“I want to ask if you’ve ever said out loud the following sentence…‘I want to be the number one in my field, I want to be the CEO of the company I work in, I want to be president,’” said Sheryl Sandberg, Facebook chief operating office, to a packed CEMEX Auditorium on Tuesday evening. “Stand up if you have.”

As some members of the audience stood up, Sandberg continued her exhortations.

“I’m excited to see people stand up,” she said. “And I’m here today to do just one thing. I’m here to get every person in this audience…to stand up the next time that question is asked.”

Sandberg spoke at Stanford as the 2013 Jing Lyman Lecturer, discussing her new book and philanthropic enterprise, “Lean In.” The book focuses on the absence of leadership roles held by women around the world in fields ranging from business to government and offers solutions to this lack of gender parity.

“I want to especially do this for the women, because the blunt truth is that men still run the world,” Sandberg said. “Unequivocally. No questions about it.”

Citing statistics that demonstrate the inadequate representation of women in leadership roles in society, such as the presence of only 21 female CEOs in the Fortune 500, Sandberg explored that inequality’s underlying causes.

Drawing on her personal life, her acquaintances and her work at Facebook and Google, Sandberg identified women’s insecurity about attributing success to themselves, social stereotypes of working men and women and an uneven burden in parenting responsibilities as factors that feed the lack of female representation.

“The studies show that starting in junior high [school], more boys than girls want to lead,” Sandberg said. “That’s true on college campuses. That’s true of companies, of divisions [and] of running for office. It is that leadership ambition gap that we need to understand, acknowledge and close.”

Sandberg argued that the institutional and societal biases that hold women back in the workplace and elsewhere emerge at a very young age and compound over time.

“These stereotypes that start in childhood are immensely self-perpetuating…and that penalty holds us back,” Sandberg said. “As men get more successful they are better liked. As women get more successful [and] more powerful, they are often less liked by men and women.”

“We still expect women to do the majority of child care and housework even though most women who are mothers in this country work full time, and they do,” she added. “I’m fully supportive of any decision any woman or man makes about children<\p>…<\p>but people should make that decision once they have children, because what I see is so many years before a woman has a child, women are quietly leaning back, making room for children and responsibilities they don’t even have, sitting next to men who are not making those compromises.”

Sandberg was hosted by the Clayman Institute for Gender Research, an organization that promotes gender equality internationally. Her Lean In organization aims to create more female leaders by organizing communities for women to exchange thoughts and stories, developing an online library of lectures in conjunction with the Clayman Institute and promoting Lean In “Circles,” support networks that aim to connect women with ambitious, like-minded peers.

Sandberg counseled that although policy and institutions matter, change stems from the individual.

“We can’t leave this just to managers,” she said. “We can’t depend on anyone else to solve that problem. We can try to educate people, and Lean In is trying to do that, but the person that’s most likely to correct this for you is you. My message, the message of Lean In, is [to] sit at the table, own your success [and] don’t let that be the reason you don’t aim for that top job.”

“When you have a chance to stand up for leadership, do it, stand up,” Sandberg said. “And just do it for yourself. Do it because every person who leans in, every woman who stands up, we do our part to change those stereotypes.”

Sandberg advocated a number of solutions to the issue of gender parity, including more mentoring specifically for women and having honest conversations with employers and partners about pregnancy and childcare. Reflecting on a hypothetical world with gender parity, Sandberg painted a utopian picture.

“We know our companies would be more productive,” Sandberg said. “When it comes to filling our leadership ranks, we are only sourcing from half the population, and when we source from the whole population, we are going to do better.”