12 th International Congress on Mathematical Education Program Name XX-YY-zz (pp. abcde-fghij) 8 July 15 July, 2012, COEX, Seoul, Korea (This part is for LOC use only. Please do not change this part.) MATHEMATICALLY GIFTED, TALENTED, OR PROMISING: WHAT DIFFERENCE DOES IT MAKE? Linda Jensen Sheffield, Ph. D. Regents Professor Emerita, Northern Kentucky University Sheffield@nku.edu Science, Technology, Engineering, and Mathematics (STEM) are critical to the economy, security, and future of the world. We need students who will become adults who understand the complexities of a technological world, who ask the essential questions to safeguard that world, and who will become the leaders, researchers and innovators in the STEM fields of the future. Too often, in the United States, these students go unrecognized, unmotivated, and under-developed at a time when they are most vital. This paper discusses whether the way we historically define these future STEM leaders and innovators has an effect upon their growth and development. Key Words: gifted, talented, promising INTRODUCTION Over ten years ago, I approached administrators in a local school that was habitually one of the lowest performing on statewide mathematics tests. We had a grant to serve mathematically gifted students, and I wanted to offer them a chance to participate. The response was, We don t have any gifted students in this school. What do you want us to do create them? In pondering this question, I thought yes, as a matter of fact, that was exactly what I wanted to do. I wanted to be able to create students who are gifted in mathematics regardless of their current performance. Teachers and administrators were willing to try, so we selected 20 of the 50 second grade students in the school to take part in our gifted math program in third grade. At the beginning of third grade as part of the baseline data, we gave the students the mathematics section of the Iowa Test of Basic Skills (ITBS) and found the average of the group on the mathematics section was at the 23 rd percentile, certainly not a typical gifted population. After a year in the program, Project M 3 : Mentoring Mathematical Minds, the average of the group on the math section of the ITBS had risen to the 71 st percentile. Test scores were still not at the level to be expected from gifted students, but they did indicate that many more than the top 5% of students could benefit from an engaging, rigorous mathematics program. It brought me back to the question of whether mathematical giftedness was something to be identified or something to be created. This paper begins with a look at a bit of the history of policies and definitions related to mathematically gifted and talented students in the United States. These lead to a abcde
number of questions about whether mathematical giftedness is a pre-existing condition or something to be produced and how conceptions of giftedness affect policies and practices on the local, state, national, and international levels. THE RISE OF IQ TESTS Over 100 years ago in 1905, Alfred Binet, a French psychologist, invented the first usable intelligence test. Binet stressed that intelligence is malleable rather than fixed, influenced by the environment, subject to variability and not generalizable. However, in many parts of the United States today, the Stanford-Binet or another IQ test continues to be the main means to identify students for gifted and talented programs. A BRIEF SELECTIVE HISTORY IN THE UNITED STATES Since the late 1900s, organizations in the United States such as the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), the National Association for Gifted Children (NAGC) and the United States Department of Education (US DoE) have held a variety of positions on the definition and status of gifted and talented education, specifically in the area of mathematics. The following are just a few of these. 1972 The Marland report to the United States Congress notes, Gifted and Talented children are, in fact, deprived and can suffer psychological damage and permanent impairment of their abilities to function well which is equal to or greater than the similar deprivation suffered by any other population with special needs served by the Office of Education. (pp. xi-xii) The current (2011) federal definition of gifted students, which is located in the Elementary and Secondary Education Act, is based on the Marland report and is Students, children, or youth who give evidence of high achievement capability in areas such as intellectual, creative, artistic, or leadership capacity, or in specific academic fields, and who need services and activities not ordinarily provided by the school in order to fully develop those capabilities. States are not required to use this definition, although many states do base their definition of gifted students on this federal definition. Continuing to the present time, almost all decisions about gifted and talented education are made at the state and local level. 1980 NCTM publishes the Agenda for Action and states, The student most neglected, in terms of realizing full potential, is the gifted student of mathematics. Outstanding mathematical ability is a precious societal resource, sorely needed to maintain leadership in a technological world. (p. 18) 1983 NCTM publishes a position statement on Vertical Acceleration and states, In almost all cases, a student would benefit more from a program of horizontal acceleration (enrichment) than from one of vertical acceleration. 1986 NCTM publishes a position statement on Provisions for Mathematically Talented and Gifted Students and states, All students deserve the opportunity to achieve their full potential; talented and gifted students in mathematics deserve no less. Abcde+3 ICME-12, 2012
