What is OGAP?

Formative Assessment System + Professional Development

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OGAP is a systemic and intentional formative assessment system in mathematics grounded in the research on how students learn mathematics. Through extensive professional development, supported by tools and resources, teachers learn how to use formative assessments in their classrooms and analyze the resulting information about student thinking to guide subsequent instruction.  OGAP is not a curriculum, but is designed to be used with an existing curriculum on a regular basis.

Research Foundation Underlying OGAP

Increasing teachers’ formative assessment skills has promise to improve student learning and close the achievement gap. A substantial research base links solid formative assessment practices to higher student achievement and they have been shown to be particularly beneficial for low-performing students (Black & Wiliam, 1998). Over the last thirty years, a wealth of research has also been conducted on children’s development of multiplicative and rational number reasoning. The growing understanding of “learning trajectories” or common pathways of development in these areas, can provide teachers with a clear progression of learning goals, how students’ thinking develops, and learning activities that are likely to move students along the pathway towards achieving those goals (Daro, Mosher, Corcoran, 2011).

Building Teacher Capacity through Ongoing Professional Development

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OGAP provides teachers of mathematics with a rich professional development experience to use the field tested item bank, learning trajectory frameworks, and a set of instructional strategies that both enhance the formative assessment process and build teacher content knowledge, curricular knowledge and pedagogical knowledge.

Through extensive professional development, teachers explore mathematics content, our growing understanding of how students learn foundational concepts, and research-based learning trajectories. Local ongoing support is provided through trained teacher leaders.

OGAP Item Bank

OGAP items are carefully designed to elicit students’ developing understandings. Each item bank has approximately 300 constructed response items organized by mathematical topics and problem structures and situations. Items are also searchable by grade level and Common Core Standards.  The item bank for Multiplicative Reasoning is organized into the following categories:


OGAP Strategies

OGAP includes strategies and tools for gathering information about student learning so that teachers can make informed instructional decisions and maximize the use of their mathematics program based on research.

  • Pre-Assessment.  Before beginning a unit on multiplication, division, or fractions, teachers gather information about their students’ pre-existing knowledge through the use of a pre-assessment. They then use the OGAP frameworks to analyze student work and guide unit planning.
  • Ongoing Questions.  Throughout the unit teachers continue to assess student progress through instructionally aligned assessment items . Teachers learn to quickly sort student responses into categories based on the relevant OGAP framework, noting student errors and misconceptions (e.g., place value or calculation errors). Based on this analysis teachers can provide more targeted feedback to students and make more informed instructional decisions.
  • Curriculum Use.  During professional development, teachers look at their mathematics program in relation to the OGAP frameworks. They can identify opportunities in the textbook for students to use a variety of models to solve problems, understand concepts or generalize ideas.

OGAP Frameworks

OGAP frameworks synthesize problem structures, problem situations, and typical learning progressions for specific mathematical topics to help teachers analyze evidence in student work and make deliberate instructional decisions.

By mapping student strategies onto the OGAP multiplicative framework, teachers have a sense of where students are, where they need to go, and how to help them progress to the next level.

Aligned with the Common Core 

The Common Core State Standards in Mathematics (CCSSM) specifically identifies problem contexts at targeted grades on a progression designed to prepare students to engage in proportional situations using multiplicative reasoning. Consistent with the CCSSM, OGAP items reflect this range of problem situations. OGAP frameworks also reflect the progression of strategies in the Common Core:  from the link between repeated addition and multiplication in an equal groups model to the development of efficient and generalizable multiplicative strategies through the open area model, and understanding of place value, properties of operations, and relationships.


OGAP eTool

The eTool is an iPad and web-based computer app that allows teachers to use the OGAP tools and strategies quickly and seamlessly. The eTool helps teachers to:

  • Intentionally select items from the item bank to administer to students. The item bank is preloaded into the iPad and teachers can search or filter items by their characteristics.
  • Record student strategies and errors/misconceptions. Teachers enter their own class lists into the program. They can tap on the iPad to record whether or not each student answered the problem correctly, along with the specific strategy used and any errors or misconceptions.
  • Analyze the results on strategy use and errors/misconceptions. Teachers can view the results by single item, across several items, or aggregated into visual graphs to see strategy and misconception/error prevalence by class.

Video | Looking at Student Work with OGAP


Black, P. B., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5(1), 7-74.

Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction (Research Report #68). Philadelphia, PA: Consortium for Policy Research in Education.