graphic organizers

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Graphic Organizers

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Graphic Organizers (GOs)

A graphic organizer is a tool or process to build word knowledge by relating similarities of meaning to the definition of a word. This can relate to any subject—math, history, literature, etc.

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Why are Graphic Organizers Important?

• GOs connect content in a meaningful way to help students gain a clearer understanding of the material (Fountas & Pinnell, 2001, as cited in Baxendrall, 2003).

• GOs help students maintain the information over time (Fountas & Pinnell, 2001, as cited in Baxendrall, 2003).

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Graphic Organizers:

• Assist students in organizing and retaining information when used consistently.

• Assist teachers by integrating into instruction through creative

approaches.

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Graphic Organizers:

• Heighten student interest

• Should be coherent and consistently used

• Can be used with teacher- and student- directed approaches

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Coherent Graphic Organizers

1. Provide clearly labeled branch and sub branches.

2. Have numbers, arrows, or lines to show the connections or sequence of events.

3. Relate similarities.

4. Define accurately.

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How to Use Graphic Organizers in the Classroom

• Teacher-Directed Approach

• Student-Directed Approach

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Teacher-Directed Approach

1. Provide a partially complete GO for students

2. Have students read instructions or information

3. Fill out the GO with students4. Review the completed GO5. Assess students using an incomplete

copy of the GO

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Student-Directed Approach• Teacher uses a GO cover sheet with

prompts– Example: Teacher provides a cover sheet

that includes page numbers and paragraph numbers to locate information needed to fill out GO

• Teacher acts as a facilitator• Students check their answers with a

teacher copy supplied on the overhead

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Strategies to Teach Graphic Organizers

• Framing the lesson• Previewing• Modeling with a think aloud• Guided practice• Independent practice• Check for understanding• Peer mediated instruction• Simplifying the content or structure of the GO

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Types of Graphic Organizers

• Hierarchical diagramming

• Sequence charts

• Compare and contrast charts

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A Simple Hierarchical Graphic Organizer

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A Simple Hierarchical Graphic Organizer - example

Algebra

Calculus Trigonometry

Geometry

MATH

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Another Hierarchical Graphic Organizer

Category

Subcategory Subcategory Subcategory

List examples of each type

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Hierarchical Graphic Organizer – example

Algebra

Equations Inequalities

2x +

3 =

15

10y

= 10

04x

= 1

0x -

6

14 < 3x + 7

2x > y

6y ≠ 15

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Category

What is it?Illustration/Example

What are some examples?

Properties/Attributes

What is it like?

Subcategory

Irregular set

Compare and Contrast

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Positive Integers

Numbers

What is it?Illustration/Example

What are some examples?

Properties/Attributes

What is it like?

Fractions

Compare and Contrast - example

Whole Numbers Negative Integers

Zero

-3, -8, -4000

6, 17, 25, 100

0

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Venn Diagram

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Venn Diagram - example

Prime Numbers

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7 11 13

Even Numbers

4 6 8 10

Multiples of 3

9 15 21

32

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Multiple Meanings

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Multiple Meanings – example

TRI-ANGLES

Right Equiangular

Acute Obtuse

3 sides

3 angles

1 angle = 90°

3 sides

3 angles

3 angles < 90°

3 sides

3 angles

3 angles = 60°

3 sides

3 angles

1 angle > 90°

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Series of Definitions

Word = Category + Attribute

= +

Definitions: ______________________

________________________________

________________________________

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Series of Definitions – example

Word = Category + Attribute

= +

Definition: A four-sided figure with four equal sides and four right angles.

Square Quadrilateral 4 equal sides & 4 equal angles (90°)

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Four-Square Graphic Organizer

1. Word: 2. Example:

3. Non-example:4. Definition

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Four-Square Graphic Organizer – example

1. Word: semicircle 2. Example:

3. Non-example:4. Definition

A semicircle is half of a circle.

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Matching Activity

• Divide into groups

• Match the problem sets with the appropriate graphic organizer

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Matching Activity

• Which graphic organizer would be most suitable for showing these relationships?

• Why did you choose this type?

• Are there alternative choices?

