Making the Implicit Explicit
in the Teaching of Chemical Equilibrium
David Yaron, Michael Karabinos,
Jodi Davenport, Jordi Cuadros
Department of Chemistry, Carnegie Mellon University
Gaea Leinhardt, Jim Greeno, Karen Evans
Learning Research and Development Center, University of Pittsburgh
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Overview of Projects
• Chemcollective (www.chemcollective.org)
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NSF CCLI and NSDL
Digital library of virtual labs and scenario based learning activities
Tutors and supported problem solving
Community building and support
• Open Learning Initiative (www.cmu.edu/oli)
– William and Flora Hewlett Foundation
– Full enactment of instruction (based on chemcollective activities)
• Pittsburgh Science of Learning Center (www.learnlab.org)
– NSF SLC
– Fundamental studies to advance the theory of learning
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Overview
Analysis of the
domain
Initial problem analysis
and selection of procedure
Implementation of computation
or procedure
Reflection on problem
solving efforts
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Supporting practice
Changing the nature of practice
Use technology to provide
hints and feedback.
http://www.chemcollective.org
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Templated feedback
Analysis of student response for common error types hints
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Pseudotutors
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Pseudotutors
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Fading
Path 3
S
Determine
target PH
Determine
target [A-]/[HA]
Path 2
Path 1
Construct
solution
with target
[A-]/[HA]
F
Determine solutions
and volumes mixed.
Schematic representation of scaffolding for design of a buffer solution.
Ovals represent episodes (pseudotutors or templated feedback).
Support is added/faded by switching paths.
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Overview
Can the problem solving
be more connected to
underlying chemical
concepts.
Initial problem analysis
and selection of procedure
Implementation of computation
or procedure
Reflection on problem
solving efforts
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Goal should be fluency
with concepts, not
procedures.
Use technology to
fundamentally change
the nature of practice.
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Virtual laboratory as a new form of practice
• Flexible simulation of
aqueous chemistry
• New mode of
interaction with
chemical concepts
• Ability to “see” inside
a solution removes
one level of indirection
in chemical problem
solving
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Taking learners beyond means-ends analysis
Typical textbook problem
“When 10ml of 1M A was mixed
with 10ml of 1M B, the
temperature went up by 10
degrees. What is the heat of the
reaction between A and B?”
Virtual Lab problem
Thermochemistry/Camping 1:
“Construct an experiment to
measure the heat of reaction
between A and B?”
• Original design goal
– The procedure is not being triggered in response to relevant prompt
• Result of student observations
– 4 sections of 30-45 students working alone; 4-5 instructors/observers
– The Virtual Lab format requires students to go beyond a strategy of matching
words to equations
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Observational studies: Knowledge refinement
“The virtual lab contains 1M solutions of A, B, C, and D. Construct
experiments to determine the reaction between these reagents”
• Intent was to give practice with determining reaction coefficients
A + 2B  3C + D
• Observation
When A is mixed with B, some A remains, 50% of students say:
A+BC+D+A
Reveals fragile understanding of limiting reagent concept (even though they could
easily perform textbook limiting reagent problems)
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Learning in a large lecture course
• Study at Carnegie Mellon
– Second semester intro course, 150 students
• Information used
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–
–
–
Pretest
9 homework activities (virtual labs with templated feedback)
3 hour exams
2 pop exams (practice exam given 5 days before hour exam)
Final exam
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Correlations
Pre
Test
Pre
test
Home-work Pop Exam
Exam
1.00
Home work 0.03
1.00
Pop
Exam
0.50
0.15
1.00
Exam
0.32
0.43
0.51
1.00
Final
0.23
0.58
0.37
0.59
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Final
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1.00
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Regression and structural equation model
•
•
•
Linear regression accounts for 48% of the variance in the final grades
Influence of homework accounts for half of the model predictions
Structural equation model supports conclusions drawn from the regression
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Assessment within online stoichiometry course
• Study design
– Treatment (20): Online course including a scenario, tutors and
virtual lab homework
– Control (20): Paper and pencil, worked examples and practice
– Assessment was traditional problem solving of quantitative
stoichiometry problems, and some qualitative questions
• Preliminary results
– Biggest predictor of learning in online course is number of
engagements with the virtual lab
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Overview
Initial problem analysis
and selection of procedure
Implementation of computation
or procedure
Reflection on problem
solving efforts
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What overall structure
are we trying to convey?
An important role we, as
chemists, can play is reconceptualizing the domain, i.e.
what should we teach, and how.
Goal of a high AP score is
different than goal of robust
learning of chemical concepts.
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Results from other domains
• Expert blind spot
– Ability to rank difficulty of math problems is worst for teachers of
that subject
• Geometry
– Sub-goal structure of proofs was implicit knowledge (Anderson,
Koedinger, Greeno..)
