Teaching to the Standards in Math

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Teaching to the Standards in Math

• Dr. Wakeman

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• Several of the slides used in this presentation
  were originally created by one or more of the
  following individuals and are used here with
  their permission. For permission to resuse any
  portion of this presentation please contact
  dbrowder_at_uncc.edu for additional information.
• Diane Browder, Katherine Trela, Bree Jimenez,
  Vicki Knight, Shawnee Wakeman

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National Council of Teachers of Mathematics

• National Council of Teachers of Mathematics 5
  main components
• Numbers and Operations
• Measurement
• Data analysis and probability
• Geometry
• Algebra

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Numbers and Operations

• Quantity and Number Sense
• Identifying numbers
• One-to-one correspondence
• Numerical order
• Place value
• Composing and decomposing s (i.e., , -)
• Sequences (e.g., first, next, last)
• Ordinal numbers (e.g., first, second, third)
• Remember
• Numbers can be represented by numerals, pictures,
  objects, or manual signing

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Number and Operations Across Grade Levels

• Early Elementary (K-2)
• 11 correspondence
• Late Elementary (3-5)
• Place value
• Fractions Decimals
• Numbers less than 0 by extending the number line
• Operations (, -, x, )
• Middle School
• Scientific and exponential notation
• Integers (i.e., positive and negative numbers)
• Applying operations to fractions, decimals, and
  percents
• High School
• Interdisciplinary applications w/very large and
  small numbers

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Algebra

• Patterns and Relationships
• Sequences (i.e., predict what comes next)
• Algebraic equations
• 3x10
• Use manipulatives and
• graphic organizers to teach

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Algebra Across Grade Levels

• Early Elementary (K-2)
• Identify patterns
• Late Elementary (3-5)
• Identify patterns and predict what comes next
• Middle School
• Use symbols to represent relationships
• Algebraic equation to solve real-world problems
• High School
• Multi-step algebraic equations
• Sophisticated formulas

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Geometry

• Spatial organization
• Not just naming basic shapes!
• Directional words (e.g., next to, parallel)
• Lines and line segments
• Points in a plane
• Maps and grids
• Coordinate plane

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Geometry Across Grade Levels

• Early Elementary (K-2)
• Explore relationships (e.g., over, near, between)
• Directional words (e.g., left, right)
• Late Elementary (3-5)
• Maps and grids
• Use Cartesian planes
• Middle School
• Coordinate plane (e.g., lines, line segments, and
  points)
• Formula for slope and y-intercept
• High School
• Transformations and matrices

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Measurement

• Attributes
• Money
• Time
• Length
• Weight
• Capacity
• Use manipulatives to teach

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Measurement Across Grade Levels

• Early Elementary (K-2)
• Use terms to describe and compare objects (e.g.,
  large, slow)
• Attributes of length, volume, weight, area, and
  time
• Late Elementary (3-5)
• Length, perimeter, area, volume, weight,
  temperature, size of angles
• Select appropriate tools for measurement
• Units in customary and metric systems
• Middle School
• Length, area, surface area, volume, angle
  measures of 2-D and 3-D shapes and objects
• Apply algebraic formulas to express relationships
  of measurements
• High School
• Interdisciplinary approach

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Data Analysis and Probability

• Graphs- actually see relationships between
  factors
• Identify how data collected
• Observe, survey
• Collect the data
• of boys and girls in class
• Summarize the data
• In graph
• Evaluate the data
• More boys or girls?

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Data Analysis and Probability Across Grade Levels

• Early Elementary (K-2)
• Pose questions and collect data
• Represent data using concrete objects, pictures,
  and graphs
• Late Elementary (3-5)
• Collect data using observations, surveys, and
  experiments
• Represent data in tables and graphs (e.g., line
  and bar graphs)
• Describe and compare data sets
• Middle School
• Formulate questions, design studies, and collect
  data
• Select representation format (e.g., pie graph,
  histogram, scatterplots, stem-and-leaf plots, box
  plots)
• Compare data sets and draw inferences about
  possible relationships
• High School
• Analyze data from various types of studies
• Understand characteristics of well-designed
  studies

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Challenges in Teaching Math and Science

• Some solutions
• Collaborate with those who know
• Work it across
• Use evidence-based practices
• New ideas from general education methods
• Math stories

• The challenges
• Math challenges
• Teaching the concept vs. something else
• Getting beyond participation to learning

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Challenge Upper Level Concepts

• Math concepts
• Slope
• Equivalence
• Sets
• Pythagorean theorem
• Angles
• Area/Perimeter/Volume

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Challenge Learning vs. Participation

• Participation in-
• Math group activity
• Science experiment
• Creating a project

• Learning-
• Processes
• Concepts
• Rules
• Terminology

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Evidence Based Practice- What is it and why use
it?

