intersection of the axes, this point is marked with a dot surrounded by some blank space.

- It's not necessary to name all the values on the axes in braille. One is enough to indicate the scale. Leave some blank space around the braille.

- Don't put the coordinates of a point in the drawing. Name the point and put additional information under the title.

- Draw the functions in thick lines. If there are several functions on one graph, use different types of thick lines (full, striped, dotted,... ) and write a legend underneath the title. Or, if the braille user isn't that experienced, split up into two or more drawings. Sometimes this is not possible, for example when the shift of functions is depicted.

example elementary functions

figure horizontal shift of parabolas


- A drawing is a fixed image. When teaching about graphs, you could also practise with objects and create alterable graphs. In the school in Berlin they use a wooden engraved board and small screws to 'draw'. In Tartu they have a plastic version of it, also usable for trigonometry. The graphs are made with Wikki Stix. A third option is to 'draw' with pins and Wikki Stix on a pinboard and a re-usable tactile drawing of a grid.

Pinboard with re-usable relief drawing, pins and Wikki Stix.

Pinboard with re-usable relief drawing, pins and Wikki Stix.

Wooden encarved board with screws

Wooden engraved board used with screws.

geo graph

Plastic board with pins and Wikki Stix.


 

7) TRIGONOMETRY

- Make a clear distinction between the various types of lines. Draw the sine, cosine, tangent and cotangent in thick full lines. The guide lines are thin and dotted. The axes are in thin full lines, and the circle itself in medium full lines.

goniometric circle: sine and cosine

- Since a drawing is a fixed image, it is a good idea to explain trigonometry during the learning phase using an alterable object to emphasize the relation between sine, cosine, tangent and cotangent. In Berlin we saw a wooden board engraved with a trigonometric circle and little holes. Little screws are used to set points. In Estonia we saw a very interesting trigonometric circle in plastic (also used to demonstrate graphs), which they use with small pins and Wikki Stix. You could also make a tactile drawing of the circle and place it on a pinboard or use it with Wikki Stix.

Re-usable drawing of goniometric circle, use with pinboard or Wikki Stix.

Re-usable drawing of goniometric circle, use with pinboard or Wikki Stix.

Wooden board with goniometric circle encarved

Wooden board with goniometric circle engraved.

geo trigono

Plastic board with goniometric circle, used with pins and Wikki Stix.