• Statistics
– Students could carry out statistical analysis procedures, but could
not select appropriate procedures (Lovett)
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Domain analysis
• 1) Utility of the domain
– Get at the conceptual knowledge that is true to the domain, and will be
generally useful
• 2) Knowledge structure of the domain
– Concepts, strategies, and procedures
– Structure may not be obvious: Knowledge may be held implicitly by the expert
• 3) Psychological aspects of the knowledge
– What is easy and hard to learn
– Based on observing student problems solving in class, student performance
data, and analysis of artifacts
– Also based on student interviews (think alouds) done on students who
completed the course a few months to a year earlier
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Domain analysis for chemical literacy
• Focused only on “Utility of the domain”
• Standards should go beyond expert opinions of what to
teach
• Evidence of the domain as practiced
– Nobel prizes for past 50 years (1952-2002)
– NY Times Science Times for 2002 (54 reports)
– Scientific American News Bites for 2002 (32 reports)
• Evidence of the domain as taught
– CA state content standards
– Best selling textbooks
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Domain map
EXPLAIN
ANALYZE
Goal
Hypothesis
Generation
Functional
Motifs
(What do you
want to know?)
Process
Hypothesis
Testing
Representational
Systems
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SYNTHESIZE
(How to determine
What you have)
Structural
Motifs
TOOLBOX
Assembly
Motifs
Quantification
Systems
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Full domain map
Is composed of
Is composed of
EXPLAIN
Is composed of
ANALYZE
SYNTHESIZE
Radioactivity
Types of
Reactions
Catalysts
Super Molecular
Structure
Acid and Base
Periodicity
Qualitative
Analysis
Redox
Materials
Molecular Structure
(What is its Structure)
Goal
Precipitation
Hypothesis
Generation
New
Elements
Quantitative
Analysis
Properties of
Gasses
Energy
(How much do you have)
Properties of
Matter
(Frameworks an expert
sifts through to construct
an explanation)
Functional
Motifs
Atomic Structure
(What do you
want to know?)
Stoichiometery
Acids and Bases
in Solution
Radioactive
Dating
What is a Metal,
Crystal, Salt?
Electromagnetism
Non-Biological
Microscopy
Techniques
Properties of
Solutions
Properties of
Atoms and
Molecules
Pharmaceuticals
Food and Health
Polymers
Biological
Scattering
Techniques
Phases of Matter
Liquid, Solid, Gas
Structural
Motifs
Investigation
Simple
Molecules
Titration
Equilibrium
Method
Spectroscopy
(How to determine
what you have)
Thermodynamics
Heat and Energy
Molecular Crystals
UV/Vis
IR
NMR
MassSpec
3-D Networks
Metals / Alloys /
Semiconductors
Simple Organic
Covalent
Bonding
Extraction
Kinetics
Catalysis
Structure
Property
Relationships
Similar structure
as an explanation
Chromatography
Separation
Paper
TLC
Gas
Column
HPLC
Chemical
Design
Non Covalent
Bonding
Distillation
Biological
Engineering
Process
Motifs
Extraction
Scavenge O2
Hypothesis
Testing
Selectively shut
down pathways
Block a
functional group
TOOLBOX
Formulation
Structure
Reactions
Molecular
Structure
Atomic Structure
Orbitals
Configuration
Lewis Dot
Filtration
Quantification
Systems
Representational
Systems
Nomenclature
Paper
TLC
Gas
Column
HPLC
Distillation
Correlate
Observables
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Chromatography
Separation
Hold one thing
fixed while
changing
another
Van der Waals /
Electrostatic
Ionic / Alloys
Filtration
Radio Label
Transition Metal
Complexes
(Metal Ligand)
Format
Units
Mole
Molarity
Partial Pressure
Stoichiometery
VSEPR
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Domain analysis
Middle school through high school: Big concepts
• Structure
– Relation to properties
• Functional groups
• Emergent properties (bonding pattern  molecular interactions - 3 d structure)
• Transformation
– Physical transformations and chemical reactions
• Energy and motion
– Heat
– Molecular motion
Materials themes: Water, gold and plastic
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Domain analysis: Chemical thermodynamics
1) Utility of domain
– Heat transfer and energy flow in systems is important
– “Camping” scenario, of heating meals ready-to-eat
2) Knowledge structure of the domain
– Heat flow from system 1  system 2
– Three processes that generate or absorb heat
• Heat/cool
• Phase change
• Chemical reaction
3) Psychological aspects of the knowledge
– Student observations suggest difficulty is correlated with “visibility” of the
heat source/drain: Hardest is heat from a chemical reaction.
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Chemical thermodynamics instruction
• Use a structured dialogue to expose a general strategy to
solving heat-exchange problems.
– Traditional instruction leaves this as “implicit knowledge”
• Structured dialogue for heat exchange
– What is the source of the heat?
• How do you describe that effect: (q=m Cv DT, q=n DH, ..)
– What is the drain of the heat?
• How do you describe that effect: (q=m Cv DT, q=n DH, ..)
