|Chris Reading (Australia)||firstname.lastname@example.org|
The development of a Profile of Statistical Understanding is aimed at providing a means of identifying the stages within the development of statistical understanding. Many studies have identified 'lack of understanding' as a major cause of students' inability to think and reason statistically. When investigating statistical understanding researchers have clearly identified the need to investigate what students 'can do'. The profile is intended to assist educators to identify what 'can be' expected of students rather than what 'should be'. Specific profiles will identify what to expect of graduating secondary students with respect to 'statistical understanding' for tertiary education or the work force.
Five basic areas of statistics have been identified: data collection; data tabulation and representation; data reduction; probability; and interpretation and inference. These five areas form one dimension of the profile under development. The other dimension covers the various levels of statistical understanding.
The research discussed involved a search for what students 'can do' in four of these areas. Probability was not investigated due to the large amount of research already being conducted in that area. Initial investigations involved 180 students from Years 7 to 12 in an Australian secondary school. All students responded to open-ended questions in each of the four areas. Then 18 students were interviewed for more in-depth responses. The analysis of the responses and interviews provided a basis for developing the profile. Using the SOLO model as a framework, student responses were ranked into hierarchies of statistical understanding within each of the four areas. SOLO was found to be a useful guide in developing the hierarchy.
Cycles of levels of responses from both the ikonic and the concrete-symbolic modes of the SOLO model were identified, within each of the four areas. Unique aspects of the responses for each level form the descriptors for the profile. Rasch analysis allowed this information to be combined to produce a measure of statistical understanding for each student. Analysis of this measure demonstrated that there was minimal growth in statistical understanding as students progressed from Year 7 to Year 12.
The profile is designed as a tool to assist educators to assess a student's level of statistical understanding. Use of the profile is not task specific, that is, a response to any task or problem which involves statistics could be assessed using the profile. Responses from students in a particular cohort could be used to present a profile of what to expect from the 'average student' in that cohort, which could be of use to both tertiary educators and employers.
The process for developing this profile is described, as well as the refinement and testing of the profile based on further data collected at other secondary schools. The profile, in its present form, is outlined, followed by plans for future expansion based on data collected involving primary and tertiary students.
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