The Florida Department of Education has partnered with the Florida Center for Research in Science, Mathematics, Engineering, and Technology (FCR-STEM) to develop a Mathematics Formative Assessment System (MFAS) for K-3 students. This project was initiated in recognition of the critical role of early learning in establishing a strong foundation for later success in advanced mathematics and for fostering interest in mathematics-related careers. The MFAS also supports the goals of RtI (Response to Instruction/Intervention) by (a) promoting evidence-based practices, (b) developing instructionally relevant assessments, (c) providing strategies for differentiating instruction, and (d) providing professional development for teachers and school leaders (Smith, 2008).

Formative assessment is a critical component of a balanced assessment system. Classroom-based formative assessments complement large-scale summative tests by providing evidence of student thinking. Teachers practicing formative assessment ask students to perform tasks, explain their reasoning, and prove their solutions. The evidence collected enables teachers to differentiate instruction based on students’ cognitive strategies rather than on incorrect answers. Misconceptions and gaps in understanding undermine the conceptual foundation essential to learn and excel in advanced mathematics. Without the evidence of student thinking obtained during formative assessment, teachers often have to target instruction at correcting symptoms (e.g., computational and procedural errors) rather than the underlying cognitive causes of chronic low performance (Bransford, Brown, & Cocking, 2000).

Research indicates that formative assessment, if well-designed and implemented correctly, is an effective strategy for enhancing student learning. Research concludes that

• Students in classes where formative assessment was implemented learned in six months what would have taken other classrooms a year to learn (Wiliam, 2006). 
• Formative assessment promotes significant gains in student self-efficacy and motivation (predictors of high school graduation) (Black, Harrison, Lee, Marshall & Wiliam, 2003).
• Regular use of classroom formative assessment could raise student achievement by 0.4 to 0.7 standard deviations (Black & Wiliam, 1998)—enough to raise the United States into the top five countries in the international rankings for math achievement (Wiliam, 2007). 
• Compared to other interventions, formative assessment has the greatest impact on learning gains and is more cost-effective.

The K-3 MFAS reflects the qualities research has identified as critical for effective educational measurement and formative assessment. The system includes 

• Classroom-based assessment tasks designed to gather evidence of student thinking and skill in core mathematics concepts and processes.
• Task-specific rubrics to assist teachers’ in evaluating and interpreting students’ performance on the tasks (e.g., using questioning strategies and student proofs to separate computational errors from misconceptions). 
• Examples of quality feedback teachers can use to differentiate and target instruction. 
• Professional development modules available through CPALMS for teachers implementing formative assessment (e.g., looking at student work, providing formative feedback, and differentiating instruction) and for administrators (e.g., implementing job-embedded professional development).

References

Black, P., Harrison, C., Lee, C., Marshall, B. & Wiliam, D. (2003). Assessment for learning: Putting it into practice. New York: Open University Press.

Black, P., & Wiliam, D. (1998) Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139-148.

Bransford, J. D., Brown, A. L., & Cocking, R. R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.

Smith, E. J. (2008). Foreword. In Statewide Response to Instruction/Intervention (RtI): Implementation plan. Tallahassee, FL: Florida Department of Education.

Wiliam, D. (2006, July 11). Does assessment hinder learning? Speech delivered at the ETS Europe Breakfast Salon. Retrieved from http://www.mission-21.com/ec/images/williams_speech.pdf.

Wiliam, D. (2007). Content then process: Teacher learning communities in the service of formative assessment. In D. B. Reeves (Ed.), Ahead of the curve: The power of assessment to transform teaching and learning (pp. 183–204). Bloomington: Solution Tree.