Particulate Representation &

Reasoning in Chemistry

S. Klemmer Aug/2013

NEACT Conference

“If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis …that all things are made of atoms.”�- Richard Feynman Six Easy Pieces 1994 �

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Norms

•  minimize side talk

•  get up whenever!

•  ask questions any time ... and?

Who are We?

Agenda •  Welcome / Who are We? •  Introductory drawing task •  Models, Modeling, and Representations •  Representation task •  Research Results: intro. college students’

particulate representations & reasoning •  Representational competence and my

classroom •  Representational competence and your

classroom

Why bother...

“Students do not learn what we teach. If they did, we would not need to keep grade books. We could, simply, record what we have taught.”!Dylan William Embedded Formative Assessment pp. 47-48!

task 1

Draw a diagram of water evaporating from a puddle.

Models & Modeling “[Models are] explicit representations that are in some way analogous to the phenomena they represent.” (Framework, p. 56)

u conceptual models u mental models

“At heart, modeling is about using tools to make sense of the world.” (pg. 56)

u explain & predict phenomena u develop, test & refine models

macroscopic ß à submicroscopic

Particulate Models in Chemistry

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§ Harrison & Treagust (Science Ed, 1996)) § Dori & Hamieri (JRST, 2003) § Johnstone (JChemEd, 1993)

“a set of skills and practices that allow a person to reflectively use a variety of representations or visualizations, singly and together, to think about, communicate, and act on chemical phenomena in terms of underlying … physical entities and processes” (Kosma & Russell, 2005, p. 131).

Representational Competence

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task 2

Draw, using submicroscopic representation(s), a diagram that helps explain the process

of water evaporating from a puddle.

Maine Governor’s Academy for Mathematics and Science Leadership

The Cu Wire Question:

Consider  a  length  of  pure  copper  wire.  Cut  the  wire  in  half  and  throw  away  one  of  the  two  shorter  wires.  Now  take  the  remaining  piece  of  wire  and  cut  that  in  half,  and  throw  away  one  piece.  Con>nue  in  the  same  way,  each  >me  cu?ng  half  of  the  remaining  wire.  Will  this  process  come  to  an  end?  Explain  your  answer.  

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Most Common Answers (Stavy & Tirosh,2000; Klemmer classroom 2011-12)

•  infinite division rule: No, the process continues forever, because you can keep dividing ½ of a ½ forever.

•  particulate model: Yes, the process ends when you get down to a single copper atom, which can’t be cut in half.

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Sabbatical!!

Preliminary Research Questions 1. What conceptual resources do college

chemistry students use when they reason about the successive cutting of a piece of copper wire? (ON LINE)

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2. What types of depictive representations do they use to support their reasoning? (INTERVIEWS)

3.  Do they use similar representations when describing other phenomena? (INTERVIEWS)

1.  College students, like younger students,

used mostly particle reasoning and/or infinite division rule reasoning to explain the cutting of the wire.

Results from preliminary research

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On-Line Results Oct 2012

rule  44%  

par>cle  34%  

tech  13%  

other  9%  

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1.  College students, like younger students, used mostly particle reasoning and/or infinite division rule reasoning to explain the cutting of the wire.

Results from preliminary research

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3.  “Rule” users supported their reasoning with purely macroscopic or mathematical representations, while “particle” users supported their reasoning with dual macro/micro representations or purely submicroscopic representations.  

2.  Particle reasoners varied in the specific conceptual resources they used in their reasoning.

Rule Reasoner Interviews Mathematical Drawings

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Rule Reasoner Interviews – Macroscopic Drawings

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Particle Reasoners – Macro/Micro Drawings

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Particle Reasoner Interviews – Submicroscopic Drawings

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1.  College students, like younger students, used

mostly particle reasoning and/or infinite division rule reasoning to explain the cutting of the wire.

2.  Particle reasoners varied in the specific conceptual resources they used in their reasoning.

3.  “Rule” users supported their reasoning with purely macroscopic or mathematical representations, while “particle” users supported their reasoning with dual macro/micro representations or purely submicroscopic representations.  

