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Transcript of How My Students...References$! Edelson,!Daniel!C.!(1997).!!Realising!AuthenDc!...
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One Way to Overcome the Math Barrier with Non-‐STEM Majors
How My Students Determined the Fate of the Universe
Steve Cederbloom University of Mount Union
Outline
ì The challenge
ì A framework for meeDng the challenge
ì My soluDon
ì New exploraDons
The challenge
ì A course for the “IntegraDve Core” – “Einstein’s Universe: The Big Bang, Black Holes, and Beyond”
ì Cosmology is an observa(onal science, not an experimental science
ì How do I get students to DO cosmology?
Authentic science practice in the classroom (Edelson, 1997)
ì APtudes
ì Tools and techniques
ì Social interacDons
Why is Inquiry Inherently Difficult?
ì “The GePng on Board Problem” (Meyer and Avery, 2010) ì ObservaDons generate the need to describe,
organize, and explain ì The resulDng paradigm suggests new observaDons
to make
Why is Inquiry Inherently Difficult?
ì “The GePng on Board Problem” (Meyer and Avery, 2010)
Empirical data TheoreDcal knowledge
Why is Inquiry Inherently Difficult?
ì “The GePng on Board Problem” (Meyer and Avery, 2010) ì ObservaDons generate the need to describe,
organize, and explain ì The resulDng paradigm suggests new observaDons
to make
ì How do you break into this cycle? ì New Ph.D students start by joining ongoing work of
mentors
A framework for meeting the challenge
ì Choose a topic for the students to explore ì The expansion of the universe
ì Choose the tools to use ì Euler’s method ì Excel
ì Backwards design -‐ scaffolding
Scaffolding
ì Making a graph ì Using only data at first ì Using equaDons also
ì EquaDons in Excel ì Cell addresses ì Copy and drag ì SePng up constants
ì Trendlines and slopes
The topic
The universe is expanding The curvature is linked to its history & desDny
The “scale factor” of the Universe, R, is governed by the Friedmann equaDon:
SoluDons tell us the possible history of the Universe
• Depend on amounts of ma_er, radiaDon, dark ma_er, & dark energy
The “scale factor” of the Universe, R, is governed by the Friedmann equaDon:
ρ changes according to conservaDon laws
Start with V and change to slope:
1! !
!= !8!"3 ! − !!!
!
!! + !Λ3!
1RΔRΔt
"
#$
%
&'2
=8πG3
ρ −kc2
R2+Λ3
Euler’s method
ΔRΔt
=R2 − R1t2 − t1
R2 = R1 +ΔRΔt
t2 − t1( )
Start with “Now”
Type in equations for one time step
The past
The future and the past
New explorations – two dimensions
ì Can these histories lead the students to new quesDons?
ì Are there other quesDons that students could invesDgate with these tools and techniques?
Embedding diagrams
References
ì Edelson, Daniel C. (1997). Realising AuthenDc Science Learning Through the AdapDon of SciencDfic PracDce. In K. Tobin & B. Fraser (Eds.), Interna(onal Handbook of Science Educa(on. Kluwer, Dordrecht, NL.
ì Meyer, Daniel Z. & Avery, Leanne M. (2010). Why Inquiry is Inherently Difficult…and Some Ways to Make it Easier. Science Educator, 19(1), 26-‐32.