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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.