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Problem Set 1

Parallelogram Rhombus

Square Quadrilateral

Polygon Kite

Irregular polygon Trapezoid

Isosceles Trapezoid Rectangle

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Problem Set 2

Counting Numbers: 1, 2, 3, 4, 5, 6, . . .

Whole Numbers: 0, 1, 2, 3, 4, . . .

Integers: . . . -3, -2, -1, 0, 1, 2, 3, 4. . .

Rationals: 0, …1/10, …1/5, …1/4, ... 33, …1/2, …1

Reals: all numbers

Irrationals: π, non-repeating decimal

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Problem Set 3Addition Multiplication a + b a times b a plus b a x b sum of a and b a(b)

ab

Subtraction Divisiona – b a/ba minus b a divided by ba less b b) a

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Problem Set 4Use the following words to organize into categories and subcategories of

Mathematics:NUMBERS, OPERATIONS, Postulates, RULE, Triangles, GEOMETRIC FIGURES, SYMBOLS, corollaries, squares, rational, prime, Integers, addition, hexagon, irrational, {1, 2, 3…}, multiplication, composite, m || n, whole, quadrilateral, subtraction, division.

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Graphic Organizer Summary

• GOs are a valuable tool for assisting students with LD in basic mathematical procedures and problem solving.

• Teachers should:– Consistently, coherently, and creatively

use GOs.– Employ teacher-directed and student-

directed approaches.– Address individual needs via curricular

adaptations.

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Resources

• Maccini, P., & Gagnon, J. C. (2005). Math graphic organizers for students with disabilities. Washington, DC: The Access Center: Improving Outcomes for all Students K-8. Available athttp://www.k8accescenter.org/training_resources/documents/MathGraphicOrg.pdf

• Visual mapping software: Inspiration and Kidspiration (for lower grades) at http:/www.inspiration.com

• Math Matrix from the Center for Implementing Technology in Education. Available at http://www.citeducation.org/mathmatrix/

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Resources

• Hall, T., & Strangman, N. (2002).Graphic organizers. Wakefield, MA: National Center on Accessing the General Curriculum. Available at http://www.cast.org/publications/ncac/ncac_go.html

• Strangman, N., Hall, T., Meyer, A. (2003) Graphic Organizers and Implications for Universal Design for Learning: Curriculum Enhancement Report. Wakefield, MA: National Center on Accessing the General Curriculum. Available at http://www.k8accesscenter.org/training_resources/udl/GraphicOrganizersHTML.asp

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How These Strategies Help Students Access Algebra

• Problem Representation

• Problem Solving (Reason)

• Self Monitoring

• Self Confidence

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Recommendations:

• Provide a physical and pictorial model, such as diagrams or hands-on materials, to aid the process for solving equations/problems.

• Use think-aloud techniques when modeling steps to solve equations/problems. Demonstrate the steps to the strategy while verbalizing the related thinking.

• Provide guided practice before independent practice so that students can first understand what to do for each step and then understand why.

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Additional Recommendations:

• Continue to instruct secondary math students with mild disabilities in basic arithmetic. Poor arithmetic background will make some algebraic questions cumbersome and difficult.

• Allot time to teach specific strategies. Students will need time to learn and practice the strategy on a

regular basis.

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Wrap-Up

• Questions

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Closing ActivityPrinciples of an effective lesson:Before the Lesson:• Review • Explain objectives, purpose, rationale for learning the

strategy, and implementation of strategyDuring the Lesson:• Model the task• Prompt students in dialogue to promote the

development of problem-solving strategies and reflective thinking

• Provide guided and independent practice• Use corrective and positive feedback

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Concepts for Developing a Lesson

Grades K-2• Use concrete materials to build an understanding of equality

(same as) and inequality (more than and less than)• Skip countingGrades 3- 5• Explore properties of equality in number sentences (e.g., when

equals are added to equals the sums are equal)• Use physical models to investigate and describe how a change

in one variable affects a second variableGrades 6-8• Positive and negative numbers (e.g., general concept, addition,

subtraction, multiplication, division)• Investigate the use of systems of equations, tables, and graphs

to represent mathematical relationships