# Errors concerning Statistics and Probability in Spanish Secondary School Textbooks
## 4 Discussion
### Research Implications  
First, we must point out that this is the first study, as far as we know, which addresses errors on statistics and probability in textbooks. In addition, we have not only detected systematic errors but have also classified them into difficulties, which can explain the errors in learning, cognitive as well as conceptual terms.  
This valuable finding is the starting point to be able to eliminate these errors--since they hinder the statistical literacy of citizens--and to propose renewed lessons that are correct and in line with the basic pillars of statistical thinking. Correcting the errors is essential to properly redirect the statistics and probability teaching-learning process. On one hand, textbooks play a crucial role in compulsory education as they contribute to the standardisation of the disciplines and they influence on teaching practices more than legislative regulations do [34; 35]. On the other hand, students deserve rigorous textbooks, including formal concepts, precise representations, and suitable contexts and applications [43]. Consequently, remove errors and inaccuracies in textbooks is necessary, and it will provide new learning opportunities.  
Beyond correcting the books, this finding raises a question about how the professionals who wrote the texts--mostly mathematicians--understand the discipline and how their point of view may skew the one of the teachers. If teachers have not questioned the contents, they will assume the errors that appear in the textbooks. This means that the teaching sequence may be contaminated; books condition teachers and they spread errors among students. These errors may have been inherited in different generations and it is possible that teachers acquired them in their student stage.  
We must reflect and research about the causes and effects of making errors in textbooks. We can infer neither that errors in textbooks are the cause of the lack of statistical literacy nor the reciprocal, that is, the lack of statistical literacy is the reason why authors make these errors. The most plausible is that both events feed back to each other, so that learning errors during the school stage cause teachers to reproduce them when they have to teach statistics in the classroom.  
Literature suggests some rational ideas to explain the difficulties to achieving statistical literacy. First, there exists differences in the preparation needed to teach statistics and the one required to teach mathematics [16]. Second, in statistics is usual the existence of false intuitions or heuristic rules [19]. Finally, there exists a conflict between mathematical and statistical thinking [14; 15]. Nevertheless, the issue is still open and our results can help experts to deep in the causes.  
Open questions arise from our result, such as whether teachers also make the same mistakes genuinely and independently of the textbooks, even with a training without errors. If so, researchers should investigate teachers' misconceptions and provide strategies to remove errors regarding statistics and probability from classrooms.  
It seems clear that textbooks needs supervision of statistics topics by experts in the field, who can contribute the elements of statistical thought that are different from the points of mathematical thought.