National Science Foundation
Linking Data to Classroom Instruction to Improve Student Learning of Mathematics
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Middle school mathematics teachers build platonic solids during a VMP graduate course entitled Geometry in the Middle Grades.

Credit: Krisan Geary, VMP Course Instructor
Permission Granted
State: Vermont

During 2006, the Vermont Mathematics Partnership (VMP), a Cohort I Math and Science Partnership project, built significantly upon its first three years of foundational research, course and materials development, and work with preK-12 partner schools and institutions of higher education (IHEs). As VMP strategies matured, and as sufficient numbers of teachers and administrators from partner schools increased their expertise in mathematics content, pedagogy, assessment and leadership, the infrastructure was built for partner schools to engage in more sophisticated, systematic use of evidence to improve mathematics teaching and learning.    

In 2003, its first summer, VMP offered one graduate course at one partner school.  During the summer of 2006, VMP offered across Vermont eleven graduate courses developed and taught by teams of mathematicians, mathematics educators, teacher leaders and assessment specialists.  Since 2003, VMP has offered more than 60 graduate courses for primary, elementary, middle school and secondary mathematics teachers. To date, there have been more than 1300 enrollments in these VMP offerings, nearly triple the project’s original estimate. In the beginning of VMP’s work, some participants balked at the high standards, claiming that VMP’s requirements were much higher than those to which they were accustomed in other graduate courses in mathematics education – particularly summer courses. Most of these courses are now full and have waiting lists, with many teachers returning as “repeat customers.” Participating teachers demonstrate statistically significant gains in their content knowledge and knowledge for teaching, as measured by pre- and post- inventories of assessment items designed by the MSP Learning Mathematics for Teaching project at the University of Michigan. 

VMP teachers and IHE faculty regularly use day-to-day, formative assessment to guide and improve instruction.  VMP staff have supported school teams in the development of common local assessments and comprehensive assessment systems to promote more equitable access to mathematics learning for all students.  These tools allow teachers to closely monitor their students’ understanding of important mathematical concepts and to modify their day-to-day instruction based on evidence of student understanding. In follow-up surveys, nearly all teachers report that this experience has had a major impact on their teaching and that they are applying formative assessment strategies to other mathematics content areas.  

Evidence of improved teaching and learning in mathematics is now documented in improved student performance. In ongoing, formative assessment pilot studies with approximately 65 elementary teachers and over 1000 students, data analyses indicate that teachers who use the VMP’s ongoing assessment tools and strategies are able to identify areas of student weakness and focus instruction more appropriately and strategically, thus improving student learning and demonstrating statistically significant gains at all grade levels (grades 2, 3, 4 and 5). A specific example can be found in the improved understanding of fractions, where, for 338 fourth grade students who took pre-assessments of their understanding of fractions, 38.2 percent made errors that demonstrated inappropriate use of whole number reasoning.  Classroom instruction was informed by this data, with participating teachers using many different mathematics programs and different teaching strategies. In post-assessments, only 7.4 percent of the students made errors that demonstrated inappropriate use of whole numbers. Teachers and administrators consistently report that students whose teachers have used systematic, formative assessment enter subsequent grades with much deeper levels of understanding of important mathematical concepts than in previous years.

Partners: Hartford School District (54), Barre Supervisory Union (61), Milton Town School District (10), South Burlington School District (16)

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Sample Pre-Post test results from VMP’s Ongoing Formative Assessment Project (OGAP). OGAP assessment tools are based on research on how students develop their understanding of mathematical concepts and where they commonly have misconceptions that may affect their learning.  As teachers systematically use OGAP items to assess their students’ understanding, prior to and during instruction, they are able to target their teaching based on a more accurate picture of their students’ knowledge.

Credit: Regina Quinn, VMP Project Director
Permission Granted

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