Novice programmers often struggle with problem solving due to the high cognitive loads they face. Furthermore, many introductory programming courses do not explicitly teach it, assuming that problem solving skills are acquired along the way. In this paper, we present 'PCDIT', a non-linear problem solving framework that provides scaffolding to guide novice programmers through the process of transforming a problem specification into an implemented and tested solution for an imperative programming language. A key distinction of PCDIT is its focus on developing concrete cases for the problem early without actually writing test code: students are instead encouraged to think about the abstract steps from inputs to outputs before mapping anything down to syntax. We reflect on our experience of teaching an introductory programming course using PCDIT, and report the results of a survey that suggests it helped students to break down challenging problems, organise their thoughts, and reach working solutions