In 1864, the Schools' Inquiry Commission was set up to inquire into the condition of post-elementary education in the country and Miss Beale was summoned to give evidence before the Commission. The fact that girls' schools were included in the investigation highlights that the government supported the notion of reforming women's education. Beale was now considered to be an educational expert; organisations such as the Schoolmistresses' Associations had helped to foster this new measure of authority and assurance.
Beale talked to the Commissioners about her teaching of mathematics and the, "principle to give as little help as possible, but to lead them to find out for themselves; under no circumstances to let them learn by heart, and to induce them to do without explanation as far as they can, so as to call out their own powers." She also spoke about how there should be no limit on mathematics, two of her pupils had taken algebra as far as the binomial theorem and were working on logarithms and one intended to go on to trigonometry. She said, "I do not see why we should limit it where we find a special taste." She also stated the importance of shared interests and experiences between boys and girls, "I think it is good for boys and girls to have similar tastes, that their minds may not be entirely bent in different ways, so that in their after life they should understand and be interested in the same things."
However, she also remarked that girls and boys do not have the same educational capacity where mathematics is concerned, "I do not think that the mathematical powers of women enable them generally - (their physical strength I dare say has a great deal to do with it) - to go so far in the higher branches of mathematics as boys." Perhaps a surprising comment from Beale, but one based solely on speculation as girls were not allowed to go as far in the higher branches of mathematics as boys at this time. The Commission, however drew different conclusions from Cheltenham Ladies' College, stating that, "there is weighty evidence to the effect that the essential capacity for learning is the same, or nearly the same, in the two sexes." It was found that girls were not so quick and accurate in arithmetic, algebra, and Euclid as boys. However it was thought that the, "inferiority of female education may be owing to the want of due method and stimulus, and to no natural causes." In 1890, Philippa Fawcett became the first woman to achieve the top score in the Mathematical Tripos exams at Cambridge, spurring wide spread debate about girls' aptitude for mathematics and modifying ideas of male superiority.
Although arithmetic was found to be the weak point in female teachers, women were still considered to be more natural teachers than their male counterparts due to their careful, patient and persevering qualities. In one of the Commissioners, Mr Bryce's report, he sensibly pointed out that, female teachers "have not themselves been well taught, and they do not know how to teach. Both of these defects are accidental, and may be remedied." Of course, he was correct and the lack of higher education for women was at the heart of the problems in girls' schools. The Schools' Inquiry Commission had concluded that in order to correct the low standards in girls' education, "the first remedy is to provide all English women of the middle class with the opportunity of higher liberal education". Overall the inquiry had a very beneficial effect on public opinion and in 1869 Girton College opened at Cambridge University, Britain's first residential college for women offering an education at degree level; Beale's evidence was central to this landmark moment.