1987 NCTM publishes Providing Opportunities for the Mathematically Gifted K 12, noting, Gifted children have become a neglected minority in our schools. (p. 3) 1994 The US DoE initiates the Jacob K. Javits Gifted and Talented Student Education Act to award grants to state and local education agencies, institutions of higher education, and other public and private agencies and organizations. These grants help talented students in elementary and secondary schools develop their abilities and reach for high levels of achievement. 1995 NCTM appoints a Task Force on Mathematically Promising students. This Task Force notes, Students with mathematical promise are those who have the potential to become the leaders and problem solvers of the future. We see mathematical promise as a function of ability, motivation, belief, and experience or opportunity. The task force goes on to state that mathematical ability, motivation to excel in mathematics, beliefs about ones capacity to be successful in mathematics, and the opportunity to experience real mathematical problem solving and problem posing are all variables that can and must be maximized in order to help students develop to their fullest mathematical potential. 1999 NCTM publishes Developing Mathematically Promising Students with 34 contributions from around the world that explore the possibilities for recognition and nurture of K 12 mathematically promising students. 2003 NCSM publishes its first volume in the Monograph Series, Activating Mathematical Talent, to stress the importance of recognizing and activating promising students mathematical talent. 2006 The National Association for Gifted Children (NAGC) Mathematics and Science Task Force is appointed with a charge to make connections with leading mathematics and science content, mathematics and science education and other organizations to develop and support research, policy statements, and resources for mathematically and scientifically promising students, their families and their educators. 2008 Foundation for Success: The Final Report of the National Mathematics Advisory Panel notes that, When children believe that their efforts to learn make them smarter, they show greater persistence in mathematics learning. (p. xx) 2009 Equity All Means ALL, NCTM Focus of the Year includes special needs students, English-language learners, students of all races, ethnicities and socio-economic status, and promising students. 2009 2010 The Common Core State Standards Initiative, a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO), develops the Common Core State Standards in Mathematics and English Language Arts. Forty-six states and Washington, DC subsequently adopt these Standards in mathematics. Very little mention is made of advanced, accelerated or gifted students. 2010 NCTM publishes jointly with NAGC and the Association for Middle Level Education (AMLE), The Peak in the Middle: Developing Mathematically Gifted Students in the Middle Grades, noting that the middle grades (grades 6 8) are a ICME-12, 2012 abcde+2
crucial time for capturing the interest and imagination and developing the potential of mathematically promising students. 2010 The National Science Board releases Preparing the Next Generation of STEM Innovators: Identifying and Developing our Nation s Human Capital with several recommendations for research and policy actions 2011 All funding ends for the Jacob K. Javits Gifted and Talented Student Education Act. The U. S. has $0 for federal programs for gifted and talented students. 2011 The NCSM approves a position statement on Improving Student Achievement by Expanding Opportunities for Mathematically Promising Students stating, Significant improvement in mathematics achievement over a sustained period requires addressing equity and expanding opportunities for our most mathematically promising students. As with all students, these special needs students deserve a least restrictive learning environment that lifts the ceiling, fuels their creativity and passions, pushes them to make continuous progress throughout their academic careers, and supports them in the fulfillment of their personal potential. In this competitive, technological world, this development of personal potential has the added benefit of maximizing the talents and abilities of those students who have the greatest potential to lead us into the future. 2011 The president of NAGC suggests Taking a Bold Step in her presidential address at the annual conference. She suggests making talent development rather than giftedness the major unifying concept with an emphasis on giftedness as a state one grows into and acquires as a result of learning and achievement. 