Laura Serpa, Kien Lim, & Ellen Esposito
College of Science
University of Texas at El Paso
March 21, 2011
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
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Mathematics is the language of science
Science inspires mathematics
Students see mathematics and science as
independent subjects
Both mathematics and science appear to
stimulate some “higher level” thinking
2008-2009
22 Pre-service teachers
26 In-service teachers (5+ years)
8 Novice teachers (0-4 years)
3 Pre-service MAT
2009-2010
17 Pre-service teachers
27 In-service teachers (2+ years)
8 Novice teachers (0-1 year)
1 Pre-service MAT
2010-2011
8 Pre-service teachers
19 In-service teachers (2+ years)
1 Novice teachers (0-1 year)
0 Pre-service MAT
So… How do we achieve our goals and create
good teachers in a program that addresses a
large number of participants from very
different backgrounds?
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•
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Problem-based lessons
Inquiry
Lesson planning
2010-11 Focus on writing curriculum:
First semester devoted entirely to 2 major activities
that integrate mathematics and science and could
form the basis for multiple lessons.
• Additional material was presented on exploring
knowledge or how to ask question
•
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Egg-Buoyancy Experiment
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Density, Buoyancy, Measurement, Ratio
Blueness Quotient Problems
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Concentration, Ratio, Weighted Average
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Why Density?
Density is a fundamental property of matter that often
explains why things work the way they do in science
 Density often controls whether things go up or down
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Why Ratio?
A critical concept for understanding measures of
intensive quantities (e.g. speed, flow rate, pressure)
 Foundational for understanding proportion
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Why Connect Density and Ratio?
Density makes ratio less abstract
 Ratio highlights the “ratio as a measure” aspect of density
which can be generalized to other measures
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This was the first activity for the new group of
participants
Participants were given a description of the
activity:
They would be given a balance; a peeled, hard-boiled egg;
and a graduated cylinder containing 500 ml of water.
 Working in small groups they must find the exact amount
of salt that must be added to the water to make the egg
float near the center of the graduated cylinder (i.e.
achieve neutral buoyancy).
 They could form their own groups but they must have no
more than 6 people in a group.
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Participants self-selected groups
A science in-service teacher group
 A math in-service teacher group
 A mixed in-service teacher group
 Two undergraduate groups
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• The science group used trial and error.
• The math group attempted to find an
equation to solve the problem .
• The mixed group could not measure the
density of the egg accurately enough to
proceed with the rest of the assignment.
They became frustrated.
• The two undergraduate group also used trial
and error. They were waiting for someone to
give them the correct answer.
The initial buoyancy experiment was followed by
several problem-sessions about density and
buoyancy
Our favorite source was: WGBH’s Voyage of doom
http://www.pbs.org/wgbh/nova/lasalle/buoyancy.html
1.
Comparing Blueness of Two Solutions
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3 beakers of blue dye + 2 beakers of water
60 beakers of blue dye + 40 beakers of water
Which solution is bluer?
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Part-part comparison vs. Part-whole comparison
3 60
3
60


2 40
3  2 60  40
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3:2
60%
Multiplicative comparison vs. A mesaure of blueness
Connection to Egg-buoyancy Experiment:
Density (concentration of particles): mass/volume
Blueness (concentration of dye): bluedye_vol/total_vol
2.
Mixing Two Solutions

Mix 5L of 40% solution with 10L of 85% solution
40% of 5L
0.0
85% of 10L
0.5
1.0
2.
Mixing Two Solutions
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Mix 5L of 40% solution with 10L of 85% solution
Multiple approaches
i. Using definition (i.e. separating blue dye and water)
40%  5  85% 10
BQ of Mixture 
5  10
ii. Adding BQs or Averaging BQs
40%  85%
BQ  40%  85% or, maybe
2
1(40%)  2(85%)
ii. Using weighted average
BQ 
1 2
Making connection: The volumes of
the solutions constitute the weights BQ  5(40%)  10(85%)
5  10
in the weighted average method
3.
You have 3000mL of Mixture R (BQ of 60%). How much
of Mixture R should you add to increase a 200mL solution
from BQ of 40% to 55%?
Solution
Mixture R
i.
An incorrect approach
200mL
3000mL
BQ = 40%
3000(60%)  200(40%)
BQ = 60%
 55%
3000  200
ii.
Guess and check approach
iii.
Algebraic approach
x(60%)  200(40%)
 55%
x  200
Connection to Egg-buoyancy Expt.
Density of salted solution = Density of Egg
M salt  M water
x  500
 1.06
 1.06
x
Vsalt  Vwater
2.165  500

How Dense Can You Be?!


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

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
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
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THANK YOU