Academic journal article Journal of Secondary Gifted Education

Conducting a Teaching Experiment with a Gifted Student

Academic journal article Journal of Secondary Gifted Education

Conducting a Teaching Experiment with a Gifted Student

Article excerpt

In this study, the teaching experiment methodology is used to observe firsthand a gifted student's mathematical learning and reasoning. A series of teaching experiments was conducted with 1 gifted and 1 average 7th-grade student to investigate how the gifted student's mathematical concepts and operation constructions differed from those of the average student. The teaching experiment approach provides opportunities for gifted and average students to be challenged by immersion in various advanced mathematical topics. The data analysis provides evidence that the gifted student was more adept at applying mathematical ideas to unfamiliar problems. As a result of being able to see mathematical patterns and to think abstractly, the gifted student was able to use analytical, deductive, and inductive reasoning to solve problems in more flexible and creative ways than the average student.


The growing popularity of educational programs tailored to the special needs of gifted students makes it especially important that educational research findings be used to support the rationale for providing such programs. One of the major challenges those in gifted education face is convincing policymakers of the need for specialized personnel and differentiated learning models to serve gifted students (Gallagher, 1997; Renzulli, 1982; Renzulli & Reis, 1998) by challenging the hackneyed idea that "gifted students can make it on their own." Communication of related research findings must create an understanding as to why traditional teaching methods in regular classrooms are inadequate for serving the needs of gifted students (Park, 1989; Westberg, Archambault, Dobyns, & Salvin, 1993).

Although mathematics is generally considered a strand in the theory of intelligence (Gardner, 1999; Sternberg, 1985), the nature of being mathematically gifted and how the needs of mathematically gifted students can be met are relatively unexplored areas. Thus far, research studies have demonstrated the need for gifted students to have access to advanced mathematical content (Johnson & Sher, 1997) and exposure to authentic and challenging mathematics problems (Johnson, 1993; Kolitch & Brody, 1992). However, mathematics curricula and instructional modifications made for gifted students are often inappropriate because of the highly repetitive nature of the courses and their lack of depth (Johnson & Sher; Kolitch & Brody; Park, 1989; Westberg et al., 1993). Thus, there is a strong need for research about the kinds of educational experiences that should be provided for mathematically gifted students, as well as research into the use of technological tools that could effectively and appropriately enhance instruction.


By conducting a series of teaching experiments, the author sought to explore individual differences between a gifted student and an average student in terms of their abstract reasoning abilities. In the early 1980s, the term teaching experiment was used to describe a research technique designed to help mathematics educators develop a greater understanding of students' mathematical constructions. This form of inquiry has since become a popular way of doing research in mathematics education. The teaching experiment was originally used to connect the practices of mathematics education research to teaching mathematics (Steffe & Thompson, 2000), and the implementation of well-developed teaching experiments enables mathematics educators to elicit evidence of students' mathematical learning and reasoning processes and to construct models that explain their responses and mathematical thinking.

Teaching experiments consist of recording and analyzing a number of teaching episodes in which the analysis of the previous session(s) is used to guide the next teaching episode. During a teaching experiment, the mathematical reasoning of the students is the focus of the researcher's attention, just as it is in a clinical interview. …

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