Results from preliminary research

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4.  While no “rule” reasoners used submicroscopic particle representations in their evaporation descriptions, half of the “particle” reasoners did.

Rule Reasoner Interviews – Purely Macroscopic Evaporation

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Particle Reasoners – purely Macroscopic evaporation

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Particle Reasoners – Macro/Micro Evaporation

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Unsure Rule Reasoner – Macro/Microscopic Evaporation

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Students have different tendencies to depictively represent submicroscopic particles. The specfic details of how much and types of particulate representation and reasoning is context-dependent, but the underlying tendency remains. That varying tendency is connected to these students’ use of particle model reasoning to explain chemical phenomena.

research claim

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More Research Data

1. conceptual resources for reasoning about the successive dilution of iced tea (ON LINE)

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2.  evaporation drawings (IN LAB) 3.  dissolving NaCl in water and

precipitation of AgCl drawings (IN LAB)

1.  Students who used submicroscopic particulate representations in drawings of evaporation were more likely to use (vs. not use) particulate reasoning in thinking about the successive division of a Cu wire or successive dilution of iced tea.

Research Results (partial – only evap)

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2.  Participants who used particulate reasoning but concluded division never ended were very unlikely to include submicro particulate representations in their evap. drawings.

3. Students were less likely to use particulate reasoning on the tea problem than on the Cu problem, and those who used it on the tea problem were very likely to have used it on the Cu problem.

Implications for Teaching  INSTRUCTION •  do my students understand the

representations I use?

LEARNING •  am I paying attention to the

representations students use? •  am I helping students use

representations to develop, test, and refine their conceptual knowledge (models)?

My Chem Classes 2013-’14

•  ask consistently for both macro/micro representations within existing demo sequence of predict/observe/explain

•  ask for macro/micro reps for labs

•  track changes (easier for labs!) over time for metacognition & formative assessment

•  be more deliberate and more transparent in my own use of representations in lecture

•  use next year’s classroom data to examine and better sequence summative assessment representational demands

•  have students use their reps to communicate, defend & refine their mental models (concepts)

Demo Format 1.  Make a sketch of what you see “before”. 2.  Predict (in words or a macroscopic sketch) what

will happen when …. . 3.  Observe. What DID happen? Make a macroscopic

sketch of what you see “after”. 4. Create a submicroscopic diagram that may

explain what you see.

Ø Share your explanation with a neighbor. Critique both models: do they explain what you saw? How are they similar/different? If you refine or amend your diagram, do so in a different color.

Ø  Apply model to explain a new demo or lab and refine.

Demo: Boyle’s Law

Demo: Boyle’s Law

Demo: Boyle’s Law

Summative Exam Example Part  3:  Observa-ons,  Models,  &  Theories  Ms.  Heal  and  Mrs.  Filip  study  mel3ng  ice  cubes.  Their  volume  data  for  cubes  A-­‐D  are  given  below.  In  all  cases  the  ice  cube’s  mass  did  not  change  when  it  melted    into  liquid  water.  

             2.  Summarize  their  observa>ons  about  mel>ng  in  1-­‐2  sentences.    3.  Scien>sts  oPen  model  maQer  as  being  made  of  >ny  spheres,  like  miniature  marbles.  Using  this  basic  idea  provide  a  possible  explana>on,  with  a  diagram,  for  what  happens  to  ice  when  it  melts.    

Sample  Label

Vol.  Ice  (mL)

Vol.  Water  (mL)

A 10.5 9.6 B 27.3 25.0 C 38.3 35.1

Which is Correct?

discussion Chemistry uses a lot of particle models and representations. What topics in chemistry are most dependent on students’particle representation skills?

-  think -  pair up and discuss

task 3 1.  Form a team of 2-3 people interested

in a common chemistry concept. 2.  What area of particulate modeling is

imprtant for understanding this concept?

