A Wrinkle in Math

My daughter has been quite fortunate this year — she has a terrific math teacher, and she has blossomed and grown in her math skills. Most critically, she’s gone from hating math to loving math, including declarations such as, “When I go to college, I want to major in math.”

But I know that across the country, many children (and their parents) are not having the same experience. Every time I hear elementary school parental frustration about “Common Core math,” I’m reminded of this passage from one of my favorite novels as a child, Madeleine L’Engle’s A Wrinkle in Time:

“Have you done your homework, Meg?”
“Not quite,” Meg said, going back into the kitchen.
“Then I’m sure Calvin won’t mind if you finish before dinner.”
“Sure, go ahead.” Calvin fished in his pocket and pulled out a wad of folded paper. “As a matter of fact, I have some junk of mine to finish up. Math. That’s the one thing I have a hard time keeping up in. I’m okay on anything to do with words, but I don’t do as well with numbers.”
Mrs. Murray smiled. “Why don’t you get Meg to help you?”
“But see, I’m several grades above Meg.”
“Try asking her to help you with your math, anyhow,” Mrs. Murray suggested.
“Well, sure, “Calvin said. “Here. But it’s pretty complicated.”
Meg smoothed out the paper and studied it. “Do they care how you do it?” she asked. “I mean, can you work it out in your own way?”
“Well, sure, as long as I understand it and get the answers right.”
“Well, we have to do it their way. Now look, Calvin, don’t you see how much easier it would be if you did it this way?” Her pencil flew over the paper.
“Hey!” Calvin said. “Hey! I think I get it. Show me once more on another one.”
Again, Meg’s pencil was busy. “All you have to remember is that every ordinary fraction can be converted into an infinite periodic decimal fraction. See? So 3/7 is 0.428571.”
“This is the craziest family.” Calvin grinned at her. “I suppose I should stop being surprised by now, but you’re supposed to be dumb in school, always being called up on the carpet.”
“Oh, I am.”
“The trouble with Meg and math,” Mrs. Murray said briskly, “is that Meg and her father used to play around with numbers and Meg learned far too many short cuts. So when they want her to do the problems the long way around at school she gets sullen and stubborn and sets up a fine mental block for herself.”

I think that for some kids, what is being marketed as the Common Core’s approach to math is intuitive and makes a lot of sense. But why are we insisting on a one-size-fits-all approach? I’m all for having kids show their work, but why do we insist that all of our kids must show the same work, rather than simply ensuring that the methods they’re using are mathematically correct and make sense to them?

For some kids, subtraction through “counting up” makes sense. For others, the traditional method of borrowing make sense. If both methods are mathematically sound, and both methods produce the same result, then why the insistence on forcing one method on all kids?

And, of course, although Meg may have been labeled “dumb in school,” at least her graduation and her future were not tied to high-stakes exams that forced her to demonstrate her proficiency at “the long way around” of completing a certain math problem (unlike the sample 3rd to 5th grade PARCC math problem that requires the kids to, one-by-one, click 48 boxes in an array to demonstrate their “understanding” of 6 x 8 = 48).

This all reminds me of this oldie but goodie from second grade math last year, with the teacher who inspired last year’s hatred of math:



Hard Times (or Everything Old is New Again)

Unfortunately, my mother-in-law took ill, and passed away last Saturday morning.  As a result, although I’ve continued to read and learn from all sides of the education policy debate, I haven’t had much of a chance to crystalize my thoughts sufficiently to finish another post.  But to whet your appetite, here’s a brief intro to a far more eloquent thinker than I could hope to be.

In reading the current education policy debates, one thing keeps nagging at me: I’ve read and heard this all before.  So I went back and re-read one of the summer reading texts I’d first encountered as an AP English Literature student: Hard Times by Charles Dickens.  And I was amazed: not only is Dickens as timely as can be when it comes to the modern education policy debates; he is also prescient regarding the class divisions between the haves and the have-nots.  I highly recommend that all modern policy makers go back and review their Dickens.  He — far more ably than I can — points out the horrors of capitalism without regulation (i.e., capitalism run amok). 

And as far as education policy goes, who can forget Mr. M’Choakumchild and Mr. Gradgrind?  

Who are our modern M’Choakumchilds and Gradgrinds?  

Gradgrind’s methods largely contributed to ruining his children’s lives.  

