Collaborative Proposal Reforming Physics:
Algebra-based Physics
with
Human Applications
Robert G. Fuller and Vicki L. Plano Clark
rfuller2@unl.edu
-
vpc@unlserve.unl.edu
University of Nebraska - Lincoln, NE
Beth Ann Thacker
Nancy Beverly
Chris Wentworth
Texas Tech Univ.
Mercy College
Mark W. Plano Clark
Doane College
Our project is rooted in the research in physics education movement;
Research in Physics Education started in the early 1970s by Arons and
Karplus.
In 1976, Arnold B. Arons and Robert
Karplus issued a call for the reform of
higher education based, in part, on their
understanding of the work of Jean Piaget.
A. B. Arons and R. Karplus,
Implications of accumulating data on
levels of intellectual development,
American Journal of Physics, 44, 396,
1976.
The
calculus reform movement
of the 1980s
25% of all calculus students reported being
in a reform section by 1994!
“PUMP NOT A FILTER”
What does it teach us?
Emphasize mathematical modeling
Physics uses mathematical models to describe the
behavior of nature. (how nature behaves, not why)
Based on physical observables
These mathematical models:
• Enable us to make predictions
• Are parsimonius
• Are developed by systematically manipulating parts of nature
• Are precise
• Are approximations of ideal situations
What kinds of students are in this course?
Who are the students enrolled in the UNL algebrabased introductory physics class?
Gender
Algebra-based Physics
Calculus-based Physics
Class Status
Algebra-based Physics
Calculus-based Physics
Career Goals
Algebra-based Physics
Calculus-based Physics
What kinds of instructional techniques
will be best for these students?
What kinds of instructional methods work best for
these students?
Research has shown multimedia to be effective for a
broad range of student abilities and interests. So
multimedia is an essential part of our modules.
Humanized Physics Multimedia
Each module we develop provides many approaches to learning physics.
Hands-on (HO) Activities
Students complete traditional hands-on experiments which
require them to manipulate equipment and take data by hand.
Students often use spreadsheets to analyze their data.
HO
a=
t
0
v
t
()
lim
Computer Modeling (CM) Activities
Students use prepared software packages such as Interactive
Physics and EM Field to model physical systems. This allows
systems to be included in the course for experimental study that
otherwise cannot be done.
CM
MBL
IV
Mathematical Modeling(MM) Activities
Students develop their ability to use mathematical models by
using graphing calculators or computer algebra software such as
Maple to analyze problems that have content appropriate to the
course but which include mathematical manipulations that would
be too time consuming or too sophisticated for the students to do
my hand.
Microcomputer-based Laboratory (MBL) Activities
Students use assorted probeware and computer-assisted data
acquisition to collect and display data in real time.
Interactive-video (IV) Activities
Students analyze real-world events which have been recorded
and digitized. This can include commercially-prepared movies or
movies which the students create themselves. Students often use
VideoPoint to collect data from these video clips.
Physics Content (PC) Activities
Students use a book or electronic database, such as CD-ROM or
suggested web sites, as textual references for this course. For
example, the Physics InfoMall CD-ROM contains nineteen
complete textbooks, over 3,000 articles from journals and
thousands of physics problems.
What kind of physics topics can motivate these students?
What contexts will be motivating for these students?
 Learning will be enhanced if interested in
what is being learned
 If learning occurs in context in which
knowledge will be used, then
 higher retention of knowledge
 more likely to appropriately apply
 Therefore, these students should learn better
if their learning takes place in an interesting,
personally-relevant context
 Human-based applications!!
Human-based Applications
 Modeling motion by studying walking, running, and
jumping
 Studying optics by building models of human vision
 Understanding the circulatory system by modeling
properties of fluid flow
 Examining simple harmonic motion with swinging leg
bones
 Modeling electrical properties of cell membranes, signal
transmission in neurons, and resistance of skin
How do we evaluate within this new learning
environment?
Second Semester College Physics
How Do We Sense, Think and Move? (5 weeks)
This module explores the fundamental aspects of physics needed to understand how
the human body is able to send messages back and forth to the its appropriate parts.
We now believe that the internal signals in our bodies that control our sensing, our
thinking and our moving are electrical signals. So we need to understand the
fundamental aspects of electricity and magnetism to understand these signals.
How Do We See Colors? (6 weeks)
Week 1: From Where Does Light Come? Spectra of two different kinds of sources with
the Pasco spectrophotometer: (a) Incandescent source.and (b) Hg spectra. Graphs of
intensity versus angle. Compare the two different types of spectra.
