Maths manipulation


Taking a look at how to help children with SEN engage with mathematics.

Teaching mathematics to children with SEN tends to concentrate on the teaching of basic skills, which are easy to teach and assess. Teachers often believe that these children cannot assimilate and retain information so there is a need for constant repetition and drills.

Research tells us, though, that children can solve problems and play with maths before they have mastered skills used to solve problems (National Council of Teachers of Mathematics, 2000). If they are given opportunities to do so, their conceptual understanding and ability to apply their knowledge is increased (Carpenter, Franke, Jacobs, Fennema and Empson, 1997).

Effective classroom practice and development of conceptual understanding is a combination of:

  • building on children’s prior experience
  • the creation of practical opportunities for children to practice
  • allowing children to investigate and choose their best strategy
  • building a climate of collaboration and talk-based learning.

Children with SEN benefit from help searching for, finding, and using patterns in learning the basic number combinations and arithmetic strategies (Baroody, 1996).

Hands-on learning

Using manipulatives is a useful way for all children to play and discover mathematical relationships and explore concepts. A maths manipulative is a concrete or visual object that allows a child to investigate maths concepts using a hands-on approach. These objects can include blocks, shapes, cubes, money or counters. Increasingly, the use of technology is providing children with a variety of manipulatives, including virtual manipulatives – digital “forms” that resemble physical objects and can be manipulated, usually with a mouse. Examples of virtual manipulatives are computer games and the use of interactive whiteboards.

Using concrete materials can enable all children to think and reason in a meaningful way. Stein and Bovalino (2001) state that by providing manipulatives, teachers can create a positive experience for children by offering a concrete form from which children can then build their conceptual understanding.

Children who use concrete and virtual manipulatives demonstrate a greater mathematical understanding than those who use physical manipulatives alone (Olson, 1988). Manipulatives that are meaningful to the child, provide control and flexibility to the learner, have characteristics that mirror, or are consistent with cognitive and mathematical structures, and assist the learner in making connections between various pieces and types of knowledge, are the most successful. For example, virtual software can connect pictured objects, such as base ten blocks, to symbolic representations. It helps children generalise and connect their game playing or their abstract experiences with concrete materials.

Conceptual understanding

Children who have difficulty in mathematics need additional resources to support and consolidate the underlying concepts and skills being learned. They need multiple experiences with models and repetition of the relevance of models with abstract, numerical manipulations.

We need to give more time to mathematics, as the curriculum does not allow enough time for the many instructional and learning strategies necessary for the maths success of the child with SEN (Lerner, 1997).

We need to make a conscious effort to build on what children know how to do, relying on children’s own strengths to address their deficits. Informal strategies provide a starting place for developing both concepts and procedures. Projects, games, collaborative and talk based activities can all help guide children’s learning. We should use direct instruction only when children are unable to invent their own strategies.

We need to ensure maths is inclusive, practical and fun for everybody. By using a talk-led, active and collaborative approach, maths is within the reach of all our children.

Further information

Melody Lowe is Innovation Director and Lead Consultant at TT Education:

Jennifer Nock Training and Consultancy


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