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The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier. At the same time, other students with requisite skills are not given access to algebra. Although studies using nationally representative data indicate strong positive outcomes for students who take algebra early, studies conducted only in contexts where all students are mandated to take algebra in eighth or ninth grade provide mixed evidence of positive outcomes, with increased achievement when policies include strong supports for struggling students. The authors conclude with a call for studies that examine the relationship among algebra policies, instruction, and student outcomes to understand the mechanisms by which policies can lead to success for all students.

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In the majority of secondary mathematics teacher preparation programs, the work of learning mathematics and the work of learning to teach mathematics are separated, leaving open the question of when and how teachers integrate their knowledge of content and pedagogy. We present a model for a content-focused methods course, which systematically develops a slice of mathematics content in the context of typical methods course activities. Three design principles are posited that undergird the design of such a course, addressing the nature of the mathematics content, the sequencing and design of activities, and the ways in which the course addresses the needs of diverse learners. Data from an instantiation of one such course is presented to illustrate the ways in which the course design framed teachers' opportunities to learn about both content and pedagogy.

Middle-grades students' understanding of proportional relationships should be fostered through problem solving and reasoning (NCTM 2000). Toward this end, instruction in proportionality should expose students to a variety of strategies and allow students to gain experience modeling proportional situations (Langrall and Swafford 2000). Students should be given ample opportunities to develop intuitive strategies based on factor- of-change (“how many times as many”) relationships (Cramer and Post 1993). Research has shown that middle-grades students are more successful at method is appropriate to use” (NCTM 2000, p. 221). We begin our discussion by focusing on the events that unfold in Marie Hanson's sixth-grade classroom during a lesson on understanding ratios and proportions (Smith et al. forthcoming), and use this lesson as a context for considering how factor-of-change relationships might be used to assist students in understanding why cross multiplication works.