Articles are listed in descending order by year (most recent first), and then by first author's last name.

**Almarode, J. T., Subotnik, R. F., Crowe, E., Tai, R. H., Lee, G. M., & Nowlin, F. (2014). Specialized high schools and talent search programs: Incubators for adolescents with high ability in STEM disciplines. ***Journal of Advanced Academics, 25*(3), 307-331.

The purpose of this study is to investigate the association between self-efficacy and maintenance of interest in science, technology, engineering, and mathematics (STEM) resulting in completion of an undergraduate degree in a science related area. To pursue this analysis, the researchers surveyed 3,510 graduates from selective specialized science high schools within the United States as well as 603 same age participants in Talent Search programs who did not graduate from a specialized science high school. Using binary logistic regression analysis, the researchers identified individual-level variables associated with the decision by both groups of high-ability adolescents to earn an undergraduate degree in STEM. These variables include self-efficacy and stability of interest in science, mathematics, and/or technology, and suggest that both specialized science high schools and Talent Search programs both serve equally well as incubators of talent for adolescents with a proclivity for STEM related disciplines.

**Assouline, S. G., & Lupkowski-Shoplik, A. (2011). ***Developing math talent: A comprehensive guide to math education for gifted students in elementary and middle school* (2nd ed.). Waco, TX: Prufrock Press.

This guide focuses on the issues involved in educating gifted and talented students in math, specifically students of elementary or middle school age. The book covers ways to identify mathematically gifted learners, strategies for advocating for gifted children with math talent, how to design a systematic math education program for gifted students, curricula and materials, and teaching strategies and approaches designed for gifted learners.

**Hanushek, E. A., Peterson, P. E., & Woessmann, L. (2010). ***U.S. math performance in global perspective: How well does each state do at producing high-achieving students?* Cambridge, MA: Harvard's Program on Education Policy and Governance, & Education Next.

This report is available here.

**National Science Board. (2010). ***Preparing the Next Generation of STEM Innovators: Identifying and Developing Our Nation's Human Capital*. Arlington, VA. Retrieved from http://www.nsf.gov/nsb/publications/2010/nsb1033.pdf

The full report is available on the National Science Board's website.

**Olszewski-Kubilius, P. (2010). Special schools and other options for gifted STEM students. ***Roeper Review, 32*, 61-70

Special schools focused on the Science, Technology, Engineering, & Mathematics (STEM) disciplines are one of the best options for gifted students with talent and interest in these areas. Such schools offer benefits, such as unique opportunities for research and mentoring, that other options cannot. In this article, I compare the advantages and disadvantages of special STEM schools in comparison to other options, such as summer programs, distance learning, mentorships, and others, as well as discuss the characteristics of students for whom each option is most appropriate. Alternatives to STEM schools, including piecing together summer programs, distance-learning programs, and other options, are also discussed and evaluated.

**Saul, M., Assouline, S., & Sheffield, L. J. (2010). ***The peak in the middle: Developing mathematically gifted students in the middle grades.* Reston, VA: The National Council of Teachers of Mathematics, The National Association of Gifted Children, & National Middle School Association.

This book outlines a variety of ways mathematically gifted students should be served in a middle school or junior high setting. Recommendations are provided for identifying mathematically gifted students, as well as serving them through acceleration, grouping, and extracurricular opportunities. The authors discuss ways to prepare teachers for mathematically talented students and provide a detailed case study of a middle school geometry classroom.

**Wai, J., ****Lubinski, D., Benbow, C. P., & Steiger, J. H. (2010).**
Accomplishments in science, technology, engineering, and mathematics (STEM) and its relation to STEM educational dose: A 25-year longitudinal study. *Journal of Educational Psychology, 102*.

Two studies examined the relationship between precollegiate
advanced/enriched educational experiences and adult accomplishments in science,
technology, engineering, and mathematics (STEM). In Study 1, 1,467 13-year-olds
were identified as mathematically talented on the basis of scores [greater than
or equal to] 500 (top 0.5%) on the math section of the Scholastic Assessment
Test; subsequently, their developmental trajectories were studied over 25 years.
Particular attention was paid to high-level STEM accomplishments with low base
rates in the general population (STEM PhDs, STEM publications, STEM tenure,
STEM patents, and STEM occupations). Study 2 retrospectively profiled the
adolescent advanced/enriched educational experiences of 714 top STEM graduate
students (mean age = 25), and related these experiences to their STEM
accomplishments up to age 35. In both longitudinal studies, those with notable
STEM accomplishments manifested past histories involving a richer density of
advanced precollegiate educational opportunities in STEM (a higher "STEM
dose") than less highly achieving members of their respective cohorts.
While both studies are quasi-experimental, they suggest that for mathematically
talented and academically motivated young adolescents, STEM accomplishments are
facilitated by a rich mix of precollegiate STEM educational opportunities that
are designed to be intellectually challenging, even for students at precocious
developmental levels. These opportunities appear to be uniformly important for
both sexes.

**Choi, K.M. (2009). ***Characteristics of Korean International Mathematical Olympiad (IMO) winners' and various developmental influences.* (Doctoral dissertation). Available from ProQuest database. (AAT 3386133)

Choi details characteristics of winners of the Korean International Mathematical Olympiad (IMO). The paper describes the roles of parents, teachers, and education in developing the mathematical talent of four of the winners of IMO. The contributions of the winners to STEM fields are also discussed.

**National Mathematics Advisory Panel. (2008). ***Foundations for success: The final report of the National Mathematics Advisory Panel*. Washington, DC: U.S. Department of Education.

The National Mathematics Advisory Panel evaluated what they identify as the “best available scientific research” to make recommendations for the mathematics education of gifted students. They write that “[m]athematically gifted students with sufficient motivation appear to be able to learn mathematics much faster than students proceeding through the curriculum at a normal pace, with no harm to their learning, and should be allowed to do so” (53).

