University of Edinburgh

Maths Early Years, Braille and Large Print

Presented in April 2005

Early Years Maths

Mary Dallas

Maths 'must-haves'! What do you think these are?

  • 100 squares either in enlarged print or overlaid in braille.  Blank tiles to go with 100 squares and cover numbers.
  • A range of number lines and cards in enlarged print or overlaid in braille
  • Flip-chart number lines for single recognition
  • Debate around use of number fans
  • All of the above are available from Synergy Learning Products.  RNIB have clear sticky backed sheets for braille

Products from RNIB

  • Tactile/large print dice and dominoes
  • Tactile ruler
  • Clear enlarged print ruler
  • Large display or talking calculator
  • A clock face with tactile markings
  • A large clear clock face
  • 100 Peg board with tactile pegs

NES Arnold

  • Large display digital timer
  • A range of beads in different shapes
  • Concrete counting resources such as Multilink
  • Coloured base ten apparatus
  • Some shapes in both 2d and 3d
  • Abacus- discs flip over


  • Cubarithm
  • Tactile protractors
  • Tactile tape measure
  • Talking thermometer
  • Talking scales
  • German film and Dycem mat to go underneath

Checklist to Determine if Diagram Should be brailled

  • If the actual object is unavailable
  • If the object is too small or too large to examine by touch and recognise details
  • If the object is dangerous to touch
  • When it is necessary to show size relationship between objects
  • When the pupil needs information to answer questions and take part in class discussions from maps/graphs etc

Checklist for Making Decisions about a Tactile Diagram

  • Why is this picture/map/figure important?
  • What are the most important elements to communicate?
  • Who will use this material?
  • Age group
  • mental and/or physical condition
  • pupil's experience or ability


How will this figure be used?

  • with or without help from a sighted teacher
  • with other children who are sighted or blind
  • with actual concrete objects

Where will the material be used?

  • in a classroom setting
  • at home for leisure reading or games
  • as part of a test
  • as an orientation map

Accessible Mathematics for Visually Impaired People

  • Some branches of mathematics can be presented in the form of tables, diagrams and graphs.
  • There are tactile equivalents and significant advances in technology in this area which are readily accessed by VI pupils.
  • Algebra presents a much greater problem.  Teaching primarily visual with no tactile equivalents.
  • There are huge problems in trying to translate advanced maths into an auditory format.
  • Imagine a maths teacher at a blackboard teaching differential calculus.  Language is an afterthought. Some maths teachers teach without using much language at all!
  • Visual Mathematical elegance is two dimensional with extensive use of subscripts and superscripts.  A square root sign can cover a complex of several variables.  Consider the visual complexity of the common equation.

Accessible Maths in Auditory Format

Even for sighted students, the content of the expression can be obscured by the formatting information.

The Maths Braille Code claims to allow blind students to braille all the necessary mathematical symbols for 'the highest level of mathematics'. Generally agreed that non-visual representations such as this are not as powerful as visual ones

Visual examination can scan the whole equation or parts of it, repeatedly, in order to seek understanding.  The pupil is in active control of this process.

Often listening is essentially a passive process with little pupil control.

Possible solutions to these problems;

  • Use of prosody - normal meaning - the study of versification (eg; poetry, blank verse or even limericks)
  • Prosody is concerned with intonation, pitch, rhythm, timing and rate of speech.  These elements may be used to translate complex visual images into auditory information.
  • to give the listener a more active role, an equation has to be broken down into smaller and logically ordered chunks.  The listener also needs to have control over access to these individual segments.

Long Term Objective

  • To formulate a system which will be accessible via the Internet
  • To develop programmes such as MathML, Mathtalk