Home » math » Data needs an interpretation to have meaning

# Data needs an interpretation to have meaning

Lesson: “Data has no meaning without a physical interpretation”

Content objectives:
1. SWBAT to identify trends in data (apparent linear plots; apparent linear data plus noise; and simple harmonic motion.)
2. SWBAT to id

Thesis: raw data doesn’t tells us anything physical phenomenon. We always first need to know what physical phenomenon we are analyzing, before we can interpret it.

Tier III vocabulary: Simple harmonic motion

Launch: Students are given graph paper, and data.  Plot the given ata points, and connect the dots in a way that they think is logical.

Question: Justify why you connected the dots in that way. Why not in some other way?

Direct Instruction/guided practice
Part A. Teacher instructions:
Print out a sine wave (attached.)
Draw a straight line across it, from upper right to lower left.
The line will intersect the sine wave at 7 points.
Overlay graph paper on top of this, and plot these 7 points.

Tag six more points from the sine wave, that are not on the original straight line.
These points should be at the wave’s maxima, minima, and zeroes, and other points.
Determine the Cartesian coordinates for them,
Give students graph papers, and at first, only 7 data points. Additional data points come afterwards.

If one were to plot only these 7 points, they would appear as a straight line. A naive reading of the raw data would lead one (mistakenly) to believe that we are studying some kind of linear phenomenon.Give examples of linear phenomenon.
One at a time, give new data points, ask them to re-draw their graph each time

Part A Student Instructions
Use the graph that you created for the Do now.
What function (line, curve, etc) best fits all of this this data? (both old and new data points.)
Draw the line/curve that best fits.

Part B: Examples of data not involving motion: Size of objects from 10^1 meters, to 10^20 meters (human-size up to galactic structures.) The Scale of The Universe (interactive applet)

Independent /collaborative work:
Part A: Justify your choice: What real world motion would produce such a function? Think-Pair-Share

After the discussion, the teacher reveals what produces such data: SHM, Simple Harmonic Motion:

Summative question, tying this all together: Why couldn’t most students plot the data correctly, even after the final data points were added? Answer: Unless you know what kind of phenomenon you are studying, you have no idea whether the data is supposed to be linear, harmonic, exponential, etc. Data – bt itself – has no meaning without a physical interpretation.

Part B: Last night they built a data table for this part of the lesson. As we use “The Scale of The Universe” (interactive applet) they’ll fill in sizes of objects at all scales.

Closure:
Query multiple students: Where do you experience SHM in your own life?
Possible answers: Moving back-and-forth on a swing, pendulum of a clock, automobile suspension system

Homework:
Textbook: Physics: Principles and Problems (Glencoe)
Read Chap. 2, Section 1, “Representing Motion”, and Section 2, “Where and When? Coordinate Systems”
Write definition for highlighted “new vocabulary” words. Page 36. Section 1 Review, #1-4.

## Learning standards

A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas (2012)

Dimension 1: Scientific and Engineering Practices: Practice 4: Analyzing and Interpreting Data.
“Once collected, data must be presented in a form that can reveal any patterns and relationships and that allows results to be communicated to others. Because raw data as such have little meaning, a major practice of scientists is to organize and interpret data through tabulating, graphing, or statistical analysis. Such analysis can bring out the meaning of data—and their relevance—so that they may be used as evidence.”