Mathematical Problem Posing

This study aims to design a scaffold of annotated expression for problem posing. The scaffold is designed on the basis of a solution tree, a hierarchical arithmetic expression with an operator, values and labels. Similarly, an annotated expression annotates every value in the expression with the meaning of the value, but remains the format of expression without using a hierarchy. This is because students are familiar with the expression format. However, when the expression involves two steps, the expression adopts a hierarchy to present the steps. For investigating the effect of problem posing by solution trees on the performance of problem solving, this study used problem posing by expressions as the control group in an experiment. The results showed that problem posing by solution trees may improve students’ performance on problem solving more than problem posing by expressions, especially on problem translation and two-step expression. Furthermore, this method can help low-ability students pose and solve mathematical word problems. In addition, the system also provides a scenario of stores. The students in the system have to play the role of store managers. With the support of annotated expression, students have to design and create a mathematical word problem which meets both the requirement of the annotated expressions and the scenarios of the assigned store. In the end, students may learn not only problem solving, but also creating their own mathematical knowledge.