Live programming is activity in which the programmer edits code while observing the result of the program. It has been exercised mainly for pedagogical and artistic purposes, where outputs of a program are not straightforwardly imagined. Most live programming environments so far target programs that explicitly generate visual or acoustic outputs. We believe that live programming is useful for data structure programming, where the programmer often has a hard time to grasp a behavior of programs. However, it is not clear what features a live programming environment should provide for such kind of programs. In this paper, we present a design of live programming environment for data structure programming, identified the problems of synchronization and mental map preservation, and proposed solutions based on a calling-context sensitive identification technique. We implemented a live programming environment called Kanon, and carried out a qualitative user experiment with 13 programmers.