Using an expression tree for adaptive learning

This article presents a model of comparing two arithmetic expressions for use in adaptive learning. The comparison model is based on a new expression non-binary tree model. The new expression tree model avoids the stable order of operands in mathematical operations and makes possible to compare two expressions that are identical in meaning but may look different. The algorithm for building the non-binary expression tree is created depends on two main methods that decide to add a new node in the tree as a parent node or as a child node. The expression tree comparison model contains expression tree normalisation, node precomputation and comparison expression trees steps. The comparison step contains an algorithm for finding similar nodes using similarity index. This index searches for similar child nodes in two expression trees to compare the original expression with the modified expression. These similar nodes are compared to obtain suggestions on how to bring the modified expression to the original expression.