Abstract:

Current era is sometimes called a post-truth era, as the distinction between truth and lie is often blurred. Every day new manipulative, false or incomplete information appears. The need to verify and work accordingly with information is therefore greater than ever. The prerequisites for this are critical thinking, the ability to provide a valid argument or reasoning strategies. One of the aims of teaching mathematics is the development of such reasoning and argumentation skills. Though the ability to reason and prove (R&P) is typically acquired implicitly throughout the whole curriculum, it is more connected with some parts of mathematics than others. This imbalance can also be observed in textbooks and might result in an uneven occurrence of R&P tasks in different math topics.

This led us to these questions:
R1: In which topics teachers most often include the argumentation and proof tasks?
R2: In what ways is the list of these topics culture or national curriculum dependent?
R3: What beliefs about the importance and concepts about R&P in classroom teachers have?

An international pilot survey was conducted by MaTeK project members (universities from Slovakia, Czech Republic, Italy, Norway and Turkey). As the curricula of different countries differ, it was necessary to find an intersection of topics that are taught in all participating countries and which are close to each other. We ended up with a general division into these topics: Geometry, Arithmetic, Algebra, Combinatorics, probability and statistics, Functions. The frequency was chosen by the teacher on a four-level Likert scale with options of not at all, sometimes, usually, and always. Several teachers from each country were also further interviewed about their beliefs concerning R&P tasks in their teaching. Currently the main data collection is underway and should be concluded by the end of the summer.

Several interesting trends could already be observed from the preliminary data. The data collected from Italian teachers show that argumentation and proof are not dependent on the topic they are currently dealing with at school. This may be due to both the length of their teaching unit (60 minutes) and the type of textbooks they use (in the form of more rigorous university-like textbooks). When analyzing collected data, we observed also the following surprising result: Although we assumed there would be similar results in the Slovak Republic and the Czech Republic, our current survey does not confirm this. This may however be due to the sample size that took part in the survey, which is why further research is important. The exception is that in both our countries teachers are least likely to prove and argue in Combinatorics, probability and statistics. Italy is in the same position. Norway and Turkey, on the other hand, least often include argumentation and reasoning in the topic of Functions. Views (or understandings) on argumentation and reasoning vary between teachers in practice and can be put anywhere on a scale from 'no argumentation' to 'rigorous deductive proof'.

Acknowledgement:
This research is a part of the H2020 project Enhancement of research excellence in mathematics teacher knowledge, acronym MaTeK, no. 951822.

Keywords:

Reasoning, proving, comparison, topics, international, curriculum.