Strategies for Numeracy Across the Curriculum

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Strategies for Numeracy Across the Curriculum

• Presented by Michelle Walker-Glenn
• Thursday, Dec. 4, 2008

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Overview

• Workshop Objectives and Expectations
• Introduction
• Rationale and Definition Numeracy
• Numeracy Strategies Across the Curriculum
• Leadership Strategies for Numeracy Across the
  Curriculum

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Workshop Objectives

• Familiarize participants with Strategies for
  Numeracy Across the Curriculum
• Understand the rationale for emphasizing numeracy
  across the curriculum
• Understand the relationship between numeracy and
  literacy
• Develop a working definition of numeracy
• Receive overview training on specific numeracy
  strategies that can be used by teachers in all
  content areas
• Develop training strategies to introduce school
  staff and administration to the implementation of
  numeracy strategies

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Why is Numeracy Important?

• To function in todays society, mathematical
  literacy (what the British call numeracy) is as
  essential as verbal literacy. These two kinds of
  literacy, although different, are not unrelated.
  Without the ability to read and understand, no
  one can become mathematically literate.
  Increasingly, the reverse is also true without
  the ability to understand basic mathematical
  ideas, one cannot fully comprehend modern writing
  such as that which appears in the daily
  newspapers.
• -- National Research Council, 2001

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Mathematical literacya serious problem in the
U.S.

• 78 of adults cannot explain how to compute the
  interest paid on a loan
• 71 cannot calculate miles per gallon on a trip
• 58 cannot calculate a 10 tip for a lunch bill
• (Philips, 2007)

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U.S. Department of Education 2008The Final
Report of the National Mathematics Advisory Panel

• Childrens goals and beliefs about learning are
  related to their mathematics performance.
  Experimental studies have demonstrated that
  changing childrens beliefs from a focus on
  ability to a focus on effort increases their
  engagement in mathematics learning, which in turn
  improves mathematics outcomes When children
  believe that their efforts to learn make them
  smarter, they show greater persistence in
  mathematics learning. Teachers and other
  educational leaders should consistently help
  students and parents to understand that an
  increased emphasis on the importance of effort is
  related to improved mathematics performance.

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U.S. Department of Education 2008The Final
Report of the National Mathematics Advisory Panel

• Mathematics performance and learning of groups
  that have traditionally been underrepresented in
  mathematics fields can be improved by
  interventions that address social, affective, and
  motivational factors. Recent research documents
  that social and intellectual support from peers
  and teachers is associated with higher
  mathematics performance for all students, and
  that such support is especially important for
  many African American and Hispanic students.

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U.S. Department of Education 2008The Final
Report of the National Mathematics Advisory Panel

• The achievement gap between students of
  differing ethnic and socioeconomic groups can be
  significantly reduced or even eliminated if
  low-income and minority students increase their
  success in high school mathematics and science
  courses.
• (Evans et al., 2006)

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Effort Based vs. Ability Based Approach

• Effort makes a difference. Academic ability can
  be grown. It is not how smart the child is, but
  how hard he or she works that determines success.
  All students are held to high expectations and
  offered opportunities to take challenging
  courses.
• Students learn at different rates and may not
  reach proficiency at the same time. A mistake is
  not an inability to perform, but a learning
  opportunity . For that reason, students may re-do
  work and retake tests.
• Effort based teachers are not necessarily
  unrealistic about their students capabilities,
  but they are unwilling to give up on them.
  Students are provided extra helpduring school,
  in the summer, and before-and after-school.

• Students of high ability receive the highest
  marks and are selected to take the most
  challenging courses. Students perceived with less
  ability are put in classes with lower
  expectations. Any academic deficiencies students
  have are attributed to low ability.
• Since time is the constant in learning, students
  that fail to finish assignments, score well on
  tests, or learn key concepts by the due dates
  receive failing marks with no second chances.
• Extra help opportunities are entirely the
  responsibility of the student. If they take
  advantage of them, thats good but no structure
  exists to ensure that students who need extra
  help get it.

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Effort Based vs. Ability Based Approach

• Students can be motivated to come to the belief
  that their effort is worthwhile, even if they do
  not believe it at the time they enter school.
• Students are provided with extensive and specific
  feedback through the learning process to make
  connections in their understanding and continue
  to learn.
• Teachers explicitly teach students how to exert
  effective efforts in learningstudy skills, time
  management, problem solving, and note-taking.

