Backwards faded scaffolding laboratory/presentation: measurement and proportion

This is the first laboratory at the start of the semester of Astronomy 210L at Cuesta College, San Luis Obispo, CA. This course is a one-semester, optional adjunct laboratory to the Astronomy 210 introductory astronomy lecture, taken primarily by students to satisfy their general education science transfer requirement.

Students are instructed on how to prepare for each weekly laboratory.

Students answer short weekly pre-lab assignments, hosted by SurveyMonkey.com.

Like Will Smith in the movie I Am Legend, students are required to look up today's sunrise and sunset times. Because as in the movie, in astronomy it is important to know when it is safe and when the zombie vampires are out there.

Students also need to look up the current phase of the moon, as knowing when the werewolves are out and about is important, too.

Students are also assigned to read selected online articles on current events in astronomy. One never knows when it might be important to convince alien abductors that Earth technology and space exploration is sufficiently advanced enough to avoid being probed like cattle.

Students take a short current events quiz during the first 10 minutes of lab on sunrise/sunset times (to within +/- 10 minutes), moon phase, and multiple-choice questions on selected astronomy news articles. This motivates students to show up promptly to lab, as the time cut-off for the quiz is strictly enforced!

Students are to work in assigned groups of 3-4 on measuring and analyzing their heights and arm spans. This is intended to be a simple activity to introduce students to working cooperatively and collaboratively on "Exploration" and "Does Evidence Match a Given Conclusion?" segments of backwards-folded scaffolding laboratories (Tim Slater, Stephanie Slater, Daniel J. Lyons, Engaging in Astronomical Inquiry, W.H. Freeman & Company, New York, 2010). Subsequent laboratories will incorporate more complete "What Conclusions Can You Draw From This Evidence?" and "What Evidence Do You Need to Pursue?" and "Formulate a Question, Pursue Evidence, and Justify Your Conclusion" sections of a complete backwards-folded scaffolded laboratory.

Purportedly the perfect human proportions are where arm spans are equal to heights. These people are called "Da Vincis."

However, "T. rexes" are people whose arm spans are shorter than heights.

Meanwhile, "monkeys" are people whose arm spans are longer than their heights. These are the people who you want covering your back in a barroom brawl.

Students check out laptops to access the course webpage, where the laboratory instructions are posted (in lieu of a printed laboratory manual). (Subsequent backwards-faded scaffolded laboratories make more explicit use of online resources for data acquisition and analysis.)

2-m sticks will be used to make measurements to the nearest centimeter.

Everyone should take off their shoes in order to measure each other's heights (to the nearest centimeter).

Also measure each other's arm spans (to the nearest centimeter).

Record your measurements on a whiteboard, and place it up at the front of the classroom.

When all tasks have been completed, all students should come to the instructor as a group and lay their reports on the counter. A four-sided die is rolled to see which one report will be representatively graded for the group.

Cuesta ThinkPad(TM) laptops (wireless networking, internet browser)
(appropriate, responsible in-class use of personal laptops allowed)
meter sticks (2 m)

Individual measurements can be statistically analyzed together to identify trends and patterns.

Students will conduct a series of inquiries about biometric measurements, as an introduction to backwards-scaffolded astronomy inquiry laboratories.

1. Exploration
Using a 2-m stick to measure the heights and arm spans, you will categorize each class member (anonymously) in terms of relative proportions.

a. Take off your shoes, and take turns measuring each group member's heights and arm spans using a 2-m stick, to the nearest centimeter.
Student: Height: Arm span:
1 ___ cm ___ cm
2 ___ cm ___ cm
3 ___ cm ___ cm
4 ___ cm ___ cm

b. Record each group members' height and arm span information on a whiteboard, and place this at the front of the classroom. (Use group and student numbers instead of student names to identify individual height and arm span data.)

c. Categorize each student in your class as a tall rectangle (height greater than arm span), square (height equal to arm span), or wide rectangle (height less than arm span). Count the total numbers of tall, square, and wide students in the classroom.

Number of tall rectangle students: __________.
Number of square students: __________.
Number of wide rectangle students: __________.

d. Make generalization statements, in a complete sentences, comparing the numbers of tall, square, and wide students in your classroom.

Generalization statements: __________.

e. Calculate the average height for your class (to the nearest centimeter), and the average arm span for your class (to the nearest centimeter).

Average height: __________.
Average arm span: __________.

f. Categorize each student in the class as either below/above average height, and also either below/above average arm span. (Also note any student(s) that may have an exact average height and/or arm span, to the nearest centimeter.) Keep a record of your results in the tally sheet below using tick marks.

Below average height, below average arm span: _____
Below average height, above average arm span: _____
Above average height, below average arm span: _____
Above average height, above average arm span: _____
Average height and/or average arm span: _____

Each person in your group should write up their own Exploration answers, to be turned in today and selected randomly to be graded for their group(*).

2. Does Evidence Match a Given Conclusion?
Consider the following generalization statements:
  1. "People are equally distributed between below-average and above-average height."
  2. "People are equally distributed between below-average and above-average arm spans."
  3. "People with above-average heights tend to have above-average arm spans."
For each of these generalization statements, agree or disagree based on the evidence obtained for your class. Cite specific numbers from your data to support or refute each statement, and explain your reasoning based on these specific numbers.
Write up your discussion on whiteboards(*), to be worked on and presented as a group.


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