Transcript Julia Aquirre - Transition Mathematics Project

Julia Aguirre, Ph.D.
University of Washington Tacoma
[email protected]
Transition Mathematics Project
Summer Faculty Institute
Leavenworth, WA
August 24, 2010
Session Goals
 Introduce a math teaching framework and student
learning outcomes that promote advancement in math
competence, confidence, and equity.
 Introduce a teaching tool to analyze and enhance math
instruction to support mathematics advancement of
all students.
Overview:
 9:00-10: 30
 ACTIVITY 1: Framing the issues for mathematical advancement
 ACTIVITY 2: Analyzing teaching from multiple dimensions
 10:30-11:00
 BREAK
 11:00-12:30
 ACTIVITY3: Analyzing our own teaching practice – Lesson plan
analysis
 Reflections & Next steps
 LUNCH
Group Share – Poster 1
 What are some reasons you have heard of (from
media, research, colleagues) that explain why
some students do well in mathematics and others
struggle?
 Any particular areas of mathematics that come
to mind?
 Any particular demographic groups?
Learning Outcomes
 Students learn that mathematics is an essential analytical tool to
understand complex issues/problems and potentially change the
world.
 Students deepen their mathematical understanding and skills through
analyzing complex social issues and problems that are important to
them and their community.
 Students become more motivated to learn and engage with
important rich mathematics.
 Students develop a intellectual and cultural competence that enable
them to maintain their cultural integrity while succeeding
academically, particularly in mathematics.
Greer et al (2009); Gutierrez (2007, 2009); Gutstein (2006); Gutstein & Peterson (2005).
Teaching Mathematics Framework (Aguirre, 2009)
Pedagogy
of
Access
Problemsolving
Funds of knowledge,
linguistic knowledge,
Informal/everyday
mathematics, country of
origin school
mathematics
Conceptual understanding,
adaptive reasoning, strategic
competence, productive
disposition, procedural
fluency, problem solving,
academic language, math
discourse
Critical Knowledge &
Critical Mathematics
Knowledge
Pedagogy of
Transformation
Problemposing
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Classical Mathematics
Knowledge
Mathematical power (core mathematical ideas,
conceptual understanding, procedural fluency,
problem-solving; standards; academic language;
mathematical discourse)
Passing the gates (standardized tests, high
school graduation, college, etc)
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Community Knowledge
Informal Math Knowledge/Funds of Knowledge: people have and
produce math knowledge outside of school tied to specific
cultural/community practices (e.g. household activities, commerce
activities, tiendas, games)
Formal Math Knowledge: people have and produce formal math
knowledge within schools that is culturally constructed (e.g. symbolic
notation, algorithms; mathematical discourse).
ABC
ABC
<ABC
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Critical Knowledge
Critical Mathematical Knowledge:
To use mathematics as an analytical tool to
understand power relations, decisions, social issues
and sociopolitical context of reality.
To use mathematics to foster positive change and/or
take action to challenge injustice.
Critical Knowledge in General:
Knowledge beyond mathematics needed to
understand the sociopolitical context. (e.g.multiple histories;
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structures, policies, and practices that create equity and inequity in society)
Access
Pedagogy of
––
Transformation
Access to classical math
knowledge, high cognitive
demand tasks, academic
language, and discourse
practices is key to advancement
in mathematics
Access to community knowledge
as a resource to learn rich and
rigorous mathematics
Access to high expectations,
high quality mathematics
content, and strong studentteacher relationships
Beyond access to
investigate, challenge and
change institutional
structures, policies, and
practices that may
perpetuate inequity (e.g.
low cognitive demand
curriculum, student tracking
and placement practices,
resource allocation)
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Pedagogy of
Problem-Solving –– Problem-Posing
Problems are derived from
learners and their contexts (i.e.
Adaptive reasoning, strategic
authentic problems; issues that
competence (NRC, 2001)
affect them and increasingly
compel them to respond and
“is learning to grapple with new and
unfamiliar tasks when relevant solution change.)
methods (even if only partially
Shared intellectual authority;
mastered) are not known.”
(Schoenfeld, 1992) co-investigators
Challenges traditional role of teacher
Teacher plays an active role in
as sole intellectual authority - (i.e. knows helping to mathematize those
all the answers).
contexts
Requires flexibility with uncertainty and Connects explicitly to critical
“experience, confidence, and selfknowledge and guides
awareness” on part of the teacher
transformative inquiry and
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action
Analyzing Mathematical Tasks
Papi’s 70th Birthday
A true story
It was Señor Aguirre’s 70th Birthday. His three children wanted to throw him a big party to
celebrate. The hall rental, mariachi, food, and decorations will cost a total of $4,500.
The brother, a special medical doctor (anesthesiologist) who makes about $20,000 per
month, suggested that the three children split the cost equally.
One of the sisters, a university professor who makes about $6,000 per month, said that
would not be fair. She suggested the following: the brother pays $3150. She would pay
$900, and the other sister, a partner in the family business and single mom with 2 boys
who makes about $3000 per month, should pay $450.
TASK*: Write a position statement using mathematical evidence (e.g. proportions, ratios,
percent) to support your conclusion to the following questions:
•Which person do you agree with and why?
•What is fair in this situation?
•Can you think of an alternative financial arrangement that might be better (more
fair)?
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Analyze Math Task
 Work on the Papi’s birthday problem
 Analyze math task for the following components:
 Cognitive Demand (high/low)
 Classical Math Knowledge
 Community Knowledge
 Critical Knowledge
 Prepare to summarize main discussion points
about: strengths limitations of the task, evidence,
and questions/concerns
Papi’s birthday
 Mathematical leverage (additive/absolute to multiplicative/
relative thinking)
 For middle school students
 Pre-service teachers
 Familiar context that is culturally grounded
 Explores facets of mathematical and social conceptions of
fairness
 High cognitive demand activity (Stein et al, 2000)
 Task is offered in two languages (e.g. English, Spanish)
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Culturally Responsive Math Teaching:
Lesson Analysis Tool
 Intellectual Support
 Depth of Knowledge and Student Understanding
 Mathematical Analysis
 Mathematics Discourse & Communication
 Student Engagement
 Academic Language Support for ELL
 Use of L1 (home language)
 Use ESL scaffolding strategies
 Funds of Knowledge/Culture/Community Support
 Use of Critical knowledge/Power/Social Justice
Video Lesson Analysis:
Division of Fractions
 Use the rubric to rate the lesson 1-5 on a specific
dimension
 Provide evidence from the lesson to support your
rating
 Discuss your rating with your table mates
 Be prepared to share your rating and evidence with
the whole group
Rethinking Math Teaching:
Analyze own lesson
 Rate your math lesson/unit based on the rubric criteria
 Provide specific evidence from your lesson to support your
rating.
 Reflect on Activity:
 What are the strengths and limitations of your lesson according to the
rubric?
 What strategies or areas would you like to strengthen as a result of this
analysis? Give an example of how you might strengthen one area (this
can be in this lesson or in subsequent lessons).
 How does this analysis help, if at all, your math lesson planning process
to meet the math learning needs of your students?
 Is there anything you would change about the rubric in relation to
helping you facilitate mathematics learning of your students? Why.
Reflection & Next Steps
 What are some key takeaways from morning activities
about advancing math for all students?
 In your own courses
 As a department/institution