Educational services to meet the academic needs of gifted students have generally been constructed based on the approaches of acceleration and enrichment. It is not a coincidence that these approaches have been developed in response to two distinct characteristics of gifted students: the pace and quality of learning. In contrast with acceleration, enrichment does not speed up the pace of the curriculum but instead intends to develop the quality of the curriculum and afford students a richer educational experience (Clark, 2008, p. 407-411; Schiever & Maker, 2003, p. 164-165). Reasoning at a more advanced level (Silverman, 1993, p. 54) and making better connections among separate ideas (Clark, 2008, p. 293; Gallagher & Gallagher, 1994, p. 85) are crucial characteristics of the gifted and suggest a need to incorporate features of depth and complexity into the core curriculum.

Existing gifted programs generally accentuate high levels of thinking of various emphases and in various manners corresponding to the goals of the program. Whereas the Integrated Curriculum Model (VanTassel-Baska & Wood, 2009, pp. 655-693) and Parallel Curriculum Model (Tomlinson, 2009, pp. 571-599) emphasize integrated thinking among or within the disciplines, The Study of Mathematically Precocious Youth (Stanley & Benbow, 1983) and Iowa Excellence Program for high school students (Assouline, Blando, Croft, Baldus and Colengole, 2009, pp. 1-17) emphasize academic acceleration. Whereas the Enrichment Triad Model (Reis and Renzulli, 2009, pp. 323-353) and The Autonomous Learner Model for the Gifted and Talented (Betts & Kercher, 2009, pp. 49-105) emphasize actualizing potential outside of the school context, the Purdue Three-Stage Model (Moon, Kolloff, Robinson, Dixon & Feldhusen, 2009, pp. 289-323) stresses critical and creative thinking skills that can be integrated into the core curriculum.

Depth and complexity are two approaches that can be embedded in any thinking skill to increase the quality or the level of thinking process. To put it differently, a higher level of thinking skills and depth and complexity are not completely unrelated constructs. However, their conceptual interrelationship makes it difficult to sort out the constructs of depth and complexity from the existing gifted programs unless their roles are stated conceptually or operationally by the program developer.

Kaplan (2009) disambiguated these constructs in her model to guide practical applications in gifted education. The author set forth the prompts of depth and complexity and their corresponding icons, definitions and sample questions. Depth prompts consist of the language of the discipline (nomenclature, lexicon or vocabulary of the study-What terms or words are specific to the work of the disciplinarian?); details (traits, attributes, characteristics to describe something-What features characterize this?); patterns (recurring events-What was the order of events?); unanswered questions (influences or forces that shape ideas-What is still not understood about this area, topic, study or discipline?); rules (stated or unstated reasons or explanations-How is this structured?); ethics (dilemmas, controversies, issues-What dilemmas or controversies are involved in this area, topic, study, or discipline?); and big ideas (generalizations, principles and theories-What general statement includes what is being studied?). Complexity prompts consist of over time (past, present, future happenings-How has time affected the information?); points of view (perspective, opinion-What are the opposite viewpoints?); and inter-disciplinary (connections between and across the disciplines-How are these ideas related or connected? (p. 242).

Dodds (2010) performed research on 88 gifted and 88 non-gifted students in the 3rd, 4th and 5th grades who were instructed by teachers trained in the use of these prompts of depth and complexity. He measured the depth and level of complex understanding of the participants in autumn 2008 as a pretest and in spring 2009 as a posttest. After evaluating the results, he concluded that (1) instruction focused on the prompts of depth and complexity developed the levels of understanding of both gifted and non-gifted students, (2) the level of understanding of the gifted students improved more than that of the non-gifted, and (3) gifted and non-gifted students found prompts of depth and complexity to be useful, interesting and challenging.

