For ALL

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For ALL Miriam Leiva
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Why this talk?
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Presentation

• From the Past to the Future
• What is the challenge? FOR ALL
• Where are we? Test results, demographics
• Attention to Mathematics
• Communication, differentiated instruction
• Representation
• Reasoning
• Implications for Educators
• Implications for Publishers

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• Teachers
• Active learning
• Group learning
• Discussions
• Communication
• Collaborative Lesson Plans
• Creative Groupings
• Manipulatives
• Modeling what goes on in classrooms

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• where the answer is right and everything is
  nice
• Carl Sandburg

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Equity in Mathematics Education

• Mathematics is a domain no longer limited to a
  select few.
• All students need to be mathematically
  proficient.
• All students must have opportunities to study
  and support to learn- mathematics
• National Research Council (2000). Adding it up.
• NCTM (2000). Principles and Standard for School
  Mathematics

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• Equity does not mean that every student should
  receive identical instruction. Rather, it
  demands that reasonable and appropriate
  accommodations be made and appropriately
  challenging context be included to promote access
  and attainment for ALL students.
• Principles and Standards for School Mathematics,
  2000

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TESOLTeachers of English to speakers of other
languages

• The purpose of contemporary education is to
  prepare ALL students for the life in the world,
  including those who enter school with a language
  other than English. 1997

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TODOS Mathematics For All An equitable,
high quality mathematics education for
ALL students, by supporting, linking,
informing their teachers and others. www.todos-mat
h.org
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the fundamental notion is not that they need
mathematics different from majority students
but rather that effective instruction for all
children must be carried out on the basis of what
is known about how children learn with
understanding.

• Hernandez, The Mathematics Bilingual Education
  Connection. Perspectives on Latinos, NCTM (1999)

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Equity

• All students must have opportunities to study
  and support to learn- mathematics.
• An equitable, high quality mathematics
  education for ALL students,
• by supporting, linking, informing
• teachers, other educators, community
• www.todos-math.org

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• Goal 1.
• To improve educators knowledge and ability to
  implement an equitable, rigorous, and coherent
  mathematics program that incorporates the role
  that language and culture play in learning
  mathematics.

TODOS Mathematics For All
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NAEP 2007 Report Math

• Upward trend in average scores continues in 2007
  at both grades 4 and 8.
• Average scores increased between 2005 and 2007 in
  23 jurisdictions at grade 4 and in 26
  jurisdictions at grade 8.
• White, Black, and Hispanic students at grades 4
  and 8 scored higher in 2007 than in all previous
  years.

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Average scale scores in mathematics, by
race/ethnicity, grade 4 19902005, NAEP
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NAEP, 07
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Grade 8 NAEP Math Gap - ELL
NAEP, Nations Report Card (2005)
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ELL NAEP 07, Math
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Average scale scores in mathematics, by students'
eligibility for free/reduced-price lunch, grade
4 19962005, NAEP
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Lunch Eligibility
NAEP 07 Math
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U.S. Department of Education, Institute of
Education Sciences, National Center for Education
Statistics, National Assessment of Educational
Progress (NAEP), 2005 Mathematics Assessment,
12th grade
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• For Every Student
• An Equal
• Opportunity
• To be different

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All learners

• Differences
• Culture, Language
• Socio-economic status
• Family, friends
• Social, School Experiences
• Previous Knowledge
• Physical and/or emotional barriers

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Key Points

• Each student is different
• Accommodations
• Differentiated Instruction
• Communication
• Strategies
• Research-Based Practices

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Key Points

• Research-Based Practices
• Accommodations, Differentiation, Intervention
• Communication
• Language Social, Academic, Mathematical
• Teaching and Learning
• Content Concepts and Skills
• Reading, Interpreting
• Representing, organizing, simplifying,
  scaffolding
• Reasoning, Solving
• Creative Grouping, Creative collaboration
• A community of Learners

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Language fluency

• English Proficiency
• It is much more than social fluency
• Level may not be apparent
• Level incorrectly designated
• Good basic social communication skills do not
  imply command of Academic English

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Strategy Develop Language Drawings Pictures Man
ipulatives Words Sentences
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• STRATEGY Assess and Plan
• Assess
• Prior knowledge
• Vocabulary
• Level of fluency
• Student confidence

