karen b. rogers [email protected] developing math talent in highly capable learners in...
TRANSCRIPT
A Quote
Karen Rogers, 2012
We all too often hear about students who are ‘bored to tears’ in math classes, their boredom stemming from frustration with the underchallenging mathematics curricula in our schools. This frustration is similar to the frustration and sense of helplessness children express when they are unaware of the destination of a trip. Mathematically talented students entering school expect to start on an exciting educational journey that will take them to their destination of talent development. However, their journey seems to go nowhere because neither the destination nor the road are readily apparent. Although educators are sincere in their commitment as teachers, their training typically has not included information about teaching mathematically talented children. Educators, as well as parents, are unsure of the educational destination of gifted students, and, for that reason they are not sure of the path to that destination. The result is a sense of helplessness and a need for guidance.
(Assouline & Lupkowski-Shoplik, 2005, p. xv)
The 12 Myths About Mathematically Talented Students
Karen Rogers, 2012
Only students identified for a highly capable program are mathematically talented
Results from standardized, year-level testing are sufficient for identifying the mathematically talented
Highly capable students respond equally well to the same curriculum as the general population
Students whose pace of instruction is accelerated cannot cover each section of the curriculum and will have gaps in their math background
Students who are mathematically talented demonstrate mastery of a topic by earning 100% on tests --including pre-tests
Mathematically talented students are computation whizzes
The 12 Myths About Mathematically Talented Students
Karen Rogers, 2012
Mathematically talented students cannot be identified until grades 9-12
Early ripe, early rotThe best option for mathematically able elementary and middle school students is enrichment
The best way to challenge mathematically talented students is to have them skip a grade and study the regular curriculum in next higher regular classroom
If mathematically able students study mathematics at an accelerated pace, they will run out of math curriculum before they get to 9th grade
Students --even those who are mathematically talented --should not study algebra until 8th or 9th grade
Talking Around the Edges of Research-Supported Maths Practices
Karen Rogers, 2012
Instructional ManagementGrouping Strategies with Sizable Academic Effects in MathFull-time gifted group, class, stream ES = .49Cluster group ES = .52Like performing cooperative dyad/group ES = .28Within class grouping ES = .34Regrouping for specific instruction ES = .79
Individualization Strategies with Sizable Academic EffectsCurriculum compacting ES = .83Cross-grading ES = .46Multi-age class ES = .38Mentorship ES = .59Credit by testing out, prior learning ES = .57
Talking Around the Edges of Research-Supported Maths Practices
Karen Rogers, 2012
Instructional Management Strategies, Continued…Acceleration Strategies with Sizable Academic EffectsGrade skipping ES = .49Vertical grouping ES = .40Subject acceleration ES = .57Dual/concurrent enrollment ES = .29Early admission to university ES = .30
Instructional Delivery StrategiesTeaching to talented students’ learning preferences for:Independent learningProject-based learning on their ownProgrammed instructional materialsLearning with a like-ability peer
Talking Around the Edges of Research-Supported Maths Practices
Karen Rogers, 2012
Instructional Delivery Strategies, ContinuedTeaching for qualitative differences in content and skill acquisition, such asLearning rate (8 times faster than slowest learners)Degree of practice, review (2-3 reviews beyond mastery)
Whole-to-part scaffold for math concepts learning Concept teachingTime for reflection/analysis, application
Curriculum Differentiation StrategiesModifications of content
Abstraction at an earlier ageComplexity/ sophisticationStudy of people, Methods of inquiryTelescoping of content
Talking Around the Edges of Research-Supported Maths Practices
Karen Rogers, 2012
Curriculum Differentiation StrategiesModifications of Process
Higher order thinking (analysis, evaluation, synthesis)
Open-endedness (paradox, analogy, visualisation, ambiguity)
Problem-Based and Inquiry approaches to math learning
Value of group productionProof and reasoning
The Three (or More) Sets of Mathematics Learners We Should Find in Bainbridge
Karen Rogers, 2012
“The General” # ______These students are ready and able to accomplish the syllabus outcomes of their year level; may or may not be motivated to learn math; are good listeners and can follow procedural directions, but may not have confidence when asked to apply their math learning
