Problem Solving Metaphors: Listening for Student Experiences CMC-South, Palm Springs, 2013
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Transcript of Problem Solving Metaphors: Listening for Student Experiences CMC-South, Palm Springs, 2013
Problem Solving Metaphors: Listening for Student Experiences
CMC-South, Palm Springs, 2013
Sean [email protected]
California State University, Fullerton
Ashley [email protected]
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 OneLiteral 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?
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?