Annotated Bibliography

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

No abstract available.

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.

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.

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.

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.

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.

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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.

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.

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.

No abstract available.

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.

No abstract available.

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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.

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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.

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.

Describes a program that identifies gifted mathematics students and places them in an accelerated program.

No abstract available.

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

No abstract available.

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.

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.

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.

No abstract available.

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

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.

No abstract available.

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.

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.

No abstract available.

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.

No abstract available.

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.

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.

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.

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