Implementing Mathematical Tasks That Promote Reasoning and Problem

Implementing Mathematical Tasks That Promote Reasoning and Problem Solving 9 -12 Dave Ebert Oregon High School dde@oregonsd. org www. oregonsd. org/webpages/debert

Task 1: Chedister, Wisconsin Teacher of Mathematics, Spring 2015

What makes this a good task?

Traditional Task

Principles to Actions: Ensuring Mathematical Success for All Eight Mathematics Teaching Practices: • Implement Tasks That Promote Reasoning and Problem Solving

Three Major Research Findings: (p. 17) • Not all tasks provide the same opportunities for student thinking and learning. • Student learning is greatest where the tasks consistently encourage high-level student thinking and reasoning, and least in classrooms where the tasks are routine and procedural in nature. • Tasks with high cognitive demands are the most difficult to implement well and are often transformed into less demanding tasks during instruction.

Implement tasks that promote reasoning and problem solving (p. 24)

5 Practices for Orchestrating Productive Mathematics Discussions Practice zero: determining the goal and selecting the task (p. 13)

Different tasks provide different opportunities for student learning (p. 15) Complete the conjecture based on the pattern you observe. The sum of any two odd numbers is ____. 1+1=2 1+3=4 3+5=8 7+11=18 13+19=32 201+305=506 Complete the conjecture based on the pattern you observe. Then explain why the conjecture is always true or show a case in which it is not true. The sum of any two odd numbers is ____.

Instructional Rounds in Education Seven Principles of the Instructional Core: • Task predicts performance. • The real accountability system is in the tasks that students are asked to do.

The Instructional Core (p. 22)

Oregon High School Theory of Action • If all OHS staff collaborate purposefully to design engaging tasks that require critical thinking, reading, writing, and problem solving… • Then all students will show growth on skills for success at OHS and in future endeavors

Mathematical Mindsets Rich Mathematical Tasks

The Design of Tasks (p. 76) 1. Can you open the task to encourage multiple methods, pathways, and representations?

The Design of Tasks (p. 76) 2. Can you make it an inquiry task?

The Design of Tasks (p. 76) 3. Can you ask the problem before teaching the method?

The Design of Tasks (p. 76) 4. Can you add a visual component?

The Design of Tasks (p. 76) 5. Can you make it low floor high ceiling?

The Design of Tasks (p. 76) 6. Can you add the requirement to convince and reason?

What makes this a good task? 1. Multiple methods 2. Inquiry 3. Ask the problem before teaching the method 4. Visual 5. Low floor / high ceiling 6. Convince and reason • What are things that you notice in your drawing? • Compare your results with your neighbors. What do you notice? Prove what you discover.

Task 2: Vector Voyage

Task 2: Vector Voyage

Task 2: Vector Voyage

What makes this a good task? 1. 2. 3. 4. 5. 6. Multiple methods Inquiry Ask the problem before teaching the method Visual Low floor / high ceiling Convince and reason

Task 3 Which is less expensive, a t-shirt at the mall for $12, or the same t-shirt at a local store for $15?

What makes this a good task? 1. 2. 3. 4. 5. 6. Multiple methods Inquiry Ask the problem before teaching the method Visual Low floor / high ceiling Convince and reason

Where to find high-quality tasks: • Illustrative Mathematics: Common Core Math Tasks www. illustrativemathematics. org • Inside Mathematics: Common Core Task & Video Collection www. insidemathematics. org • Mathematics Assessment Project: Tasks, Assessments & Lesson Collection http: //map. mathshell. org • National Council of Teachers of Mathematics: Principals to Actions Toolkit http: //www. nctm. org/Pt. AToolkit • Youcubed tasks http: //www. youcubed. org/tasks/

Illustrative Mathematics example Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said, I wonder whether the dollar belongs inside the cash box or not. The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found$200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?

Take-Home Task: Angle Chase

What makes this a good task? 1. 2. 3. 4. 5. 6. Multiple methods Inquiry Ask the problem before teaching the method Visual Low floor / high ceiling Convince and reason

Implementing Mathematical Tasks That Promote Reasoning and Problem Solving 9 -12 Dave Ebert Oregon High School dde@oregonsd. org www. oregonsd. org/webpages/debert