**Matthews, M. S., & Farmer, J. L. (2008). Factors affecting the Algebra I achievement of academically talented learners. Journal of Advanced Academics, 19, 472-501. **

Matthews, M. S., & Farmer, J. L. (2008). Factors affecting the Algebra I achievement of academically talented learners. Journal of Advanced Academics, 19, 472-501. [Keywords: Achievement and Motivation]

Understanding student performance in Algebra I is important because this course serves as the gateway to advanced coursework in mathematics and science through the remainder of high school and into post secondary education. In the current study, we analyzed secondary data to evaluate the relationship between selected indicators of mathematics and the Algebra I performance of academically able and gifted learners who participated in above-level talent search testing. We used structural equation modeling to examine the relationship among selected CO variables and students' scores on a standardized measure of Algebra I achievement. Variables included prior mathematics ability, parental education level, whether a student was identified as gifted, participation in after school activities, the time spent on homework, and the amount of class time spent on discussions and lectures. Results indicate the strongest relationships were between mathematics reasoning and Algebra I achievement. Although gifted status was a strong predictor of mathematics reasoning, it was not strongly related to Algebra achievement, which supports the need for differentiated instruction for gifted learners. The amount of class time spent on discussion had a significant effect on the amount of time spent weekly on Algebra I homework. Rather than reliance on traditional lecture-based instruction, teachers should consider incorporating more classroom discussion on mathematical topics.

**Subotnik, R. F., Edmiston, A. M., & Rayhack, K. M. (2007). Developing national policies in STEM talent development: Obstacles and opportunities. In P. Csermely, K. Korlevic, & K. Sulyok (Eds.), ***Science education: Models and networking of student research training under 21* (pp. 28-38). Washington, DC: IOS Press.

The goal of this chapter is to analyze the current U. S. approach to serving adolescents who are talented and interested in science, technology, engineering, and mathematics (STEM). The first section of this chapter reviews to status of national government investments in STEM and contrasts it with private and local funding. The second section addresses key problems we view as obstacles to meeting national goals. Next we describe policy proposals that might be implemented in the future. We close by posing a challenge to our colleagues, the response to which could assist us in restoring the appeal of STE< careers for our talented youth, and perhaps offer insights into the obstacles and opportunities that exist in our colleagues' own nations.

**Webb, R. W., Lubinski, D., & Benbow, C. P. (2007). Spatial ability: A neglected dimension in talent searches for intellectually precocious youth. ***Journal of Educational Psychology, 99*(2), 397-420.

Webb, Lubinski, & Benbow suggest that another meaningful way to identify gifted students in mathematics and science is by considering the students’ spatial ability. The article discusses the use of triangulation of data to determine that students who are talented in spatial ability are also talented in mathematics and science.

**Burris, C. C., Hubert, J. P., & Levin, H. M. (2006). Accelerating mathematics achievement using heterogeneous grouping. ***American Educational Research Journal, 43*(1), 105-136.

Burris, Hubert, and Levin outline the effects of having all students enroll in accelerated mathematics classes throughout middle and high school. The study uses longitudinal data over a span of 6 years to document the improvement in achievement data for all students in the area of mathematics as a result of the accelerated program. The article outlines the methods for acceleration by placing students in heterogeneous mathematics classes. The study compares the achievement data results from three sixth grade cohorts that were tracked to three sixth grade cohorts that were integrated in to accelerated mathematics classes. According to Burris, Hubert, and Levin, as a result of all students being exposed to higher expectations in the mathematics classroom, students in the accelerated mathematics class both performed better on achievement data over the course of the six year study and stayed in upper level mathematics classes longer. (This is the same case addressed in Burris, Hubert, Levin, 2004).

**Coleman, L. J., & Southern, W. T. (2006). Bringing the potential of underserved children to the threshold of talent development. ***Gifted Child Today, 29*(3), 35-39.

Coleman and Southern outline the Accelerating Achievement in Mathematics and Science in Urban Schools (AAMSUS) program in this article. The purpose of the program is to identify students from economically disadvantaged families, who may not have otherwise been identified as talented and gifted students, and give them the opportunity to enroll in a program to prepare them for acceleration and enrichment in their secondary schooling. The purpose of this article was to report baseline data only. Data was collected on approximately 182 students from urban areas. The outcome from the four year program was a wide range of achievement data; however, anecdotal evidence gathered from the students’ teachers indicated that after enrolling in AAMSUS students had better attitudes about school and better homework completion rates.

**Feist, G. J. (2006). The development of scientific talent in Westinghouse finalists and members of the National Academy of Sciences. ***Journal of Adult Development, 13*(1), 23-35.

Feist discusses the results of two studies addressing the development of scientific talent among finalists in the Westinghouse Science Competition and members of the National Academy of Sciences. The article sampled four cohorts of finalists to explore their education and career outcomes. The study found that a high proportion of both males and females stayed in the scientific field; however, more men (91%) than women (74%) pursued a career in the sciences. Age of talent recognition was a predictor of lifetime productivity in the area of scientific contribution.

**Lubinski, D., & Benbow, C. P. (2006). Study of Mathematically Precocious Youth after 25 years: Uncovering antecedents for the development of math-science expertise. ***Perspectives on Psychological Science, 1*(4), 316-345.

This review provides an account of the Study of Mathematically Precocious Youth (SMPY) after 35 years of longitudinal research.Findings from recent 20-year follow-ups from 3 cohorts, plus 5- or 10-year findings from all 5 SMPY cohorts (totaling more than 5,000 participants), are presented. SMPY has devoted particular attention to uncovering personal antecedents necessary for the development of exceptional math-science careers and to developing educational interventions to facilitate learning among intellectually precocious youth.

**Ma, X. (2005). A longitudinal assessment of early acceleration of students in mathematics on growth in mathematics achievement. ***Developmental Review, 25*, 104-132.

