1. Science Instruction by Inquiry:
D. Livelybrooks, J. Baxter University of Oregon

2. Science by Inquiry Inquiry defined Example: World Cup Soccer Kick
Mathematical opportunities in statistics and data analysis
‘Inquiry’ is a way of learning science that:
* explicitly represents science as a process.
* can closely couple mathematics (data analysis, algebra, calculus) with science instruction.
* can involve context-rich situations, such as “World Cup Soccer Kick!’

3. Inquiry Defined Learn & use scientific processes:
Pose question, identify variables
Refine into a hypothesis
Make a prediction
Experiment to test prediction
Revise hypothesis if necessary

4. Example: World Cup Soccer Kick
Ask a question.
Review prior knowledge.
Energy conservation
Momentum conservation
Newton’s Laws
Pose hypothesis predict.
My question: “how does the initial height of the ‘foot’ affect the distance the ball travels?”
My prior knowledge: Energy conversation to get velocity of foot prior to strike. Energy and momentum conservation to ‘solve’ for ball velocity (just) after strike.
Kinematics to relate distance traveled to velocity of ball after strike.
Hypothesis: “distance traveled is proportional to post-strike ball velocity. If I double the height of the foot, I double the kinetic energy, which is proportional to
Velocity squared. So I expect doubling the height to increase distance traveled by sqrt(2).”

5. Example: World Cup Soccer Kick
Hypothesis:
x  v;
KE  h  v2;
ergo, x2  h
Expect doubling h results in x  sqrt(2)
My question: “how does the initial height of the ‘foot’ affect the distance the ball travels?”
My prior knowledge: Energy conversation to get velocity of foot prior to strike. Energy and momentum conservation to ‘solve’ for ball velocity (just) after strike.
Kinematics to relate distance traveled to velocity of ball after strike.
Hypothesis: “distance traveled is proportional to post-strike ball velocity. If I double the height of the foot, I double the kinetic energy, which is proportional to
Velocity squared. So I expect doubling the height to increase distance traveled by sqrt(2).”

6. Example: World Cup Soccer Kick
A hypothesis and prediction involve:
Independent variable (height)
Dependent variable (ball distance)
Constant variables (mass, etc.)
Students would normally choose according to their question/hypothesis.
For today we have chosen already.
‘Constant variables’ are list of ‘Independent variables’ for next inquiry project.

7. Multiple trials– each ‘foot’ height.
Collect Data
Multiple trials– each ‘foot’ height.

8. Math Analysis
Mathematical opportunities in statistics and data analysis:
Represent data
Describe data
Interpret data

9. height (m) distance (m) 0.085 0.21 0.085 0.85 0.085 0.24 0.085 0.22
Table, Data
height (m) distance (m)

10. Bar Graph

11. X-Y Graph Mention bar graphs, frequency plot, etc.
How is this plot different from a plot of the mean for each height?

12. Describe Data Mathematical Opportunities… Range: variation
Mode: most frequent
Median: middle value
Mean: arithmetic average
Define, back up a page. Talk about context of analysis part of inquiry.
Example: tendency is to use arithmetic (cookbook) mean (from primary school) predisposes to use mean exclusively, later.

13. What if…? Interpret data: What if…? Interpolate values between
data points
Extrapolate values beyond
Slope
What would happen if height were increases to .385 m?
Inquiry question: why is variability increasing with height?
Slope, does it decrease as per our prediction? Or is it constant?

14. Video Analysis
An Aside: One can use a standard videocamera and videotape the experiment. Download (QuickTime) movie to file, and use Vernier Logger Pro to analyze each frame of the movie (dots) for the position of the foot and ball over time. Then can make graphs and ‘model’ them.

15. In Summary Together, Science Inquiry and Mathematical Opportunities:
Identify meaningful context
Pose hypothesis/conjecture
Collect data
Analyze data
Support or modify hypothesis
Good inquiry isn’t always simple physics (or math)

16. Science Instruction by Inquiry:
D. Livelybrooks, J. Baxter University of Oregon