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 (20^{th} 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?

**A**

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

** B**

- 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).