An Effective Mathematics and Science Curriculum Option for Secondary Gifted Education.In recent years, many research studies have attempted to determine an appropriate method for educating gifted high school students in the areas of mathematics and science. Early college enrollment and dual enrollment are successful options for many gifted students (Stanley, 1991. However, there is a clear need for appropriate mathematics and science curricula for gifted students who remain in high school for four years. This study seeks to determine if an integrated mathematics Integrated mathematics is a style of mathematics education which integrates many topics or strands of mathematics in a real-life context. Instead of presenting a series of classes in algebra, geometry, trigonometry, and statistics in tracks for advanced, average, and remedial and science program can provide effective instruction for secondary gifted students. Review of the Literature Gifted secondary students are a diverse population. It is important to consider the needs of the individual student when choosing appropriate curriculum. Charlton (1994) followed the educational and career outcomes of 12 youths who received rapid educational advancement. Several students in the study noted that although advancement was a successful choice for some, rapid educational advancement may not be the optimal path for others. It appears that to meet the needs of gifted students an array of services is necessary. It is important to make certain that gifted students who elect to remain in high school have curriculum which is appropriate. Recently, mathematics and science curriculum options for advanced high school students have received considerable media attention. The Third International Math and Science Study (TIMMS TIMMS Trends in International Mathematics and Science Study (formerly known as the Third International Mathematics and Science Study) TIMMS TMDE (Test, Measurement, and Diagnostic Equipment) Integrated Maintenance Management System , 1998) compared a sample of the best science students in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. to the best students in other countries. U.S. twelfth graders outperformed only two of the 21 participating countries in mathematics and science. The TIMMS data emphasizes the need to examine how curriculum for advanced students is presented. It has become increasingly important to determine which programs present curriculum in mathematics and science in the most effective manner. In light of the TIMMS data, educators of the gifted should determine the types of programs secondary gifted students need to facilitate their acquisition of higher level mathematics and science curriculum. Effectively integrating the mathematics and science curriculum for gifted students might offer an opportunity for increased learning. Francis and Underhill (1996) described aspects of an integrated program for math and science that emphasized guidelines guidelines, n.pl a set of standards, criteria, or specifications to be used or followed in the performance of certain tasks. from the National Council of Teachers of Mathematics The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally. , Advancement of Science, and the National Research Council. The guidelines compiled by the council indicate connections must be made within the curriculum to both promote and extend student learning. Sherman (1986) proposes that effective integration of the curriculum will strengthen and reinforce student understanding in new areas and will connect to life in the real world. Sherman noted that when mathematics and science are integrated students see the utility and beauty of mathematics, as well as the language and structure of science. Few teachers of the gifted have the time or resources to develop and implement an integrated mathematics and science curriculum at the school level. Noskin (1995) indicates that in order for curriculum integration to be successful, teachers must be treated as professionals, and allowed to form interdisciplinary teams interdisciplinary team, n a group that consists of specialists from several fields combining skills and resources to present guidance and information. with the power to make curricular decisions. Teachers who have had opportunities to participate in such planning teams to develop integrated curriculum found curriculum presented in meaningful contexts more effective than curriculum presented in isolation and in the format of drill (McFaden, Nelson, & Randall, 1996). Research Questions This current study of various curriculum delivery models seeks to answer the following: * Can a differentiated mathematics and science program housed in the high school environment assist gifted students with their acquisition of higher level mathematics and science curriculum? * Are the academic needs of gifted students met in heterogeneously grouped classrooms? * Is an integrated, teacher developed, science and mathematics curriculum effective in improving science and mathematics achievement test scores for secondary gifted students? Method Students The objective of the GA-GEMS program was to give students with high potential in mathematics and science, but not necessarily high verbal ability, an opportunity to explore the disciplines of mathematics and science in an enriched environment. Participants in Project Ga-GEMS, students at a large mid-Georgia High School, were identified using a matrix that considered many different criteria for selection (Table 1). All eighth grade students performing