Transcript Driscoll Heck Chval DRK12PI_nov09

Mathematics Teachers Teaching
English Language Learners: What
Knowledge Do They Need?
The Challenge
• Mathematics teachers of English Language
Learners (ELLs) are increasingly expected to
help ELLs learn academic language while
learning mathematics.
• Many are understandingly challenged by this
expectation, possibly viewing it as something
beyond supporting student learning of
mathematics content.
Teacher Knowledge
• Teachers must develop and draw from
numerous knowledge bases to effectively
teach mathematics to all their students.
• Shulman, 1986; Grossman, 1990; Magnusson,
Krajcik, and Borko, 1999; Hill, Ball, and
Schilling, 2008 have conceptualized teacher
knowledge and developed frameworks for
consideration.
Outline of Session
• Introduction of our work and guiding
principles
• Analysis of a mathematical task
• Discussion of relevant teacher knowledge
Kathryn’s CAREER Grant
• CAREER: A Study of Strategies and Social
Processes that Facilitate the Participation of
Latino English Language Learners in
Elementary Mathematics Classroom
Communities
Research Question
In what ways and under what contexts do
the identified research-based strategies
facilitate Latino ELLs’ participation in
elementary mathematics classrooms?
Influence expectations and norms?
Fostering Mathematics Success of
English Language Learners
(FMSELL)
A Collaboration of EDC and Horizon Research,
Inc.
What led us to link geometry to ELLs:
Fostering Geometric Thinking
Fostering Geometric Thinking
Toolkit
Published by Heinemann, Inc.
FMSELL Research Questions
• Does participation in FGTT increase teachers’
geometric content knowledge?
• What effects does teachers’ participation in FGTT
have on their attention to students’ thinking and
mathematical communication when teachers
analyze student work?
• What effects does teachers’ participation in FGTT
have on instructional practices, especially those
known to benefit ELLs?
• What impact on ELLs’ problem-solving strategies
is evident when teachers participate in FGTT?
3 Guiding Principles
• The Challenging Mathematical Tasks Principle
• The Multimodal Communication Principle
• The Academic Language Principle
Principle 1: The Challenging
Mathematical Tasks Principle
No matter what category ELLs fit into—from
students newly arrived in the country and just
beginning to learn English, to those who have
advanced to “Former Limited English
Proficient”—it is both possible and important
to engage all these students in regular
mathematical work that challenges them to
reason, solve problems, conjecture, and
convince.
Principle 2: The Multimodal
Communication Principle
Classroom environments that make ample use
of multimodal communication—pictures,
diagrams, presentations, oral explanations,
written explanations, and gestures—afford
ELLs the means to express the thinking behind
their reasoning and problem solving.
Principle 3: The Academic
Language Principle
In the mathematics classroom, ELLs can learn
to express their mathematical thinking and
reasoning in precise academic language,
provided mathematics teachers work to
understand and apply the ways in which
language is implicated in the learning of
mathematics. In brief, mathematics teachers
of ELLs need to recognize that they also are
language teachers.
The Dissections Problem
Fostering Geometric Thinking Toolkit
(Published by Heinemann, 2008)
The Dissections Problem – Purpose
• Explore your own and your colleagues’
geometric thinking
• See the principles in action
– in particular, we’ll unpack the use of multi-modal
communication
• Prepare to analyze students’ language and
geometric thinking on this problem
The Dissections Problem – Plan
• (5 min) Begin Exploring Problem 1 Individually.
• (15 min) Explore Problem 1 in Small Groups.
– If you finish you can move on to Problem 2.
• (10 min) Prepare to share convincing mathematical
explanations.
– Each group will be given instructions about how to share.
• (10 min) Share thinking with full group.
• (5 min) Debrief use of multi-modal communication and
academic language.
The Dissections Problem – Sharing
• Purpose:
– Share and explore geometric thinking
– Develop language around convincing mathematical
explanations
– Consider the affordances of different modes of
communication
• Directions:
– Listen to or watch five different types of geometric
thinking presentations
– Take notes on the Presentation Notes handout
What helped you understand
presenters’ geometric thinking?
Group Discussion
What knowledge do teachers of
mathematics need in order to support
the learning of ELLs?
How do we help preservice and
practicing teachers develop this
knowledge?
What Knowledge is Needed?
• Strategies for engaging ELLs in oral and
written production in the classroom
• Strategies for scaffolding and structuring
mathematics tasks to heighten access for ELLs,
without watering down the cognitive
challenges in the tasks
• Strategies for facilitating productive peer
interactions
• Strategies for negotiating meanings
What Knowledge is Needed?
• Knowledge of at least some basic ways in
which language is implicated in the learning of
mathematics—e.g., awareness that words like
‘same’ and ‘any’ underscore the importance of
precision in mathematical language, as well as
the privileged meaning of some words and
phrases in mathematics
• Knowledge of how to interpret gestures and
other non-verbal modes of expressing
mathematical thinking
What Knowledge is Needed?
• How to assess and interpret oral and written
mathematical work by ELLs, to see both
evidence of mathematical thinking and
evidence related to academic language
development.
• Mathematical tools—e.g., technology,
manipulatives, symbolic representations—for
supporting ELLs in mathematical
investigations and communication of their
thinking