Ma compares attitudes about mathematics of gifted, honors, and regular students who have been accelerated and not accelerated. The author specifically considers student attitudes toward mathematics and the amount of anxiety these different groups of students feel toward mathematics. Ma used student self-reported anxiety and attitude toward mathematics data collected as part of the Longitudinal Study of American Youth (LSAY) survey. The LSAY was administered to 60 seventh grade students at each school in 52 school districts nationwide. The results of the LSAY were that accelerated and non-accelerated gifted students showed a small decline in attitude toward mathematics between seventh and twelfth grade. A larger difference in anxiety existed between gifted and honors students who were both accelerated in their mathematics education.

**Ma, X. (2005). Early acceleration of students in mathematics: Does it promote growth and stability of growth in achievement across mathematical areas? ***Contemporary Educational Psychology, 30*(4), 439-460.

This study looked at mathematical achievement of accelerated and non-accelerated students from seventh through twelfth grade. The objective of this study was to determine whether early acceleration into formal algebra promoted significant academic growth and balanced academic development throughout the secondary school years. The author used hierarchical linear modeling to analyze results from the Longitudinal Study of American Youth. Students were grouped as high- or low-achieving based on their performance on seventh grade math tests. The same students were then grouped based on their access to acceleration in mathematics. Students who took Algebra I in seventh or eighth grade were defined as accelerated in mathematics.
Students who were accelerated into formal algebra at the beginning of middle school grew more quickly in basic skills, algebra, geometry, and quantitative literacy than students who were not accelerated. Student and school characteristics did not significantly impact the rates of growth. Interestingly, students who had low initial mathematics achievement showed higher rates of growth than their non-accelerated peers. Initially low-achieving students improved at a faster rate than students who were initially high achievers. However, the author acknowledges a potential “ceiling effect” for high achievers, who may have already learned all of the content in basic skills and quantitative literacy, leaving less room for improvement. As a result, a lack of substantial growth in this group is not an effective argument against acceleration for high-achieving students.
The results suggest that the challenge of more advanced mathematical problems in formal algebra motivates students and prevents boredom. Students who were initially high achievers and those who were initially low achievers both improved their mathematical skills at a higher rate than their non-accelerated peers. Early acceleration in mathematics was not found to decrease the stability in development of basic skills, algebra, geometry, or quantitative literacy in either group.

**Burris, C. C., Hubert, J. P., & Levin, H. M. (2004). Math acceleration for all. ***Educational Leadership, 61*(5), 68-71.

Burris, Hubert, and Levin outline the effects of having all students enroll in accelerated mathematics classes throughout middle and high school. The study uses longitudinal data over a span of 6 years to document the improvement in achievement data for all students in the area of mathematics as a result of the accelerated program. The article outlines the methods for acceleration by placing students in heterogeneous mathematics classes. The study compares the achievement data results from three sixth grade cohorts that were tracked to three sixth grade cohorts that were integrated in to accelerated mathematics classes. According to Burris, Hubert, and Levin, as a result of all students being exposed to higher expectations in the mathematics classroom, students in the accelerated mathematics class both performed better on achievement data over the course of the six year study and stayed in upper level mathematics classes longer.

**Reed, C. F. (2004). Mathematically gifted in the heterogeneously grouped mathematics classroom: What is a teacher to do? ***The Journal of Secondary Gifted Education, 15*(3), 89-95.

Reed outlines specific ways to differentiate instruction in a heterogeneously grouped Geometry classroom. Differentiation strategies include extensions or applications of current class work, the completion of open-ended questions, and student-selected problems. Content specific to Geometry covering the Pythagorean Theorem and proving triangle congruence are given.

**Rotigel, J. V., & Fello, S. (2004). Mathematically gifted students: How can we meet their needs? ***Gifted Child Today, 27*(4), 46-51.

Rotigel and Fello outline appropriate ways to identify mathematically gifted students as well as appropriate programming for students who have been identified as gifted in mathematics. The article discusses the use of above-level testing for students scoring in the 95th percentile or higher on their grade-level tests. The importance of combining standardized test data with teacher observations, classroom assessments, and the student’s emotional needs is also addressed. Effective programming for mathematically gifted students includes differentiated instruction and the use of technology to further accelerate students in mathematics.

**Ysseldyke, J., Tardrew, S., Betts, J., Thill, T., & Hannigan, E. (2004). Use of an instructional management system to enhance math instruction of gifted and talented students. ***Journal for the Education of the Gifted, 27*(4), 293-310.

This article discusses the educational effects of using the computerized Accelerated Math instructional management system. All students in the study completed the standard school curriculum, but some students also used the Accelerated Math program. In post-tests, gifted students whose teachers used the computer program outperformed gifted students whose teachers did not use the program.

**Etkina, E., Matilsky, T., & Lawrence, M. (2003). Pushing us to the edge: Rutgers Astrophysics Institute motivates talented high school students. ***Journal of Research in Science Teaching, 40*(10), 958-985.

The authors detail the Rutgers Astrophysics Institute (RAI), a summer program for gifted students in science, in which students have the opportunity to work with an expert astrophysicist. The goals of the program are to identify gifted students in science, to engage them in higher level scientific methods, and to keep them interested in science. Etkina, Matilsky, and Lawrence collect a variety of data to measure the success of the program according to these goals. Overall, students who enrolled in RAI expressed greater interest in pursuing science and performed as well on the AP physics exam as their counterparts that enrolled in AP physics.

**Hsu, L. (2003). Measuring the effectiveness of summer intensive physics courses for gifted students: A pilot study and agenda for research. ***Gifted Child Quarterly, 47*(3), 212-218.

This article addresses the claim that intensive summer physics courses for gifted students could be used to replace the year-long physics course during the school year. Hsu uses student scores on the Force Concept Inventory (FCI) exam to compare student scores from the summer intensive course to those scores of students taking full year physics during the school year. 128 students participated in the study. Overall, students participating in the summer intensive physics course performed about as well as students enrolling in the year-long physics course.

**Karp, A. (2003). Thirty years after: The lives of former winners of mathematical Olympiads. ***Roeper Review, 25*(2), 83–87.

