You might want to start considering this question by analysing Chapter Six, "Sleary's Horsemanship," and comparing it with the rest of the novel up unto this point. It is in this chapter that we see the world of the circus, or the world of fancy and the imagination that Sissy Jupe inhabits. What indicates that this chapter presents us with a strong contrast is the name of the inn where the circus folk are staying. Having had a pointed lesson on the precise definition of a horse, we are know visiting the Pegasus's Arms. Having told Sissy Jupe firmly that we do not cover our walls or houses with pictures of imaginary horses, Mr. Gradgrind is confronted with exactly this:
Framed and glazed upon the wall behind the dingy little bar, was another Pegasus--a theatrical one--with real gauze let in for his wings, golden stars stuck on all over him, and his ethereal harness made of red silk.
Having told Louisa in Chapter Five that she must "never wonder," we are suddenly plunged into the world of fantasy and imagination that stands for everything that Mr. Gradgrind is against. The strange assortment of entertainers we are presented with are able to magically transform the monotonous world in which they live into a place of mystery and magic by the simple use of their imaginations. You might want to consider how Kidderminster fulfils this role. In reality, he is an angry, mischievous young boy, but in his role as Cupid, he pleases the spectators and is very adorable:
Made up with curls, wreaths, wings, white bismuth, and carmine, this hopeful young person soared into so pleasing a Cupid as to constitute the chief delight of the maternal part of the spectators; but, in private, where his characteristics were a precocious cutaway coat and an extremely gruff voice, he became of the Turf, turfy.
Through exercising their imaginations, the circus performers please others and themselves, in stark contrast to the grey and solemn existence of Louisa.
Firstly, you talk about how the linguistic and ideological contexts show how language is used in the text. Dickens shows two opposite worlds on his book. The first being, system and fact. The second being, fancy and life. These are two contradictory worlds and there is the desire to show that how these two worlds need to be controlled in their own way.
The themes help to show the contrasting worlds in Hard Times. Dickens shows how there is no difference between signifier and signified in the world of Fact. Dickens shows this when he describes Mr. Bounderby's house and how everything in his house represents himself. Even the name written outside his house is written in a way "very like himself". Hence there is no difference between the material things that the character has and the character himself. However, in the world of Fancy there is a difference between the signifier and the signified.
Also, there is a difference in language in the two worlds. Where in the Fact world everything is defined as calculation, payment etc. But in the Circus world, even calculations can be left to imagination and there is no set rule. There is always room for imagination in the circus world.
The world of Gradgrind describes fact and anything not going according to fact is disagreeable. However, in the circus world, realism is exceeded and imagination comes in.
Fairy-tale is hence important where imagination allows a system to be formed but not like the one present in the world of Gardgrind and Bounderby. In the circus world it is seen how efficiency causes inefficiency and how that inefficiency is good. That is anything bad is good in the circus world and how it can be differently defined. The language helps to show these things and the themes present both the world very clearly.
In the fancy world, everything is different. In the world of Fact, everything is same and is ironically described in metaphor. The language of Sleary and Sissy's misinterpretation of statistics clearly shows how such unclearness leads to clarity.
The world of utilitarianism is about satisfaction and wants being met, where Bitzer does not leave Thomas alone when Gradgrind tells him to. Because Bitzer did not owe anything to Gradgrind, he had paid for his education. Hence utility had occurred. Whereas in the world of Fancy, there is no such thing as doing one thing for another for payment. There is no compensation needed.