What different gender norms are contrasted in the novel? How are they in conflict with one another? Are there any implicit values connected to specific gender roles in Matilda?

There are certainly a number of gender norms that are discussed and challenged in Ronald Dahl's brilliant novel, Matilda. Matilda is an exceptionally smart girl with telekinetic powers who is faced with abusive parents and an abusive brother. Matilda's father and mother consistently punish Matilda for seeking knowledge, and Matilda's father becomes furious when Matilda expresses her intelligence. The implication is that girls are not supposed to be intelligent, and are certainly not supposed to challenge the intelligence of the male figures in their lives. Matilda's mother reinforces this oppressive ideology when she mocks Miss Honey for having chosen a life dedicated to education and the pursuit of knowledge, rather than a shallow life devoted to looks and obtaining a husband. The values connected to gender roles in this context, then, are that women who prioritize looks and being desirable to men are held within a higher regard in society than educated women.
Matilda and Miss Honey both must struggle against gender-based stereotypes of how girls and women are supposed to behave. Miss Honey is an independent, single woman who is making her own living in spite of the challenges she faces. Matilda admires Miss Honey and eventually is adopted by Miss Honey, who then becomes a an independent, single parent who provides Matilda with the love and support she had never received within her biological, nuclear family structure. Miss Honey dismantles the patriarchal notion that she needs a man in her life in order to thrive or provide a good life for her child.
One could even argue the Miss Trunchbull is held unfairly under the scrutiny of assumed gender roles. She is an incredibly strong and robust woman who is loud and brazen. At one point, she mocks the manner in which students learn to spell "difficulty". When the student sings "Mrs. D, Mrs. I, Mrs. FFI, Mrs. C, Mrs. U, Mrs. LTY. That spells difficulty.'' Miss Trunchbull replies in disgust, ''How perfectly ridiculous!...Why are all these women married?” Miss Trunchbull, though she is horribly cruel and abusive, also feels the oppression of gendered expectations. Miss Trunchbull's physical appearance, strength, and brazen demeanor can be seen as a physical representation of her cruel attitude, which is an unfortunate connection to make as it reinforces the notion that acceptable women aren't strong or loud like men.