How many lives are we willing to ruin in service to ideals that Dickens rejected in 1854?

To get you started, here (with thanks to Project Gutenberg) are the first three chapters of Dickens’ Hard Times, which make the point that true education is about so much more than stuffing a child’s head full of facts.  The modern analogue, of course, is that true education is about so much more than turning our children into trained test-taking monkeys.



‘Now, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them. This is the principle on which I bring up my own children, and this is the principle on which I bring up these children. Stick to Facts, sir!’

The scene was a plain, bare, monotonous vault of a school-room, and the speaker’s square forefinger emphasized his observations by underscoring every sentence with a line on the schoolmaster’s sleeve. The emphasis was helped by the speaker’s square wall of a forehead, which had his eyebrows for its base, while his eyes found commodious cellarage in two dark caves, overshadowed by the wall. The emphasis was helped by the speaker’s mouth, which was wide, thin, and hard set. The emphasis was helped by the speaker’s voice, which was inflexible, dry, and dictatorial. The emphasis was helped by the speaker’s hair, which bristled on the skirts of his bald head, a plantation of firs to keep the wind from its shining surface, all covered with knobs, like the crust of a plum pie, as if the head had scarcely warehouse-room for the hard facts stored inside. The speaker’s obstinate carriage, square coat, square legs, square shoulders,—nay, his very neckcloth, trained to take him by the throat with an unaccommodating grasp, like a stubborn fact, as it was,—all helped the emphasis.

‘In this life, we want nothing but Facts, sir; nothing but Facts!’

The speaker, and the schoolmaster, and the third grown person present, all backed a little, and swept with their eyes the inclined plane of little vessels then and there arranged in order, ready to have imperial gallons of facts poured into them until they were full to the brim.


Thomas Gradgrind, sir. A man of realities. A man of facts and calculations. A man who proceeds upon the principle that two and two are four, and nothing over, and who is not to be talked into allowing for anything over. Thomas Gradgrind, sir—peremptorily Thomas—Thomas Gradgrind. With a rule and a pair of scales, and the multiplication table always in his pocket, sir, ready to weigh and measure any parcel of human nature, and tell you exactly what it comes to. It is a mere question of figures, a case of simple arithmetic. You might hope to get some other nonsensical belief into the head of George Gradgrind, or Augustus Gradgrind, or John Gradgrind, or Joseph Gradgrind (all supposititious, non-existent persons), but into the head of Thomas Gradgrind—no, sir!

In such terms Mr. Gradgrind always mentally introduced himself, whether to his private circle of acquaintance, or to the public in general. In such terms, no doubt, substituting the words ‘boys and girls,’ for ‘sir,’ Thomas Gradgrind now presented Thomas Gradgrind to the little pitchers before him, who were to be filled so full of facts.

Indeed, as he eagerly sparkled at them from the cellarage before mentioned, he seemed a kind of cannon loaded to the muzzle with facts, and prepared to blow them clean out of the regions of childhood at one discharge. He seemed a galvanizing apparatus, too, charged with a grim mechanical substitute for the tender young imaginations that were to be stormed away.

‘Girl number twenty,’ said Mr. Gradgrind, squarely pointing with his square forefinger, ‘I don’t know that girl. Who is that girl?’

‘Sissy Jupe, sir,’ explained number twenty, blushing, standing up, and curtseying.

‘Sissy is not a name,’ said Mr. Gradgrind. ‘Don’t call yourself Sissy. Call yourself Cecilia.’

‘It’s father as calls me Sissy, sir,’ returned the young girl in a trembling voice, and with another curtsey.

‘Then he has no business to do it,’ said Mr. Gradgrind. ‘Tell him he mustn’t. Cecilia Jupe. Let me see. What is your father?’

‘He belongs to the horse-riding, if you please, sir.’

Mr. Gradgrind frowned, and waved off the objectionable calling with his hand.

‘We don’t want to know anything about that, here. You mustn’t tell us about that, here. Your father breaks horses, don’t he?’

‘If you please, sir, when they can get any to break, they do break horses in the ring, sir.’

‘You mustn’t tell us about the ring, here. Very well, then. Describe your father as a horsebreaker. He doctors sick horses, I dare say?’

‘Oh yes, sir.’

