# Levels – PEN

The Period Of The Pendulum

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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