"By George, she's got it!"

These are the words of Professor Higgins in My Fair Lady when Eliza shows significant progress in her learning! We use a lot of different idioms to indicate that we understand something or do not understand something. For example, for understanding, we might say things like:

• Oh, I see! 
• Now it’s clicked. 
• Everything is falling into place. 
• I think I've cottoned on! 
• I get the picture. 
• My eyes have been opened! 

And for not understanding, we have phrases like these:

• Sorry, I don’t get it. 
• I’m still in the dark. 
• I can’t see the sense in that! 
• That's as clear as mud! 
• You're talking double Dutch! 
• It just went over my head. 

What's your favourite way of saying 'I understand' or 'I do not understand'?

Expressions like those above reveal a number of insights into the nature of understanding. They show, for example, the importance to us of understanding things, of making sense of them, rather than just learning by rote. We can see within the expressions used a clear sense of closure, of things fitting into place, a sense of relief almost, when we 'get it'. And, by contrast, phrases that indicate not understanding reveal a sense of frustration. Understanding or not understanding is as much an emotional experience as a cognitive one!

Then we might notice that understanding brings clarity and light to the learner. Many of the phrases we use for understanding talk about 'seeing' something, having our eyes opened, or, by contrast, being in the dark.

Finally, these expressions for understanding support the idea that learning with understanding is all about making connections: connecting some new experience with other experiences or existing understandings. So, we talk about understanding as though it feels like things 'clicking' (like two Lego pieces fitting together), or 'falling into place' (like a piece in a jigsaw connecting with other pieces and suddenly making sense), or 'getting the picture'. And when we don't understand, the words 'go over our head', so we have a sense of not being able to connect them to anything and embed them in our minds. 

To learn that mathematics can be learnt with understanding in the ways indicated by these idioms is the most important thing for children to learn about this subject by the time they leave primary schools.