Complexity

Differentiating the complexity of content means making it more complex for high ability students, those eager to think about complicated ideas and relationships. The complexity of the content of a lesson, unit or course is determined by the density and sophistication of connections between concepts involved in it. In other words, it focuses on the interconnections among concepts, principles, generalizations and theories.

It is easy to confuse complexity of the content with it’s abstractness. What is the difference? Abstractness of content is based on the richness of individual concepts in the content. Complexity of content is based on the relationships among the concepts. The two forms of differentiation are closely related. Concrete content will not be complex because the ideas in it are not related, they are discrete.

Examples

The examples below show simple content and more complex content that includes the simple content. High ability students are capable of learning complex versions. They can learn the simple within the complex. Less able students may be able to learn complex content but they will need more time and support to learn the complex version.

Simple (and Concrete) Complex
Definitions of individual punctuation marks Expressions of joy
Individual events on a timeline Issues and forces that cause wars
Individual math single digit math facts that result in a sum of “7”

6 + 1 = ?
3 + 4 = ?
the different types of relationships (mathematical operations) between numbers less than ten that might generate “7” as a result

___ + ___ = 7

Content organized around an interdisciplinary theme is usually more complex than content relevant to a single discipline so choosing a theme is a good place to begin efforts to create curriculum with complex content. “Change,” “Power,” and “Patterns” are all interdisciplinary themes. The next table presents a collection of “Universal Themes and Generalizations” developed by Dr. James Curry and John Samara.[16]

 

CHANGE

  • Change generates additional change.
  • Change can be either positive or negative.
  • Change is inevitable.
  • Change is necessary for growth.
  • Change can be evolutionary or revolutionary.
 CONFLICT

  • Conflict is composed of opposing forces.
  • Conflict may be natural or human-made.
  • Conflict may be intentional or unintentional.
  • Conflict may allow for synthesis and change.
 EXPLORATION

  • Exploration requires
  • recognizing purpose and responding to it.
  • Exploration confronts “the unknown.”
  • Exploration may result in “new findings” or the confirmation of “old findings.”
FORCE

  • Force attracts, holds, or repels.
  • Force influences or changes.
  • Force and inertia are co-dependent.
  • Force may be countered with equal or greater force.
 RELATIONSHIPS

  • Everything is related in some way.
  • All relationships are purposeful.
  • Relationships change over time.
 POWER

  • Power is the ability to influence.
  • Power may be used or abused.
  • Power is always present in some form.
  • Power may take many forms (chemical, electrical, political, mechanical).
ORDER AND CHAOS

  • Order may be natural or constructed.
  • Order may allow for prediction.
  • Order is a form of communication.
  • Order may have repeated patterns.
  • Order and chaos are reciprocal.
  • Order leads to chaos and chaos leads to order.
 PATTERNS

  • Patterns have segments that are repeated.
  • Patterns allow for prediction.
  • Patterns have an internal order.
  • Patterns are enablers.
 STRUCTURE

  • Structures have parts that interrelate.
  • Parts of structure support and are supported by other parts.
  • Smaller structures may be combined to form larger structures.
  • A structure is no stronger than its weakest component.

 

Interdisciplinary units of study can be found and created around themes. One example is the theme of patterns. Students of all ages can develop rich understandings of patterns that are relevant to the arts, sciences and humanities through their study of patterns in botany. These understandings can be revisited and enhanced throughout their education without repeating content. Increasingly sophisticated versions of content relevant to patterns in growth and development can be introduced over the years. They might explore and analyse patterns related to the growth and development of bean seedlings by tracking changes in their size, structure, appearance, responses to changes in access to light, water, nutrients, etc. They can take the role of botanists, identifying patterns that influence the life of their plant, seeking relationships among light, water and nutrients that might enhance (or end) the life of the plant or make its beans more (or less) nutritious or its foliage more (or less) attractive, etc. Students may identify and investigate patterns in other disciplines as well, exploring those patterns, taking on the role of a professional who would work with them. Examples include, meteorologists studying weather patterns, authors who use a “formula” in their writing, architects who design buildings, and so on.





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