Depth and Complexity

Language of the Discipline: What vocabulary terms are specific to the content or discipline?

Way to apply this in math: terms, signs, symbols, algebraic terms, variables, functions, operations

Details: What are the defining features or characteristics? Find examples and evidence to support opinions and ideas.

Way to apply this in math: numbers, factors, points, lines, curves, algorithms

Patterns: What elements reoccur? What is the sequence or over or events? Make predictions based on past events.

Way to apply this in math: number lines, geometric patterns, problem solving, polynomials, order of operations, algorithms, standard measurements

Unanswered Questions: What information is unclear, missing, or unavailable? What evidence do you need? What has not yet been proven?

Way to apply this in math: Equations, historical math problems, unforeseen relationships, special measurements, organization of data

Rules: What structure underlies this subject? What guidelines or regulations affect it? What hierarchy or ordering principle is at work?

Way to apply this in math: rules of: problem solving, operations, computation, algebra rations, accuracy

Trends: Note factors (Social Economic, Political, Geographic) that cause events to occur. Identify patterns of change over time.

Way to apply this in math: application of math principles and procedures, tools and machines of measurements, data collection and representation

Ethics: What moral principles are involved in this subject? What arguments could emerge from a study of this topic?

Way to apply this in math: misleading statistics, problem-solving techniques, interpretation/application of solution, logic, probability, applied mathematics

Big Ideas: What theory or general statement applies to these ideas? How do these ideas relate to broad concepts such as change, systems, chaos vs. order, etc.? What is the main idea?

Way to apply this in math: math principles, laws, accuracy, systems, validity, scale and strucure

Across the Disciplines: Relate the area of study to other subjects within, between, and across disciplines.

Way to apply this in math: geometry- architecture, art-maps, operations-computation-agriculture-business, economics, money-banking-credit, data collection and analysis, interest-taxation

Changes Over Time: How are elements related in terms of the past, preset, and future? How and why do things change? What doesn’t change?

Way to apply this in math: Interpretation of data, problem solving related to time, time measurement, origins, history of math discipline and subject

Different Perspectives: How would others see the situation differently?

Way to apply this in math: interpretation of data, representation of data, statistics and points of view, charts and graphs, geometric structures