at or above the 90th%ile in mathematics and science on the ITBS ITBS Iowa Test of Basic Skills ITBS Iliotibial Band Syndrome ITBS Industrial Technologies Business Solutions (Iowa Test of Basic Skills The Iowa Test of Basic Skills (ITBS) are a set of standardized tests given annually to school students in the United States. These tests are given to students beginning in kindergarten and progressing until Grade 8 to assess educational development. ) were considered for placement in Project Ga-GEMS. The pool of applicants was given a standardized standardized pertaining to data that have been submitted to standardization procedures. standardized morbidity rate see morbidity rate. standardized mortality rate see mortality rate. individual intelligence test (Wechsler Intelligence Test Wechsler Intelligence Test Definition The Wechsler Intelligence Scales are a series of standardized tests used to evaluate cognitive abilities and intellectual abilities in children and adults. for Children-III) and additional group achievement test scores in science and mathematics were obtained and considered when needed. All potential student participants were administered a pretest pre·test n. 1. a. A preliminary test administered to determine a student's baseline knowledge or preparedness for an educational experience or course of study. b. A test taken for practice. 2. which accompanies the Algebra algebra, branch of mathematics concerned with operations on sets of numbers or other elements that are often represented by symbols. Algebra is a generalization of arithmetic and gains much of its power from dealing symbolically with elements and operations (such as I textbook textbook Informatics A treatise on a particular subject. See Bible. published by Harcourt Brace and Jovanovich. This test is purported pur·port·ed adj. Assumed to be such; supposed: the purported author of the story. pur·port  ed·ly adv. to measure ability to understand
sequences. All potential student participants completed two standardized
instruments, the Gifted Evaluation Scale (GES GES GTN (Global Transportation Network) Exercise SystemGES General Estimates System (NHTSA) GES Ghana Education Service GES Government Economic Service (UK) )(McCarney, 1987) and the Dimensions of Self-Concept Scale (DOSC DOSC Digital Optimum Servo Control (Kenwood) )(Michael, Smith, & Michael, 1989). Table 1
Student Identification Form
Used to Determine Program Participation
Percent or Low Average-Above High Superior
Percentile 0-49 Average 50-84 85-95 96-99
1. Standardized Intelligence Test Score
Test -- Date --
Test -- Date --
Test -- Date --
2. Achievement Test
a. Composite
Test -- Date --
Test -- Date --
b. Science
Test -- Date --
Test -- Date --
c. Math
Test -- Date --
Test -- Date --
3. Teacher Recommendation (GES)
a. Total
b. Intellectual
c. Creativity
d. Academic Apt.
e. Leadership
4. Self-Evaluation (DOSC)
Aspiration
Academic Interest
a. Leadership
b. ID Vs. Alienation
5. Academic Grades
a. Total
b. Science
c. Math
The GES was designed so that teachers with primary observation opportunities could objectively report on students. Specifically, the scale was designed to provide information that may assist in the identification of gifted students. Subscale scores are provided in the areas of: Intellectual, Creativity, Specific Academic Aptitude, Leadership Ability and Performing and Visual Arts visual arts npl → artes fpl plásticas visual arts npl → arts mpl plastiques visual arts npl → . Reported measures for validity and reliability fall in the acceptable range. The DOSC is a self-report inventory Noun 1. self-report inventory - a personality inventory in which a person is asked which of a list of traits and characteristics describe her or him or to indicate which behaviors and hypothetical choices he or she would make self-report personality inventory of five school-related factors of self-concept. The instrument provides five factor scales in the areas of: Aspiration aspiration /as·pi·ra·tion/ (as?pi-ra´shun) 1. the drawing of a foreign substance, such as the gastric contents, into the respiratory tract during inhalation. 2. , Anxiety, Academic Interest and Satisfaction, Leadership and Initiative, and Identification vs. Alienation alienation, in property laws: see tenure. alienation In the social sciences context, the state of feeling estranged or separated from one's milieu, work, products of work, or self. . For the secondary school population, reports of validity and reliability fall in the acceptable range. After obtaining information on all possible student participants, an identification profile was completed for each student (Table 1). An identification team was formed consisting of a science teacher, a mathematics teacher, a secondary curriculum coordinator, and the program director for gifted education Gifted education is a broad term for special practices, procedures and theories used in the education of children who have been identified as gifted or talented. Programs providing such education are sometimes called Gifted and Talented Education (GATE) or . Parents were informed of the program and student interviews with potential participants were conducted. Student placement in the Ga-GEMS program was determined by a juried team based decision. The Ga-GEMS program included a total of 32 students out of 48 who were eligible. To form a control group, Ga-GEMS participants were matched with students from two similar schools within a 30-mile radius of the intervention A procedure used in a lawsuit by which the court allows a third