Depth

In the context of the study, depth is defined as understanding core meanings by building causal connections among events or situations (Egan, 2010; Lehrer, 2001, Jensen & Nickelsen, 2008; Kaplan, 2009; Salmon, 1998; VanTassel-Baska & Stambaugh, 2006). One of Gowin’s (1970) observations in school science laboratories is that students are occupied with observing, making records and transforming data to tables, diagrams and graphics. During these activities, however, an essential aim can be neglected, that of the need to refer to concepts, principles and theories to grasp their underlying reasons (as cited in Novak & Gowin, 1984, p. 56-58). From Gowin’s standpoint, actions dealing with operations more than explanations draw a line between depth and superficiality. Reasons establishes deeper understanding for the happenings around the environment. Assume that a student is confronted with a person who has an allergic of butter. If he concludes that some people has allergy, some people do not, this conclusion seems superficial compared to an effort to understand what makes his body allergic to butter.

Complexity

Understanding, as described by Gallagher (as cited in Folk, 2006, p. 29), can never be complete and can always be enriched and expanded with the formation of new meanings over time. Complexity suggests possibilities and multiplicity in thinking so that comprehension can be extended to new dimensions. In this respect, as the level of complexity increases, the relationships among components increase (Pollock, Chandler, & Sweller, 2002, p. 64). In such processes, as van Merrienboer and Sweller (2005, p. 148-149) explained, an individual is forced to handle a considerable number of simultaneous multiple processes. Several components of knowledge being used simultaneously increases the load of knowledge and processes in the working memory, which activates mental accumulation (van Merrienboer, Kirschner, & Kester, 2003, p. 9). Nonetheless, it should be noted that the primary purpose in complexity is not to expand knowledge by absorbing a surplus of facts and ideas but to simplify meanings by developing relationships among them. This interpretation supports the discussions in the studies of Clark (2008, p. 293), Kaplan (2009), van Merrienboer and Kirschner (2007) and VanTassel-Baska and Stambaugh (2006). The construct of complexity may be described as establishing different relationships among the variables to shift an individual’s understanding into a more general one.

Depth and Complexity in Science

As explained in earlier subsections, depth and complexity are distinguished by their way of channeling thinking processes. Although depth and complexity may be described differently, the relationship between these constructs should not be overlooked. Grotzer’s (2005, p. 3) clarifications indicate that these constructs are closely intertwined. When establishing causal relations in a situation lacking complexity, there are specific flawed assumptions one might rely on erroneously. Students seeking more explicit causes and effects fail to notice the role that passive agents, cannot be easily detected, but having casual connection with the happening in some way, play in scientific explanations. Specifically, Resnick (1996) concluded that students think of causality as being centered and deterministic rather than distributed and probabilistic. On this basis, it can be claimed that the intertwined relationship between depth and complexity in science is due to two underlying principles:

• Scientific explanations basically require causality among the associations of objects (Salmon, 1998, p.5).
• Events are not limited to one natural occurrence but should be observed in a larger network of a system (Page, 2011; Taylor, 2003).

The results of Dodds’ findings suggest promise in the use of depth and complexity in gifted education. However, other than Kaplan’s and Dodds’ studies, there appears to be a lack of studies in the literature focusing on the use of these constructs in the education of gifted students. The scarcity of studies regarding depth and complexity in the role of gifted education suggests a need to explore these constructs both theoretically and experimentally. The current experimental study was conducted with the aim of demonstrating the use of depth and complexity in science education to attain a high level of achievement.

This study aimed at examining the effects of using a science curriculum differentiated in terms of the depth and complexity with gifted 5th-grade students. The effectiveness of this differentiated science curriculum as designed by the researcher was evaluated against three criteria: academic achievement, science process skills and attitude toward science education.

Given the importance of depth and complexity, this study seeks to answer the following question. What are the impacts, in terms of (a) academic achievement, (b) scientific process skills, and (c) attitude toward science education, of instructing gifted students using a science curriculum differentiated on the basis of depth and complexity versus instructing gifted students using a general science curriculum?