Sensorimotor (birth -2) Schemes are formed mostly from behaviors and perceptions. Children have a difficult time focusing on or thinking about anything not immediately in front of them. Trial-and-error Exploration and manipulation of an object to determine its properties Object permanence The acknowledgement that objects retain their properties even when not physically present Symbolic thought Begins to develop at the end of the stage. Physical objects and events can be represented through symbols
Preoperational (2-6/7 yrs) Due to language and thought development, children are capable of utilizing symbolic schemas to talk about things beyond their immediate presence. Logical reasoning is not yet developed. egocentric Students tend to think about the world only from their perspective. centration inability to focus on two dimensions simultaneously Lacks Reversibility child does not recognize that physical objects retain their properties when changing position Animism the belief that all things are alive and living
Concrete Operational (6/7 -11/12 yrs) Students can now reason using logic, but thinking is often limited to manipulation of physical (i.e., “concrete”) objects class inclusion the ability to classify objects by two or more classifications simultaneously conservation the realization that the amount remains the same, despite alterations in shape or arrangement transductive thinking belief that when two events occur simultaneously, one must have caused the other.
Formal Operational (11/12 + yrs.) Students can now apply logical reasoning processes to abstract ideas and contexts. Proportional reasoning Students can conceptually understand fractions, percentages, ratios, decimals. Hypothetical reasoning Ability to logically deduce conclusions from completely abstract notions. Separating/ Controlling variables Ability to test hypotheses by manipulating one factor while holding others contstant.
Teach the commutative property of mathematics e.g., 2+1 = 3 and 1+2=3 Teach decimal place value Teach fractions to 4th graders which variable, weight, length or height of initial drop, affects a pendulum’s oscillation rate?