• Plan Instruction accordingly

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• Comparing
• Heights
• 1st grade
• Carl has more height than Chelsea

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Communication

• Communicate to Learn mathematics
• Learn to Communicate mathematically
• Speak, Write, Read,
• Listen, Interpret
• NCTM (2000). Principles and Standard for School
  Mathematics, p. 60

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NCTM Position Math for ELL

• communication "as an essential part of
  mathematics and mathematics education.
• all students, and ELL in particular, need to
  have opportunities and be given support for
  speaking, writing, reading and listening in math.
  classes.
• to help ELL overcome barriers that will
  facilitate "communicating to learn mathematics
  and learning to communicate mathematically."

Principles and Standards (2000), NCTM
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• To enable (students)
• to achieve in mathematics
• the teacher must help them develop language
  skills that go beyond mere social fluency
• Peixotto. Teaching Mathematics and Science to
  English-Language Learners, NWREL (2002)

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The language of Mathematics
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One inch of rain is equivalent to ten inches of
snow.
s 10 x r
r 0.10 x s
Represent
Rain
Snow
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One inch of rain is equivalent to ten inches of
snow.

• Rain to snow 110 or 1/10
• Snow to rain 101 or 10/1
• Amount of snow
• 10 times of the amount of rain
• Amount of rain
• 10 of the amount of snow

Represent
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Teaching mathematics requires instructional
settings and situations where students are
engaged in solving interesting real-life problems
that encourage both critical thinking and basic
skills development and practice.National
Clearinghouse for Bilingual Education, 1997
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Math Test Un-Real Applications
Bobby has 10 minutes to solve four word problems
and no idea how to do them. If he leaves on a
train traveling 55 mi/hr, how long before his
teacher realizes he is gone?
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• Communication Dialogue, discussion
• Beyond Words, Vocabulary, and Exercises
• Participation in math. discussion
• Generalizing, Abstracting
• Being precise (any, all, each, there is)
• Reaching certainty, proving, justifying
• Using multiple meanings and representations
• Beyond language TO mathematics communication,
  reasoning, meanings
• To individualize instruction.
• To build a community of mathematics learners

Moschkovich (2002) A situated and sociocultural
perspective on bilingual mathematics learners.
Math. Thinking and learning. Erlbaum.
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Implications for Publishing

• Use advanced technology See, hear, interact, do,
  solve
• Utilize the Web, Internet for individualized
  programs
• Promote/support the best teaching strategies
• Students are together in ONE classroom
• Focus on language, FOR ALL
• The problem with word problems
• Problems grounded in the students world
• Professional Development on using materials
• Implicit and Explicit motivation
• It takes a village include all other
  stakeholders

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Implications for Teachers

• Teach in many different ways
• Manipulatives, Visuals, Technology
• Multiple Representations
• Vocabulary building English, Math
• Engage students, active participation
• Questions, explanations, justification
• in other words why
• Creative grouping, creative collaboration
• Select and use materials appropriately

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Research-Based Practices

• High expectations
• knowledge, reasoning, work, discipline
• Provide for differences
• Learning styles
• Prior knowledge, experiences
• Flexibility
• Materials
• Communication and connections
• Assessment
• on going, seamless, to inform

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Predictors of Success

• Expectations
• Previous academic achievement
• The teacher, the principal, the school
• Appropriate materials for teacher, students
• Creative teaching and outreach programs
• Support from all the community the village
• Thomas Collier. School effectiveness for
  language minority students. NCBE. (1997)

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Key Points

• Research-Based Practices
• Accommodations, Differentiation, Intervention
• Communication
• Language Social, Academic, Mathematical
• Teaching and Learning
• Content Concepts and Skills
• Reading, Interpreting
• Representing, organizing, simplifying,
  scaffolding
• Reasoning, Solving
• Creative Grouping, Creative collaboration
• A community of Learners

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Problem Solving   What to do when you dont
know what to do!     engaging in a task for
which the solution method is not known in
advance.   Principles and Standards for School
Mathematics, NCTM
 
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Math Test Un-Real Applications
Bobby has 10 minutes to solve four word problems
and no idea how to do them. If he leaves on a
train traveling 55 mi/hr, how long before his
teacher realizes he is gone?
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StrategyScaffolding

• Guide students
• To build on
• Prior knowledge, experiences
• To explore and inquire
• To construct the foundation
• Through planned sequencing, questioning

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The Problem with Words

• The cars on the Ferris Wheel hold 3 children
  each. There are 20 children
• How many rides are needed for all children to
  ride?

