 # Levels – PEN

The Period Of The Pendulum

Levels Of Conceptualization And Related Knowledge

Levels Of Conceptualization

•  Representation of the phenomenon which does not include length of string as a relevant factor
•  Representation of the phenomenon which incorporates but does not isolate the effect of the length of string
•  Discovery of positive covariation between length of string and period (i.e. as length of string increases — period increases)
•  Discovery that length of string is the only factor that covaries with the period
•  Representation of linear relationship between length of string and period
•  Discovery of non-linearity of relationship between length of string and period
•  Unsuccessful attempt to formulate a mathematical representation of a non-linear relationship between string length and period
•  Successful mathematical representation of a non-linear relationship between string length and period [e.g. period proportional to square root of length, T (time) = approximately 2 * the square root of the length]

RELATED KNOWLEDGE
`K1′ – Knowledge Related to Period of the Pendulum

#1-Measurement of Time:

•  DOES NOT FORMALLY1 MEASURE TIME
•  USES AN INSTRUMENT TO MEASURE TIME
•  USES MEASUREMENT INSTRUMENT CORRECTLY AND EXPRESSES THE UNITS OF MEASUREMENT CORRECTLY

1FORMALLY = using a measurement instrument

`K1′ – Knowledge Related to Period of the Pendulum

#2-Measurement of Distance:

•  EYES DISTANCES
•  USES A MEASUREMENT INSTRUMENT
•  USES MEASUREMENT INSTRUMENT CORRECTLY AND EXPRESSES THE UNITS OF MEASUREMENT CORRECTLY
• `K1′ – Knowledge Related to Period of the Pendulum

#3-Ratio – Theoretical Knowledge

•  DOES NOT MENTION “RATIO(S)”
•  USES THE TERM “RATIO”

#4-Ratio – Practical Knowledge

•  DOES NOT FORMULATE RATIOS
•  FORMULATES RATIOS

`K1′ – Knowledge Related to Period of the Pendulum

#5- Proportions – Theoretical Knowledge

•  DOES NOT MENTION PROPORTIONS
•  USES THE TERM “PROPORTIONS”

#6-Proportions – Practical Knowledge

•  DOES NOT FORMULATE PROPORTIONS
•  FORMULATES PROPORTIONS