person who was not originally a party to the suit to become a party, by joining with either the plaintiff or the defendant. site. The control group consisted of 32 students who were matched with the Ga-GEMS group on age (within six months), sex, grade, mathematics and science scores on the ITBS (within five percentile percentile, n the number in a frequency distribution below which a certain percentage of fees will fall. E.g., the ninetieth percentile is the number that divides the distribution of fees into the lower 90% and the upper 10%, or that fee level points), race and family income. All student participants attended schools where tracking was in place for mathematics and science and all participants were in the highest track. During the academic year, control group students participated in their regular mathematics and science classes while Project Ga-GEMS students participated in the newly developed integrated mathematics and science curriculum. Curriculum The curriculum was designed to facilitate the development and use of higher order thinking skills The concept of higher order thinking skills became a major educational agenda item with the 1956 publication of Bloom's taxonomy of educational objectives. The simplest thinking skills are learning facts and recall, while higher order skills include critical thinking, and incorporate visual and tactile tactile /tac·tile/ (tak´til) pertaining to touch. tac·tile adj. 1. Perceptible to the sense of touch; tangible. 2. Used for feeling. 3. experiences to reinforce concepts and to help students generate basic knowledge of the disciplines of science and mathematics. Specifically, Ga-GEMS engaged students in hands-on experiences created to enhance learning by teaching mutually reinforcing concepts across the subject areas of mathematics and science. Ten teachers spent one-year reviewing and realigning curriculum in biology, chemistry, physical science, Algebra II, and geometry geometry [Gr.,=earth measuring], branch of mathematics concerned with the properties of and relationships between points, lines, planes, and figures and with generalizations of these concepts. . The curriculum for the Ga-GEMS program was written by four secondary mathematics teachers, four secondary science teachers and two middle school teachers. Using acceleration and curriculum compacting, students covered the content normally taught in Algebra II, geometry, chemistry, biology, physics and physical science. Content presentation differed significantly from the typical classroom. For example, prior to balancing equations in chemistry, appropriate mathematics concepts were introduced and mastered. When set theory was taught in Algebra II, classification systems were covered in Biology. Teachers realigned the curriculum so that mutually reinforcing concepts could be presented across the subject areas of mathematics and science (See Table 2). A team teaching approach was used by the teachers implementing the curriculum. A mathematics and science teacher were paired together for the blocked instructional period. The paired team determined the classroom teaching responsibilities based on the subject area. In all, teachers spent more than 1000 hours preparing the curriculum with an additional 105 hours of consultation during the first year of implementation of the curriculum. Table 2
Curriculum Chart Indicating Relationship Between
Topics Taught and Subject Areas During the First
Semester of Project Ga-GEMS
Math Science Math and Science
Sets Sets/Classification
Process Skills/Lab
Safety
Measurement
Basic Operations Matter Structure of Matter
Algebraic Expressions Scientific Notation
Exponents
Angle Measurement
Linear Equations Minerals/Rocks Model Mineral
Volcanoes/Heat Construction
Earth Forces/Energy Mechanical Forces
Coordinate Geometry Motion/Gravity/Work
Force Formulas Machines
Slope Mechanical
Advantage
Teachers implementing the curriculum used a team teaching approach, and both teachers had a common planning period. Students were assigned as·sign tr.v. as·signed, as·sign·ing, as·signs 1. To set apart for a particular purpose; designate: assigned a day for the inspection. 2. to participate in the new curriculum for two hours and forty-five minutes a day for two academic years. The blocked time permitted extended labs and exploratory activities, and lunch was scheduled to accommodate labs or field trips. Students might spend two hours a day for one week or more on science oriented o·ri·ent n. 1. Orient The countries of Asia, especially of eastern Asia. 2. a. The luster characteristic of a pearl of high quality. b. A pearl having exceptional luster. 3. activities under the direction of the science teacher assisted by the mathematics teacher. Similarly, the mathematics teacher might be responsible for an extended period of classroom learning time in mathematics. To reinforce interrelated in·ter·re·late tr. & intr.v. in·ter·re·lat·ed, in·ter·re·lat·ing, in·ter·re·lates To place in or come into mutual relationship. in concepts, similar topics such as balancing equations in both algebra and chemistry were covered during the same class period. At the close of the two-year program, data were collected on all student participants and the control group. Results Quantitative Data Collection The Science and Mathematics sections of the ACT (American College American College is the name of:
Table 3
T-Tests Comparing the Act Scores of the
Central High Ga-Gems Participants to the
ACT Scores of the Control Group
Variable N Mean
(*)Science
Control 32 47.96
Ga-GEMS 32 60.00