Karp seeks to answer questions about former Mathematical Olympiad winners. He surveys a large group of winners from St. Petersburg, Russia in 1991 (ages ranging from 35 – 45) and conducts a follow-up survey in 2001. He attempts to answer the following questions: How did their lives turn out? What became of these people who were considered mathematically gifted in childhood? What are their own views regarding the Olympiads and their mathematical education as a whole? The results of his survey show approximately half of the winners pursued a doctorate degree and about half of the respondents had a career at an academic institution. The average number of publications per winner was about ten. Nearly all respondents rated their university mathematics department as “high quality.”

**Ma, X. (2003). Effects of early acceleration of students in mathematics on attitudes toward mathematics and mathematics anxiety. ***Teachers College Record, 105*(3), 438-464.

Ma compares attitudes about mathematics of gifted, honors, and regular students who have been accelerated and not accelerated. The author specifically considers student attitudes toward mathematics and the amount of anxiety these different groups of students feel toward mathematics. Ma used student self-reported anxiety and attitude toward mathematics data collected as part of the Longitudinal Study of American Youth (LSAY) survey. The LSAY was administered to 60 seventh grade students at each school in 52 school districts nationwide. The results of the LSAY were that accelerated and non-accelerated gifted students showed a small decline in attitude toward mathematics between seventh and twelfth grade. A larger difference in anxiety existed between gifted and honors students who were both accelerated in their mathematics education.

**Cope, E. W., & Suppes, P. (2002). Gifted students' individual differences in distance-learning computer-based calculus and linear algebra. ***Instructional Science, 30,* 79-110.

This article discusses the performance of high school students on online AP Calculus courses, as well as college-level linear algebra courses. All students in this article were offered these courses as part of the Education Program for Gifted Youth (EPGY) at Stanford University. The average age of students taking the online courses was 14.9 and all students had to score in the top 15% on a standardized aptitude test to be eligible for the courses. 103 students participated in this study. Although the type of student taking the online courses was narrowly defined, the range of scores on time of course completion, error rate, and calendar days enrolled in the course varied greatly. Cope & Suppes conclude that this is an indicator of the wide range of needs for the gifted student in mathematics.

**Jones, B. M., Fleming, D. L., Henderson, J., & Henderson, C. E. (2002). Common denominators: Assessing hesitancy to apply to a selective residential math and science academy. ***The Journal of Secondary Gifted Education, 13*(4), 164-172.

The
Texas Academy of Mathematics and Science (TAMS) is a state-supported,
tuition-free residential high school at the University of North Texas, one of
14 similar academies in the U.S. TAMS students earn dual high school and
college credit, graduating in 2 years with 60 or more transferable college
credits. Some 200 high school juniors are admitted each fall from a competitive
statewide pool based on exceptional SAT scores and other credentials. While
hundreds of highly capable students seek admission each year, hundreds of others
withhold applications. Responding to a survey, gifted nonapplicants reported an
unwillingness to leave home 2 years earlier than usual and a reluctance to
abandon varsity athletics and associated extracurricular activities.
Recruitment implications are discussed, along with suggestions for further study.

**Ma, X. (2002). Early acceleration of mathematics students and its effect on growth in self-esteem: A longitudinal study. ***International Review of Education, 48*(6), 443-468.

Ma compares attitudes about mathematics of gifted, honors, and regular students who have been accelerated and not accelerated. The author specifically considers student attitudes toward mathematics and the amount of anxiety these different groups of students feel toward mathematics. Ma used student self-reported anxiety and attitude toward mathematics data collected as part of the Longitudinal Study of American Youth (LSAY) survey. The LSAY was administered to 60 seventh grade students at each school in 52 school districts nationwide. The results of the LSAY were that accelerated and non-accelerated gifted students showed a small decline in attitude toward mathematics between seventh and twelfth grade. A larger difference in anxiety existed between gifted and honors students who were both accelerated in their mathematics education.

**Schenkel, L. A. (2002). Hands on and feet first: Linking high-ability students to marine scientists. ***The Journal of Secondary Gifted Education, 13*(4), 173-191.

Schenkel discusses the student-perceived benefits of their participation in the Science Fair Summer Camp program at the Harbor Branch Oceanic Institute in Fort Piece, Florida. The students designed and carried out hands-on scientific experiments relating to issues in marine science. This study addressed the following questions: 1) Does the program align with recommendations for science education reform? 2) What do students gain by participating in the program? 3) Are there any benefits from this program that could not be addressed through regular classroom experiences? These questions were answered through two student surveys, which indicated that participants in the program were engaged in experiences appropriate for gifted learners and, as a result of their participation in the program, had a better attitude about science and scientists.

**Webb, R. W., Lubinski, D., & Benbow, C. P. (2002). Mathematically facile adolescents with math-science aspirations: New perspectives on their educational and vocational development. ***Journal of Educational Psychology, 94*(4), 785-794.

Webb, Lubinski, and Benbow conducted a longitudinal study tracking 1110 students identified as mathematically gifted at the age of 13. The students expressed interest in pursuing a mathematics or science undergraduate major. The study followed the students to see if their high school educational experiences, abilities, and interests predicted whether students pursued majors and careers in mathematics and science. The study found that more male than female students pursued careers in the STEM fields.

**Hébert, L. (2001). A comparison of learning outcomes for dual-enrollment mathematics students taught by high school teachers versus college faculty. ***Community College Review, 29*(3), 22-38.

Hébert discusses the use of dual enrollment credits as they serve high school students. This study followed two groups of students: high school students earning dual enrollment credit from a high school year and high school students earning dual enrollment credit from a college professor. The findings of this quasi-experimental study found that students earning dual enrollment credit from high school teachers were better prepared for college coursework than students who had been taught by college professors while still in high school. The study found no significant difference between grade distributions in the dual enrollment class when comparing students taught by high school teachers versus those taught by college professors.

**Partenheimer, P. R., & Miller, S. K. (2001). ***Eighth grade algebra acceleration: A case study of longitudinal effects through the high school pipeline.* Paper presented at the Annual Meeting of the American Educational Research Association, Seattle, WA.

