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Chapter 13

Chapter 13. Reaching Exceptional Learners. Geometrical & Spatial Reasoning. Mathematical Routine: Shape puzzles. Conversation in Mathematics. Discuss how the lesson was accessible to all the students in the class. What did the teacher do to differentiate the lesson?. Exceptionality.

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Chapter 13

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  1. Chapter 13

  2. Reaching Exceptional Learners Geometrical & Spatial Reasoning

  3. Mathematical Routine:Shape puzzles

  4. Conversation in Mathematics • Discuss how the lesson was accessible to all the students in the class. What did the teacher do to differentiate the lesson?

  5. Exceptionality • Pedagogy

  6. How We Learn

  7. Access and Equity • Equal access versus identical instruction • High expectations • Providing modifications for students with an IEP versus unidentified students • Importance curriculum and instruction plays • Teachers of students of special needs must be familiar with the grade level curriculum and practices of general education students

  8. Role of Assessment • Individual assessments provide the most information • Modification of assessments for children with language difficulties (are we testing language or math?)

  9. Differentiating Instruction

  10. Advanced Learners or Gifted Students

  11. Struggling Learners

  12. Specified Learning Disabilities & ADD/ADHD • For a child to be considered having a specific learning disability, there must be a significant gap between his intelligence and achievement in one ore more of the following areas: • Oral Expression • Listening comprehension • Written expression • Basic reading skills • Reading comprehension • Math calculations • Math reasoning

  13. Possible Barriers • Memory • Self-regulation • Visual procession • Language processing • Related academic skills • Motor skills

  14. Removing Barriers

  15. Dyscalculia • Disorder in calculation • May perform inconsistently from one year to the next - quality of instruction is critical! • May perform at grade level in other subject areas, such as reading.

  16. Students with Severe Learning Needs • All students need to pass through the same steps: concrete/semi-concrete/abstract. • They basically need to make the same generalizations, but they may take much longer to do so.

  17. Geometric & Spatial Reasoning • Content

  18. The Four Geometric Systems • Topological Geometry • Transformational Geometry • Euclidean Geometry • Coordinate Geometry

  19. Spatial Reasoning • A combination of Topological and Transformational Geometry • symmetry • flip • slide • rotation (rotational point outside the shape; rotational point inside the shape)

  20. Tessellations

  21. Euclidean Geometry(two and three-dimensional figures) • Polygon sort • Three-dimensional solids (always use actual solids before introducing pictures - each pair of children need to be able to manipulate their own set of solids).

  22. Coordinate Geometry • The Cartesian Plane • Ordered Pairs • Translations

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