Complementary to existing normative models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical processes, a descriptive model seemed essential. The juxtaposition of models from the literature and our empirical analyses enabled us to generate such a descriptive model of problem-solving processes. For the generation of our model, we reflected on the following questions: (1) Which elements of existing models for problem-solving processes can be used for a descriptive model? (2) Can the model be used to describe and discriminate different types of processes? Our descriptive model allows one not only to capture the idiosyncratic sequencing of real problem-solving processes, but simultaneously to compare different processes, by means of accumulation. In particular, our model allows discrimination between problem-solving and routine processes. Also, successful and unsuccessful problem-solving processes as well as processes in paper-and-pencil versus dynamic-geometry environments can be characterised and compared with our model.

作为对现有规范模型的补充，本文提出了一个描述性的问题解决阶段模型。实际的，不理想的解决问题的过程包含错误，绕道和周期，并且它们没有遵循规范模型中所假定的预定顺序。为了表示和强调经验过程的非线性，描述性模型似乎必不可少。来自文献的模型的并置和我们的经验分析使我们能够产生这样的描述性解决问题的过程模型。在生成模型的过程中，我们思考了以下问题：（1）现有的解决问题模型的哪些元素可用于描述性模型？（2）该模型可以用来描述和区分不同类型的过程吗？我们的描述性模型不仅可以捕获实际解决问题过程的特质顺序，而且可以通过积累的方式同时比较不同的过程。特别是，我们的模型允许区分解决问题的流程和常规流程。此外，可以描述成功和失败的问题解决流程，以及纸笔与动态几何环境中的流程，并与我们的模型进行比较。