This study features a program evaluation of a policy that allows gifted 8th-grade mathematics students to take algebra. The study is longitudinal and looks at the effects of taking algebra in the 8th grade and the subsequent four years of mathematics in high school. Among the specific research questions in the study are: (1) To what degree do students in 8th-grade algebra progress through upper level mathematics after early entry? (2) To what extent do some of these accelerated students have negative experiences? and (3) Does the elementary school mathematics curriculum (self pacing versus traditional) affect the mathematics profile for 8th-grade algebra and subsequent mathematics courses? The study concludes that the policy of accelerating students in mathematics at this particular school had a negative impact for many of those students.

**Ma, X. (2000). Does early acceleration of advanced students in mathematics pay off? An examination of mathematics participation in the senior grades.*** Focus on Learning Problems in Mathematics, 22*(1), 68-79.

Examines advanced students' course taking procedures and their senior year mathematics participation. Concludes that students who took early algebra demonstrated a substantially higher participation rate in advanced mathematics in the later grades of high school than students who did not.

**Schrecongost, J. (2000). ***An analysis of the selection criteria for the eighth grade algebra I accelerated mathematics program in Harrison County, West Virginia.* Master of Arts Thesis, Salem-Teikyo University.

This study analyzed the criteria used in Harrison County, WV, to select students to participate in an accelerated mathematics program. The program's main component is an eighth grade Algebra I course that enables the students to complete five years of college preparatory mathematics, ending with calculus. The scores used as selection criteria, CTBS concepts, CTBS computation, and pre-algebra grades, were all found to be good predictors of success. The results indicate, however, that the current standards need to be raised. Requiring higher scores would eliminate a significant number of program dropouts (currently 51%). A fourth selection criterion, a 65th percentile on the Iowa Algebra Aptitude Test, could not be evaluated since there was no record of such test results. However, other studies indicate that both an algebra prognosis test and an assessment of interest would be helpful.

**Benbow, C.P., Lubinski, D., & Sanjani, H.E. (1999). Our future leaders in science: Who are they? Can we identify them early? ***Talent Development III,* 59-70.

The article uses what the Study of Mathematically Precocious Youth (SMPY) has learned about the characteristics of people likely to be distinguished in STEM fields. The questions answered in the article include: Who are these people? What were their educational experiences? How did they feel about them? The study explores categories such as gender and selected field of study in college as they relate to identifying future scientific leaders. Benbow, Lubiniski, & Sanjani analyze the data as a way to illustrate deficiencies in a pull out program for highly gifted students in elementary and secondary school.

**Lupkowski-Shoplik, A. (1998). ***Guiding Mathematically Talented Elementary Students.* Retrieved April 2, 2009, from http://www.cmu.edu/cmites/guidemath.html

Lupkowski-Shoplik outlines ways parents can advocate for their mathematically gifted students within the typical elementary school setting. The article also discusses appropriate methods for identifying a student as talented and gifted in the area of mathematics. Lupkowski-Shoplik also offers resources available for parents to help find appropriate activities and programs for their mathematically talented student.

**Shayer, M. (1997). ***Cognitive acceleration through science education (CASE). *Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL.

"Thinking Science," the Cognitive Acceleration through Science Education (CASE) curriculum, is a program designed for 11-14 year olds (in the first two years of secondary school) which encourages them to reflect on their own thinking and to develop their reasoning power in tackling novel problems. This study presents results that represent the first large-scale long-term test of the process of raising standards in schools by concentrating on a thinking skill approach. Overall, about 4,500 pupils in the CASE schools have been featured in the data in this report. Seventeen schools' data have been compared with added-value data from a greater number of control schools. Results indicate that the CASE methodology, even when tried for the first time, produced an average increase on the order of half as much gain in the percentage of pupils obtaining C-grade and above at the GCSE examination (an increase from a national average of 44% to 63% for science in 1996, and an increase from 43% to 57% in science for 1995. In addition, there was the same relative order of increase in achievement in mathematics and a somewhat lower improvement, though still substantial, in English. In schools where teachers had two or more previous years of experience with this approach, the schools more than doubled the proportion of their pupils showing National Curriculum achievement at level six or above in all three subjects.

**Stanley, J. C. (1996). In the beginning: The Study of Mathematically Precocious Youth. In C. P. Benbow & D. Lubinski (Eds.), ***Intellect and talent: Psychology and social issues* (pp. 225- 235). Baltimore: Johns Hopkins University Press.

This paper contains a brief description of the founding and early years of the Study of Mathematically Precocious Youth (SMPY) from 1968 to the present. Several of the guiding principles behind SMPY are discussed. SMPY led to the formation of strong regional, state, and local centers that now blanket the United States with annual talent searches and academic summer programs. Among their main tools are the assessment tests of the College Board including the SAT, high school achievement tests, and Advanced Placement Program (AP) examinations. Identifying, via objective tests, youths who reason exceptionally well mathematically and/or verbally is the initial aim of SMPY and its sequels. The 12- or 13-year-old boys and girls who score high are then provided the special, supplemental, accelerative educational opportunities they sorely need.

**Ravaglia, R., Suppes, P., Stillinger, C., & Alper, T. (1995). Computer-based mathematics and physics for gifted students. ***Gifted Child Quarterly, 39*(1), 7-13.

This article follows three groups of middle and high school students who have completed online accelerated mathematics and physics courses as part of the EPGY project at Stanford University. The courses offered in this project were Calculus AB, Calculus BC, and Physics C. In all three groups 88-100% of students enrolled in the courses earned a score of 4 or 5 on the corresponding Advanced Placement exams. Advantages of the EPGY courses include student access and success with courses that would not otherwise be available to them for two to three more years of formal schooling. The students are also able to control the pace of the class, as they completed assignments for the computer based lessons on their schedule, and they can enroll in the course at any time during the year.

**Ravaglia, R., Suppes, P., Stillinger, C., & Alper, T. M. (1995). Computer-based mathematics and physics for gifted students. ***Gifted Child Quarterly, 39*(1), 7-13.

