Teacher Toolbox
Learning Strategies - Mathematics

Concept Knowledge

Children need to grasp ideas that provide a foundation for subsequent learning and  support a variety of tasks and procedures that go beyond a single activity. It is important for instruction to be focused around a central mathematic concept to enable children to develop understanding and to build upon their prior knowledge.

Examples of the central mathematic concepts children need to understand in order to support learning of more complex math include:

Examples of Central Math Concepts
  • Number
  • Sequence and Pattern
  • Sets and Set Relationships
  • Operations
  • Representation of Quantity  - Numeric and Nonnumeric
  • Shape, Space, and Geometric Forms
  • Money
  • Time, Movement, and Speed
  • Measurement – Standard and Nonstandard Units
  • Data Representation and Interpretation

Children need to have adult mediated experiences to help them develop the necessary mathematic concepts to support their learning.  Pointing out specific information and relationships and encouraging children to tell about their thought processes helps to stimulate learning in math and in other areas.

Children benefit from direct instruction and independent exploration to form math concepts.

Use Manipulatives During Instruction to Demonstrate the Targeted Concept.

When using manipulatives it is beneficial to consider:

  • Match the materials to the concept being modeled.  For example, if using manipulatives to introduce addition, select individual counters instead of bundled sticks or rods from a base 10 set if used to represent one number, especially if the child has only acquired one-to-one correspondence.  The stick bundles can be interpreted as one group or an amount determined by the number in that bundle.
  • If introducing a new material, allow students time to explore with the objects before using them for teaching purposes.  This will provide opportunities for children to explore concepts as well as remove the novelty of the materials.
  • Clearly state the purpose of the manipulatives.  This helps to link the concept to its purpose as well as lead toward learning about a procedure.
  • Once children efficiently demonstrate the concept using the manipulatives, gradually model how to represent the concept in different way, such as using pictures or symbols.
  • Gradually phase out the use of manipulatives as children master the concept.
  • As children become proficient with the concept, provide novel problems for children to solve that use that concept

The National Council of Teachers of Mathematics (NCTM) web site links to Illuminations, a valuable and useful web site that provides lesson plans, instructional suggestions, and information about mathematic instructional standards to help teachers provide effective math instruction as well as other resources. www.nctm.or.