Special Education Teacher Preparation

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Special Education Teacher Preparation

• Inclusive Education, Intensive, Personalized
  Education, and Mathematics Instruction

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Quick survey

• Pick one
• I like mathematics
• I love mathematics
• I can live with it or without it
• I try to avoid mathematics

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Special Educators CCSS

• What do special educators need to know in the
  context of
• Common Core State Standards Inclusive Education?

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An Attempt at an Answer

1. Goals of the Common Core in Mathematics
2. FRACTIONS (teacher understanding and proficiency
   must precede improved instruction)
3. Other aspects of algebra readiness
4. Research base on effective instruction (and the
   gaping holes)
5. RtI in mathematics strengths and vulnerabilities

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Goals intent of Common Core in Mathematics (in
a nutshell)

• Focus on fewer Mathematical Ideas and Procedures
  in depth
• Why? To ensure understanding as well as
  proficiency fluency
• Why? Understanding of arithmetic is key to
  success in algebra more advanced mathematics
• Why? In part mathematics proficiency involves
  higher levels of abstraction abstracting out
• Why else more depth time on each topic? Mastery
  proficiency criticalendless spiraling not good

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Goals intent of Common Core in Mathematics
(cont.)

• Capitalize on insight from cognitive research
  (Rittle-Johnson Siegler, 2001) and working
  knowledge of mathematicians
• Conceptual procedural knowledge develop in a
  reciprocal fashion
• Problem solving must be integrated into the mix
  as it enriches both (provides meaning to the
  computational procedural work, provides a logic
  for why things are done)

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Goals intent of Common Core in Mathematics
(cont.)

• Coherence
• Includes demonstrating connections between the
  various ideas in geometry arithmetic/algebra
  between arithmetic algebra
• Involves allowing students to solve problems, at
  times, in a variety of ways
• Precision of mathematical language

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Key Issue

• Special education students must work on all these
  fronts. Older belief that practice on computation
  is the only means to teach does not address
  Common Core standards and will be increasingly
  frowned on.

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Fractions

• Many American teachers do not know much about
  fractions (Ball, 1990 Ma, 1999)
• Many teachers struggle with both solving fraction
  problems explaining, for example, what division
  of a fraction is

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Fractions (cont.)

• Many teachers do not have automatic access to
  various common interpretations of fractions
• Part of whole
• Parts of a whole (e.g. 7/3)
• Parts of a set
• A specific point on a number line (measurement
  implications)
• Equivalent to division

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Sense of Betrayal

• Students learn fractions as part of a whole in
  grade 3. Example
• Half of the class went to museum the first day.
  There are 18 students in the class. How many
  went?
• Put 9/4 on a number line

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Teaching fractions

• To teach fractions well, teachers must understand
  the mathematics
• Special education students often are unlikely to
  intuit all the interpretations nuances

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Minimum fraction Knowledge for special educators

• At a minimum, special educators should know the
  interpretations of fractions
• part(s) of units such as circles, pizzas,
  buildings
• parts of a set
• equivalent to division
• a point on a number line determined by numerator
  denominator
• Achievable objectives through PD work with
  mathematics educators or texts

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Algebra readiness critical foundations

• Properties of Arithmetic Multiplication
• Commutative
• Associative Property
• Distributive Property
• Fractions
• It is beginning of road to abstraction. Example
  one number but looks like two numbers (e.g. 4/7)
• Word Problems (path to abstraction)
• Fact Fluency (to be able to understand
  mathematics)

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What else about algebra readiness?

• Gateway coursetrue for both algebra 1 2
• Both require a full year of successful navigation
  of abstractions
• Universal graduation requirement high failure
  rates

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Overview of relevant research for mathematics
intervention sources

• Gersten, R., Beckman, S., Clarke, B., Foegen, A.,
  Marsh, L., Star, J. R., Witzel, B., Dimino, J.,
  Jayanthi, M., Newman-Gonchar, R., Monahan, S.,
  Scott, L. (2009). Assisting students struggling
  with Mathematics Response to intervention
  (RtI) for elementary and middle schools (NCEE
  2009-4060). Washington, DC National Center for
  Education Evaluation and Regional Assistance,
  Institute of Education Sciences, U.S. Department
  of Education.
• Gersten, R., Chard, D. J., Jayanthi, M., Baker,
  S. K., Morphy, P., Flojo, J. (2009).
  Mathematics Instruction for Students with
  Learning Disabilities A Meta-Analysis of
  Instructional Components. Review of Educational
  Research, 79, 1202-1242.
• Also see Center on Instruction website at
  http//www.centeroninstruction.org/
• Or google Center on Instruction, look for
  mathematics
• (Note may be removed Sept. 30, 2012)

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IES Practice Guide
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Levels of evidence
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(No Transcript)
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Major Challenges of rti in mathematics

• Must include foundational skills relevant to
  grade level content
• e.g. division for fractions, fractions for
• simple linear equations
• Common Core Progressions are excellent source
• http//ime.math.arizona.edu/progressions/
• Interventions must include activities that cover
  mathematical ideas but use some of the empirical
  base on effective instruction for at- risk
  learners

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Rti in mathematics a few contemporary issues

• Screening measures strongest in K 1
• In my view, grades 3 up need rethinking for
  both screening progress monitoring

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why?

• Do they measure what Common Core sets as
  proficiency (understanding, problem solving,
  representation modeling of mathematical ideas)?
• What do grades 4 to 8 screening measures add
  above beyond prior years state assessment? Key
  question to ask

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Why?

• Will interventionists teach to the test?
• i.e. if progress monitoring measures focus
  heavily on easy to score items (computations,
  easy problems) will this determine content of
  intervention?
• Given technology advances with item response
  theory, can progress monitoring provide
  diagnostic information placement information?

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Thank you