Using Math Tasks to Promote High Level Thinking

Using Math Tasks to Promote High Level Thinking in Grades 7 -12 Robin Conti Senior Secondary Mathematics Specialist Office of School Improvement @Educate. IN @Robin. LConti

In Today’s Session Our purpose is to: Explore tasks aimed at increasing student engagement, risk-taking, and sense-making alongside productive struggle. @Educate. IN @Robin. LConti Our purpose is to: Discuss ways to open up Need typically closed tasks to promote student discourse.

A Vision for Ambitious Instruction • Mathematics learning is an ACTIVE process. • Students construct mathematical knowledge through exploration, discussion, and reflection. • Teachers are facilitators of student learning, as they engage students in rich tasks. (NCTM, Principles to Actions, 2014) @Educate. IN @Robin. LConti

Eight Effective Math Teaching Practices @Educate. IN @Robin. LConti

Tasks, Talking, and Telling What are your big takeaways after watching? @Educate. IN @Robin. LConti

The Design of Rich, Mathematical Tasks 1. Open task to encourage multiple methods, pathways, and representations 2. Make it an inquiry task 3. Ask before teaching 4. Add a visual component 5. Low floor high ceiling 6. Add requirement to convince and reason @Educate. IN @Robin. LConti

What is an irrational number? @Educate. IN @Robin. LConti

Rank these birds in terms of speed. @Educate. IN @Robin. LConti

Change the Question, Change the Task Reversibility question: Typical question: Simplify 4(3 + 5 y) Reverse the question: Find an expression that can be simplified to 12 + 20 y. Generalization question: Find an algebraic expression with four terms that can be simplified to one with two terms. What do you notice about the terms? Find an algebraic expression with three terms that cannot be simplified. What do you notice about the terms? @Educate. IN @Robin. LConti

Change the Question, Change the Task Flexibility question: Write an equivalent expression to 3 b - 5. Write another equivalent expression to 3 b - 5. @Educate. IN @Robin. LConti Flexibility question: Simplify each. 5(4 x - 3) 5(4 a - 3) 5(4 y + 3) 5(3 + 4 y) (4 x - 3)5

Opening Up Closed Tasks Closed OR Open Simplify each. Choose any pair of expressions and add multiples together of each. Can you find a way to get an answer of 5 x + 8 y in each case of combining distinct expressions together? @Educate. IN

The Original @Educate. IN @Robin. LConti

The Upgrade @Educate. IN @Robin. LConti

Funneling vs. Focusing Funneling Questions Focusing Questions ❏ Teacher guides a student down the teacher’s path to find the answer ❏ Teacher is doing the cognitive work ❏ Hints at answer ❏ Gives the illusion of deep learning ❏ Support students doing the cognitive work of learning by pushing their thinking forward ❏ Encourage students to figure things out for themselves ❏ Opens up kids’ thinking and show them where to look Adapted from: John Hattie’s Visible Learning for Mathematics p. 89 (2017) @Educate. IN @Robin. LConti

Funneling vs. Focusing Funneling Questions ❏ How do you find the mean of the data? What about the median and mode? Interquartile range? ❏ How can I get rid of the 2? What do I have to do to the other side? ❏ How do I find the area of this trapezoid? Do you see the rectangle and triangles? I can just add them up. @Educate. IN @Robin. LConti Focusing Questions ❏ What do you notice about the data? How would you describe them to someone? What makes you say that? What other ways might you be able to describe them? ❏ What do you think about when you see this equation? How do you want to solve it? ❏ I want to know the area of this trapezoid, but I’m not sure how to find it. Any ideas?

Wafers and Creme @Educate. IN @Robin. LConti

Three Act Tasks Act 1 - The Tease How many points is each shape worth? Write down a guess. @Educate. IN @Robin. LConti

Three Act Tasks Act 2 - The Information What information would be useful to figure this out? Write down some questions you may have in your head right now. @Educate. IN @Robin. LConti

Three Act Tasks Act 3 - The Reveal! @Educate. IN @Robin. LConti

Would You Rather. . . @Educate. IN @Robin. LConti

Don’t Just Plug and Chug! Students must find the values for the dimensions (no repeats) so that all figures have the same area. @Educate. IN @Robin. LConti

Slow Reveal Graphs @Educate. IN

Rollover Numbers @Educate. IN #INspir. EDmath

Frayer Models (Examples and Non-Examples) @Educate. IN @Robin. LConti

In Summary ★ The most productive discourse involves students thinking about, reasoning about, and making sense of mathematical ideas, problems, concepts, or even procedures. ★ Engaging in mathematically rich tasks that challenge students somewhat beyond what they already know can set the stage for rich discourse around mathematical ideas. ★ Students get used to the notion that it’s ok to struggle a bit over a challenging problem, even to make a mistake, knowing that the discussion that evolves from their struggle is likely to lead to better understanding. ★ NCTM has suggested that the most effective student learning arises when tasks are carefully selected to elicit thinking and when the teacher poses questions that support the development of reasoning. @Educate. IN @Robin. LConti

Explore and develop rich tasks that support the eight mathematics teaching practices Interactive and engaging full day session with guided implementation and collaboration opportunities embedded throughout the day Open up traditionally closed problems to promote student discourse, provide opportunities for productive struggle, and to support students in risk-taking and sense-making Classroom teachers and coaches are the target audience, although the support of building level administrators is highly encouraged! Go to bit. ly/Math. PD 2019 to register! @Mrs. Bruning @Robin. LConti

Updates From IDOE Office of School Improvement Literacy Mathematics Social-Emotional Learning High Ability Indiana Academic Standards @Robin. LConti #INspir. EDmath

Assessment Contact Information Dr. Charity Flores Tricia Stephens Dr. Kristine David Stephanie Thompson Director of Assessment cflores@doe. in. gov Assistant Director of Assessment, Content kdavide@doe. in. gov Sholonda Trice Assistant Director of Assessment strice@doe. in. gov Kelly Connelly Senior Assessment Specialist, ILEARN kconnelly@doe. in. gov @Educate. IN @Robin. LConti Assessment Specialist, Test Security tstephens@doe. in. gov Assessment Specialist, I AM sthompson 2@doe. in. gov Mary Williams Assessment Specialist, High School, Formative mwilliams@doe. in. gov Mark O’Malley Assessment Specialist, IREAD-3 momalley@doe. in. gov

Resources for Understanding ILEARN Released Items Repository • Sample Items (at least 10 per grade and content area) & Scoring Guides • Student Supports and Tools IDOE Guidance • Technology & BYOD Policies • Scheduling & Timing Guidance • ILEARN ECA Participation • Accessibility & Accommodations • Calculator Policy • Educator Scoring Flyer • Updated FAQ @Robin. LConti #INspir. EDmath Content Resources • Test Blueprints • Item Specifications • Content-Specific Webinars • Performance Level Descriptors • Scoring Rubrics Assessment Literacy • Educator & Parent Brochures • Assessment Development Infographic • Recorded Training Webinars

bit. ly/OSIMath 2019 Robin Conti Senior Secondary Math Specialist rconti@doe. in. gov @Robin. LConti Digital Supports Document @Educate. IN @Robin. LConti