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Productive Struggle and Problem Solving in the Grades 9-12 Classroom

WMC Annual ConferenceMay 4, 2017

Tammy Moynihan, Wisconsin Mathematics Council Grades 9-12 RepresentativeOconto Falls High School

tammy.moynihan@of-ps.org

Introduce yourself to your neighbor

Where are you from?

What do you teach?

Cup Stacking Challenge

Agenda1. Define productive struggle. 2. A supportive classroom environment:

a. Growth Mindset/Mistakesb. Teamwork/Collaborationc. Engaging Tasks

3. Tasks to support productive strugglea. Building a New Playground Taskb. Productive Struggle Video Clip

4. Questioning

What does productive struggle look like in the classroom? What doesn’t it look like? Turn and talk.

Definition of Productive Struggle

Productive struggle refer to a student’s

‘‘effort to make sense of mathematics, to

figure something out that is not immediately

apparent’’ (Hiebert & Grouws 2007, p.287; Robert Q. Berry, III, Ph.D. MPES Presentation!)

Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships. (NCTM, 2014)

Teachers must create a classroom culture that demonstrates “struggle as a natural part of the learning process” (Star, 2015) and allows students to see the potential in persevering.

Mindset Monday!

Growth Mindset & Struggle

When my students make mistakes in math they believe they are not good at math.

1 2 3 4 5

Agree Somewhat agree Not Sure Somewhat Disagree Disagree

How Can We Change the Ways Students View Mistakes?

EMBRACE MISTAKES!

CELEBRATE MISTAKES!

My Favorite No

What message(s) does this activity send to students?

Algebra 1 Examples

What are teachers doing? What are students doing?

• Anticipating what students might struggle with during a lesson and being prepared to support them productively through the struggle.

• Giving students time to struggle with tasks, and asking questions that scaffold students’ thinking without stepping in to do the work for them.

• Helping students realize that confusion and errors are a natural part of learning, by facilitating discussions on mistakes, misconceptions, and struggles.

• Praising students for their efforts in making sense of mathematical ideas and perseverance in reasoning through problems.

• Struggling at times with mathematics tasks but knowing that breakthroughs often emerge from confusion and struggle.

• Asking questions that are related to the sources of their struggles and will help them make progress in understanding and solving tasks.

• Persevering in solving problems and realizing that is acceptable to say, “I don’t know how to proceed here,” but it is not acceptable to give up.

• Helping one another without telling their classmates what the answer is or how to solve the problem.

Principles to Actions. NCTM, 2014

Collaboration

Engaging Tasks

Engaging Tasks

BUILDING A NEW PLAYGROUND (Part A only)The City Planning Commission is considering building a new playground. They would like the playground to be equidistant from the two elementary schools, represented by points A and B in the coordinate grid that is shown.

PART A

1. Determine at least three possible locations for the park that are equidistant from points A and B. Explain how you know that all three possible locations are equidistant from the elementary schools.

2. Make a conjecture about the location of all points that are equidistant from A and B. Prove this conjecture.

(Principles to Actions Toolkit: http://www.nctm.org/)

1. Work on task individually.2. Share solution(s) with elbow partner.3. Share with smaller groups.

a. How would students solve this problem?b. Any student misconceptions you can

anticipate? c. How might you implement this task in a

classroom?

Proximity Partners: 2 chairs, 1 table, 1 corner of the room

Supporting Productive Struggle: Video Clip

As you watch the video, how does the teacher support student learning and engagement in the classroom?

Be prepared to share - citing line numbers will help!

Redefining Student and Teacher Success handoutTake a moment to read several of the boxes...

Supporting Productive Struggle: Video Clip

Evidence of growth mindset?Evidence of collaboration?Evidence of an engaging task?

Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships. (NCTM, 2014)Looking back at the transcript, identify Purposeful Questions. Be ready to share!

Question Type Description

Gathering Information Students recall facts, definitions, or procedures

Probing Thinking Students explain, elaborate, or clarify their thinking, including articulating the steps in a solution methods or the completion of a task.

Making the Math Visible Students discuss mathematical structures and make connections among mathematical ideas and relationships

Encouraging reflection and justification

Students reveal deeper understanding of their reasoning and actions, including making an argument for the validity of their work.

Link to Handout

How might you apply what you’ve learned today to your classroom?

Tammy Moynihantammy.moynihan@of-ps.org