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Big picture of chemical thermodynamics
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Chemical equilibrium / Acid-base chemistry
1) Utility of the domain
–
How is this knowledge used in organic chemistry and molecular
biology
1) Compare pH to pKa to determine ionization state
2) Buffers used to control pH (qualitative not quantitative)
3) Titration as an analytical technique
–
Current instruction
1: Almost a footnote (in the indicators section)
2-3: Coverage may not be sufficiently qualitative
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Chemical equilibrium / Acid-base chemistry
2) Knowledge structure
– Flexibility with “progress of reaction” is required in problem
analysis
– General strategy can be constructed based on
• First, determine concentration of “majority species”
• Second, determine concentration of “minority species”
3) Psychological aspects of the knowledge
– LeChatlier (especially with addition/removal of a species) is most
retained concept
– Broad confusion regarding “progress of reaction”
• Q vs. K
• Meaning of “initial” vs. “equilibrium” state
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Some features of the instruction
• Sequencing
– LeChatlier’s principle plays role of “prior knowledge”
– Human respiration is scenario to which to attach “initial” vs.
“equilibrium” state
• Blood entering lungs and muscles experiences a new initial state
• Blood leaving lungs and muscles has reached new equilibrium
• Progress of Reaction
– Concept of progress of reaction (and Q) introduced before K
– Visualizations used
• General strategy for equilibrium problem analysis
– Majority vs. Minority Species
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Majority/minority species
Protein 
Drug
 Protein:Drug
K  108
Initial
1.2x10-6
3.0x10-3
0
STEP 1 (Majority species): Thought experiment with K  
Change
1.2x10-6
1.2x10-6
1.2x10-6
K 
0
3.0x10-3
1.2x10-6
Now know that [Drug]=3.0 mM and [Protein:Drug]=1.2 M
STEP 2 (Minority species): Use K=Q
K  10
8
Protein:Drug 

1.2x10-6


 Protein  Drug   Protein  3.0x10-3
Traditional approach
1.2x10-6  x
1.2x10-6
10 



-3
 x   3.0x10  x 
 x   3.0x10-3 
8
assume x  1.2x10-6
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Old vs new instruction
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Majority vs. minority species
• A general strategy for equilibrium thinking/problem
analysis?
– Examine state of solution and select all strong reactions (K>>1)
• Acid base: OH- + H+ ; HA + OH• Solubility: M+ + X- and M+ + L
and A- + H+
– Thought experiment: Assume large K’s are infinite and do a
limiting reagent calculation
• All species that do not go to zero, are majority species and you now know
their concentration
– Determine minority species, via equilibrium expressions
• Replaces “small x approximation” with a conceptual framework
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Big picture of acid-base chemistry
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Back to domain analysis
• How is this knowledge used in organic chemistry and
molecular biology
1) Compare pH to pKa to determine ionization state
2) Buffers used to control pH (qualitative not quantitative)
3) Titration as an analytical technique
• How is this addressed by new instruction
 A-  
pH  pK a  log10    
  HA  


Operates in  if A - and HA are majority species (buffer)
– 1 and 2
Operates in  if A - and HA are minority species (protein in blood)
– 3) Virtual labs involving titrations
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Development status
• Stoichiometry
– Full set of tutorials and supported problems (virtual lab and tutors
released on ChemCollective and OLI)
• Thermochemistry
– Supported problems, based on structured dialogues (virtual labs
and tutors): Fully tested and in process of release.
• Equilibrium/Acid-Base
– Supported problems on buffer design and mechanism (with
fading): Fully tested.
– Combined instruction/supported problems implementing new
strategy: In final development, most has been tested.
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Research status
•
Study of the factors influencing learning in large chemistry classrooms (J. Chem.
Ed., in press)
– Online homework activities contribute substantially to learning
– Benefits are not correlated with pre-test
•
Controlled study of online stoichiometry course
– Karen Evans’ thesis to be defended this summer, replicate in next academic year
– Virtual lab engagement strongest predictor of learning in the course
•
Expert/novice comparison of problem solving in acid-base chemistry (see
Davenport poster)
– Results influenced instructional design described here.
•
Controlled studies of new instructional approaches (see Davenport poster)
– Majority/minority instruction improves performance on
2A+3B
4C
K = 1.4 x 1010
From 22% to 58% correct. (Finer grained analysis underway.)
– Studies on full instructional modules being analyzed, and further studies planned.
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Discussion points
• How different is majority/minority strategy from traditional
instruction?
• What aspects of the chemistry domain most need to be
re-conceptualized?
• Should we shift emphasis in freshman course towards
literacy?
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Thanks To
Carnegie Mellon
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Michael Karabinos
Jodi Davenport
Donovan Lange
D. Jeff Milton
Jordi Cuadros
Rea Freeland
Emma Rehm
William McCue
David H. Dennis
•
•
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•
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Tim Palucka
Jef Guarent
Amani Ahmed
Giancarlo Dozzi
Katie Chang
GRC 2007
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Erin Fried
Jason Chalecki
Greg Hamlin
Brendt Thomas
Stephen Ulrich
Jason McKesson
Aaron Rockoff
Jon Sung
Jean Vettel
Rohith Ashok
Joshua Horan
Funding
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NSF: CCLI, NSDL, SLC
William and Flora Hewlett
Foundation
Howard Hughes Medical
Institute
Dreyfus Foundation
LRDC, University of Pittsburgh
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•
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Gaea Leinhardt
Jim Greeno
Karen Evans
•
Baohui Zhang
http://www.chemcollective.org
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