2012 osep project directors conference washington, dc july 24, 2012 russell gersten, ph.d. director,...
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2012 OSEP Project Directors ConferenceWashington, DC
July 24, 2012
Russell Gersten, Ph.D.Russell Gersten, Ph.D.Director, Instructional Research GroupDirector, Instructional Research Group
Professor Emeritus, University of OregonProfessor Emeritus, University of Oregon
Inclusive Education, Intensive, Personalized Education, and
Mathematics Instruction
Pick one:1. I like mathematics2. I love mathematics3. I can live with it or without it4. I try to avoid mathematics
What do special educators need to know in the context of
Common Core State Standards & Inclusive Education?
1. Goals of the Common Core in Mathematics
2. FRACTIONS (teacher understanding and proficiency must precede improved instruction)
3. Other aspects of algebra readiness4. Research base on effective
instruction (and the gaping holes)5. RtI in mathematics: strengths and
vulnerabilities
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 critical…endless spiraling not good
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)
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
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.
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
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
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
To teach fractions well, teachers must understand the mathematics
Special education students often are unlikely to intuit all the interpretations & nuances
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
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)
Gateway course…true for both algebra 1 & 2
Both require a full year of successful navigation of abstractions
Universal graduation requirement & high failure rates
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)
Must include foundational skills relevant to grade level content
e.g. division for fractions, fractions for simple linear equations
Common Core Progressions are excellent sourcehttp://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
Screening measures strongest in K & 1
In my view, grades 3 & up need rethinking for both screening & progress monitoring
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
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?