Computer-based instruction allows gifted middle school and early high school students to complete advanced mathematics and physics courses several years early. The progress of three groups of students (grades 7-12) who took Advanced Placement level calculus or physics courses at an education program for the gifted was examined. Advanced Placement examination scores were high, and attrition rates were low. Gender differences were not apparent. It is concluded that acceleration is appropriate for gifted students if they are allowed to move at their own pace and required to demonstrate mastery of the material throughout. If students are able to learn material faster, keeping them from doing so does not appear to improve their education.

**Charlton, J. C., Marolf, D. M., & Stanley, J. C. (1994). Followup insights on rapid educational acceleration.*** Roeper Review, 17*(2), 123-129.

Too little is known about what happens to youths who reason extremely well mathematically. This article discusses mathematically precocious youth. A comment on this article by a group of guest editors is appended.

**Elmore, R. F., & Zenus, V. (1994). Enhancing social-emotional development of middle school gifted students. ***Roeper Review, 16*(3), 182-185.

Elmore and Zenus outline the effects of a twelve-week program for mathematically gifted middle school students on self-esteem and academic achievement. The students worked collaboratively during the 12 sessions. Students were administered a pre- and post-test for self-esteem and mathematical ability. At the conclusion of the program, all students had higher scores on both tests. The lower-achieving mathematically gifted students showed a greater increase in scores than their higher-ability counterparts.

**Lupkowski-Shoplik, A. E., & Assouline, S. G. (1994). Evidence of extreme mathematical precocity: Case studies of talented youths.*** Roeper Review, 16*(3), 144-151.

This article presents four case studies of extreme mathematical precocity in two boys and two girls. Problems in providing appropriately challenging instruction for these children are noted. The article concludes with 11 recommendations for programming for exceptionally talented students.

**Bell, D., & Leroux, J. (1992). Acceleration: A case study of home schooling. ***Canadian Journal of Special Education, 8*(2), 167-175.

This paper describes an accelerative instructional program in algebra provided to a sixth-grade boy, highly able in mathematics, by parental home tutoring. The boy's high intrinsic motivation and teaching sensitive to his needs and abilities led to successful achievement.

**Kolitch, E. R., & Brody, L. E. (1992). Mathematics acceleration of highly talented students: An evaluation.*** Gifted Child Quarterly, 36*(2), 78-86.

This study examined the precollege mathematics preparation of first-year college students (n=69) with very high mathematical aptitude. Despite most students' radical acceleration (as part of the Study of Mathematically Precocious Youth), achievement in coursework was high. Gender differences were found in degree of acceleration and choice of college major.

**Lynch, S. J. (1992). Fast-paced high school science for the academically talented: A six-year perspective. ***Gifted Child Quarterly, 36*(3), 147-154.

This study of 905 academically talented students (ages 12-16) who completed a 1-year course in high school biology, chemistry, or physics in a 3-week summer program found that the fast-paced courses effectively prepared subjects to accelerate in science, and that talented students could begin high school sciences earlier than generally allowed.

**Lynch, S. J. (1992). Fast-paced high school science for the academically talented: A six-year perspective.*** Gifted Child Quarterly, 36*(3), 147-154.

This study of 905 academically talented students (ages 12-16) who completed a 1-year course in high school biology, chemistry, or physics in a 3-week summer program found that the fast-paced courses effectively prepared subjects to accelerate in science, and that talented students could begin high school sciences earlier than generally allowed.

**Stanley, J. C. (1991). An academic model for educating the mathematically talented.*** Gifted Child Quarterly, 35*(1), 36-42.

This article traces the origin and development of special educational opportunities offered to students who are exceptionally able in mathematics, focusing on the Study of Mathematically Precocious Youth at Johns Hopkins University and the Center for the Advancement of Academically Talented Youth.

**Swiatek, M. A., & Benbow, C. P. (1991). A 10-year longitudinal follow-up of participants in a fast-paced mathematics course. ***Journal for Research in Mathematics Education, 22*(2), 138-150.

Participants in a fast-paced mathematics course and qualified nonparticipants were surveyed 10 years later with respect to undergraduate record, graduate experience, attitudes toward mathematics/science, and self-esteem. In general, participation was associated with stronger undergraduate records for all students and with more advanced graduate accomplishment for females.

**Lynch, S. J. (1990). Credit and placement issues for the academically talented following summer studies in science and mathematics.*** Gifted Child Quarterly, 34*(1), 27-30.

Students (n=570, aged 12-16) who attended university-sponsored science and mathematics summer classes reported on their subsequent status at their regular schools pertaining to credit and placement issues. Advanced placement was given more often than credit, although in most cases both were awarded, particularly for high school level coursework.

**Stanley, J. C., Lupkowski, A. E., & Assouline, S. G. (1990). Eight considerations for mathematically talented youth.*** Gifted Child Today, 13*(2), 2-4.

The article considers how accelerative and enrichment options complement each other to provide appropriate challenges for mathematically talented students. Eight principles of educating such youth are presented, based on experience of the Study of Mathematically Precocious Youth at Johns Hopkins University.

**Thomas, T. A. (1989). ***Acceleration for the academically talented: A follow-up of the academic talent search class of 1984.* (ERIC Documents Reproduction Service No. ED307303).

This paper reviews and synthesizes the results from 42 research reports dealing with acceleration of mathematics programs for talented junior high school students. The effects of acceleration and enrichment are compared, and it is concluded that acceleration is preferable. The question of optimal grade level for initiating accelerated programs, and that of the advisability of providing slower paced programs for low achievers are raised. Annotations are provided for each of the reports reviewed. Each annotation gives bibliographic information, a brief description of the study, and a list of findings.

**Stanley, J. C. (1988). Some characteristics of SMPY's 700-800 on SAT-M before age 13 group. ***Gifted Child Quarterly, 32*(1), 205-209.