(*)Math Total
Control 32 60.37
Ga-GEMS 32 75.42
(*) Pre-Algebra/Elementary Algebra
Control 32 63.50
(*)Ga-GEMS 32 77.42
(*)Intermediate Algebra/Coordinate Geometry
Control 32 45.08
Ga-GEMS 32 69.27
(*)Plane Geometry/Trigonometry
Control 32 63.08
Ga-GEMS 32 75.69
(*)p < .05 Qualitative Data Operational definitions were developed for the seven categories of classroom activity specified in Table 4. Three graduate research assistants rated a sample 45-minute videotape videotape Magnetic tape used to record visual images and sound, or the recording itself. There are two types of videotape recorders, the transverse (or quad) and the helical. . The videotape was analyzed an·a·lyze tr.v. an·a·lyzed, an·a·lyz·ing, an·a·lyz·es 1. To examine methodically by separating into parts and studying their interrelations. 2. Chemistry To make a chemical analysis of. 3. using a 3-minute variable interval schedule. Classroom activities were rated using a rating sheet that delineated de·lin·e·ate tr.v. de·lin·e·at·ed, de·lin·e·at·ing, de·lin·e·ates 1. To draw or trace the outline of; sketch out. 2. To represent pictorially; depict. 3. the types of activities that were present in the classroom (Table 4). Inter-rater reliability Inter-rater reliability, Inter-rater agreement, or Concordance is the degree of agreement among raters. It gives a score of how much , or consensus, there is in the ratings given by judges. among the three graduate assistants was recorded at .92. Table 4
Percent of Occurrences of Various
Classroom Activities in Ga-GEMS and
Control Classrooms
Activity Ga-GEMS Control
Classroom Classroom
Lecture 27% 45%
Lab Work 22% 0%
Seat Work 5% 14%
Question and Answer 14% 17%
Group Work 23% 8%
Teacher Giving Directions 6% 9%
No Structured Activities 3% 7%
Videotapes were taken of the control classroom and the five classrooms that served the control group students. The Ga-GEMS classroom and the control group classes were each taped for a period of 45 to 55 minutes on 10 occasions. The videotapes were analyzed using a 3-minute variable interval schedule. Classroom activity was rated using a rating sheet that delineated the types of activities that were present in the classroom (See Table 4). The frequency with which certain activities in the Ga-GEMS classroom occurred was different from the frequency of similar activities in the control classrooms (see Table 4). Students spent more mathematics and science classroom time doing hands-on activities in the Ga-GEMS classrooms as opposed to the control classrooms. In the control classrooms, 20% more time was spent in lecture. As they exited the Ga-GEMS programs, students completed a written survey which asked each student to explain their reason for electing to remain in high school and participate in the Ga-GEMS program as opposed to electing to participate in early college entrance. Of the 28 students who responded to the survey, 25 indicated that extracurricular activities such as sports, elected offices, and cheerleading The examples and perspective in this article or section may not represent a worldwide view of the subject. Please [ improve this article] or discuss the issue on the talk page. had influenced their choice to remain in high school. Three students indicated that financial concerns had influenced their decision to remain in high school. Follow-up Testing As Ga-GEMS participants exited high school, the Scholastic Aptitude Test ap·ti·tude test n. An occupation-oriented test for evaluating intelligence, achievement, and interest. scores of Ga-GEMS participants and the control group, were compared (See Table 5). Four student had moved during the course of the study, leaving 28 pairs of students for the final post-intervention comparison. Ga-GEMS participants scored significantly higher on the mathematics and total score areas of the SAT. There was no significant difference in verbal scores. Table 5
T-Tests Comparing the SAT Scores of the
Ga-GEMS Participants to the SAT Scores
of the Control Group
Variable N Mean
(*)Math
Group
Control 26 570.77
Ga-GEMS 26 594.77
(*)Verbal
Control 26 552.69
Ga-GEMS 26 590.00
(*)Total
Control 26 1123.46
Ga-GEMS 26 1184.77
(*)p < .05 Discussion Limitations Although the data supporting Project Ga-GEMS appears quite impressive, there are some limitations to the study. It took over 1000 hours to develop the curriculum for Project Ga-GEMS. Many school districts cannot afford the costs or man hours to undertake such an extensive curriculum development project. Project Ga-GEMS contains many components which have purportedly pur·port·ed adj. Assumed to be such; supposed: the purported author of the story. pur·port influenced the achievement level of gifted students: superior teachers, blocked scheduling, homogenous homogenous - homogeneous grouping, extended laboratory time and intenerated curriculum. The current study cannot determine which component or which combination of components of the project is responsible for student achievement gains in mathematics and science. A research design which looked separately at the variables would help in determining the effectiveness of various components of Project Ga-GEMS. The implementation of Project Ga-Gems was limited to one site. The generalizability of the results is called into question because of the limited implementation. To further determine the effectiveness of the Ga-GEMS curriculum, the curriculum would need to be implemented in additional sites. Strengths Accelerated programs such as early college entrance and dual enrollment accommodate the needs of some