Week 2: How Does Light Get to Your Eyes? Absorption using filters and MBLBouguer's Law, exponential modeling. Introduce Optical Density(O.D.)
Week 3: How Does the Medium Change What You See? Absorption Versus
Wavelength using a Spectrometer and color filters. Plot both transmission percent and
O.D. as functions of wavelength.
Week 4: How Can You Use Light to Measure Other Properties? Beer's Law using
Colorimeters, finding an unknown concentration.
Week 5; How Does Your Eye Form Images? Reflection and Refraction. Forming Images
Using Plane Mirrors and Converging and Diverging Lenses. Apply the thin lens
equation.
Week 6: How Does Your Brain Understand Colors? Explore properties of own eyes –
accommodation, visual acuity, blind spot, near point, and astigmatism. Model function
and defects of the human eye with Cenco eye model – accommodation,
nearsightedness, farsightedness, astigmatism, compound effects, and removal of the
lens.
How Do We See Inside Ourselves? (3 weeks)
This module explores the fundamental concepts from physics needed to
understand how we can use energy to see what is inside of our bodies.
In order for us to use ionizing radiation to make images of what is inside of us, the
radiation must go completely through our bodies, or be reflected back out, and it must
also leave some of its energy in our bodies so we can detect a change between the
incident energy and the transmitted, or reflected, energy. It is a kind of yin and yang of
image versus dose, what we want to see versus how much radiation energy we want to
deposit in our bodies.
Week 1: Nuclear Physics and Radioactivity
Week 2: Ionizing Radiation The Inverse Square Law for Isotropic Radiation
Week 3 : Radiation: Dosimetry and Imaging
How do we evaluate student learning within this new learning
environment?
We need to develop new evaluation tools and assessment instruments
In addition to the attitude and expectations survey, we have to find appropriate physics
content measures. We are trying to develop more relevant and individualized physics
problems. The following are examples of some of the problems we have developed.
4.00
Interactive Lecture Demonstration #6
up to 6 points
3.75
3.50
Names:
,
3.25
and
3.00
You can earn up to 6 points based on your work.
You are a forensic pathologist investigating a motorcycle accident that occurred at the
intersection of 17 and South Street sometime last night. The blood from the
unconscious victim was rushed to your crime lab in south Lincoln. To determine the
time of the accident, you measure the light-transmitting properties of a thin smear of
the victim's blood at 2:30 PM. You find that the blood sample has an optical density of
2.75
2.50
2.25
th
2.00
1.75
1.50
1.25
2.30  0.01. To determine how the light-transmitting properties of blood change with
time, you look up some calibration data from your files. You find that fresh human
blood transmits 50% of incoming light, blood that has been exposed to air for 2.8 hours
transmits 20% of incoming light, and blood that has been exposed to air for 4.0 hours
transmits 13.5% of incoming light.
Since you are somewhat
sophisticated about blood
physics, you expect that
percent transmission vs. time
since exposed to air will be an
exponential function, i.e.
linear on a semi-log graph.
(See graph on the reverse side
of the page.)
1.00
0.75
0.50
0.25
0.00
0
2
4
6
8
10
1. (2 points) To convince
police of your estimate for the
time of the accident, you
make a graph of Optical
Density vs. Time exposed to
air. Label your axes.
12
14
16
18
20
22
24
2. (2 points) To be sure you can communicate your reasoning, you determine the
equation of your OD vs Time relationship.
3. (2 points) And, of course, you must estimate the time of the accident.
Be sure to explain your reasoning in language that both policemen and
lawyers can understand!
Sample 2:
Skin Burning Intensity of Sun light
Human skin is not equally sensitive to all types of ultraviolet(UV) radiation. The
Erythemal Response Spectrum is a scientific expression that describes human skin
sensitivity to UV.
Skin sensitivity to Ultraviolet Radiation - the Erythemal Response
Spectrum
Exposing skin to UV light leads to redness or burning
once a threshold dose has been exceeded. However,
sunburn is not simply proportional to the total absorbed
energy of ultraviolet light. Skin sensitivity to Erythema
depends strongly on the UV wavelength. Although overall
sensitivity to sunburning varies among individuals, the
relative sensitivities to separate wavelengths remain the
same. The Erythemal Response Spectrum (shown on the
graph) demonstrates erythemal skin sensitivity for UV
wavelengths.
The Erythemal Relative Response Spectrum
Relative response vs. wavelength
UV Radiation contained in Solar Light at the Earth's Surface
Relative Solar UV Spectrum at the
Earth's Surface for Different Ozone
Thicknesses 2.0 mm, 2.6 mm, 4.0 mm
The intensity of UV radiation reaching the Earth's
surface is not uniform in UV wavelength components.