‘Very well, then. He is a veterinary surgeon, a farrier, and horsebreaker. Give me your definition of a horse.’

(Sissy Jupe thrown into the greatest alarm by this demand.)

‘Girl number twenty unable to define a horse!’ said Mr. Gradgrind, for the general behoof of all the little pitchers. ‘Girl number twenty possessed of no facts, in reference to one of the commonest of animals! Some boy’s definition of a horse. Bitzer, yours.’

The square finger, moving here and there, lighted suddenly on Bitzer, perhaps because he chanced to sit in the same ray of sunlight which, darting in at one of the bare windows of the intensely white-washed room, irradiated Sissy. For, the boys and girls sat on the face of the inclined plane in two compact bodies, divided up the centre by a narrow interval; and Sissy, being at the corner of a row on the sunny side, came in for the beginning of a sunbeam, of which Bitzer, being at the corner of a row on the other side, a few rows in advance, caught the end. But, whereas the girl was so dark-eyed and dark-haired, that she seemed to receive a deeper and more lustrous colour from the sun, when it shone upon her, the boy was so light-eyed and light-haired that the self-same rays appeared to draw out of him what little colour he ever possessed. His cold eyes would hardly have been eyes, but for the short ends of lashes which, by bringing them into immediate contrast with something paler than themselves, expressed their form. His short-cropped hair might have been a mere continuation of the sandy freckles on his forehead and face. His skin was so unwholesomely deficient in the natural tinge, that he looked as though, if he were cut, he would bleed white.

‘Bitzer,’ said Thomas Gradgrind. ‘Your definition of a horse.’

‘Quadruped. Graminivorous. Forty teeth, namely twenty-four grinders, four eye-teeth, and twelve incisive. Sheds coat in the spring; in marshy countries, sheds hoofs, too. Hoofs hard, but requiring to be shod with iron. Age known by marks in mouth.’ Thus (and much more) Bitzer.

‘Now girl number twenty,’ said Mr. Gradgrind. ‘You know what a horse is.’

She curtseyed again, and would have blushed deeper, if she could have blushed deeper than she had blushed all this time. Bitzer, after rapidly blinking at Thomas Gradgrind with both eyes at once, and so catching the light upon his quivering ends of lashes that they looked like the antennæ of busy insects, put his knuckles to his freckled forehead, and sat down again.

The third gentleman now stepped forth. A mighty man at cutting and drying, he was; a government officer; in his way (and in most other people’s too), a professed pugilist; always in training, always with a system to force down the general throat like a bolus, always to be heard of at the bar of his little Public-office, ready to fight all England. To continue in fistic phraseology, he had a genius for coming up to the scratch, wherever and whatever it was, and proving himself an ugly customer. He would go in and damage any subject whatever with his right, follow up with his left, stop, exchange, counter, bore his opponent (he always fought All England) to the ropes, and fall upon him neatly. He was certain to knock the wind out of common sense, and render that unlucky adversary deaf to the call of time. And he had it in charge from high authority to bring about the great public-office Millennium, when Commissioners should reign upon earth.

‘Very well,’ said this gentleman, briskly smiling, and folding his arms. ‘That’s a horse. Now, let me ask you girls and boys, Would you paper a room with representations of horses?’

After a pause, one half of the children cried in chorus, ‘Yes, sir!’ Upon which the other half, seeing in the gentleman’s face that Yes was wrong, cried out in chorus, ‘No, sir!’—as the custom is, in these examinations.

‘Of course, No. Why wouldn’t you?’

A pause. One corpulent slow boy, with a wheezy manner of breathing, ventured the answer, Because he wouldn’t paper a room at all, but would paint it.

‘You must paper it,’ said the gentleman, rather warmly.

‘You must paper it,’ said Thomas Gradgrind, ‘whether you like it or not. Don’t tell us you wouldn’t paper it. What do you mean, boy?’

‘I’ll explain to you, then,’ said the gentleman, after another and a dismal pause, ‘why you wouldn’t paper a room with representations of horses. Do you ever see horses walking up and down the sides of rooms in reality—in fact? Do you?’

‘Yes, sir!’ from one half. ‘No, sir!’ from the other.

‘Of course no,’ said the gentleman, with an indignant look at the wrong half. ‘Why, then, you are not to see anywhere, what you don’t see in fact; you are not to have anywhere, what you don’t have in fact. What is called Taste, is only another name for Fact.’ Thomas Gradgrind nodded his approbation.

