Formative Re-Engaging Lessons

The information that is most valuable for teaching must focus on student thinking. Dylan Wiliam states that, "The central idea of formative assessment, or assessment for learning, is that evidence of student learning is used to adjust instruction to better meet student learning needs." He describes formative assessment practice as students and teachers using evidence of learning to adapt teaching and learning to meet immediate learning needs, minute-to-minute and day-by-day. Most teachers don't actively use these practices, in part because few teachers are trained to use formative assessment and have no apprenticeship implementing its use in classrooms.

Quality math performance assessments, coupled with effective professional development for classroom teachers and leaders, can support improved instruction and student achievement. Teachers need in-depth understanding of mathematical concepts and effective strategies for instruction. Without these in-depth understandings, it is challenging to design instructional experiences that drive significant student achievement. Teachers can improve instructional effectiveness by using a cycle of formative assessment practice. As they examine the student thinking revealed in the assessments and consider each student's current knowledge and misconceptions, teachers also clarify and strengthen their own understanding of mathematical concepts.

Re-engagement is not re-teaching. Re-teaching presents the same material again to a group of students. Re-engagement involves students in thinking about mathematical concepts in a new way. Formative re-engaging lessons are directly tied to the results of formative assessments. They reengage students in the core mathematical ideas of the assessment task in order to deepen their understanding of the core math and build a better conceptual foundation to learn further mathematics. The follow-up or re-engagement lessons featured here model strategies for designing lessons using the formative re-engagement process.

To do so, teachers engage in a process of examining student work. It's common for test results in a class to range from students indicating little success to those students who successfully complete the task. A well-designed re-engagement lesson addresses students' learning needs across this continuum.

One way to get started with formative re-engagement is to use student work from the class or the MARS tasks. The work is transcribed to assure anonymity. Students are asked to examine the work, determine if it is mathematically sound and either to justify the findings or show where the work lacked mathematical accuracy or logic. The challenge of critiquing and explaining other students' thinking and misconceptions requires and develops high cognitive skills.

Asking the class to explore the student thinking in unique or mathematically interesting approaches, or in intuitive and logical approaches which contain mathematical flaws, are productive ways to deepen student understanding. Comparing alternative approaches is also valuable. The teacher may select a few different approaches and have the class examine and compare the methods to make connections between ideas and representations. The elaborated level of the task might also be explored through the examination of other students' thinking.