Problem Solving Metaphors: Listening for Student Experiences

CMC-South, Palm Springs, 2013

Sean Yee

syee@fullerton.edu

California State University, Fullerton

Ashley Thune-Aguayo

athune@fullerton.edu

California State University, Fullerton

Game Plan

• (20 min) Theoretical Background & Results

• (20 min) How this has helped teachers• (20 min) Watch Student and Teacher

Video• (15 min) Design of Professional

Development• (15 min) What’s Next? Questions?

What are Conceptual Metaphors?

Each Literal Metaphor has a Conceptual Metaphor.

A Conceptual Metaphor is a mapping, attaching two different ideas together.

Metaphora - Greek - A Transfer

What are Conceptual Metaphors?

Literal Metaphor: “Once I read it I kind of understood what it was saying”

Conceptual Metaphor: WRITTEN PROBLEMS ARE SPOKEN PROBLEMS

TARGET DOMAIN IS () SOURCE DOMAIN

Try One

Literal Metaphor“To solve it for me, it meant that I had to find it somehow.”

Conceptual MetaphorPROBLEM SOLVING IS SEARCHINGABSTRACT IDEA IS CONCRETE EXPERIENCE(Structural Metaphor)

One More…

Literal Metaphor“So I don’t think this would be a route that I would immediately jump to.”“I think I know where to go”“I’m lost”

Conceptual MetaphorPROBLEM SOLVING IS A JOURNEY

Metaphors Describe Shared Experiences.

• “So I don’t think this would be a route that I would immediately jump to.”

• “I think I know where to go”• “I’m lost”

My Work• 2011 I began applying this to

problem solving (Pilot study with 9 high students)

• 2012 22 Student Video Interviews• 2013 23 Teacher Video Interviews

Students’ Most Frequented

Source Domains

(22 Students)

Students’ Most Popular Source

Domains

(22 Students)

Teachers’ Most Frequented Source

Domains

(23 Teachers)

Teachers’ Most Popular Source

Domains

(23 Teachers)

26% JOURNEY 95% JOURNEY 26% JOURNEY 100% JOURNEY

18% SEARCHING 86% VISUALIZING 13% SEARCHING 96% SEARCHING

13% VISUALIZING 82% SEARCHING 10% DISCOVERY 91% DISCOVERY

12% DISCOVERY 73% PROCESS 10% VISUALIZING 91% BUILDING

9% PROCESS 68% BUILDING 9% PARTITIONING 87% VISUALIZING

8% BUILDING 68% DISCOVERY 7% BUILDING 78% PARTITIONING

8% PARTITIONING 55% PARTITIONING 3% PROCESS 52% PROCESS

3% REMEMBERING 35% RECOGNIZING

26% REMEMBERING

Problem Solving is…• JOURNEY• SEARCHING• DISCOVERY• BUILDING• PARTITIONING• PROCESS• VISUALIZATION

Something Happened• I became a better teacher from CMT

analysis.• I began to use CMT in real time.

• I listened to students, not for answers.• Brent Davis (1991)

CMT Analysis for Listening

INTEGERSADDITION

Example: CLOSURETeaching Math for Elementary Teachers

CoPI Ashley Thune-Aguayo

STUDENT: hit on-target with the first shot, and would hit the core with the second shot.

ASHLEY: If I shoot an arrow, and it hits a target, could I then shoot a second arrow, and hit the same target?

STUDENT: Well, yes.

ASHLEY: Could I hit two completely separate targets with a single arrow? STUDENT No.

ONE ARROW (one input) TWO TARGETS (two outputs) NOT POSSIBLE.

Functions *(paraphrased)

CoPI Ashley Thune-Aguayo

Ordered Pairs (3,7)

Misconception:North/South THEN East/West

AdjustmentEast/West THEN North/South

X-Y Plane

Your turn!!!• Geometry Problems on first page of

handout.

• Student Transcript, try to identify, a common metaphor with the Bolded words.

• Teacher Transcript, try to identify, a common metaphor with the Bolded words.

Theta 2

T23

What did you think?• Were you overwhelmed?

• Did your listening change?

• What Conceptual Metaphors did people identify?

• Can you see this being helpful for teachers?

Current Work• 2013 Intramural Grant creating Teacher

Professional Development.• 2014 Pilot Professional Development

with 4-8 teachers in local high schools on improving listening through CMT analysis.

• 2015 Aim for NSF Discovery K-12 Grant with 30 teachers from multiple high schools.

Professional Development

• 1. Learn CMT with video, transcripts, and rewinding.

• 2. Learn CMT with video.• 3. Learn CMT with each other in real time.• 4. Learn CMT in conversations with

classroom.• 5. Generate Lesson Plans with CMT

Measuring Results• Pre-Test

– Teacher Listening Style Profile– Student Perceptions of Teacher Listening– Time Teacher Spends in Class Listening

• Summer Two-Week Professional Development• Teacher-Generated Lesson Plans• Post-Test

– Teacher Listening Style Profile– Student Perceptions of Teacher Listening– Time Teacher Spends in Class Listening

• SPRING 2013-PRELIMINARY DATA COLLECTION• -Collect initial data by recording teachers in classroom (time spent listening, type of

listening).• -Teacher’s students complete initial survey about teacher listening (Student

Perception Survey, SPS).• -Teachers complete both initial surveys about listening (Listening Styles Profile, LSP;

Teacher Listening Survey, TLS)

• SUMMER 2014-PROFESSIONAL DEVELOPMENT: TEN, 2-HOUR SESSIONS OVER TWO WEEKS.

• • FALL 2014-FINAL DATA COLLECTION• -Collect data by recording teachers in classroom (time spent listening, type of

listening).• -Teacher’s students complete surveys about teacher listening (Student Perception

Survey, SPS).• -Teachers complete both surveys about listening (Listening Styles Profile, LSP;

Teacher Listening Survey, TLS).• -Data is analyzed by PI and Co-PI to look for changes in teacher listening behavior

and pedagogical practices.

Any Questions?

If you are interested in collaborating…

Sean Yeesyee@fullerton.edu

Ashley Thune-Aguayoathune@fullerton.edu

Thank you!

Conceptual Metaphor Theory(CMT)

• 1980’s Lakoff-”Metaphors We Live By” Cog Sci• 1990’s Sfard, English, Moschkovich

DISCOURSE Davis (1991) Listening Theory• 2000’s Linguists (Kovecses) develop

metaphorical systems as descriptive, not prescriptive. CMT Analysis used on mathematics (invented vs discovered)

• 2007 Marcel Danesi uses CMT analysis to deconstruct the complexity in LEARNING mathematical concepts.

Trying CMT Listening in Real Time…

• Imagine you had a piece of string. How would you shape this string to make a triangle bounded by the string with the greatest area?