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Strategy Scaffolding

• 20 children are going to ride on the Ferris
  Wheel.
• There are 6 cars on the Ferris Wheel.
• Each car holds 3 children.
• What is the question?
• In your group
• Make up a problem
• Solve it

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Problem Solving

• Reading with Understanding
• Language, Communication
• Visuals, Models
• Context, Connections
• Group Work
• Reasoning

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Read and interpret Reason patterns, experience,
Represent relationships with models
Represent, Resolve symbols, graphs,
Reflect, Analyze results Relate, Communicate
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The present and future

• Realistic problems their world
• Connected to other disciplines
• Success in P.S. based on
• Reasoning
• Communication

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Learning is contextual

• What is connected to how
• Models, visuals
• Active participants, groups
• Dialogues, communication

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Strategy No Numbers

• Ruth buys ___ tickets for the concert.
• Tickets cost ___ each.
• Ruth has _____
• How much money does she have left after buying
  the tickets? ____

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Strategy Tiered Lesson

• Ruth buys ___ tickets for the concert.
• Tickets cost _____ each.
• Ruth has _____
• How much money does she have left after buying
  the tickets? _______
• 60 4 10 20

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Teaching and Communication

• Discussion to promote thinking, clarity
• Discussion to connect to other ways of solving,
  other representations, other problems
• Dialogue and other communication to explain,
  justify, defend, support solutions deepens
  understanding.

National Research Council (2001). Adding it up.
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An artist designs and makes rugs using
arrangements of rectangles A rectangular rug
has an area of 12 m2 Describe possible
dimensions of the rug        
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Good practices

• High expectations demand
• knowledge, reasoning, work, discipline
• Provide for differences
• Learning styles
• Prior knowledge, experiences
• Flexibility
• Communication and connections
• Assessment on going, seamless, to inform

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Language and Assessment

• Seamless Approach
• Curriculum, Instruction, Assessment
• Assess
• Barriers linguistic or academic
• L1 followed by L2 as appropriate
• Test driven curriculum trivializes teaching
• Inaccurate data on student progress, instruction

Mathematics Standards and the Language Minority
Student. National Clearing House for Bilingual
Education (1997)
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Predictors of Success

• Expectations
• Previous academic achievement
• The teacher, the principal, the school
• Appropriate materials for teacher, students
• Creative teaching and outreach programs
• Support from all the community the village
• Thomas Collier. School effectiveness for
  language minority students. NCBE. (1997)

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• Rich Appropriate Content
• Problem Solving
• Reasoning
• Communication
• High Expectations
• Equal Access
• If you believe it
• you will see it

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All Educators, Community

• Support
• Equity
• High Standards
• Professional Development
• Involve, Educate Communities
• Enlist Support - Promote Linkages
• Expect more from ALL

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For All Students

• Rigorous Math Program
• High Expectations
• Access

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• For every student
• An equal opportunity
• to
• succeed

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One child at a time
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If you believe it you may see it! It takes much
more
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go to the children teach them Thomas
Aquinas
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TODOS Mathematics For All An equitable, high
quality mathematics education for ALL
students, by supporting, linking,
informing their teachers and others. Reception
Room 007 D 530 pm maleiva_at_carolina.rr.com
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Miriam Leiva

• maleiva_at_carolina.rr.com
• www.todos-math.org

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Miriam Leiva maleiva_at_carolina.rr.com
TODOS Mathematics for ALL  www.todos-math.org
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TODOS Mathematics For All An equitable and high
quality mathematics education for all students
www.todos-math.org
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All students must have opportunities to study
and support to learn- mathematics. Equity does
not mean that every student should receive
identical instruction instead, it demands that
reasonable and appropriate accommodations be made
as needed to promote access and attainment for
all students. PSSM, NCTM (2000)