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This chapter outlines the evolution of one of the counterarguments generated by the girls in order to illustrate how multiple knowledge bases (knowledge about the needs of the community, knowledge about math, and knowledge about ways to critique the district) interacted within this hybrid math learning space. A distinguishing characteristic of this particular space was the fluid movement between space in the math club and the community context of the investigations. This movement between spaces supported the interaction amongst knowledge bases, as knowledge bases are often tied to particular spaces. Ultimately, this hybrid learning space fostered an alternative kind of mathematical activity that challenged the often exclusionary, yet dangerously portrayed as neutral, role of the discipline of math, and opened up entry points for the collective development of mathematical and critical knowledge for the students. Statistics on educational attainment and achievement suggest that the disconnect between students' school experiences and their lives outside of school can have devastating consequences. Math education should not only empower students with the skills and understandings to succeed academically, but also prepare them to critically investigate, challenge, and act upon issues in their lives and communities.

Math and science hold uniquely powerful places in contemporary society. These domains open doors to high-paying professions; provide a knowledge base for more informed conversations with health care workers, educators, and business and community leaders; and demystify issues of global importance, such as air and water quality standards, population density, toxic dumping, and the economy. Schools play a crucial role in mediating access to math and science. The call to make equitable math and science instruction has tended to reside in the policy sector with extension into curricula, rather than in any systematic line of inquiry into what this should look like and why. This chapter sheds light on specific needs of urban learners in the effort to promote science and math for all. High-quality science and math education is a civil right for all students, one which is especially significant for those from non-dominant groups. Studies of equal treatment and equal outcome have played, and continue to play, powerful and historically important roles. Most researchers are generally familiar with the chilling statistics that describe high-poverty and minority urban and rural students' differential access to resources in US schools, and are aware that these trends have changed little in the past three decades.

This chapter, “Training Numeracy,” focuses on improving numeric competencies to provide backdoor assistance to adults who want to make better decisions. The chapter reviews research on the roles of formal schooling in childhood and numeracy training in adulthood. It particularly highlights current evidence on adult trainings for objective numeracy and subjective numeracy and their causal effects in decision making. Although more intervention research is needed (especially to increase effect sizes), it is simply not the case that people cannot change their numeric ability. Instead, emerging interventions can build adult numeric capacity and propel decision makers to bring knowledge to bear on decisions, think probabilistically, use heuristic processing less, consider alternative scenarios, and reason better numerically. Finally, the chapter introduces the question of how much numeracy improvement is necessary to drive better decisions and outcomes if objective numeracy has cumulative effects across time.

A beautiful large stained-glass window dominates the end of the Great Hall of Birmingham University. My great-grandfather was one of the glaziers who made it—my family were Birmingham artisans, craftsmen, and engineers. His son, my grandfather, remembered being taken to the opening of Birmingham University in 1902—Joe Chamberlain, the founder of the university, believed that the workers who had built it should be invited, not just the academics. From a distance it looks like the stained-glass window in an ancient cathedral with figures of saints, but close up you see the radicalism of Joe Chamberlain’s vision. It is dedicated to the arts and sciences. Instead of saints and bishops the figures represent disciplines like geometry or music, but alongside them, equally prominent, are contemporary trades: there is an electroplater, a rather Michelangelesque miner, and a demure bookkeeper too. It is a celebration of the range of trades and professions of the early twentieth century, ‘as practised in the university and in the City’, said the local paper. England’s first university in one of its great bustling industrial cities was claiming a new role for the university based on its civic commitment. This great window embodies a very different idea of the university from the Oxbridge tradition. It is a vigorous statement in an argument that was raging within Government at the very time that Chamberlain was planning his new university. The question was whether public funds should go to help pay for higher education courses outside Oxbridge on a systematic basis and if so which courses at which institutions. (At this point what would become our Redbrick universities were typically university colleges teaching for the external degree of the University of London and funded locally, though with occasional public grants.) The question came to the Chancellor of the Exchequer in 1895, who replied: ‘As an old Oxford man myself I must confess to a feeling, which you may call a prejudice, that University education, in the full sense of the term, can hardly be obtained except at our old Universities.’ The Treasury consulted Oxford and Cambridge on what they should fund.

The value of universities is not simply their contribution to human capital and economic growth, welcome though these are. Universities should enable a graduate to lead a flourishing, fulfilled life. That must mean the capacity to engage with the wide range of extraordinary intellectual and cultural achievements to which we are heirs and to which we should add for the next generation. It is the most important single responsibility of our universities and it is where the most significant reform is required. English education requires 16-year-olds to take life-changing decisions to specialize in just three subjects, and indeed allows students to drop a range of subjects at the age of 14. No other major Western country does this. It is the source of many of the other problems which we worry about. Fewer girls do STEM subjects after the age of 16 than in most other countries because in England they are presented with irreversible decisions to give them up when they are much too young. We suffer particularly acutely from C. P. Snow’s two cultures because our teenagers can join one of two apparently deeply hostile gangs—the humanities or the sciences, the Montagues and the Capulets of intellectual life—when most other countries avoid promoting such divisions. When employers complain about employability they often mean that young people have been force-fed for a narrow academic curriculum without a wider range of subjects and skills. Above all, as I look back on my education, my greatest regret—and that of many friends and contemporaries as we get older—is that we missed out on great scientific or cultural achievements of our age because of early decisions whose long-term significance we completely failed to recognize. I greatly enjoyed studying History, English, and German for my A levels but now I am shocked at the barbarism of a system which restricted my studies to those three subjects at the age of 16. This is the intellectual and cultural damage inflicted by our educational system when above all it should broaden our horizons and enlighten us. That this system is preserved on the claim it is necessary for high academic standards is even more scandalous.