How do you learn maths?

For reasons subtly related to children's maths learning experiences and notions of learning (and less subtly related to the school context of the interviews) there is overwhelmingly more descriptive material on maths learning as Work than on maths learning as a Gift in my material.

Maths learning as a Gift

In terms of learning of the effortless variety, we have already heard children talking about learning as just having the ability (by oneself) or discovering its presence, given the occasion to use it - or as getting the information (from others) when this is taken for granted to equal learning. The following excerpt illustrates the sudden, unexpected emergence of ability in its simplest form, trial and immediate success:

 

E:	Kommer du ihåg när du lärde dej å räkna?	Do you remember when you learned how to count?
M:	... ... ... ... ... ... ... Nää... Kommer jante ihåg...	... ... ... ... ... ... ... Noo... I don't remember...
E:	... ... Men du hante alltid kunnat räkna till hundra?	... ... But you haven't always been able to count to one hundred?
M:	Nää.	Noo.
E:	Nää.	Noo.
M:	... ... ... ... ... ... ... ... De börja me att ja hörde-hh... ... en kompis, att hon hade räknat te hundra mens hon for te mej då. I bilen.	... ... ... ... ... ... ... It started with... I heard-hh... a friend, she had counted to one hundred while she was like, going to me. In the car.
E:	Hm m...	Umm...
M:	— dåså... bara gick de när ja skulle försöka...	And then like... it just worked when I tried...
	(Marie, initial interview)

There are a number of statements (from children who succeed well in maths) with a more specific focus on the experience of maths learning as the event of just hitting upon - or being struck by - the proper state of things:

In these excerpts learning is described as taking place all of a sudden, when a convincing solution makes its appearance or as one finds oneself able to make numbers fit together properly. This experience may even be expressed in explicit contrast to kinds of learning that take time:

Then, sometimes you may notice things, like how pleased you get:

And in the next example it is easiness that is foregrounded. Ina tells a story of easy learning that combines the notion that it is possible that she knew some maths before she was aware of her ability with the notion that once informed about the principle of addition, she had understood it. First she just had not had reason to pursue the matter, then she was told that "plus" is just "putting together." From that point on it was easy:

If we listen to and share the experience of children who talk about learning as a timely, gratuitous emergence of ability, we can see that to these children learning makes its appearance only as an aspect of the novel ability showing that you have appropriated some thematic aspect of maths. Learning is not a longdrawn process. It is not even an event in the present, but something that has always already taken place. When learning is conceived of in this way there simply isn't much to notice and describe. What you experience is that now you are able, as opposed to some earlier time when you were not able - or when you were not aware of your ability, because this aspect of maths had not been visible to you. So, now that you are able, you must have learned, and the aspects of your experience that may indicate learning must be that slight surprise, the excitement, or joy, that feeling of lightness constituting an aspect of your first successful performance with numbers.

In the extreme case you were in some way always able - maths learning as a Gift fuses with being so gifted that you do not have to learn:

M:	Aa a, men dom... som min kompis gjorde... han... kunde nästan... han kunde allt... Matte... han bara satt så. Han behövde aldrig lära sej nått enda tal...	Aa ah, but they... like my friend did... he... knew almost... he knew everything... Maths... he just sat like that. He never had to learn a single sum...
E:	Jasså. Han bara kunde dom...	Oh. He just knew them...
M:	Han kunde allting...	He knew everything...
	(Mac, final interview)

The intangible character of these experiences of learning tells us something about why descriptions of maths learning as a Gift are both scarcer and shorter than descriptions of maths learning as Work . Experiences that continue to be thematic for a long time would presumably give richer material for narrative than experiences passing in a moment, never to come back (you cannot learn the something more than once).

The meaning structure of maths learning as a Gift also appears in another form, as a negation of maths learning as Work. When proper maths learning is understood as a gift had for free, then it may be reasonable to perceive anything that demands work as counterproductive to learning:

D:	Ja, man kan ju inte hålla på- ... Om man skulle hålla på och räkna hela tiden så skulle man aldrig lära sej.	Well, you can't keep on- ... If you kept counting all the time then you would never learn.
E:	... Hur då menar du?	... How do you mean?
D:	Nä man kante hållaå- ... sitta å hh-hh ... tänka igenom hela tiden så där... "ew-ew-ew- Hur ska man räkna nu då?" ... ... Då går det inte å lära sej då nästan.	No, you can't keep-uh ... sit there hh - hh ... thinking it through all the time like that... "ew-ew-ew- How do you count now?" ... ... Then you'd learn almost nothing, you know.
	(Drew, initial interview)

Drew expresses similar objections to the notion that learning takes labour in both interviews. To him, and to other children as well - although Drew certainly produces the most articulate arguments - their understanding of what maths learning means stands in opposition to the notion that work is a prerequisite for learning. Drew may be the only one to claim expressly that work actually obstructs learning, but he is not alone in maintaining that the essential learning event has nothing to do with exertion, that it must be something else. It is interesting to note that the children who articulate an opposition to the notion that learning entails exertion are among the children who do enter school with a fair proficiency with numbers. It seems reasonable that their experience of maths learning so far has indeed been of something coming easy.

In this section I have presented a picture of a distinct way of structuring the meaning of maths learning as a Gift - something that you just get for free. Learning understood in this fashion is experienced as the smooth (and sudden) emergence of an ability to handle numbers properly. Strictly speaking, learning is not experienced as a separate phenomenon but as a quality of newness in a person's actual performance in maths. The way children describe this quality is as (unexpected), easy success. If things do not come easy you are not learning, but failing. With learning defined in this way the extended and systematic occupation with maths activities provided at school will not be understood as genuine learning, but as imposed chores, affording few, if any, opportunities for true learning.