Fig. 3

The relationship between variable PNS and Step 3 of word problem. This figure is a graph of logistic regression. Logistic regression is this a mathematical modelling approach in which the best-fitting, yet least-restrictive model is desired to describe the relationship between several independent explanatory variables and a dependent dichotomous response variable. In our case, a straight line reflects the probability that respondent resolved the Step 3 of a problem if the PNS scale reached a certain score. In Step 3 which is based on Step 1, just the subtraction operation was needed. X-axis displays the independent variable. It is a score achieved by individual respondents in a PNS scale. The y-axis shows the dependent variable of interest. One stands for the correct solution, zero for the incorrect solution. The blue circles represent the number of respondents who reached a certain score on the PNS scale and who were successful/unsuccessful in Step 3 of the problem. For example, six students who reached 45 points on the PNS scale, correctly solved the Step 3. On the contrary, four of the respondents who were unsuccessful in Step 3, had 55 points on the scale PNS