3.  Identify a demo, lab or other activity that would allow students to create, test, and refine their own mental models around this concept. What will you be looking for?

4.  Be prepared to share an insight or a question.

Resources

Questions?

Thank You!!

Interview Design

•  draw “water evaporating from a puddle” •  “think aloud” what happens when copper wire is

successively cut in half •  support explanation with drawing •  elicit possible alternative explanations •  “think aloud” on provided particulate and infinite

division rule explanations •  probe further

o  if cutting stops, what would happen if you tried to cut further? is it still copper?

o  if cutting never ends, draw a row of 8 atoms and show what happens as continue to cut

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Particulate vs. Rule Thinking in Cu vs. Evap

35% of respondents (131/373) showed some evidence of particle thinking in their Cu responses. 1.  Of these 131:

a.  the vast majority concluded that cutting the wire ended (120/131 = 92%). b.  35% (46/131) also used submicroscopic elements in their evap drawings,

compared to 16% (39/242) of those who included submicroscopic elements in the evap drawing but showed no particulate thinking in their Cu responses.

2.  The 120 participants who decided that cutting Cu would end and showed evidence of particulate reasoning were twice as likely to include submicro structure in their evap. drawings (45/120 = 38%) than ????????

3.  Of the 11 participants that showed evidence of particulate ideas in their Cu responses but concluded that cutting never ends, nearly all (10/11 =91%) did NOT include submicroscopic elements in their evaporation drawing. The LACK of submicro representation in the evaporation drawing strongly correlated to the problematic use of particulate ideas in the cutting Cu problem. 9/11, including the one who had structure in evap, indicated that copper atoms (7), subatomic particles (1), or molecules (1) could continue to be divided. 45  

Particulate vs. Rule Thinking in Tea vs. Evap

1.  Of the 360 participants both answered the online tea question and did the evaporation drawing, only 14% (52/360) showed some evidence of particle thinking in their tea responses. Compared to 35% for Cu.

2.  Of the 52 participants that showed some evidence of particulate ideas in the tea question:

a.  about half concluded that diluting ended: (28/52 = 54%). Compared to 92% for Cu.

b.  about a third also used submicroscopic elements in their evap drawings (46/131 = 35%), compared to 68/308 = 22% without particulate thinking in tea who had microstructure in their evaporation drawings.

c.  Of the 24 participants that showed evidence of particulate ideas in their tea responses but concluded that diluting never ends, a large majority (20/24 = 83%) did NOT include submicroscopic elements in their evaporation drawing. Compared to 91% for Cu. The LACK of submicro representation in the evaporation drawing strongly correlated to the problematic use of particulate ideas in the tea dilution problem.

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Problematic Particulate Thinking in Tea particulate language but no clear reasoning (16/36)

part + rule reasoning (10/36)

part + tech reasoning 2/36)

homogeneity reasoning 6/36)

idiosyncratic reasoning 2/36)

“ No because there will always be a small fraction of the tea mixture left, assuming the molecules are evenly distributed through the water”.

“No, because the concentration of ice tea flavoring is only being decreased by 1/2 every time she pours out her glass so the number of ice tea "molecules" per he glass will only get infinitely small.’

“ No because the particles get mixed together. There will always be a small amount of tea particles floating in the water.”

“ No because the tea is homogenous, and there will always be tea molecules in the solution.”

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Particulate vs. Rule Thinking in Cu vs. Tea

58/195 = 30% of respondents who used particle reasoning on the Cu problem also used part reasoning on the tea problem, vs. 58/83 = 70% of respondents who used part reasoning on the tea problem also used part reasoning on the Cu problem.

Far fewer respondents used particle reasoning on the tea problem (83/497 = 17%) than on the Cu problem (195/497 = 39%), while rule reasoning only rose slightly: 251/497 = 51% on Cu and 278/497 = 56% on tea.

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Distribu>on  of  Cu  Reasoning  

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Distribu>on  of  Tea  Reasoning  

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