Depth and Complexity in My Classroom

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

Terms, signs & symbols of math areas

algebraic terms

variables, functions

operations

axioms & theories

metric and US measurements

Details:What are the defining features or characteristics?

numbers

factors

points

lines

curves

algorithms

Patterns:What elements reoccur? What is the sequence or order of events?

number lines

geometric patterns

problem-solving

probability

polynomials

order of operations

algorithms

standard measurements

Unanswered Questions:What information is unclear, missing, or unavailable?

equations

historical math problems

unforeseen relationships

nanoseconds & other special measurements

organization of data

Rules:What structure underlies this subject? What guidelines or regulations affect it?

the rules of:

problem solving

operations

computations

almost everything in arithmetic, geometry and algebra

ratios

accuracy

Trends:Note factors that cause events to occur. Identify patterns of change over time.

application of math principles & procedures

tools and machines of measurement

data collection and representation

Ethics:What moral principles are involved in this subject? What controversies exist?

misleading statistics

problem-solving techniques

interpretation/application of solutions

logic, probability

applied mathematics

Big Ideas:What theory or general statement applies to these ideas?

math principles, laws

accuracy

systems

validity

scale & structure

Across Disciplines:Relate the area study to other subjects.

geometry-architecture

art-maps

operations-computation-agriculture-business

economics

money-banking-credit

data collection & analysis

interest-taxation

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

interpretation of data

problem solving related to time

time measurement

origins

history of math disciplines & subjects

Multiple Perspectives:How would others see the situation differently?

interpretation of data

representations of data

statistics & point of view

charts, graphs

geometric constuctions