Berkshire Mathematics

Types of Models

Continuous materials are those where the mathematics information is
obtained through visual-spatial means. Cuisenaire rods, Base 10 Material
and Unifix are continuous materials because their colour, size and shape are
the basis of their use.

Discontinuous materials are those where the mathematics information is
found through the counting process. Fingers, the number line, the abacas,
the Invicta Balance, Unifix cubes and counting blocks are discontinuous
materials because counting is the basis of their use.

Some materials are both because they can be used in both ways. For
example Unifix cubes are discontinuous when the colour is disregarded and
they are simply counted. However when used for teaching place value, a
white cube could represent a unit, an orange cube a ten, and so on. This use
of the colour means that the material is being used in a continuous way.

Discontinuous materials emphasise sequencing, transitivity and deductive logic, whereas continuous materials help children see patterns and inductive logic. Therefore both kinds of material are necessary in order to develop the child’s visual perception and strategy skills.

Mahesh Sharma is Professor of Education at Cambridge College,
Cambridge, Massachusetts, USA .

He is the Director of the Center for Teaching/Learning of Mathematics.
He edits Focus on Learning Problems in Mathematics, an international and interdisciplinary journal dealing with the learning and teaching of
mathematics, in particular with issues dealing with learning problems
in mathematics such as: dyscalculia, acalculia, mathematics anxiety
and specific learning disabilities in mathematics.
He also writes Math Notebook, a newsletter for teachers and parents.

His Center for Teaching and Learning of Mathematics is affiliated to
Berkshire Mathematics in the U.K. run by Patricia Brazil.
She organises Prof. Sharma’s lectures and courses, and produces videos / DVDs, which are for sale along with the U.S. publications.

Tel: 0118 947 4864 Fax: 0118 946 1574
Email: info@berkshiremathematics.com