This paper discusses the thought processes involved in statistical problem solving in the broad sense from problem formulation to conclusions. It draws on the literature and in-depth interviews with statistics students and practising statisticians aimed at uncovering their statistical reasoning processes. From these interviews, a four-dimensional framework has been identified for statistical thinking in empirical enquiry. It includes an investigative cycle, an interrogative cycle, types of thinking and dispositions. We have begun to characterise these processes through models that can be used as a basis for thinking tools or frameworks for the enhancement of problem-solving. Tools of this form would complement the mathematical models used in analysis and address areas of the process of statistical investigation that the mathematical models do not, particularly areas requiring the synthesis of problem-contextual and statistical understanding. The central element of published definitions of statistical thinking is "variation". We further discuss the role of variation in the statistical conception of real-world problems, including the search for causes.

Summary. There is a compelling case, based on research in statistics education, for first courses in statistical inference to be underpinned by a staged development path. Preferably over a number of years, students should begin working with precursor forms of statistical inference, much earlier than they now do. A side benefit is giving younger students more straightforward and more satisfying ways of answering interesting real world questions. We discuss the issues that are involved in formulating precursor versions of inference and then present some specific and highly visual proposals. These build on novel ways of experiencing sampling variation and have intuitive connections to the standard formal methods of making inferences in first university courses in statistics. Our proposal uses visual comparisons to enable the inferential step to be made without taking the eyes off relevant graphs of the data.This allows the time and conceptual distances between questions, data and conclusions to be minimized, so that the most critical linkages can be made. Our approach was devised for use in high schools but is also relevant to adult education and some introductory tertiary courses.

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