The Ongoing Assessment Project (OGAP) is both the product and subject of research. First, OGAP was developed upon important research-based principles of student learning and mathematics instruction. Second, OGAP has been the subject of a number of studies that assess its impact on teachers and students. Here both the research foundation for OGAP and the evidence of its impacts on teachers and students are summarized.

**The Research Foundation of OGAP**

The foundation underlying OGAP is both the strong research base for formative assessment and the field’s growing understanding of how students learn mathematics. Research reviews of formative assessment practices indicate that teachers’ skill with formative assessment is a key factor for improving student learning (Kluger & DiNisi, 1996; Wiliam, 2007). In their extensive review of the literature on formative assessment, Black and Wiliam (1998) found substantial evidence linking formative assessment with higher student achievement, with typical effect sizes ranging from an impressive 0.4 to 0.7. Across these studies, formative assessment was shown to be particularly beneficial for low-performing students, which suggests that increasing teachers’ skill with formative assessment has promise for closing the achievement gap.

Over the last thirty years, a parallel set of research has been conducted on children’s development in such mathematical concepts as multiplicative reasoning, rational number reasoning, and proportional reasoning (Behr, Harel, Post, & Lesh, 1992; Harel & Confrey, 1994; Lamon, 2007; Steffe & Olive, 2010; Tournaire** **& Pulos, 1985; Sherin & Fuson, 2005), (e.g., Confrey, 2009). The growing understanding of the “learning trajectories” or common pathways of development in these areas have the potential to provide teachers with a clear articulation of learning goals, how students’ thinking should develop, and learning activities that are likely to move students along the path towards achieving those goals (Heritage, 2008; Sztajn, Confrey, Wilson, & Edginton, 2012).

The ability to tie assessment evidence to subsequent instruction involves understanding the trajectory of student learning and having instructional strategies that help learners move along that trajectory (Andrade, 2010). Some evidence suggests that research-based frameworks of how students build mathematical understanding can enhance teacher’s ability to interpret evidence of student learning and respond productively in light of that evidence (Clements, Sarama, Spitler, Lange & Wolfe, 2011; Wilson, 2009).

Building on this research through a decade of their own research and development, the Vermont Mathematics Partnership is an effort to use formative assessment processes informed by the research on students’ mathematical learning. OGAP materials were developed through the distillation of hundreds of studies and articles on mathematics education research on multiplicative reasoning and fractions; more than 50,000 samples of student work; and the study of over 27 teacher-leader projects in which OGAP has trained teachers working in Michigan, Alabama, Nebraska, New Hampshire, and Ohio using the OGAP materials for fractions and multiplicative reasoning.

A key aspect of OGAP is that the program translates research into practice for teachers. For example, the OGAP framework for multiplicative reasoning is used by teachers on an ongoing basis to chart students’ progress towards more efficient and generalizable strategies when solving problems. Research has shown that in multiplicative situations, as students interact with new concepts, new and/or more complex problem situations, and new problem structures, they may move back and forth between multiplicative, transitional, additive, and non-multiplicative strategies (e.g., Ambrose et al., 2003;** **Carpenter et al., 1998; Greer, 1992; Kaput, 1989; Lamon, 1994; Nesher, 1998). This research base is synthesized in the three interrelated elements of OGAP: 1) problem structures (e.g., number of digits, number of factors, properties); 2) problem situations with sample problems (e.g., equal groups, multiplicative change and comparisons, rate); and, 3) the main stages in the learning trajectory for multiplication and division and evidence in student work.