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CONNECTING MATH AND SCIENCE

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CONNECTING MATH AND SCIENCE Powered By Docstoc
					Laura Serpa, Kien Lim, & Ellen Esposito
           College of Science
      University of Texas at El Paso
            March 21, 2011
   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?
•   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
   Egg-Buoyancy Experiment
       Density, Buoyancy, Measurement, Ratio


   Blueness Quotient Problems
       Concentration, Ratio, Weighted Average
   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

   Why Ratio?
     A critical concept for understanding measures of
      intensive quantities (e.g. speed, flow rate, pressure)
     Foundational for understanding proportion

   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
   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.
   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
• 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
         3 beakers of blue dye + 2 beakers of water
         60 beakers of blue dye + 40 beakers of water
         Which solution is bluer?
        Part-part comparison vs. Part-whole comparison
                3 60                   3      60
                                         
                2 40                 3  2 60  40
                  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              85% of 10L




         0.0                         0.5                     1.0
2.   Mixing Two Solutions
        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%)
         in the weighted average method                 5  10
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           3000mL      200mL
          3000(60%)  200(40%)            BQ = 60%    BQ = 40%
                                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
          Vsalt  Vwater          2.165  500
                                    x
   How Dense Can You Be?!
       Maria Davis, Roberto Morales, Alexandra Navarro, Gabriel Rocha
   Integrating Math and Science Using the Human Body
       Nancy Aguirre , Bernle Licon , Becky Calderon, Salina Ohman
   How to Teach for Conceptual Understanding
       Adolfo Payan, Alfonso Vasquez, Veronica Jimenez, Alma Alvarez
   Integrating Math & Science with a focus on ELL strategies
       Sarah Escandon, Joann Estrada, Robert Garcia
   Integrating Math & Science using Interactive Notebooks
    and Foldables with Resources from Dinah Zikes
       Austin Campbell, Evangelina Martinez, Danielle Pena, Hevila Ramos
THANK YOU

				
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