delicate balance is required between letting the child have some time and freedom to develop his own approach to strategy to problem solving, and sensitive questioning which develops the child’s thinking (Hopkins et al. 1996).

Beginning with the problem-solving framework, the teacher has a very specialized and highly-involved role in the education of the students, and the recognition of the likely effect of intervention and non-intervention are critical. In this paper, teaching strategies will be presented which promote problem solving and mathematical thinking in the developing children of the United Kingdom.

Solving problems is one crucial component of using and applying mathematics. According to the 1999 Framework for teaching mathematics, numeracy is a proficiency that requires a child to have an ability to solve problems when given different contexts. Problem solving for the children from primary years one to six has been embedded into mathematics teaching and learning, thereby becoming an integral part of the children’s work.

This progression analysis highlights the increasing complexity of the mathematical problems that the children tackle as they move from one year to the next. Through years one to six Block A covers counting, partitioning, and calculating; securing number facts and understanding shape in Block B; handling data and measures in Block C; calculating, measuring and understanding shape in Block D; and securing number facts, relationships and calculating in Block E (Tanner & J1s 2000).

In Block A, each student should be able to solve problems, recognise and utilize the number system, recognise prior experience with mathematic operations, and communicate the abstract concepts of math in a concrete, tangible form. In Block B, they name shapes and their characteristics, forming a basis for the examination of 2-D and 3-D shapes which extends through Year five. In Block C, they sort and present information in diagrams and use units of
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