Statistics are presented concerning background characteristics of 292 students who scored well on the mathematical sections of the Scholastic Aptitude Test at age 12 or younger. Discussed are the ratio of girls to boys, geographic distribution, verbal ability, parents' education level and occupational status, siblings, and educational acceleration.

**Stanley, J. C. (1987). Making the IMO team: The power of early identification and encouragement.*** Gifted Child Today, 10*(2), 22-23.

Stanley describes four members of the United States 1985 International Mathematical Olympiad team that also took part in Study of Mathematically Precocious Youth (SMPY). Through discussions with these team members, Stanley outlines the importance of identifying mathematically talented students early in their formal schooling. Identification of these students is important because acceleration, encouragement, and talent development proved to be important predictors of a gifted student’s success in mathematics and science.

**Stanley, J. C. (1987). State residential high schools for mathematically talented youth.*** Phi Delta Kappan, 68*(10), 770-773.

Proposes that states promote the preparation of mathematically and scientifically talented high school students through the establishment of special residential high schools.

**Stanley, J. C., & Benbow, C. P. (1986). Youths who reason exceptionally well mathematically. In R. J. Sternberg and J. E. Davidson (Eds.), ***Conceptions of giftedness *(pp. 361-387). Cambridge, England: Cambridge University Press.

Stanley and Benbow describe the Study of Mathematically Precocious Youth (SMPY) program, the validity of using SAT-M scores to identify mathematically talented students, and the importance of acceleration - rather than enrichment - for the gifted student. The authors outline three main problematic aspects of grade-level enrichment in mathematics for highly gifted students: busywork used as “enrichment,” irrelevant academic enrichment (enrichment that does not address a student’s specific areas of giftedness), and cultural enrichment.

**Stanley, J. C., & Stanley, B. S. K. (1986). High school biology, chemistry, or physics learned well in three weeks. ***Journal of Research in Science Teaching, 23*(3), 237-250.

At ages 11-15, 25 intellectually highly-able youths studied high school biology and 12 studied chemistry intensively for 3 summer weeks, after which their median score on the College Board's achievement test was 727 (biology) and 743 (chemistry). Implications of these and other results for science instruction are discussed.

**Wolfle, J. A. (1986). Enriching the mathematics program for middle school gifted students. ***Roeper Review, 9*(2), 81-85.

Wolfle suggests ways that middle school mathematics teachers can better serve mathematically talented youth in their classrooms. Particularly because middle school students undergo many emotional changes, middle school teachers need to keep in mind both the emotional and academic needs of their high-ability students. A common mistake in middle schools is grouping younger high-ability students with older lower-ability students.

**Stanley, J. C. (1985). Finding intellectually talented youths and helping them educationally. ***Journal of Special Education, 19*(3), 363-372.

Discusses the first 14 yrs (1971-1985) of the Study of Mathematically Precocious Youth at Johns Hopkins University. Many youths who reasoned exceptionally well mathematically were identified, studied further, and aided. Issues discussed include the need for longitudinal teaching teams, the identification of students with high mechanical reasoning, and use of the Scholastic Aptitude Testing in screening.

**Reynolds, A. S. (1983). ***Identifying mathematically talented sixth grade students in an upper-middle income community.* Unpublished master's thesis, Hayward State University.

This study examines predictors of success and continuance in an accelerated high school mathematics program based on 21 variables. A multiple regression analysis found that the two best predictors of student success and continuance in an accelerated mathematics program were students’ middle school and algebra mathematics grades. Further, Reynolds’ data analysis found that, of the students who self-accelerate, 88% of the students were male. Based on the results of the study, Reynolds recommends that more students be placed in honors mathematics in middle school to ensure that more students are selected for an accelerated algebra program in eighth grade.

**Stanley, J. C., & Benbow, C. P. (1983). SMPY's first decade: Ten years of posing problems and solving them.*** Journal of Special Education, 17*(1), 11-25.

The Study of Mathematically Precocious Youth (SMPY) began in 1971 with the purpose of devising ways of identifying and facilitating the education of such students. The solutions and their longitudinal evaluation are described. Use of the Scholastic Aptitude Test (SAT) was shown to be an effective way of identifying students in the 7th grade who would achieve academically at a superior level in high school. Moreover, acceleration was deemed an effective alternative for educating gifted children. Curricular flexibility rather than special programs for the gifted has proved the most effective way to facilitate the education of precocious students. For the mathematically precocious, SMPY devised fast-paced mathematics classes. These were shown to have long-term effects. SMPY has also discovered large sex differences in mathematical reasoning ability and in mathematics and science achievements in high school.

**Pizzini, E. L. (1982). Appropriate experiences for the gifted science student. ***Roeper Review, 4*(4), 7-8.

Pizzini highlights a variety of ways gifted students can be appropriately challenged in science. The article discusses three specific types of enrichment or acceleration for the gifted science student: extension programs offered by a university or other outside professional organization (such as Iowa-SSTP, at the University of Iowa); online accelerated science courses; and individual science projects completed by students with a field-expert mentor.

**Stanley, J. C. & Benbow, C. P. (1982). Educating mathematically precocious youths: Twelve policy recommendations.*** Educational researcher, 11*(5), 4-9.

Presents recommendations based on 13 years of work by the Study of Mathematically Precocious Youth. Holds that mathematically talented students are essential to our country's scientific and technological progress and that their abilities must be cultivated to a far greater extent than is permitted by current educational programs.

**Mezynski, K., & Stanley, J. C. (1980). Advanced placement oriented calculus for high school students.*** Journal for Research in Mathematics Education, 11*(5), 347-355.

Two supplementary calculus classes for high school students are described. Both classes were projects sponsored by the Study of Mathematically Precocious Youth (SMPY) of Johns Hopkins University.

**George, W. C., & Stanley, J. C. (1979). The study of mathematically precocious youth.*** Gifted Child Quarterly, 23*, 518-525.

The article describes the Johns Hopkins University Study of Mathematically Precocious Youth (SMPY), which identifies and studies mathematically precocious seventh graders to provide information on which to base special education efforts on their behalf. Some SMPY publications are listed, and several books on SMPY activities and findings are described.

