Allison: A case study of spatial visualization in mathematical problem solving

There has been a long history of research work done on spatial visualization by scientists, psychologists and researchers in mathematics education. To date, much theory has been written on it. In particular, Bishop (1983) proposed two types of spatial ability constructs ' Interpreting figural information (IFI) and Visual Processing (VP). Today, spatial visualization is widely acknowledged as an important component of mathematics education. The current focus is on the roles spatial visualization play as a tool for mathematical reasoning and its processes in problem solving. The Singapore problem solving curriculum acknowledges and reflects this focus. This paper provides an interpretation of the problem solving behaviour of a fourth grader, Allison, in her attempts to solve a set of word problems. The word problems were Primary School Leaving Examination (PSLE)-type problems. The PSLE in Singapore is a national examination which aims to assess pupils' attainment in mathematics at the end of primary education with respect to the objectives of the primary mathematics curriculum. These word problems required the modeling approach to arrive at the solution. Allison, a visualizer, displayed the tendency to visualize the problem situation in her mind, and the use of diagrams to solve the word problems. Allison's solution strategies remind us that ability to select the correct operations and to perform accurate computations do not always lead to the correct solution. Knowledge on issues related to the strengths and difficulties associated with spatial visualization will better equip classroom teachers to help their students overcome challenges in mathematical problem solving