New Math Resources: Understanding Proficiency — Learning from Student Work on Performance Tasks

by Jessica Arnold


College- and career-ready math standards require students to demonstrate a complex set of knowledge, skills, and abilities that go beyond math concepts and procedures. Students need to solve complex problems, explain their thinking, defend their solutions, and attend to precision.

Next-generation assessments use performance tasks to measure how well a student can integrate knowledge and skills across multiple content standards. These performance tasks are designed to reveal student competency in 21st century skills —critical thinking, problem solving, and communicating reasoning — which cannot be adequately assessed by constructed-response and selected-response items alone.

Many teachers are asking: How can we use assessment both of and for learning to support students in meeting these important learning standards? For teachers, the processes of examining, scoring, and discussing students’ work on performance tasks can deepen understanding of the standards in practice; provide insight into assessment of student knowledge, skills, and abilities; and suggest the kinds of classroom experiences that students need in order to be truly college- and career-ready.

Understanding Proficiency is an online resource designed to support educators in analyzing and learning from student work on performance tasks. The site — developed by WestEd in partnership with the Stanford Center on Assessment, Learning, and Equity (SCALE) — launched in 2016 with a robust collection of scored student responses to Smarter Balanced English Language Arts (ELA) performance tasks.

We are excited to add a full complement of math resources to the Understanding Proficiency site. Like the ELA resources, these new math materials include student responses that have been annotated by practicing educators and that illustrate the full range of performance levels for each task. Understanding Proficiency aims to use Smarter Balanced performance tasks and sample responses to support professional learning and to inform and enhance instruction for all students.

The Understanding Proficiency website features ELA and mathematics tasks in grades 3 through 8 and high school. In addition to providing scored, annotated student samples, Understanding Proficiency features the following resources:

  • Analyses of student responses across all the questions in the performance tasks, with discussion of instructional implications and next steps for each student.
  • Interviews with educators about what they learned from scoring student responses.
  • Tools to support educators in using these resources for professional learning.

These materials can be used by individuals or teams of educators who want to gain a deeper understanding of Smarter Balanced performance tasks and scoring tools, develop a sense of how students can demonstrate mastery of the Common Core State Standards through performance tasks, and consider the instructional implications of offering all students opportunities to develop college- and career-ready skills.

Visit the Understanding Proficiency math collection on Raising the Bar to see a sample collection of grade 4 mathematics and ELA resources, or visit the Understanding Proficiency site for resources at every grade level and for videos and professional learning tools.

Understanding Proficiency was developed with generous support from The Leona M. and Harry B. Helmsley Charitable Trust. For more information on the Trust and its programs, visit

Senior Program Associate, Center for Prevention & Early Intervention, WestEd