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Good Thinking vs. ‘The Right Answer’

Posted by Philosophy Foundation on February 20, 2009

Here’s a question for you. Imagine a teacher asks this question: “what does 2 + 2 equal?” and child A responds with, “four, because its my lucky number,” but child B counts along the number line but makes a small error and says, “five.” Which would you consider to be the better answer and why?

I was leading a staff meeting where a debate ensued following this question about the importance of understanding when giving the right answer. Some two and a half thousand years ago Socrates, the ancient Greek philosopher written about by Plato, said that a right answer is not worth much until it is ‘tethered’ by good reasons. As a philosopher who works with children and teachers, I subscribe to this view and would always prefer a wrong answer with good reasoning to a right answer with faulty or no reasoning (“Four, because it is my lucky number.”)

The Cambridge Primary Review report (20th February) has voiced concerns about the shortcomings of the current ‘testing-culture’ in education, and I would like to add to the many voices by saying that I think this education approach seems to favour the right answer over good reasoning. Let me provide some examples that have come to my attention through the work that I do in primary schools.

If you were shown a necker cube how would you answer the question whether it is 2D or 3D?

I have been in discussion with primary school children where many have said that it is 3D (including many teachers) but where some have pointed out that it is 2D because… “Even though it looks like a 3D shape, it’s really only 2D because it’s flat and you can’t turn it round, so it’s a 2D drawing of a 3D shape.” A perfectly sound bit of reasoning, surely. Now think about this: what sort of answer do you think would be expected of a child in a SAT situation? 3D perhaps?

Again, in a SAT situation, when asked what the definition of a square is, which of these lists would you prefer, A or B?


  • 4 straight sides
  • Equal sides
  • 2D
  • Opposite parallel lines
  • Sides connected by right angle


  • 4 straight sides
  • Equal sides
  • 2D
  • Sides connected by right angle 

I witnessed a discussion where the children removed ‘opposite parallel lines’ from the list because they said, “You don’t need it, because if you’ve got four straight, equal sides connected by right angles then you’ve already got opposite parallel lines.” (Interestingly, it was only originally included because one of the children was ‘cheating’ and reading off a wall chart that I was unaware of).  The teacher then felt the need to recommend that they still include it to get the marks. Whether or not they really would get less marks for list B, the teacher’s concern demonstrates the kind of thinking that is preferred and therefore encouraged in the children: expected answers over clearer thinking and better understanding.

If education is about teaching our children to think, then the current model seriously needs to be looked at, if not utterly reformed when it prefers an unthinking answer to a thinking one. 

Socrates and ‘Necessary and Sufficient Conditions’

Socrates is famous for going about the market place of Athens in the years running up to his death in 399 BC, and challenging the beliefs of many of its citizens by asking them philosophical questions such as what is justice? and what is courage?

He is one of the first historical figures to have insisted that people provide clear and precise definitions of words that they are using, such as ‘justice’ or ‘courage’ in order to make discussions about them fruitful. Later in philosophy this criteria for accuracy would be known as necessary and sufficient conditions. It sounds daunting but can be translated as ‘what is needed and what is enough’. When we speak of a square there are certain things that are needed, such as ‘sides’ or ‘right angles’, but they are not, by themselves enough to say that we have a square – any rectangle will have both sides and right angles. So philosophers would say that ‘sides’ and ‘right angles’ are necessary for a square but not sufficient.

What the children had done in the above example was identify that ‘opposite parallel lines’ are not even necessary for the definition of a square when they considered what else they had already listed (equal, straight lines connected by right angles). 



7 Responses to “Good Thinking vs. ‘The Right Answer’”

  1. Red Baron said

    Unfortunately it is a feature of the new consumer market education that has been created that the whole process is seen as being a means to an end, therefore as education is not seen as important in its own right it is merely important to pass the respective tests in order to achieve what is perceived as a higher purpose, in this instance a career. Whilst it is disappointing that there is a singular lack of any dissent of the marketisation of education from students it is only to be expected given the education system they will have grown up under. When paying a substantial amount of money in fees and mortgaging one’s future in student loans the current trend of thinking is to expect something tangible from it. Self-advancement in the inner sense is not seen as being worth the outlay whilst a job in the corporate sector is and this is perhaps the most damming indictment of our education system as it stands. Thus in order to follow the now well-worn path into industry it is only important to tick the right boxes, industry does not wish to employ young naive mavericks it wishes to have corporate cannon fodder, sycophantic yes men that will preserve the status quo, and for that end free-thinking far from being an advantage is in fact an anathema.

  2. thephilosophyshop said

    Should we try to change it? Or is it so ingrained now that this becomes an impossibility? Would we need a total overhaul of society in order to change our education system, or, if we start to change the education system will society take care of itself?

  3. Red Baron said

    We cannot leave it as it is, it is too shambolic and the fallout of this is long-term and catastrophic. The overhaul of society is started by the education system, no major change can be carried out without it. There is so much to do though and it doesn’t take care of itself. Education/Welfare/Borders/Health etc must all be radically restructured but the first step is educating people to see the need for that change.

  4. thephilosophyshop said

    That’s where we’re starting…lets hope it works, or makes some impact.

  5. Red Baron said

    Sorry guys I think that comment is a spam one – it’s the Making Money link that seems to give it away, you get lots of them when you start out until akismet learns and the it sorts them out automatically. It’s just me sat here in the corner smoking fags and talking shite. I know it ain’t the Left Bank but hey we all have to start somewhere!

  6. thephilosophyshop said

    Thought so, the grammar should have given it away too, but nevermind, as you say we all start somewhere.

  7. The Philosophy Shop said

    Re: the necker cube example, many teachers have said that they encounter the same problem in reverse: they are given a box of 3D (albeit flat) shapes to teach children the idea of 2D shapes. Another of many mixed messages which highlights the discrepancy between good thinking and learning expectations.

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