‘This is a new principle, a discovery, a great discovery,’ said the gentleman. ‘Now, I’ll try you again. Suppose you were going to carpet a room. Would you use a carpet having a representation of flowers upon it?’

There being a general conviction by this time that ‘No, sir!’ was always the right answer to this gentleman, the chorus of No was very strong. Only a few feeble stragglers said Yes: among them Sissy Jupe.

‘Girl number twenty,’ said the gentleman, smiling in the calm strength of knowledge.

Sissy blushed, and stood up.

‘So you would carpet your room—or your husband’s room, if you were a grown woman, and had a husband—with representations of flowers, would you?’ said the gentleman. ‘Why would you?’

‘If you please, sir, I am very fond of flowers,’ returned the girl.

‘And is that why you would put tables and chairs upon them, and have people walking over them with heavy boots?’

‘It wouldn’t hurt them, sir. They wouldn’t crush and wither, if you please, sir. They would be the pictures of what was very pretty and pleasant, and I would fancy—’

‘Ay, ay, ay! But you mustn’t fancy,’ cried the gentleman, quite elated by coming so happily to his point. ‘That’s it! You are never to fancy.’

‘You are not, Cecilia Jupe,’ Thomas Gradgrind solemnly repeated, ‘to do anything of that kind.’

‘Fact, fact, fact!’ said the gentleman. And ‘Fact, fact, fact!’ repeated Thomas Gradgrind.

‘You are to be in all things regulated and governed,’ said the gentleman, ‘by fact. We hope to have, before long, a board of fact, composed of commissioners of fact, who will force the people to be a people of fact, and of nothing but fact. You must discard the word Fancy altogether. You have nothing to do with it. You are not to have, in any object of use or ornament, what would be a contradiction in fact. You don’t walk upon flowers in fact; you cannot be allowed to walk upon flowers in carpets. You don’t find that foreign birds and butterflies come and perch upon your crockery; you cannot be permitted to paint foreign birds and butterflies upon your crockery. You never meet with quadrupeds going up and down walls; you must not have quadrupeds represented upon walls. You must use,’ said the gentleman, ‘for all these purposes, combinations and modifications (in primary colours) of mathematical figures which are susceptible of proof and demonstration. This is the new discovery. This is fact. This is taste.’

The girl curtseyed, and sat down. She was very young, and she looked as if she were frightened by the matter-of-fact prospect the world afforded.

‘Now, if Mr. M’Choakumchild,’ said the gentleman, ‘will proceed to give his first lesson here, Mr. Gradgrind, I shall be happy, at your request, to observe his mode of procedure.’

Mr. Gradgrind was much obliged. ‘Mr. M’Choakumchild, we only wait for you.’

So, Mr. M’Choakumchild began in his best manner. He and some one hundred and forty other schoolmasters, had been lately turned at the same time, in the same factory, on the same principles, like so many pianoforte legs. He had been put through an immense variety of paces, and had answered volumes of head-breaking questions. Orthography, etymology, syntax, and prosody, biography, astronomy, geography, and general cosmography, the sciences of compound proportion, algebra, land-surveying and levelling, vocal music, and drawing from models, were all at the ends of his ten chilled fingers. He had worked his stony way into Her Majesty’s most Honourable Privy Council’s Schedule B, and had taken the bloom off the higher branches of mathematics and physical science, French, German, Latin, and Greek. He knew all about all the Water Sheds of all the world (whatever they are), and all the histories of all the peoples, and all the names of all the rivers and mountains, and all the productions, manners, and customs of all the countries, and all their boundaries and bearings on the two and thirty points of the compass. Ah, rather overdone, M’Choakumchild. If he had only learnt a little less, how infinitely better he might have taught much more!

He went to work in this preparatory lesson, not unlike Morgiana in the Forty Thieves: looking into all the vessels ranged before him, one after another, to see what they contained. Say, good M’Choakumchild. When from thy boiling store, thou shalt fill each jar brim full by-and-by, dost thou think that thou wilt always kill outright the robber Fancy lurking within—or sometimes only maim him and distort him!


Mr. Gradgrind walked homeward from the school, in a state of considerable satisfaction. It was his school, and he intended it to be a model. He intended every child in it to be a model—just as the young Gradgrinds were all models.

