Animal studies can throw some useful light on aspects of basic number fact learning such as how experiences of number facts need to turn into knowledge of those facts.
The BBC documentary Smart Animals commented on the turning of experience into knowledge. "If you can't remember what you have done you haven't learned a thing! For knowledge, memory is key."
It went on to show us from recent research with pigeons how important memory is.
In a study which aimed to throw light on how pigeons find their way home, pigeon trainer Jeremy Davis teamed with scientists from Oxford University, They were equipped with GPS navigational devices.
Davis trained newly fledged pigeons over 12 weeks. Scientists were present at their first release, just 8km from home which was practically visible in a nice straight line. Study of the paths taken by the birds showed that navigation was not instinctual.
One bird, for example, travelled every-which-way for 60km before arriving home. It was clear the way home had to be learned.
In subsequent weeks Davis gave the birds the opportunity to learn. He released them further and further from home.
In the 12th week the scientists returned to check on progress. They studied the release of the birds from a place they did not know, 70km from home.
As the reporter said, "Off they confidently flew - but in the wrong direction!
"But they knew what they were doing. They headed for the nearest town, followed a road and river to a roundabout, then flew over a camping park whose rows of caravans were visible for miles. In short, they followed obvious landmarks all the way home!"
What is the point? The pigeons "turned the learning experiences they were given into real know-how".
Memory was the crucial thing that helped them create and navigate from internal maps. Memory was key.
If we turn to another kind of know-how, knowledge of basic number facts or "tables", is memory again the key?
Traditionally teachers placed high value on memorisation and prided themselves on the methods by which they helped their students become quick and accurate. Instant recall was the aim.
We went through a period when memorisation was looked down on and tended towards being equated with rote learning without understanding.
In theory we have come away from that. Ministry people will say yes - number fact knowledge is required and recall should be instant. But the methods advocated to make this happen too often do not do so, as studies now show.
Memory is hugely important in our daily life. Without it we could not do anything useful with our computer or our golf stick or our car ... Alzheimer's gives unpleasant reminders.
We would do well to think of memory as a sort of world. It's a living thing. It's a place we can move mentally around in and do things in. It holds a number of neat data bases. We go to our "roading" database, for example, when we head off for the motorway or our local mall. There is a heap of information there - mental pictures - and subconsciously we rely on these with every turn of our wheel.
Pigeons fly about with map databases in their heads. If they are well developed they arrive home quickly and safely. If not, they arrive home late, or not at all.
Our children need good sound number fact databases within which to think freely, see connections, solve problems. If they have them, they have a future in maths.
Without them their whole future in maths and perhaps in life is in jeopardy.
Des Rainey is an Auckland education consultant who supplies maths programmes to schools.