Design and Evaluation of a Hypothetical Learning Trajectory to Confidence Intervals based on Simulation and Real Data

Abstract This article discusses the design of a hypothetical learning trajectory to introduce the confidence intervals in a basic university course, from an informal perspective based on the use of data obtained from surveys and samples simulation. The trajectory consists of four activities and was evaluated as part of a first improvement cycle with a group of 11 students (19-21 years) of international studies career at a Mexican university. The results were obtained from the analysis of the worksheets and software files delivered by the students at the end of each activity, in addition a set of items selected from the AIRS test (Assessment Inferential Reasoning in Statistics), which were answered by the students in a final evaluation. The results show that it is possible to reason adequately with complex concepts that underlie a statistical inference, using data with real contexts and dynamic and interactive computer tools that allow real time visualization of the sampling results. However, some concepts were particularly difficult for the students, as the distinction between population, sample and sampling distribution, properties of sampling distributions and confidence intervals.