There were five young Gradgrinds, and they were models every one. They had been lectured at, from their tenderest years; coursed, like little hares. Almost as soon as they could run alone, they had been made to run to the lecture-room. The first object with which they had an association, or of which they had a remembrance, was a large black board with a dry Ogre chalking ghastly white figures on it.

Not that they knew, by name or nature, anything about an Ogre Fact forbid! I only use the word to express a monster in a lecturing castle, with Heaven knows how many heads manipulated into one, taking childhood captive, and dragging it into gloomy statistical dens by the hair.

No little Gradgrind had ever seen a face in the moon; it was up in the moon before it could speak distinctly. No little Gradgrind had ever learnt the silly jingle, Twinkle, twinkle, little star; how I wonder what you are! No little Gradgrind had ever known wonder on the subject, each little Gradgrind having at five years old dissected the Great Bear like a Professor Owen, and driven Charles’s Wain like a locomotive engine-driver. No little Gradgrind had ever associated a cow in a field with that famous cow with the crumpled horn who tossed the dog who worried the cat who killed the rat who ate the malt, or with that yet more famous cow who swallowed Tom Thumb: it had never heard of those celebrities, and had only been introduced to a cow as a graminivorous ruminating quadruped with several stomachs.

To his matter-of-fact home, which was called Stone Lodge, Mr. Gradgrind directed his steps. He had virtually retired from the wholesale hardware trade before he built Stone Lodge, and was now looking about for a suitable opportunity of making an arithmetical figure in Parliament. Stone Lodge was situated on a moor within a mile or two of a great town—called Coketown in the present faithful guide-book.

A very regular feature on the face of the country, Stone Lodge was. Not the least disguise toned down or shaded off that uncompromising fact in the landscape. A great square house, with a heavy portico darkening the principal windows, as its master’s heavy brows overshadowed his eyes. A calculated, cast up, balanced, and proved house. Six windows on this side of the door, six on that side; a total of twelve in this wing, a total of twelve in the other wing; four-and-twenty carried over to the back wings. A lawn and garden and an infant avenue, all ruled straight like a botanical account-book. Gas and ventilation, drainage and water-service, all of the primest quality. Iron clamps and girders, fire-proof from top to bottom; mechanical lifts for the housemaids, with all their brushes and brooms; everything that heart could desire.

Everything? Well, I suppose so. The little Gradgrinds had cabinets in various departments of science too. They had a little conchological cabinet, and a little metallurgical cabinet, and a little mineralogical cabinet; and the specimens were all arranged and labelled, and the bits of stone and ore looked as though they might have been broken from the parent substances by those tremendously hard instruments their own names; and, to paraphrase the idle legend of Peter Piper, who had never found his way into their nursery, If the greedy little Gradgrinds grasped at more than this, what was it for good gracious goodness’ sake, that the greedy little Gradgrinds grasped it!

Their father walked on in a hopeful and satisfied frame of mind. He was an affectionate father, after his manner; but he would probably have described himself (if he had been put, like Sissy Jupe, upon a definition) as ‘an eminently practical’ father. He had a particular pride in the phrase eminently practical, which was considered to have a special application to him. Whatsoever the public meeting held in Coketown, and whatsoever the subject of such meeting, some Coketowner was sure to seize the occasion of alluding to his eminently practical friend Gradgrind. This always pleased the eminently practical friend. He knew it to be his due, but his due was acceptable.

He had reached the neutral ground upon the outskirts of the town, which was neither town nor country, and yet was either spoiled, when his ears were invaded by the sound of music. The clashing and banging band attached to the horse-riding establishment, which had there set up its rest in a wooden pavilion, was in full bray. A flag, floating from the summit of the temple, proclaimed to mankind that it was ‘Sleary’s Horse-riding’ which claimed their suffrages. Sleary himself, a stout modern statue with a money-box at its elbow, in an ecclesiastical niche of early Gothic architecture, took the money. Miss Josephine Sleary, as some very long and very narrow strips of printed bill announced, was then inaugurating the entertainments with her graceful equestrian Tyrolean flower-act. Among the other pleasing but always strictly moral wonders which must be seen to be believed, Signor Jupe was that afternoon to ‘elucidate the diverting accomplishments of his highly trained performing dog Merrylegs.’ He was also to exhibit ‘his astounding feat of throwing seventy-five hundred-weight in rapid succession backhanded over his head, thus forming a fountain of solid iron in mid-air, a feat never before attempted in this or any other country, and which having elicited such rapturous plaudits from enthusiastic throngs it cannot be withdrawn.’ The same Signor Jupe was to ‘enliven the varied performances at frequent intervals with his chaste Shaksperean quips and retorts.’ Lastly, he was to wind them up by appearing in his favourite character of Mr. William Button, of Tooley Street, in ‘the highly novel and laughable hippo-comedietta of The Tailor’s Journey to Brentford.’

