Innovative pedagogies tend to focus on two things: how students learn and the function of the teacher. These pedagogies might suggest new ways of using digital technology, propose student-centred approaches, advocate personalised learning or stress the importance of giving students the fishing rod rather than the fish.

But what is often overlooked when considering how students can best access the content of learning is that content itself. And yet these issues are interlinked. The question of how to deliver the curriculum is a question of what is in the curriculum. How we learn is shaped by what we learn.

Let’s say that you want your students to become inquisitive and intrepid thinkers rather than - or in addition to - knowledgeable and adept learners. And let’s say that your subject is physics. How are you going to achieve this end? Instead of simply bestowing answers on your students, you could teach them to think like scientists. Perhaps you spend time expounding the scientific method, examining the path that can take us from an observation to a theory. When your students know the right sorts of questions to ask and the right techniques to employ, they will discover many answers for themselves.

Your students are now independent, which is terrific, but are they intrepid? Have you developed their inquisitiveness? They are capable of taking the wheel - are they capable of inventing it? Though you have shown your students how to navigate a predetermined path, the intrepid thinker does more than this. An intrepid thinker is not someone who finds their own way, they discover somewhere else entirely. Finding your own way, in other words, is not the same as going your own way.

Nevertheless, if facts are facts, how is it possible to go your own way? The amount of time it takes an object to travel a certain distance is not up for invention, it is determinate. The curriculum can’t change the conclusiveness of facts; intrepidity isn’t always possible. With most subjects there is a fixed structure of information that students must learn to inhabit.

Facts, however, do change. Our ideas about time, for instance, have changed. Although time may not be in question, it is not absolute, as it was once thought to be. Einstein showed that what seems like an object of simple fact is actually complex, variable and circumstantial. Facts may still be facts but, according to Einstein, they are variegated.

This isn’t to suggest that students should be discovering relativity in the classroom. The point is that a curriculum conducive to developing thinkers rather than learners would be one that drew attention not only to the multifaceted nature of truths but also to the revolutionary changes - such as Einstein’s - that punctuate the course of history. If we want students who go beyond learning, who become dissentient thinkers, we need a curriculum that reflects the contentious and erratic nature of human endeavour. We need to overturn the impression that paths are predetermined and structures absolute.

True or false

Whereas the thinker challenges, the learner complies; the thinker is animated by questions, the learner seeks only answers. As it stands, the curriculum is more on the side of learners than thinkers. It fails to convey the aliveness of its subjects. It does not illustrate how knowledge grows, how beliefs change, how styles evolve and fall away. It presents human endeavour as a solid lump, neglecting the ebb and flow, the ways in which culture is in perpetual mutation and fuelled by the iconoclastic, the idiosyncratic and the subversive. We should not be too focused on imparting truths. As philosopher Karl Popper argued, it is not truth but falsity that keeps knowledge in motion.

The curriculum fails to stress how everything that students are taught may be wrong or temporary. The essential incompleteness of understanding and desire is swept under the rug. Students are led to believe that they are entering a ready-made world rather than a malleable one. No matter how ingenious our pedagogical methods are, if we want thinkers rather than learners we need a curriculum with a different spirit. We need to approach subjects by spending more time exploring the conflicts, the arguments, the things that don’t make sense, emphasising the mysteries and the things that we don’t know.

One way in which this might be done is by introducing a philosophical element. There are those who argue that philosophy (the only major academic subject not represented in schools) should enter the curriculum as an autonomous subject. An alternative to this would be for it to take a systemic place in the curriculum. Challenging foundations, testing conceptual limits and considering alternative frameworks - this is the philosopher’s bread and butter. These are also the abilities that take human endeavour to exciting places, abilities you find in an Einstein, a James Joyce or a Miles Davis. And these are abilities that are essential to all specialists, whatever their area.

Every subject has its own internal philosophical questions; every subject tests itself and requires self-reflection. And in this sense every subject teacher is potentially, and in part, a philosophy teacher. The philosopher-historian, for example, might raise questions of historiography and engage in ethical evaluations of the past; the philosopher-mathematician might wonder what numbers are and how mathematical knowledge grows; the philosopher-artist might question the value of form over content and the importance of intentions.

Subject-specific philosophy involves asking questions that address the scope and limits of the subject itself, as well as addressing moments of electrifying and revolutionary change. Embedding philosophy into every subject - offering class time in which students can discuss challenging and open questions - would be one step towards offering a curriculum that does not promote learning to the detriment of thinking, one that enables students to become free and intrepid thinkers.

David Birch works with the Philosophy Foundation, an educational charity. His book Provocations: philosophy for secondary school is published by Crown House