Due to ozone absorption, UV rays with wavelengths
shorter than 290nm (often classified as the UV-C range)
are of negligible intensity. For the intermediate UV-B
range (290-320nm) the ozone absorption is substantial,
but UV radiation still reaches the Earth's surface. The UVA range (320-400nm) is little absorbed by the Earth's
ozone layer. The graph shows the relative Solar UV
Spectrum for three ozone thicknesses: 2.0 mm, 2.6 mm,
and 4.0 mm. Data for noon time, clear sky, latitude 40o,
equinox, at the Earth's surface. The curves are normalized
to 1 at 400nm.
| |
2.0 mm 4.0 mm
The Effective UV Spectrum - The "Skin Burning Intensity"
The Effective UV Spectrum is the mathematical product of Solar UV Spectrum and the
Erythemal Response Spectrum. It can be interpreted as the "skin burning intensity" of
individual wavelengths of sunlight.
Based on the information contained on "The problem of measuring "skin burning
intensity" of sun light" above the following questions:
1. Determine the relative
"Skin Burning Intensity' as a
function of UV wavelength
for the ozone thicknesses of
2.0 mm and 4.0 mm. Label
each curve by ozone
thickness.
2. Discuss the relationship between ozone thickness and skin burning. Compare
quantitatively the skin burning intensity for the two different ozone thicknesses, 2.0 mm
and 4.0 mm.
3. Explain how these data can be related to the experiments you did in Physics 142
laboratory this week.
Individualized Homework
Using Student ID Numbers
Features:
-
Gives every student a chance to do an individualized problem
-
Shows that physics problems can be worked with more than one set of
numbers
-
Easily graded using a spreadsheet answer page
Select digits from the ID number
(use the =MID(Text, Start_num, Num_chars)
Write your solution functions in the cells
- Solutions can be readily posted in a sort by numbers
Examples:
Kinematics:
Your younger brother is rushing back and forth on "O" street on a little scooter. You decide to
study his motion. You write down how far he travels each second for exactly nine seconds. You
are quite surprised to discover that the distance he traveled in meters in each second exactly
matches each of the nine digits in your student ID number, if you replace any zero with a ten.
You further discover that when the number is odd he was going east and when the number is
even he was going west. For example, if the first digit of your student ID number is a 7, then
your younger brother traveled 7 meters east during the first second, and so forth.
a) (Two points)
How far did your younger brother travel and in which direction, each second?
Time
1st s
2nd s
3rd s
4th s
5th s
6th s
7th s
8th s
9th s
distance(m)
dir.(E or W)
b) (Two points) At the end of the nine seconds, where was your younger brother with
respect to his location when you started measuring his motion?
c) (Two points) During what time period(s) was the magnitude of his average
velocity, i.e. his speed, the greatest? How much was it?
d) (Two points) During what time period(s) was the magnitude of his average
velocity, i.e. his speed, the least? How much was it?
e) (Two points) Between which two time period(s) was the magnitude of his average
acceleration the greatest? How much was it?
f) (Two points) Betweeen which time period(s) was the magnitude of his average
acceleration the least? How much was it?
g) (Two points) Write a verbal description of your younger brothers motion for the
whole nine seconds.
For full credit, 8 points
Professor Edgerton from
Aurora,NE, took a strobe
photograph of an sphere projected
horizontally near the surface of the
earth in a vacuum. He has given
you the photograph. See the figure.
Of course, you are quite surprised
to discover, when you measure the
vertical distance (h) from the
surface of the earth to the initial
location of the sphere that it is
exactly three meters plus some
hundredths of a meter determined
by the 6th and 7th digits of your
student ID number.
h = 3. 41 m (1 pt)
Furthermore, the horizontal
distance that the sphere travels
before it hits the floor is exactly 2
plus some hundredths of a meter
determined by the 8th and 9th digits
of your student ID number.
w = 2. 69 m (1 pt)
a) ( 2 pts) Using only symbolic algebra with g for the acceleration of gravity on the earth
and N the number of flashes for the sphere to hit the surface of the earth, write
the expressions for t, the time between adjacent strobe light flashes and vx , the
horizontal speed of the sphere, in terms of g, N, h and w.
b) (1 pts) Compute a numerical value for vx , the horizontal speed of the sphere, to three
significant figures if g = 9.80 m/s2.
c) (1 pts) Compute the number of flashes that the strobe made per minute.
n = __________ per minute
d) (2 pts) Compute the velocity of the sphere where it hits the surface of the earth.