Thomas Gradgrind took no heed of these trivialities of course, but passed on as a practical man ought to pass on, either brushing the noisy insects from his thoughts, or consigning them to the House of Correction. But, the turning of the road took him by the back of the booth, and at the back of the booth a number of children were congregated in a number of stealthy attitudes, striving to peep in at the hidden glories of the place.

This brought him to a stop. ‘Now, to think of these vagabonds,’ said he, ‘attracting the young rabble from a model school.’

A space of stunted grass and dry rubbish being between him and the young rabble, he took his eyeglass out of his waistcoat to look for any child he knew by name, and might order off. Phenomenon almost incredible though distinctly seen, what did he then behold but his own metallurgical Louisa, peeping with all her might through a hole in a deal board, and his own mathematical Thomas abasing himself on the ground to catch but a hoof of the graceful equestrian Tyrolean flower-act!

Dumb with amazement, Mr. Gradgrind crossed to the spot where his family was thus disgraced, laid his hand upon each erring child, and said:

‘Louisa!! Thomas!!’

Both rose, red and disconcerted. But, Louisa looked at her father with more boldness than Thomas did. Indeed, Thomas did not look at him, but gave himself up to be taken home like a machine.

‘In the name of wonder, idleness, and folly!’ said Mr. Gradgrind, leading each away by a hand; ‘what do you do here?’

‘Wanted to see what it was like,’ returned Louisa, shortly.

‘What it was like?’

‘Yes, father.’

There was an air of jaded sullenness in them both, and particularly in the girl: yet, struggling through the dissatisfaction of her face, there was a light with nothing to rest upon, a fire with nothing to burn, a starved imagination keeping life in itself somehow, which brightened its expression. Not with the brightness natural to cheerful youth, but with uncertain, eager, doubtful flashes, which had something painful in them, analogous to the changes on a blind face groping its way.

She was a child now, of fifteen or sixteen; but at no distant day would seem to become a woman all at once. Her father thought so as he looked at her. She was pretty. Would have been self-willed (he thought in his eminently practical way) but for her bringing-up.

‘Thomas, though I have the fact before me, I find it difficult to believe that you, with your education and resources, should have brought your sister to a scene like this.’

‘I brought him, father,’ said Louisa, quickly. ‘I asked him to come.’

‘I am sorry to hear it. I am very sorry indeed to hear it. It makes Thomas no better, and it makes you worse, Louisa.’

She looked at her father again, but no tear fell down her cheek.

‘You! Thomas and you, to whom the circle of the sciences is open; Thomas and you, who may be said to be replete with facts; Thomas and you, who have been trained to mathematical exactness; Thomas and you, here!’ cried Mr. Gradgrind. ‘In this degraded position! I am amazed.’

‘I was tired, father. I have been tired a long time,’ said Louisa.

‘Tired? Of what?’ asked the astonished father.

‘I don’t know of what—of everything, I think.’

‘Say not another word,’ returned Mr. Gradgrind. ‘You are childish. I will hear no more.’ He did not speak again until they had walked some half-a-mile in silence, when he gravely broke out with: ‘What would your best friends say, Louisa? Do you attach no value to their good opinion? What would Mr. Bounderby say?’ At the mention of this name, his daughter stole a look at him, remarkable for its intense and searching character. He saw nothing of it, for before he looked at her, she had again cast down her eyes!

‘What,’ he repeated presently, ‘would Mr. Bounderby say?’  All the way to Stone Lodge, as with grave indignation he led the two delinquents home, he repeated at intervals ‘What would Mr. Bounderby say?’—as if Mr. Bounderby had been Mrs. Grundy.