Do reasoning skills of students improve when we teach logic? This is a question that has been investigated for university students (Lehman-etal-effects-on-reasoning-1988, Stenning-etal-graphical-effects-1994, Stenning-etal-cognitive-theory-1995, Stenning-etal-contrasting-cognitive-effects-1995, Stenning-embedding-logic-1996, Stenning-seeing-reason-2002) but how well secondary school students reason and whether a logic curriculum can improve these skills has only recently become the object of interest (Bronkhorst-logical-reasoning-2019, Bronkhorst-logica-vwo-2006, Bronkhorst-etal-leren-logisch-redeneren-2018).

One source of interest lies, in part at least, in the fact that for the first time in the Netherlands, logic has become part of the mathematics curriculum "Wiskunde C". Cf. the final report entitled "Denken & doen. Wiskunde op havo en vwo per 2015" which was presented to the Dutch Minister for Education. This curriculum raises natural questions on a secondary school level: what it is that we are teaching secondary school students and how well do we succeed in it?

An important question in this respect is what we mean when we use the term reasoning skill. For many psychologists this questions boils down to a capacity of how well one is able, given some reasoning task, to competently adhere to a fixed reasoning model deemed to be the golden standard of rationality. As we will see below, we will follow stenning-etal-human-reasoning-2008 and take a much broader conception of logic and reasoning. In this conception reasoning skills are considered a more encompassing activity involving interpretative processes which should be evaluated differently.

Cognitive psychologists have studied reasoning performance for decades. The field of psychology of reasoning started with Wason-rule-1968 's selection task and empirically investigates how people factually reason and how competently they do this. Developmental psychologists have focused much attention on the reasoning skills of children in the age group from 4 till 12. However, as an age group, adolescents (roughly children with an age from 12 until adulthood, i.e., 18) have not received similar attention.

The conclusions of Wason-rule-1968 were pessimistic:

Could it then be that the stage of formal operations is not completely achieved at adolescence, even among intelligent individuals? Wason-rule-1968, p. 281.

The picture that further emerges from the studies that followed Wason's selection task (Johnson-Laird-etal-deduction-1991, sperber-etal-relevance-1995, cosmides-social-exchange-1989) is that reasoning is a procedure that follows predetermined rules. Specifically, in many such studies the laws of classical logic are assumed to be the standard for (human) reasoning without any motivation.

stenning-etal-human-reasoning-2008 extensively criticize the view where competence is tested with classical logic as a yardstick without further motivation. Instead, their position on logic and reasoning is much broader. For instance, they make a distinction between reasoning to an interpretation and reasoning from an interpretation. According to this view, in order to perform a reasoning task, the reasoner needs to set relevant parameters in order to come to an interpretation of the task ("reasoning to"). After these relevant parameters have been set it is mathematically fixed what follows ("reasoning from"). Note that although a distinction between these two types of reasoning is made, they are not to be considered linearly ordered in time, but rather proceed interactively.

The parameters that need setting in reasoning to an interpretation include a choice of a formal language, a semantics and notion of logical consequence and setting these parameters is what is involved in imposing a logical form on the task. stenning-etal-human-reasoning-2008 stress that the full range of interpretative choices a subject faces when performing a reasoning task (in particular in Wason's selection task) should be taken seriously. Firstly, because subjects visibly worry about setting such parameters when solving a task, secondly, it is only once the parameters have been fixed that reasoning from an interpretation, i.e., deriving a conclusion, can be evaluated to be valid or not.

Evaluating if and to what degree students' reasoning skills improve when we teach logic will have to take into account the different components that are necessary for executing a reasoning task, i.e., the interpretative choices subjects face. Many of the choices that subjects face in performing a reasoning task happen unconsciously. In this respect an educational programme is likely to gain a lot by raising awareness of these interpretative possibilities.

Using their formal framework stenning-etal-human-reasoning-2008 analyzed reasoning tasks (e.g., the selection task and the suppression task) and believe that their method, which, in particular includes interviewing subjects (see in particular stenning-etal-human-reasoning-2008, chapter 3.5) will be instrumental when it comes to investigating the reasoning skills of adolescents.

The PhD project consists of four subprojects which will lead to a number of articles to be submitted for publications. The PhD thesis will then collect of all these articles.