The Purpose of the Formative Instructional and Assessment Tasks

The Formative Instructional and Assessment Tasks are provided as tools to use to assess students’ mathematical understanding as specified in the NC Standard Course of Study: Common Core State Standards for Mathematics (CCSS-M).

Mathematical Concepts Assessed The Formative Instructional and Assessment Tasks are designed to reveal the extent to which a student knows and understands specific concepts. Moving beyond only whether an answer is right or wrong, the tasks focus attention on the thinking and processes that all students use in solving the tasks, with opportunities to demonstrate his or her knowledge, skill, and understanding.

Therefore, the tasks assess the Common Core State Standards and highlight Standards for Mathematical Practice that may emerge as students explore the tasks. The rubric specifically addresses the conceptual understandings indicated in the CCSS-M. The Standards for Mathematical Practice that are likely to emerge are indicated in bold for each task.

Since both written and oral correct answers and appropriate processes are valued in mathematics, teachers find that observing students and talking with them are ways to provide students with opportunities to demonstrate what they know and can apply in new situations. Thus, the teacher is encouraged to ask the student clarifying questions during the assessment or after the assessment to gain a more accurate picture of what the student knows and understands. Insight into children’s thinking helps teachers build on what students understand, not just what they can do by memorizing processes.

The Role of the Classroom Teacher The classroom teacher uses the tasks in a formative manner. As defined by North Carolina Department of Public Instruction, formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to help students improve their achievement of intended instructional outcomes. Therefore, a teacher may use these tasks to:

Determine prior knowledge regarding a concept that is about to be taught.

Assess understanding throughout an instructional sequence to gain an understanding of how to best meet the needs of all of the students in an on-going basis.

Determine if the student is not yetproficient on a particular concept or if the student is proficient, demonstrating proficiency.

Assess understanding after the instructional sequence to determine if all students are proficient with that concept and are ready to move forward.

The teacher may administer the tasks to a whole class, small group of children, or an individual student, depending on the purpose for collecting data. For example, the teacher may decide that s/he would like to gain awareness of the entire class’ understanding of a particular concept. Thus, the task(s) selected would then be administered to all of the students in the class. Other times the teacher may need to determine what a particular student, or small group of students, understands in order to plan the most effective mathematical experiences. Thus, the task(s) selected would then be used with the selected student(s). Therefore, the assessment tasks can be used in multiple ways with the purpose of informing instructional planning and practice.

The Role of the Local Education Agency (LEA) A school district may decide to use the assessment tasks to create benchmark assessments, aligning a collection of tasks to their unique pacing guide to be administered district-wide at several points throughout the year. The classroom teacher scores the quarterly benchmark assessments, sees students’ answers, observes misconceptions, and uses the data gathered to inform further instruction and plan interventions or enrichments as needed (Joyner & Muri, 2011). The district uses the data from the benchmark assessments to gain a global view of how students are performing within particular domains or clusters, determine which additional instructional materials and resources may be needed, and discern particular topics and concepts that teachers may need additional support or growth and work with principals and teachers to plan professional development and coaching opportunities accordingly.

These state-developed assessment tasks are aligned with the North Carolina Standard Course of Study: Common Core State Standards for Mathematics and may be adopted or modified as appropriate for individual school districts. As they are used with students, please add to and adapt the materials in order to make them useful for each school’s unique situation. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource. Feedback should be sent to NCDPI Elementary Mathematics Consultant Kitty Rutherford kitty.rutherford@dpi.nc.gov or Denise Schulz denise.schulz@dpi.nc.gov.

References Joyner, J. & Muri, M. (2011). INFORMative assessment: Formative assessment to improve math achievement. Sausalito, CA: Math Solutions.

## The Purpose of the Formative Instructional and Assessment Tasks

TheFormative Instructional and Assessment Tasksare provided as tools to use to assess students’ mathematical understanding as specified in theNC Standard Course of Study: Common Core State Standards for Mathematics (CCSS-M).Mathematical Concepts AssessedThe

Formative Instructional and Assessment Tasksare designed to reveal the extent to which a student knows and understands specific concepts. Moving beyond only whether an answer is right or wrong, the tasks focus attention on the thinking and processes that all students use in solving the tasks, with opportunities to demonstrate his or her knowledge, skill, and understanding.Therefore, the tasks assess the

Common Core State Standardsand highlightStandards for Mathematical Practicethat may emerge as students explore the tasks. The rubric specifically addresses the conceptual understandings indicated in the CCSS-M. TheStandards for Mathematical Practicethat are likely to emerge are indicated inboldfor each task.Since both written and oral correct answers and appropriate processes are valued in mathematics, teachers find that observing students and talking with them are ways to provide students with opportunities to demonstrate what they know and can apply in new situations. Thus, the teacher is encouraged to ask the student clarifying questions

duringthe assessment orafterthe assessment to gain a more accurate picture of what the student knows and understands. Insight into children’s thinking helps teachers build on what students understand, not just what they can do by memorizing processes.The Role of the Classroom TeacherThe classroom teacher uses the tasks in a formative manner. As defined by North Carolina Department of Public Instruction, formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to help students improve their achievement of intended instructional outcomes. Therefore, a teacher may use these tasks to:

not yetproficienton a particular concept or if the student isproficient, demonstrating proficiency.The teacher may administer the tasks to a

whole class,small groupof children, or anindividualstudent, depending on the purpose for collecting data. For example, the teacher may decide that s/he would like to gain awareness of the entire class’ understanding of a particular concept. Thus, the task(s) selected would then be administered to all of the students in the class. Other times the teacher may need to determine what a particular student, or small group of students, understands in order to plan the most effective mathematical experiences. Thus, the task(s) selected would then be used with the selected student(s). Therefore, the assessment tasks can be used in multiple ways with the purpose of informing instructional planning and practice.The Role of the Local Education Agency (LEA)A school district may decide to use the assessment tasks to create benchmark assessments, aligning a collection of tasks to their unique pacing guide to be administered district-wide at several points throughout the year. The classroom teacher scores the quarterly benchmark assessments, sees students’ answers, observes misconceptions, and uses the data gathered to inform further instruction and plan interventions or enrichments as needed (Joyner & Muri, 2011). The district uses the data from the benchmark assessments to gain a global view of how students are performing within particular domains or clusters, determine which additional instructional materials and resources may be needed, and discern particular topics and concepts that teachers may need additional support or growth and work with principals and teachers to plan professional development and coaching opportunities accordingly.

These state-developed assessment tasks are aligned with the North Carolina Standard Course of Study: Common Core State Standards for Mathematics and may be adopted or modified as appropriate for individual school districts. As they are used with students, please add to and adapt the materials in order to make them useful for each school’s unique situation. The North Carolina Department of Public Instruction appreciates any suggestions and feedback, which will help improve upon this resource.Feedback should be sent to NCDPI Elementary Mathematics Consultant Kitty Rutherford kitty.rutherford@dpi.nc.gov or Denise Schulz denise.schulz@dpi.nc.gov.ReferencesJoyner, J. & Muri, M. (2011).

INFORMative assessment: Formative assessment to improve math achievement. Sausalito, CA: Math Solutions.