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Supporting Rigorous Mathematics Teaching and Learning

Making Sense of Numbers and OperationsFraction Standards via a Set of Tasks

Tennessee Department of EducationElementary School MathematicsGrade 3-5 [*Note: Slides for Math CCSS Grades 6-8 are the same except for the tasks and the grade level standards. 6th & 7th grade Focus – Making Sense of the Number System Standard via a Set of Tasks.]

Rationale

Tasks form the basis for students’ opportunities to learn what mathematics is and how one does it, yet not all tasks afford the same levels and opportunities for student thinking. [They] are central to students’ learning, shaping not only their opportunity to learn but also their view of the subject matter.

Adding It Up, National Research Council, 2001, p. 335

By analyzing instructional and assessment tasks that are for the same domain of mathematics, teachers will begin to identify the characteristics of high-level tasks, differentiate between those that require problem-solving, and those that assess for specific mathematical reasoning.

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Session Goals

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Overview of Activities

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Analyzing Tasks as a Means of Making Sense of the CCSS

Number and OperationsFractions

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TASKS

as they appear in curricular/ instructional materials

TASKS

as set up by the teachers

TASKS

as implemented by students

Student Learning

The Mathematical Tasks Framework

Stein, Smith, Henningsen, & Silver, 2000

Linking to Research/Literature: The QUASAR Project

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TASKS

as they appear in curricular/ instructional materials

TASKS

as set up by the teachers

TASKS

as implemented by students

Student Learning

The Mathematical Tasks Framework

Stein, Smith, Henningsen, & Silver, 2000

Linking to Research/Literature: The QUASAR Project

Setting Goals Selecting TasksAnticipating Student Responses

Orchestrating Productive Discussion• Monitoring students as they work• Asking assessing and advancing questions• Selecting solution paths• Sequencing student responses• Connecting student responses via Accountable

Talk® discussionsAccountable Talk® is a registered trademark of the University of Pittsburgh

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Analyzing Tasks: Aligning with the CCSS(Small Group Discussion)

Determine which Content Standards students would have opportunities to make sense of when working on the task.

Determine which Mathematical Practice Standards students would need to make use of when solving the task.

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Analyzing Tasks: Aligning with the CCSS(Whole Group Discussion)

How do the tasks differ from each other with respect to the content that students will have opportunities to learn?

Do some tasks require that students use Standards for Mathematical Practice that other tasks don’t require students to use?

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The CCSS for Mathematical Content − Grade 3

Common Core State Standards, 2010, p. 54, NGA Center/CCSSO

Number and Operations-Fractions 3.NF

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The CCSS for Mathematical Content − Grade 3

Common Core State Standards, 2010, p. 55, NGA Center/CCSSO

Number and Operations-Fractions 3.NF

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The CCSS for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Common Core State Standards, 2010, p. 6-8, NGA Center/CCSSO

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Reflecting and Making Connections

• Are all of the CCSS for Mathematical Content in this cluster addressed by one or more of these tasks?

• Are all of the CCSS for Mathematical Practice addressed by one or more of these tasks?

• What is the connection between the cognitive demand of the written task and the alignment of the task to the Standards for Mathematical Content and Practice?

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Differentiating Between Instructional Tasks and Assessment Tasks

Are some tasks more likely to be assessment tasks than instructional tasks? If so, which and why are you calling them assessment tasks?

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Instructional Tasks Versus Assessment TasksInstructional Tasks Assessment TasksAssist learners to learn the CCSS for Mathematical Content and the CCSS for Mathematical Practice.

Assesses fairly the CCSS for Mathematical Content and the CCSS for Mathematical Practice of the taught curriculum.

Assist learners to accomplish, often with others, an activity, project, or to solve a mathematics task.

Assess individually completed work on a mathematics task.

Assist learners to “do” the subject matter under study, usually with others, in ways authentic to the discipline of mathematics.

Assess individual performance of content within the scope of studied mathematics content.

Include different levels of scaffolding depending on learners’ needs. The scaffolding does NOT take away thinking from the students. The students are still required to problem-solve and reason mathematically.

Include tasks that assess both developing understanding and mastery of concepts and skills.

Include high-level mathematics prompts. (The tasks have many of the characteristics listed on the Mathematical Task Analysis Guide.)

Include open-ended mathematics prompts as well as prompts that connect to procedures with meaning.

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Reflection

• So, what is the point?

• What have you learned about assessment tasks and instructional tasks that you will use to select tasks to use in your classroom next school year?

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Bridge to Practice

• Select a high-level task.

• Analyze the task and determine the alignment to the Mathematical Content Standards and the Standards for Mathematical Practice.

• Describe if the task is an instructional task or an assessment task and explain why you decided on the label. If necessary, refer back to slide 33 for assistance. Use the set of examples of tasks to differentiate between the two types of tasks .