February 12, 2022
Heuristic Trees as a Digital Tool to Foster Compressionand Decompression in Problem‑Solving
This design-based study addresses the issue of how to digitally support students’problem-solving by providing heuristics, in the absence of the teacher. The problemis that, so far, digital tutoring systems lack the ability to diagnose students’ needsin open problem situations. Our approach is based on students’ ability to self-diag-nose and find help. To this purpose, we introduce a new type of digital, interactive,help-seeking tool called a heuristic tree. Students’ use of this tool is supported by ahelp-seeking flowchart. The design of heuristic trees is based on our reinterpretationof the notion of heuristic in terms of terms of compression. Our research questionis: How do heuristic trees and the help-seeking flowchart influence students’ prob-lem-solving behaviour? This question was studied in the context of a number theorycourse for in-service mathematics teachers. During five weeks, fifty students workedon fifty-five problems supported by heuristic trees. Our data consists of video obser-vations of two small groups of students, a teacher log, interviews with these twogroups, and a survey filled in by twenty-three students. The main results are that thesupport by heuristic trees and the help-seeking flowchart allows students to work inthe absence of a teacher and to engage strongly with problems, maintaining owner-ship of the solution methods. Moreover, as intended by the tree structure, studentslearned to focus not just on the small steps of the solutions, but also on the generalheuristic techniques, theorems, and concepts that should be learned in the process offinding those solutions.