The Use of Algorithmic Models to Develop Secondary Teachers’ Understanding of the Statistical Modeling Process

Figures & data

Fig. 1 Recursive partitioning example used to predict whether a person will play tennis or not depending on the temperature and humidity. Integers in squares indicate the order of the partitioning. Blue areas represent predictions of “Yes,” yellow areas represent predictions of “No.”

Fig. 2 Corresponding prediction rules for recursive partitioning depicted in Figure 1.

Fig. 3 The decision tree indicates a set of partitioning rules (algorithm) for predicting whether a person will play tennis or not depending on the temperature and humidity. The terminal nodes of “Play” and “Do not play” are predictions made by the model.

Fig. 4 The decision tree after pruning using a 10% inclusion threshold.

Table 1 Model building and evaluation process for classification tree and logistic regression using the tennis example.

Process	Classification tree	Logistic regression
Model building	Determine set of candidate predictors (Humidity, Temperature)	Determine set of candidate predictors (Humidity, Temperature)
	CART algorithm outputs set of decision rules to classify cases as “plays tennis” or “Does not play tennis”	Maximum likelihood (or other estimation method) outputs coefficient estimates and dispersion parameters based on a specified functional form and link function. The estimates can be used to determine the probability of “playing tennis”
Model evaluation	Decision rules are retained/pruned by comparing the model evaluation metric for the classification tree that includes that rule to one that does not	Predictors are retained/omitted by comparing the model evaluation metric for the logistic regression model that includes that predictor to one that does not
	Model evaluation metric is a measure of how well the cases were classified (e.g., percentage of correct classifications), often on a validation set of data	Model evaluation metric is typically a p–value. Sometimes it is some other global index of model performance (e.g., AIC, proportion of deviance explained). While cross-validation can be used, it rarely is used in traditional presentations

Fig. 5 Timeline showing the chronology of the PD activities and individual assignments.

Fig. 6 Partitioning of the dot plot (Panel 1) corresponding to the 10-rule overfitted model (Panel 2) created by one pair of teachers.

Fig. 7 Initial tree diagrams (first column) and pruned tree diagrams (second column) produced by each group or teachers during the second part of the spring professional development session.