“The Mathematically Able” # ______These students are 1 to 1 1/2 years ahead of their grade level’s syllabus outcomes, may or may not be motivated to learn math, can follow procedural directions and have confidence in their ability to apply math learning
“The Mathematically Talented” # ______These students are 1 1/2 to several years ahead of their grade level’s syllabus outcomes ,reason in qualitatively different ways about mathematical ideas and concepts, are motivate to learn math, can follow procedural directions, especially if presented at a rapid pace, and have confidence in their ability to apply math learning
Mathematical Needs of “The General” Population of Math Learners
Karen Rogers, 2012
Compacting so that they only learn what they do not already know
Enrichments that broaden or deepen their mathematical understanding (often found in the text adopted by the district at the end of each chapter or unit)
Fun with math, but incorporating practice into the fun
Spiral approach to concept learningProblem solving opportunities and applications with every concept or skill taught
Mathematical Needs of “The Mathematically Able” Population
Karen Rogers, 2012
Extensive compactingSome “general population” opportunities
Little spiraling of concepts and skills
Content presentation 2 times faster than “general” class pace
Cut down number of revisions for concepts to less than half those provided for “the general” math students
Mathematical Needs of “The Mathematically Talented”
Karen Rogers, 2012
Place in like performing classesPresent whole concept up front in its entirety and then go to the parts that make up the whole (e.g., quadratic equations concept)
No spiraling of math concepts and procedures; eliminate almost all practices of concepts once mastered (extensive compacting
Accelerated pacing (2-3 times faster than “general” class pace)
Begin at their current performance level and expect to accomplish 2 or more years’ curriculum per year
Provide opportunities for competition through math contests, Olympiads, etc.
Real world applications of advanced math conceptsSome enrichments when group feels they are “moving too fast”
Mathematical Needs of “The Most Mathematically Talented”
Karen Rogers, 2012
Consider “individualizing” math instruction (e.g., Josh Zucker)
MentorshipsPresent “whole” concept in a few words, then let student work, and give a few more words if first ones didn’t do it!
Distributed practice of concept as it is being learned
Subject acceleration with goal of at least 2 years’ math accomplished for each year in school (repeated!!)
For Further Reading
Karen Rogers, 2012
Assouline, S., & Lupkowski-Shoplik, A. (2005). Developing math talent: A guide for educating gifted and advanced learners in math. Waco, TX: Prufrock Press.
Bartovitch, K. G., & Mezynski, K. (1981). Fast-paced precalculus mathematics for talented junior high students: Two recent SMPY programs. Gifted Child Quarterly, 24, 73-80.
Benbow, C. P., & Lubinski, D. (1996). Intellectual talent: Psychometric and social issues. Baltimore, MD: Johns Hopkins Press.
For Further Reading (2)
Karen Rogers, 2012
Kaizer, C., & Shore, B. M. (1995). Strategy flexibility in more and less competent students on mathematical word problems. Creativity Research Journal, 8(1), 113-118.
Krutetskii, V.. A. (1976). The psychology of mathematical abilities in schoolchildren. Chicago, IL: University of Chicago Press.
Lupkowski-Shoplik, A., & Assouline, S. G. (1993). Evidence of extreme mathematical precocity: Case studies of talented youths. Roeper Review, 16, 144-151.
For Further Reading (3)
Karen Rogers, 2012
Malpass, J. R., O’Neil, H. F., Jr., & Hocevar, D. (1999). Self-regulation, goal orientation, self-efficacy, worry, and high-stakes math achievement for mathematically gifted high school students. Roeper Review, 21, 281-288.
Mason, M. M., & Moore, S. D. (1997). Assessing readiness for geometry in mathematically talented middle school students. Journal of Secondary Gifted Education, 8, 105-110.
Mills, C. J., Ablard, K. E., & Lynch, S. J. (1992). Academically talented students’ preparation for advanced-level course work after individually-paced precalculus class. Journal for the Education of the Gifted, 16, 3-17.
For Further Reading (4)
Karen Rogers, 2012
Ravaglia, R. Suppes, P., Stillinger, C., & Alper, T. M. (1995). Computer-based mathematics and physics for gifted students. Gifted Child Quarterly, 39, 7-13.
Sheffield, L. J. (1994). The development of gifted and talented mathematics students and the National Council of Teachers of Mathematics standards. Storrs, CT: National Research Center on the Gifted and Talented.
Shore, B. M. (2000). Metacognition and flexibility: Qualitative differences in how gifted children think. In R. C. Friedman & B. M. Shore (Eds.), Talents unfolding: Cognition and development (pp. 167-187). Washington, DC: American Psychological Association.