Instruction that is differentiated for highly able students must increase the complexity of the content as well as the process by which the students learn so that depth and breadth are demonstrated in the products by which they present their learning (Kingore, 2004).

Elements of Abstract Thinking, Complexity, and Depth (Kingore, 2004)

Abstractions: Abstract thinking poses and reconciles paradoxes and involves the application of symbols and metaphorical thought.
• Which symbols could represent the Allies in WWII?
• How is a hornet’s nest like an atom?

Change Over Time: Students consider the past, present, and future concepts with enduring value is an area of study as they analyze change over time.
• How has the Colorado Rockies changed over time?
• How has time affected people’s attitudes toward new technologies?
• Based upon economic recessions in the past, what are the future trends of economics in the United States?

Essential Questions: Open-ended questions that represent the heart of exploring and interpreting the big ideas of a topic and related areas such as:
• How is observation crucial to scientific advancement?
• What patterns exist in story structure?
• How is mathematics useful in daily life?
• What interrelationships are essential among the systems of the human body?

Ethics: Ethical concerns are revealed by the dilemmas or controversies related to a topic.
• How has bias affected the topic of civil rights?
• What is your interpretation of the judgment, “Asian students are better mathematicians than American students”?

Generalizations: Inferred ideas that express understanding of relationships among data or principles.
• What is the key relationship among resources and renewable energy sources?
• What overarching meaning can be drawn from the history of space exploration?

Interdisciplinary Content: Exploring a topic across two or more academic disciplines enriches the depth and breadth of student understanding.
• What are the common elements of the scientific method and the writing process?
• Which events influenced the renaissance movement in art or literature?

Issues: Disputed aspects of a topic whose resolutions are significant to the public.
• Why is the resolution of the issue of limited fossil fuel resources significant to the public?
• How relevant is the issue of racism today?

Language and Terminology: Involve the use of more sophisticated words and specific vocabulary related to a field of study.
• Which five words are most important to the topic of habitats?
• Which terms best describe the process of mathematical problem solving?
• What terminology is specific to the field of medicine?

Methodology: Involves procedural knowledge and how proficiently students carry out a process.
• Which method is most relevant to this experience?
• How would a professional poet complete this writing assignment?

Patterns: Identify recurring events, elements, behaviors, and ideas within a topic or event.
• What is the implied mathematical rule?
• What are the recurring ideas involved in Shakespeare’s literature?

Perspectives: Involves the multiple or unique viewpoints possible when people respond to ideas, events, or behaviors.
• What are the opposing viewpoints regarding the conflict in Iraq?
• How does your perspective affect the meaning of the book?

Resources and Technology: Involve the use of more sophisticated resources that are more concept-dense than resources typical of the grade level. Technology use is sophisticated and reflects a student’s technological proficiency.
• How can you determine bias in the resources you choose?
• How can you demonstrate technological proficiency?

Tips for Differentiating with Abstract Thinking, Complexity, and Depth (Kingore, 2004)

1. The teacher incorporates abstract thinking, complexity, and depth as criteria on rubrics.
2. The teacher refers to the elements of abstract thinking, complexity, depth to increase challenge through inquiry and tiering.
3. The teacher uses the elements to focus student’s thinking and advanced investigations.
4. The teacher selects the elements.
5. The teacher and student collaboratively select the elements.
6. The students self-select elements to enhance their learning.