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Rethinking Transition Mathematics for Advancement: A Teaching Analysis Tool for Lesson Planning and Practice. Julia Aguirre, Ph.D. University of Washington Tacoma jaguirre@u.washington.edu. Transition Mathematics Project Summer Faculty Institute Leavenworth, WA August 24, 2010. - PowerPoint PPT Presentation
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Julia Aguirre, Ph.D.University of Washington Tacoma
jaguirre@u.washington.edu
Transition Mathematics ProjectSummer Faculty Institute
Leavenworth, WAAugust 24, 2010
Session GoalsIntroduce 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 analysisReflections & 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).
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Problem-solving
Problem-posing
Conceptual understanding, adaptive reasoning, strategic competence, productive disposition, procedural fluency, problem solving, academic language, math discourse
Critical Knowledge &
Critical Mathematics Knowledge
Funds of knowledge, linguistic knowledge, Informal/everyday mathematics, country of origin school mathematics
Pedagogy ofAccess
Pedagogy of Transformation
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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)
Classical Mathematics Knowledge
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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
Community Knowledge
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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;
structures, policies, and practices that create equity and inequity in society)
Critical Knowledge
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Pedagogy of Access –– 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 student-teacher 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
Adaptive reasoning, strategic competence (NRC, 2001)
“is learning to grapple with new and unfamiliar tasks when relevant solution methods (even if only partially mastered) are not known.”
(Schoenfeld, 1992)
Challenges traditional role of teacher as sole intellectual authority - (i.e. knows all the answers).
Requires flexibility with uncertainty and “experience, confidence, and self-awareness” on part of the teacher
Problems are derived from learners and their contexts (i.e. authentic problems; issues that affect them and increasingly compel them to respond and change.) Shared intellectual authority; co-investigators
Teacher plays an active role in helping to mathematize those contexts
Connects explicitly to critical knowledge and guides transformative inquiry and action
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Analyzing Mathematical Tasks
Papi’s 70th BirthdayA 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)?
Analyze Math Task
Work on the Papi’s birthday problemAnalyze math task for the following
components:Cognitive Demand (high/low)Classical Math Knowledge Community KnowledgeCritical Knowledge
Prepare to summarize main discussion points about: strengths limitations of the task, evidence, and questions/concerns
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Papi’s birthdayMathematical 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)
Culturally Responsive Math Teaching: Lesson Analysis Tool
Intellectual SupportDepth of Knowledge and Student
UnderstandingMathematical AnalysisMathematics Discourse & CommunicationStudent EngagementAcademic 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 matesBe prepared to share your rating and
evidence with the whole group
Rethinking Math Teaching: Analyze own lessonRate your math lesson/unit based on the rubric
criteriaProvide 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 StepsWhat are some key takeaways from morning
activities about advancing math for all students?In your own coursesAs a department/institution
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