• Students have the responsibility to motivate
  themselves. If they do not believe they can do
  well in school, they probably wont.
• Feedback to students is limited, often occurring
  only in the form of a numerical grade or letter
  grade.
• Teachers assume that students should have these
  skills by the time they reach their classroom.
• Taken from Masters for Motivation by Jonathan
  Saphier. Chapter 5 in On Common GroundThe Power
  of Professional Learning Communities by Dufour,
  Eaker, Dufour

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3 Reasons Why Numeracy is Important

• Economy/Employability
• I advise my students to listen carefully the
  moment they decide to take no more mathematics
  courses. They might be able to hear the sound of
  closing doors.
• --James Caballero, 1991
• National Security
• National Security Agency www.nsa.gov
• Democracy
• To develop an informed citizenry and to support
  a democratic government, schools must graduate
  students who are numerate as well as literate.
• --Lynn Arthur Steen, 1999

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Why is Numeracy important for ALL students?

• A strong grounding in HS mathematics through
  Algebra II or higher correlates powerfully with
  access to college, graduation from college, and
  earning in the top quartile of income from
  employment.
• The correlation is even stronger for African
  American and Hispanic students!

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Transforming Traditional Mathematics Instruction
intoInstruction with an Emphasis on Mathematical
Literacy
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What is Numeracy?

• At homeness with numbers
• Appreciation of mathematics
• Confidence in math
• Reason
• Mental math ability
• Use symbols
• Sense of numbers
• Use mathematical models
• Interpret data
• Read and interpret graphs

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Verbal Literacy and Numeracy
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SREBs Definition of Numeracy

• The ability to interpret and understand numeric
  symbols and relationships
• The ability to communicate and represent
  mathematical concepts in a variety of ways
• The development of mathematical culture and way
  of thinking and looking at the world in a
  mathematical way
• Appreciation for aesthetics, history and
  application of math
• Source SREB, 2007

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Activity Defining Numeracy

• What are some characteristics of a numerate
  person (student)?
• What are some examples of innumeracy in our
  society?
• What does good teaching of numeracy look like?
• What does poor teaching of numeracy look like?

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Adding It Up (National Research Council)

• UNDERSTANDING (conceptual understanding)comprehen
  sion of mathematical concepts, operations, and
  relations, knowing what mathematical symbols,
  diagrams and procedures mean.
• COMPUTING (procedural fluency)Skill in carrying
  out procedures such as adding, subtracting,
  multiplying and dividing flexibly, accurately,
  efficiently, and appropriately.
• APPLYING (strategic competence)Ability to
  formulate, represent, devise strategies and solve
  mathematical problems using concepts and
  procedures appropriately.
• REASONING (adaptive reasoning)Capacity for
  logical thought, reflection, explanation, and
  justification, extending something known to
  something not yet known.
• ENGAGING (productive disposition)Habitual
  inclination to see mathematics as sensible,
  useful, and worthwhile, coupled with a belief in
  diligence and ones own efficacy. Mathematics is
  useful and doable if one works at it.

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Adding it UpNational Research Council(2001)
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UnderstandingConceptual Understanding Strand
1/3
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Understanding Conceptual Understanding Strand
1/2 of 1/3
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ComputingProcedural Fluency Strand

• 1/2 x 1/3 1/6

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ApplyingStrategic Competence Strand

• Charles went to the kitchen and saw that there
  was some pudding left in the pan. He noticed that
  about 1/3 of the pudding was left in the pan. He
  ate 1/2 of the remaining pudding. What fraction
  of the original pudding did he not eat?

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ReasoningAdaptive Reasoning

• 1/2 plus 1/3 does not equal 2/5.
• Explain why this statement is true.
• OR
• "Five out of four people have trouble with
  fractions.
• (Steven Wright)
• Explain how this quote is an example of irony.

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EngagingProductive Disposition Strand

• What good are fractions?

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Why Teach Numeracy Across the Curriculum?

• Learning is about making connections
• Brain research supports the need for connected
  learning

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Organization of Guidebook

• Introduction
• Rationale and definitions
• Strategies for Improving Numeracy Across the
  Curriculum
• Seven strategies
• Leadership for Numeracy Across the Curriculum
• Leadership activities, self-assessements,
  planning tools

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What can all teachers do NOW to enhance Numeracy?

