You're going to run into problems attempting to operationalize a variable like 'critical reasoning', in order to demonstrate, scientifically, its empirical validity. In fact, you'll need the help of philosophers, who have been studying various ways of interpreting what critical reasoning actually means[1], and how to properly operationalize variables[2].
Reasoning - using logic to form conclusions, inferences, judgements - is a process defined, taught, and professionally applied by philosophers. So, teach students philosophy and some other 'control subject'. They learn logic, rhetoric, and how to follow complex chains of complex thought.
It seems to be a difficult claim to make, that this experiment would some somehow not show an improvement in critical reasoning - however you operationalize it.
[1] https://plato.stanford.edu/entries/self-knowledge-externalis...
[2]https://plato.stanford.edu/entries/operationalism/#OpeUniAna...