**McKnight, C. C. (1979). ***Acceleration vs. sophistication in mathematics: An either/or case? Development Report Number 2.* Urbana, IL: Illinois University at Urbana Curriculum Laboratory.

This document discusses the importance of acceleration vs. sophistication in mathematics programs and curricula for gifted students. The discussion proceeds through three steps. First, an attempt is made to model how various kinds of gifted students interact with three dimensions of the curriculum. These dimensions are acceleration, sophistication (depth), and enrichment (breadth). Second, a description is given of the way in which one program has tried to respond to this model. This program is the mathematics program for gifted students at the University High School, the laboratory school of the University of Illinois. Finally, an attempt is made to draw a few conclusions and practical guidelines for dealing with gifted students.

**Stanley, J. C. (1979). The study and facilitation of talent for mathematics. In A.H. Passow (Ed.),***The gifted and the talented: Their education and development* (pp. 169-185). Chicago: University of Chicago Press.

Brief discussions of general vs. special ability and of mathematical reasoning ability form the introduction of this paper on the education of mathematically gifted students. The second section of the paper describes the annual mathematics talent searches conducted by the Study of Mathematically Precocious Youth (SMPY). The third section covers SMPY's special educational provisions for the mathematically talented, including the basic components of the program, importance of fast pace, and other aspects of the offerings (skipping grades, part-time college study, credit by examination, early college entrance, college graduation in less than four years, and by-passing the bachelor's degree). Two illustrations of how selected students progressed through the program comprise the fourth section of this paper, while the final section summarizes SMPY's position concerning the education of mathematically precocious youth.

**Stanley, J. C. (1976). ***Brilliant youth: Improving the quality and speed of their education.* Proceedings from the Annual Meeting of the American Psychological Association, Washington, DC.

The three phases (finding seventh and eighth grade mathematically talented students, studying them, and helping them educationally) of the Study of Mathematically Precocious Youth (SMPY) are detailed, and examples of the superiority of educational acceleration over educational enrichment are pointed out. Results of standardized intelligence tests are seen to be less helpful than scores on the mathematics part of the College Entrance Examination Board's Scholastic Aptitude Test in identifying gifted students for SMPY. Four types of enrichment (busy work, irrelevant academic, cultural, and relevant academic) are described and contrasted with academic acceleration. Presented is the case of 11-and-one-half-year-old boy who was helped educationally by entering college before completing high school. Stressed is the need for flexibility that makes a variety of educationally accelerative possibilities (such as grade skipping and college courses for credit) available for the student.

**Stanley, J. C. (1976). Identifying and nurturing the intellectually gifted.*** Phi Delta Kappan, 58*(3), 234-238.

Stanley outlines four types of instructional strategies used in schools to meet the needs of gifted students. Of these four, three do not actually serve the needs of such students. The strategies identified in the article are: busy work, irrelevant academic enrichment, cultural enrichment, and relevant academic enrichment. The first three instructional strategies for the gifted learner do not help to cultivate skills in students’ areas of giftedness. Many times the strategies are used as a way to keep the learner on task in a classroom setting. Stanley writes that the best way to implement the fourth instructional strategy, relevant academic enrichment, is through acceleration in the student’s area(s) of giftedness.

**Stanley, J. C. (1976). Special fast-mathematics classes taught by college professors to 4th-12th graders. In D.P. Keating (Ed.),*** Intellectual talent: Research and development.* Baltimore: Johns Hopkins University Press, 132-159.

This book chapter details the methods and outcomes of teaching 24 students in grades 4 – 7 algebra by college professors. Each of the students was taught for one hour each week during their regular school day by a college mathematics professor of the same sex. Stanley emphasizes the importance of quality instruction and the possible benefits of homogonous grouping when teaching talented students in the area of mathematics.

**Stanley, J. C. (1976). The case for extreme educational acceleration of intellectually brilliant youths.*** Gifted Child Quarterly, 20*(1), 66-75.

Presents several detailed case studies demonstrating good effects of acceleration in educating mathematically precocious youth who had been identified in a longitudinal study.

**Stanley, J. C. (1976). The student gifted in mathematics and science. ***Bulletin of the National Association of Secondary School Principles, 60*, 28-37.

The article outlines the Study of Mathematically Precocious Youth (SMPY) program at Johns Hopkins University. Stanley describes the way students are selected to be part of the program and the types of activities the program offers. Stanley discusses the use of acceleration (as opposed to enrichment) in mathematics and presents a case study of an SMPY student.

**Stanley, J. C. (1976). Youths who reason extremely well mathematically: SMPY's accelerative approach.*** Gifted Child Quarterly, 20*(3), 237-238.

Statistics are presented concerning background characteristics of 292 students who scored well on the mathematical sections of the Scholastic Aptitude Test at age 12 or younger. Discussed are the ratio of girls to boys, geographic distribution, verbal ability, parents' education level and occupational status, siblings, and educational acceleration.

**Stanley, J. C., Keating, D. P., & Fox, L. H. (Eds.) (1974). ***Mathematical talent: Discovery, description, and development.* Baltimore: Johns Hopkins University Press.

The book discusses ways to foster mathematical ability among mathematically precocious students. In addition to the editors of the book, Helen S. Astin, Anne Anastasi, Daniel S. Weiss, Richard J Haier, Susanne A. Denham, & Stanley Wiegand author chapters describing the educational development of mathematically gifted students and detailing ways to design a mathematics program to foster precocious mathematics achievement.

**Holmes, J. E. (1970). Enrichment or acceleration? ***Math Teacher, 63*(6), 471-473.

Holmes’ article advocates the use of enrichment in high school mathematics curriculum, as opposed to acceleration. He argues that too many students take calculus their senior year in high school, only to have to repeat it when they get to college because of insufficient scores on the Advanced Placement calculus exam. The author gives specific examples of ways the high school mathematics teacher can enrich a pre-calculus course.