# Levels – PEN

The Period Of The Pendulum

Levels Of Conceptualization And Related Knowledge

Levels Of Conceptualization

• [1] Representation of the phenomenon which does not include length of string as a relevant factor
• [2] Representation of the phenomenon which incorporates but does not isolate the effect of the length of string
• [3] Discovery of positive covariation between length of string and period (i.e. as length of string increases — period increases)
• [4] Discovery that length of string is the only factor that covaries with the period
• [5] Representation of linear relationship between length of string and period
• [6] Discovery of non-linearity of relationship between length of string and period
• [7] Unsuccessful attempt to formulate a mathematical representation of a non-linear relationship between string length and period
• [8] 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:

• [0] DOES NOT FORMALLY1 MEASURE TIME
• [1] USES AN INSTRUMENT TO MEASURE TIME
• [2] 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:

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

#3-Ratio – Theoretical Knowledge

• [0] DOES NOT MENTION “RATIO(S)”
• [1] USES THE TERM “RATIO”

#4-Ratio – Practical Knowledge

• [0] DOES NOT FORMULATE RATIOS
• [1] FORMULATES RATIOS

`K1′ – Knowledge Related to Period of the Pendulum

#5- Proportions – Theoretical Knowledge

• [0] DOES NOT MENTION PROPORTIONS
• [1] USES THE TERM “PROPORTIONS”

#6-Proportions – Practical Knowledge

• [0] DOES NOT FORMULATE PROPORTIONS
• [1] FORMULATES PROPORTIONS
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