• Policy
• NCLB challenged schools to use evidence-based
  practice to help students meet standards

• Research
• Researchers began to define what constituted
  evidence-based practice (pre-NCLB to current
  time)
• More that one study
• Quality of research design
• Effect size

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Math Research

• Browder, D. M., Spooner, F., Ahlgrim-Delzell, L.,
  Wakeman, S.Y., Harris, A. (2008). A
  meta-analysis on teaching mathematics to students
  with significant cognitive disabilities.
  Exceptional Children, 74, 407-432.

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From Prior Research

• Task analytic instruction
• Systematic prompting with feedback
• Incorporate assistive technology to promote
  student responding

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Math Equity

• All students, regardless of their personal
  characteristics, backgrounds, or physical
  challenges must have opportunities- 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.
• National Council of Teachers of Mathematics
  (2002)

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Accommodations

• Task-Analytic Instruction
• (Browder, Trela, Jimenez, 2007 Jimenez,
  Browder, Courtade, in press)
• Concrete-Representational-Abstract presentation
  of problem
• (Maccini Hughes, 2000)
• Assistive Technology
• Low tech graphic organizers with manipulatives
• High tech voice output devices, switch access to
  digital graphic organizer

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Touch Math- Elementary

• Began in 1975
• Symbolic representation with the digits quantity
  included using dots.
• Multi sensory approach to math
• Supplemental program typically
• See Example

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Access to Secondary Math

• Algebra- use algebraic expressions to model and
  solve problems
• Geometry- broaden use of coordinate plane and
  spatial organization
• Data Analysis collect, organize, and interpret
  data to solve problems
• Measurement/Numbers and Operations- perform
  operations with real numbers to solve problems
• North Carolina Department of Public Instruction,
  Standard Course of Study Competencies

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Template for Teaching Math Standards

• TASK ANALYSIS
• Task analyze the steps to solve the math problem
• STORY
• Write a story for the math problem
• CONCRETE MANIPULATIVES
• Create a jig or use manipulatives to compensate
  for unlearned math operations
• ASSISTIVE TECHNOLOGY
• Develop student response board or select AT
• TEACH
• Teach the task analysis using systematic
  prompting and feedback until student masters

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Geometry Example

• Read story based problem
• Identify problem statement
• Identify locations needed to solve problem
  (points, line segments, plane)
• Organize locations named in story
• Identify location to solve story problem
• Restate solution in story context
• Trela, Jimenez, Browder. (2008). Teaching to
  the Standards in Math A Literacy-Based Approach
  for Students with Moderate to Severe
  Developmental Disabilities. Verona, WI
  Attainment Co.

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Measurement/Numbers and Operations Example

• Read story-based math problem
• Identify problem statement
• Use Next Dollar Strategy and number line to solve
  problem
• State solution in story context
• Trela, Jimenez, Browder. (2008). Teaching to
  the Standards in Math A Literacy-Based Approach
  for Students with Moderate to Severe
  Developmental Disabilities. Verona, WI
  Attainment Co.

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Data Analysis

Interpreting Organizing Data
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Graphing and Data Display

• Count and record own behavior
• Tally and compare attributes of our class (number
  of boys vs. girls)
• Bar graph for canned food drive

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The Language of Data Analysis

• Introduce the Y axis, This is the Y axis, it
  runs vertical (up and down.)
• Introduce the X axis,
• Common Terms
• Votes
• Most/least
• Winner
• Data

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Measurement

• One More Than Strategy

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Measurement

• Money
• Time
• Temperature
• Distance
• Length
• Weight

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MONEY management

• Concern for teachers parents
• Pay too much and lose money.
• Still not able to count out coins
• Takes too long.
• VERY IMPORTANT SKILL

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Teaching Idea One More Than strategy

• Next dollar amount to make a purchase
• Denny Test, 1995

• Price is 6.25
• Repeat first number six
• Count out six dollars
• And one more is

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Story Graphic Organizer Task Analysis
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Student Learning
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Math Work

• More examples from Math Work
• Geometry
• Data Analysis
• Next Dollar
• Notebooks for Data Analysis and Geometry

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Break
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Remember work it across?

• Lets try another
• Math angles
• 3 parts
• What materials will you need to present?
• What do you expect students to do?
• How will the concept be taught?
• Remember you work by a students symbolic levels
  across the page starting with typically
  developing students to students with significant
  cognitive disabilities who use abstract symbolic
  to concrete symbolic to presymbolic.
• Save on a eboard as group works across.