Standard P.4. Assessing Student Understanding and Learning

P.4.a. Engaging in the formative assessment cycle 

In their work with students, EMSs assess for student understanding and growth by selecting, modifying, or creating assessment opportunities to elicit information on students’ progress toward rigorous mathematics learning goals. In using assessments, EMSs recognize and attend to the many valued mathematical learning outcomes, such as conceptual understanding, procedural fluency, reasoning, and problem solving, as well as to productive mathematical disposition. They use a variety of both formal and informal assessments, including pre-assessment and classroom-based formative assessment tools and strategies as well as summative assessments. In doing so, EMSs gather evidence of students’ mathematical thinking in ways suitable for children and sensitive to their backgrounds, and that allow for varying knowledge demonstration. EMSs understand the purposes, strengths, and limitations of each assessment technique and strategy they implement. They use formative assessments (e.g., observations, questioning, conferring)  throughout a lesson in order to monitor and build upon students’ mathematical strengths and provide needed scaffolds, supports, modifications, and extensions. 

EMSs analyze and reflect upon assessment information and data to support the learning of each student. They regularly collect information on students’ progress and use information or data from informal (e.g., observations, interviews) and formal (e.g., assessment tasks, end-of-unit assessments) assessments to analyze progress of individual students, groups of students, and the class as a whole toward meeting rigorous mathematics learning goals. In order to mitigate bias, EMSs are acutely aware of the potential of their own culture and background affecting their judgment when analyzing student understanding. Using an asset-based view, analysis of assessment information and data should illuminate students’ mathematical thinking and strengths, as well as learning progress and needs to support responsive teaching. This analysis should also be used to reflect upon the effectiveness of their planning and instruction, including how particular teaching moves supported or inhibited student understanding and subsequent instructional steps. 

EMSs modify instruction based on analysis and reflection, grounding their instructional decisions in evidence of student thinking and reasoning. They assess progress toward rigorous mathematics learning goals and adjust instruction continually in ways that support and extend learning. These adjustments should improve learning for each and every student, whether during in-the-moment instruction or a subsequent lesson. They build upon students’ mathematical strengths and productive beginnings, while addressing early, partial, or alternate conceptions (i.e., common errors, partial solutions, overgeneralizations)(93). In particular, formative assessment within a lesson allows responsiveness to learners, knowing when to support and scaffold or when to allow students to productively struggle. EMSs understand the connection between assessment and feedback and create a classroom culture that recognizes the importance of teacher-to-student, student-to-teacher, and student-to-student feedback (94). These opportunities may be written or verbal, with the intent of fully engaging students in the assessment process. 

Further, EMSs recognize the value in not grading all assignments, such as cognitively-demanding instructional tasks (95). They recognize the limitations of a traditional grading approach for classroom-based formative assessments. They explore ungrading techniques (96), and competence-based approaches where the emphasis is feedback, so students can focus on understanding and growth rather than points and grades. In addition to students being able to grapple with tasks without apprehension of everything being graded, they should be encouraged to revisit and revise their solutions to tasks in order to develop a deeper understanding of the mathematical content (97). 

P.4.b. Using summative assessments formatively   

EMSs use student summative assessment data (e.g., end-of-unit tests, benchmark assessments) to evaluate and modify instructional units and support student learning. They analyze and reflect upon assessment results and use this information to guide their subsequent design of instructional units, such as lesson planning around mathematical goals, instructional tasks, and tools. They also use this information to guide areas where some students may need an opportunity to re-engage with particular mathematics concepts. Summative assessments should be used to promote students’ self-monitoring and self-regulation of their learning. EMSs use these assessments as a form of feedback to students on their learning, through: sharing results before or without scores, highlighting accurate and emerging understandings, providing actionable steps on what and how to improve responses, and offering opportunities to revise responses.

EMSs modify summative assessments in ways that reflect knowledge of their students, such as altering story problem contexts and providing choices about number sizes, just as they do instructionally. Further, for some students in which additional assessment information is not needed, EMSs revise summative assessments so that students do not respond to the full set of provided items. EMSs understand the limitations and potential biases of summative assessments and, as needed, make changes. Finally, EMSs strive to use and support others in using tools and strategies that are ethically grounded and developmentally, culturally, ability, and linguistically appropriate to document developmental progress and promote positive outcomes for all children (98).