2012 NAGC publishes Using the Common Core State Standards in Mathematics with Advanced and Gifted Learners to provide classroom teachers and administrators examples and strategies to implement the Common Core State Standards (CCSS) for advanced learners at all stages of development in K-12 schools. DISCUSSION In the more than 100 years since the publication of the first IQ test, the concept of giftedness in the United States has come to be regarded as a fixed trait that can be identified through testing and other identification measures. In a similar manner, mathematically gifted students have often been identified using results from a paper-and-pencil test. In 1995, NCTM suggested using the term promising rather than gifted, purposely broadening the definition to include a much greater range of students. Promise was defined to be something that could change and grow, consisting of a number of variables that could be maximized including ability, motivation, belief, and experience or opportunity. In 2006, Dweck published Mindset: The New Psychology of Success describing her research that found that middle grades students with a growth mindset that saw intelligence as malleable rather than fixed were much more successful in middle grades mathematics than students with a fixed mindset. Abcde+3 ICME-12, 2012
When Paula Olszewski-Kubilius, the current president of the National Association for Gifted Children, suggested that NAGC take a bold step in redefining what it means to be gifted, it again brought up the question of the correlation/effect of the label chosen as well as the definition of what it means to be mathematically gifted, talented, promising, creative, innovative, etc. on the creation of these students and the policies and procedures that influence the development of future STEM innovators. CONCLUSIONS The history of mathematics education for gifted, talented, creative, and promising students in the United States has been spotty at best. With an ever-increasing need for innovation in the STEM fields, the importance of developing gifted and creative mathematics students has never been more critical. The following are a few questions that I would like to see addressed by the field. Is it time to change from a focus on mathematically gifted as an unchanging, identifiable trait to a focus on the development of mathematical talent? Is mathematical giftedness an end product of nurture and development rather than a pre-existing, ever-present state? Does it matter how we identify mathematical giftedness or even whether we identify it? Does the use of the term mathematically gifted, mathematically promising, or the development of mathematical talent affect the teaching, learning, number and level of top mathematics students? How do educators and researchers in other countries define, identify, and develop their most outstanding mathematics students? Can we create gifted mathematics students, and thus the outstanding, innovative mathematicians and STEM leaders of the future? Can we afford not to? References Binet, A. (1909). Les idées modernes sur les enfants. Paris: Flammarion. (Published in English as Modern ideas about children. Menlo Park: CA: Suzanne Heisler, 1984) Council of Chief State School Officers (CCSSO) (2010). Common Core State Standards Initiative. Retrieved April 3, 2012 from www.corestandards.org/ Dweck, C. (2006). Mindset: the new psychology of success. New York: Random House. Gavin, M. K., Sheffield, L. J., & Chapin, S. (2011). Math innovations: Moving math forward through critical thinking and exploration. Dubuque, IA: Kendall Hunt. Marland, S. P., Jr. (1972). Education of the gifted and talented: Report to the Congress of the United States by the U.S. Commissioner of Education and background papers ICME-12, 2012 abcde+2
submitted to the U.S. Office of Education, 2 vols. Washington, DC: U.S. Government Printing Office. National Association for Gifted Children (In press). Using the Common Core State Standards in Mathematics with advanced and gifted learners. Washington, DC: NAGC. National Council of Supervisors of Mathematics (2011). Improving student achievement by expanding opportunities for mathematically promising students. NCSM Position Statement. Denver, CO: NCSM. National Council of Teachers of Mathematics (2010). The peak in the middle: Developing mathematically gifted students in the middle grades. Edited by Mark Saul, Susan Assouline and Linda Sheffield. Reston, VA: NCTM. ----------- (1999). Developing mathematically promising students. Edited by Linda Sheffield. Reston, VA: NCTM. ------------ (1995). Report of the NCTM Task Force on Promising Students. Reston, VA: NCTM. ----------- (1987). Providing opportunities for the mathematically gifted K-12. Edited by Peggy House. Reston, VA: NCTM. ----------- (1986). A position statement on provisions for mathematically talented and gifted students. Reston, VA: National Council of Teachers of Mathematics. ---------- (1983). A position statement on vertical acceleration. Reston, VA: NCTM. ---------- (1980). An agenda for action: Recommendations for school mathematics of the 1980s. Reston, VA: NCTM. National Science Board. (2010). Preparing the next generation of STEM innovators: Identifying and developing our nation s human capital. Arlington, VA: National Science Foundation. Olszewski-Kubilius, P. (2011). Taking a bold step. NAGC Presidential address, New Orleans, LA: NAGC. United States Department of Education (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: ED Pubs. ---------- (1994). Jacob Javits gifted and talented students education act. Washington, DC: US DoE. Vogeli, B. R. and Karp, A. (2003). Activating mathematical talent. Golden, CO: NCSM. Abcde+3 ICME-12, 2012