• Be a good role model. Showcase the way you use
  mathematics in your professional life as well as
  your specific content area.
• Make mathematics an integral part of daily
  instruction. Strive to make a connection during
  each class.
• Provide time in class for students to work on
  mathematics that relates to instructional
  objectives for your content area.
• Incorporate logical reasoning and problem
  solving opportunities daily, as it relates to
  your content.
• Provide resources for students such as
  calculators, rulers, scale models, graphic
  organizers, charts, graphs, statistical data,
  etc., to enable students to experience
  mathematical connections to various topics across
  the curriculum.
• Create and/or gather samples of mathematical
  connections to your specific content area. Share
  newspaper articles, magazine articles, and
  professional journal articles that show how
  mathematics is utilized in your academic
  discipline.
• Allow students choice about their completion of
  assignments that incorporate mathematics and
  problem solving.
• Source Adapted from SREB, 2003

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• Invite students to incorporate data and data
  analysis as part of writing to authentic
  audiences for authentic reasons about which they
  truly care.
• Provide students with prompt feedback about
  content as well as mathematical reasoning, when
  appropriate.
• Avoid teaching computation in isolation. It
  should be addressed in the context of students
  own authentic problem solving.
• Analyze student work to determine instructional
  implications and make adjustments in instruction
  to address areas of need.
• Look at student work with an eye for logical
  reasoning, use of multiple representations,
  incorporation of data, and use of graphs that
  make cross-curricular connections.
• Read professional literature about incorporating
  mathematical concepts into your specific content
  area.
• Focus on improving each students knowledge and
  ability to apply mathematical thinking and
  reasoning skills across content areas rather than
  just developing computational skills in
  isolation.
• Avoid sharing any personal math phobias or a
  personal dislike of mathematics. Educators never
  boast of being illiterate, yet we often freely
  share that we are innumerate!
• Source Adapted from SREB, 2003

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Numeracy Strategies Jigsaw Activity

• Familiarize yourself with your assigned strategy
  (10 minutes). Working with a partner or group,
  give a summary (3-5 minutes) of the strategy. Use
  chart paper if necessary. Give examples of how
  you could use this strategy in your classroom.
• Strategy 1 p. 12
• Strategy 2 p. 15
• Strategy 3 p. 21
• Strategy 4 p. 23
• Strategy 5 p. 28
• Strategy 6 p. 33
• Strategy 7 p. 37

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Activity Are We Implementing Across the
Curriculum?

• Read through the list of statements on p. 42 and
  put a check mark next to those that you believe
  are true for your school.
• For statements marked not true, discuss the
  next steps necessary to make these into true
  statements.
• Generate a list of 3-5 immediate actions that can
  be taken to support increased numeracy across the
  curriculum
• Be prepared to share your action steps with the
  group.

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Activity Numeracy Survey for School Leaders

• Complete the Numeracy Survey for School Leaders
  p. 76 without putting your name on it. Be honest!
• Crumple survey and toss into a pile in the center
  of the room.
• Select a survey from the pilenot your own.
• Create human bar graph.

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Closing Activity

• Key Ideas
• Next Steps
• What will you do differently tomorrow morning?
• What will you do differently next week/month?
• What will you do differently this school year?

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Homework Creating Lesson Plans with a Focus on
Numeracy

• Math Teachers Work with non-math colleagues to
  develop 3 lesson plans in non-math content areas
  using the Numeracy Strategies (p. 12-37). Bring
  copies of your plans for the group and be
  prepared to share.
• Non Math Teachers Use Numeracy Strategies (p.
  12-37) to develop 3 lesson plans that incorporate
  numeracy across the curriculum. Bring copies of
  your plans for the group and be prepared to
  share.
• Non Teachers Complete at least 1 leadership
  activity (p. 40-82) with a team. Be prepared to
  share the results of your activity.

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Homework Bring HSTW or MMGW 2008 Assessment Data

• All Participants Bring a copy of your schools
  HSTW or MMGW 2008 Assessment Data
• High School
• Page 1 - Executive Summary
• Page 2 Key Indicators of Student Achievement
• Page 4 2008 Mean Math Scores
• Page 7 Percent Meeting Math Goals
• Page 11 Percent Taking HSTW Rec. Math Curr.
• Page 15 Emphasis on Numeracy Across the
  Curriculum
• Page 28 Emphasis on Numeracy Across the
  Curriculum
• Pages 85-96 Math Demographic Data
• Pages 216-217 Teacher Survey on Challenging
  Math Content

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Extra Credit for Math Teachers

• Review all of the questions listed on a test or
  quiz.
• Identify whether each question addresses
• Conceptual understanding
• Procedural fluency
• Strategic competence (applying to story problem)
• Adaptive reasoning (justifying answers/explaining)
  
• Productive disposition (what good is ___ ?)
• Do your assessments enable students to develop
  all 5 strands of the rope?

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Thank You

• Contact Information
• Michelle Walker-Glenn
• shellw_at_cinci.rr.com
• A man is like a fraction whose numerator is what
  he is and whose denominator is what he thinks of
  himself. The larger the denominator, the smaller
  the fraction. Leo Tolstoy