+ Improving Student Problem Solving Through Reasoning & - - PowerPoint PPT Presentation

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Improving Student Problem Solving Through Reasoning & Revision

Jessica Murk, Windsor High School Math Teacher February 19, 2015 Sonoma County Leadership Network

+A Case for Revision

 The definition of mathematical proficiency has

changed

+A Case for Revision

 Previous definition:

CALIFORNIA HIGH SCHOOL EXIT EXAM

+A Case for Revision

 New Definition:

SMARTER BALANCED ASSESSMENT CLAIMS

+A Case for Revision

 The new expectations for students require new instructional

strategies.

Showing students exactly how to do a problem and then having them practice doing problems of the same type may work for Claim 1, but it will not work for Claims 3 and 4. Those require instructional strategies more like a writing class than a traditional math class.

+A Case for Revision

 The new expectations for students requires new

instructional strategies.

 One becomes a better writer by writing, getting

feedback, and revising.

 One does not improve by only writing first drafts.  Math class often is about getting a certain

percentage of problems “correct” and then moving

• n.

 Communicating reasoning and mathematical

modeling are processes that can always be improved.

+The Target has Changed!

OLD DEFINITION OF PROFICENCY NEW DEFINITION OF PROFICENCY

Tools for Reasoning and Revision

+

+Overview of Our Time Together

OVERARCHING HABITS OF MIND

• 1. Make sense of problems and persevere in

solving them

• 6. Attend to precision

REASONING AND EXPLAINING

• 2. Reason abstractly and quantitatively
• 3. Construct viable arguments and critique the reasoning of
• thers

MODELING AND USING TOOLS

• 4. Model with mathematics
• 5. Use appropriate tools strategically

SEEING STRUCTURE & GENERALIZING

• 7. Look for and make use of structure
• 8. Look for and express regularity in repeated reasoning

+Goals

 Big Picture of CCSS Shifts  Some specific strategies to use in your

classroom that can help with these shifts

 Give your students opportunities to engage in

the SMPs using our current curriculum

+Tools for Reasoning & Revision

 Bongard Problems  Developing Definitions  Peer Feedback Template

+

Reasoning Revision Tool #1: Bongard Problems

The Problem: Students struggle with abstract reasoning

+Reasoning Revision Tool #1: Bongard Problems

 Students can test their rules on their own

(Agency)

 The template allows them to write down

their initial thoughts and then revise as they hear other ideas (Attend to precision)

 The “puzzle” element lowers fear and

anxiety for students (Access/Equity)

+Bongard Problems

M.M. Bongard (1924 – 1971) was a Russion computer scientist interested in cognition and artificial

• intelligence. He introduced a

set of problems (now called Bongard Problems) in his 1967 book Проблема Узнавания.

+Let’s Try One

The goal is to identify a simple rule or property that applies to each of the figures on the left hand side AND none of the figures on the right hand side.

+

I would like to add an option for their first draft and then a revised rule.

+Bongard Problem #94

+Student Responses

+Student Responses

+Student Responses

+Challenge

+Let’s Try Another One

+Revising as a Class: A written record of revision

+Reasoning Revision Tool #1: Bongard Problems

 Students can test their rules on their own

(Agency)

 The template allows them to write down

their initial thoughts and then revise as they hear other ideas (Attend to precision)

 The “puzzle” element lowers fear and

anxiety for students (Access/Equity)

+

Reasoning Revision Tool #2: Developing Definitions

The Problem: Students don’t understand the difference between a “mathematical” definition and a dictionary definition

+Reasoning Revision Tool #2: Developing Definitions

 Access student prior knowledge in an

authentic way (Use of assessment)

 They are not blank slates (Access/

Identity)

 Make connections between what they

already know and the more precise, mathematically rigorous definition (Cognitive Demand)

+Teaching Vocabulary

+Developing Definitions: Old School

 Look terms up in a dictionary  Provide students the formal definition

from the textbook through direct instruction

+Developing Definitions: New School

 Asking students what they already know  Making connections between their prior

knowledge and more precise, mathematically rigorous definitions

+Access Prior Knowledge

 We know it’s a good idea (research and

credential programs tell us so)

 But HOW?!?  How can we access a student’s prior

knowledge in an authentic way?

+Geometry Vocabulary

+Geometry Vocabulary

+Geometry Vocabulary

+Geometry Vocabulary

Are these points collinear? Can we think of the freeway as a segment? Or is it more of a line? Which towns are the endpoints

• f the

freeway?

+Reasoning Revision Tool #2: Developing Definitions

 Access student prior knowledge in an

authentic way (Use of assessment)

 They are not blank slates (Access/

Identity)

 Make connections between what they

already know and the more precise, mathematically rigorous definition (Cognitive Demand)

+

Reasoning Revision Tool #3: Peer Feedback Template

The Problem: Students lack experience in critiquing the reasoning of others

+Reasoning Revision Tool #3: Peer Feedback Template

 The authority shifts from teacher to

student (Authority)

 Developing mathematical definitions

and constructing arguments (Mathematics)

 Revising their definitions based on

feedback (Cognitive demand)

+Peer Feedback with Revision

 Peer Feedback Template  First Draft ≠ Final Draft  Building on the ideas and conjectures

that students have about reflections

 Goal is to help students move toward a

more formal definition, which will ultimately be provided by the teacher

+Giving Feedback… A Gentle Reminder

 Unnatural in a math class  Students have very little experience  Rarely receive this type of feedback in a

math class

 It takes practice!!!

+Giving Feedback

+A Little Help

+Let’s Try One

+Peer Feedback: Our Purpose

+Peer Feedback: Some Suggestions

• Students write their

argument individually

• Each argument gets rotated

to another table

• Pairs work together on

providing feedback to two arguments

• This happens twice
• Arguments are returned to
• riginal authors
• Students read through

feedback to consider where they might revise their original argument and write a second draft

+Peer Feedback

+Student Work – Lizbeth

+Student Work – Emily

+Student Work – Nicole

+Reasoning Revision Tool #3: Peer Feedback Template

 The authority shifts from teacher to

student (Authority)

 Developing mathematical definitions

and constructing arguments (Mathematics)

 Revising their definitions based on

feedback (Cognitive demand)

+Tools for Reasoning & Revision

 Bongard Problems  Developing Definitions  Peer Feedback Template

+Thank You!!

 Jessica Murk

 Email: jmurk@wusd.org  Blog: themathymurk.blogspot.com  Twitter: @JessicaMurk13