Buxton, Derbyshire
August 1834

Our tour of the Industrial North ends in the sleepy little spa town of Buxton. Lady Gosford is here – she is a friend of Mamma’s – with her two little girls, Olivia and Annabella. My cat, Mistress Puff, now a venerable old lady, is on almost permanent loan to them now. Grey-tinged, as though dipped in ash, she is irascible on occasion, her hind legs rheumatism-stiff. But she still enjoys chasing the sparrows that hop across the terrace in the morning sunshine, and mewing for milk, and I shall always remember the time when – as a lonely, book-gobbling child – I looked upon Puff as my only friend.

There is, as is often the case with spa towns, not much to do in Buxton. More out of boredom than anything else, I offer one day to tutor the little girls in mathematics. I am rather delighted both by the selflessness of this gesture, and the idea of Ada the Tutor. (Also: I have realised, rather to my embarrassment, that I do not really think about others very often.)

Lady Gosford is enchanted. ‘But that is a charming idea,’ she says. ‘Livvy, Bella, you are lucky little girls, to have Ada to teach you.’

Mamma also smiles on my proposal, but I can’t help but detect a very slight disbelief in her expression. I remember her telling me at the allotments that I did not have the temperament of a teacher; I never forget such criticisms. Then again, she herself leaves much to be desired as an instructress; every time she took charge of my education, we both suffered for it.

I do not prepare much for the first arithmetic lesson, since I don’t see why I should need to. I possess all the knowledge, and shall merely be imparting it.

‘We will begin with the simple things,’ I tell the girls, as we make ourselves comfortable in an unoccupied corner of the hotel dining room. ‘Addition, subtraction, multiplication, division; and later, some simple trigonometry.’

Their little blonde heads gleam with purpose; they smile and nod and look at me with expectation. I decide that being a teacher is a straightforward business. Puff, who is curled up on the banquette beside me, must find it a curious reversal, since she herself has been present at many lessons – hundreds – in which I was the pupil, not the teacher.

Each girl has her commonplace book, and for each I write ten sums of differing complexity. It takes them far longer than I think that it should to do the work, and at first I make a variety of impatient remarks, unable to stop myself.

‘Goodness, Livvy!’ I exclaim, when that dear girl asserts that seven sixes are forty-eight. ‘How can you think such a thing?’

But I can see at once from the slump of Olivia’s shoulders, her instant dejection, how disheartening my words have been.

‘The sums are hard,’ says Bella, who has as much trouble holding her pencil as I used to have when holding a pen. When I propose that they construct a triangle in their books, neither girl is able to do it. It is as though they have never attempted such a thing before. Soon enough, they are both close to tears, and I am full of remorse.

‘It seems that I have begun with the wrong things,’ I tell them, pointing out that the fault lies with me entirely. ‘Let us start again.’

The girls are young – seven and five – and I decide that I will not expect as much of them as Mamma expected of me, for such expectations are not fair ones. They will not be forced to lie still on a board if they do not complete their work to the highest standard; I will not bribe them with tickets for work well done, either – they should be proud of what they can achieve regardless. I remember Miss Stamp, who always allowed me the time I needed to correct myself, and try to be more like her. I change my tone of voice, making it softer and more encouraging. I simplify the sums, asking them now to count up in twos, say, or in tens. I slow down too, allowing them far more time for the sums. I might pat a sleeve in gentle support, or scribble a useful reminder on a page.

After a quarter of an hour or so, I am transformed – and so are they.

‘That’s very good,’ I say. ‘Perhaps check your work, Bella, here – and here...’

The time passes so quickly that I am surprised when Lady Gosford comes to claim her children.

Later on, a further realisation dawns: in order to be a teacher, I must also be a student. I don’t have many of my arithmetic books with me, but I do have Pasley’s Practical Geometry Method, and Euclid, of course, and I consult them as I prepare my notes for the next day’s lesson with the girls. I have always known, if not admitted, that there are holes in my knowledge – perforations where I have flitted too fast (as Mamma would say) from one idea to another – and a more thorough approach on my part, ensuring that those holes are filled, can only be a good thing. In teaching them, I will teach myself too. All the better for my studies with Mary Somerville – for I sometimes think she is too polite to point out that I have weaknesses, as well as strengths.

In addition to this, I realise, I must be patient – not speak too quickly, nor remonstrate with them if they do not understand. I must be the kind of teacher that I myself would have appreciated – as witty and wise as Mary Montgomery; as passionate and dedicated as Miss Stamp. Yes: I, Ada, can be all those things: patient and witty and passionate and kind.

As I go to sleep, I wonder whether perhaps this is something I can do with my future.