gifted students. For those who prefer to stay in high school because of interests in other areas such as leadership, sports, and social/emotional areas, Project Ga-GEMs offers an opportunity for gifted students to continue to pursue their interests while receiving challenging and appropriate curriculum in mathematics and science entire academic program in the areas of mathematics and science. Instead of developing a similar curriculum, interested school systems could make adjustments to the curriculum developed by Project Ga-GEMS. Since the Ga-GEMS curriculum is in place, replications of the study would be much less expensive. In light of the recent TIMMS data, clearly, it is time we considered major modifications in the curriculum for gifted students. Project Ga-GEMS offers a feasible alternative for educating gifted students in the areas of mathematics and science. Replications of the project to further study effectiveness are certainly indicated. REFERENCES American College Test, (n.d.). Iowa City Iowa City, city (1990 pop. 59,738), seat of Johnson co., E Iowa, on both sides of the Iowa River; founded 1839 as the capital of Iowa Territory, inc. 1853. Among its manufactures are foam rubber, animal feed, paper, and food products. The city is the seat of the Univ. , IA: American College Testing (new edition each year). Charlton, J.C. (1994). Follow-up insights on rapid educational acceleration. Roeper Review, 17(2), 123-130. Francis, R. & Underhill, R.G. (1996). A procedure for integrating math and science. School Science and Mathematics, 96(3), 114-119. Lemley, D. (1994). Motivating underachieving gifted secondary students. Gifted Child gifted child Child naturally endowed with a high degree of general mental ability or extraordinary ability in a specific domain. Although the designation of giftedness is largely a matter of administrative convenience, the best indications of giftedness are often those Today, 17, 40-41. McCarney, S.B. (1987). Gifted Evaluation Scale, Hawthorne Educational Services, Colmbia, MO. McFaden, D.M., Nelson, B.A.,& Randall, C.M. (1196). Redesigning the model: A successfully integrated approach to teaching and learning. Bulletin, 80, 1-6. Michael, W. B., & Smith, R. A. (1989). Technical manual for the Dimensions of Self-Concept. San Diego San Diego (săn dēā`gō), city (1990 pop. 1,110,549), seat of San Diego co., S Calif., on San Diego Bay; inc. 1850. San Diego includes the unincorporated communities of La Jolla and Spring Valley. Coronado is across the bay. : Edits. Noskin, D.P. (1995). Seeking coherence coherence, constant phase difference in two or more Waves over time. Two waves are said to be in phase if their crests and troughs meet at the same place at the same time, and the waves are out of phase if the crests of one meet the troughs of another. through interdisciplinary teaching Interdisiplinary teaching is a method, or set of methods, used to teach a unit across different curricular disciplines. For example, the seventh grade Language Arts, Science and Social Studies teachers might work together to form an interdiscipinary unit on rivers. . American Secondary Education, 24(1), 34-40. Sherman, L. A. (1986, November). Cooperative strategies in secondary mathematics and science classes: Three comparative studies. Paper presented at the annual meeting of the School Science and Mathematics Association, Lexington, KY. US Department of Education, National Center for Educational Statistics. (1998). Initial findings from the Third International Mathematics an Science Stud stud 1. purebred. 2. a place, usually a farm, at which purebred animals are maintained and reproduced. stud animal an animal registered in a stud book. ), (TIMMS): A study of the US twelfth-grade mathematics and science achievement in international context. Washington, D.C.: US Government Printing Office Manuscript manuscript, a handwritten work as distinguished from printing. The oldest manuscripts, those found in Egyptian tombs, were written on papyrus; the earliest dates from c.3500 B.C. submitted April, 1998. Revision accepted May, 1999. Tandra Tyler-Wood is the Special Education Program Coordinator in the Department of Technology and Cognition cognition Act or process of knowing. Cognition includes every mental process that may be described as an experience of knowing (including perceiving, recognizing, conceiving, and reasoning), as distinguished from an experience of feeling or of willing. at the University of North Texas. She developed and ran the Summer Opportunities Program for Gifted Students at State University of West Georgia In recent years, the university has been named by the Princeton Review as one of the Best Southeastern Colleges and one of America's Best Value Colleges. Its 109 programs of study include 60 at the bachelor's level, 45 at the master's and specialist's, two at the doctoral level and two for ten years. Mark Mortensen is an Assistant professor in the Department of Technology and Cognition at the University of North Texas. His research interests include multimedia systems, distance education and digital media production. Michael Cass is Associate Professor in the Special Education Department at the State University of West Georgia. His research interests include effective programming for special needs students. Dawn Putney is Assistant Dean at the State University of West Georgia. Her research interests include the development and implementation of effective curriculum for learners with special needs. |
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