Abstract:

Technology is needed in the study of correlation and regression, given its ability to compute, produce graphs and simulations. The Spanish curricular guidelines for Science and Social Science high school students suggest that students should work with statistical projects and real data, using the spreadsheet.

In this paper, we describe an experience aimed at training prospective high school teachers to teach correlation and regression using the spreadsheet, real data and other tools available from the United Nations web server. Twenty-five prospective teachers who had previously finished a Bachelor in Mathematics, Statistics or Sciences/Engineering/Architecture took place in a workshop with four (2-hour long) sessions where participants had access to computers and Internet. They were given a statistical project to investigate the relationship between the life expectancy in different countries and different international indicators of human development. They were provided with an Excel file with the data set, containing data from nine variables from 193 countries, and some questions to ignite project work.

In this paper, we analyse a task aimed to evaluate and develop the participants’ Technological Knowledge of Content (TKC). The task consisted in fitting a regression model for each of the eight independent variables, using Excel. At the same time, the activity serves to indirectly reinforce Content Knowledge (CK) of participants; specifically, participants were asked to reflect on the convenience of using different fitting functions to predict a variable, and should relate the correlation and determination coefficients in cases in which the dependence is or is not linear. To decide the best fit, the simplicity of the expression and the increase of the determination coefficient value should be considered.

Most participants fitted different models to life expectancy of one or more independent variables provided in the data file. These models included linear, logarithmic, exponential and polynomial functions of different degrees, which suggest their Content Knowledge of various elementary functions and their Technological Knowledge for using Excel to work with regression and correlation. Most participants compared the determination coefficient of several models to choose the one that maximizes their value, although the model did not always coincide with that predicted in our analysis. In this respect, the future teachers were divided into two groups: those that used the maximum variance explained and those that opted for a simpler model (for example, linear) if the explained variance changed little. Twenty-four participants made a correct fit, in graphically representing the data, and changing the scale of the scatter plot produced by Excel to better visualize the data. Consequently, they showed an adequate Technological Content Knowledge of correlation and regression and a very advanced reading level of the scatter plot. Only a teacher found difficulties in the task, because he did not change the scale for the different variables in the graphs, and then he decided to apply the linear model in all variables, even in cases in which the graph clearly showed that the fit was not linear.

Keywords:

Training teachers, technology, correlation and regression, project work.