The theme of modelling is pervasive through the whole of science education. I have chosen to restrict the topic to chemical equations, largely because I have a lot of material on it both historical and philosophical, and it is central theme in school chemistry in all countries, but also because it exemplifies ideas about representation that are common across all the sciences. It also bridges the tension between conceptual understanding and quantitative calculations that are present in chemical education and chemistry.
History: Article on The Era of Alchemy by Greg Goebel, in the public domain; do read the section on The Rise of Scientific Ideas for comments about the challenges of studying gases when they can not be contained. The article suggests that 'the long-lost atomic ideas of Democritus, who had correctly envisioned air as particles bouncing around in a vacuum' 'had resurfaced in the 15th century, and made a convert in the form of the French philosopher Pierre Gassendi (1592:1655), who spread the word'. A biography of Democritus is in Wikipedia
Whether Democritus understood a vacuum (void) in the same way that we do now is debatable.
Both Boyle and Toricelli in the 17th century created models of air based on quantitative data about air, e.g. the effect of pressure on air volume at a fixed temperature. Bernoulli developed these in 1738.
Philosophy Democritus' views on epistemology, and whether senses can discover truth are discussed in the Wikipedia biography . This is further discussed in the Stanford text. The Stanford text contains an excellent discussion of ancient Greek philosophy in a reasonably accessible tone, for teachers. The ideas of the Greeks came from thinking, i.e. philosophy, not empirical and practical investigation. A Wikipedia biography of Pierre Gassendi is available but is tough reading, in line with the ideas of the time!
Avoidance of whiggishness:
Looking at whether Democritus' ideas about a void and atoms are the same as today. Learner material:
Biography of Democritus
Biography of Toricelli Teacher material (other than that provided for learners):
Clues about compounds: law of constant composition as an indicator of atoms
Clues about law of conservation of mass: efforts to represent atoms.Third level of representation ie symbolic. Issues about balancing equations.
History: Law of constant composition (definite proportions) from Wikipedia See pictures of balances from Science and Society picture library. Note Ramsden's balance from late 18th century, and the 'self-indicating balances designed by Da Vinci, 1452-1519'.
Lavoisier computed masses, using an accountant's expertise (he did work as in the Ferme Generale collecting taxes for the French government, for which he was beheaded in 1794 on the guillotine) and his tables (reproduced here) look very similar to financial tables.
'The oldest surviving balance used for a published series of chemical experiments is said to be that used by ... Joseph Black', described in his doctoral thesis of 1754 (quoted here). Black's balance had a sensitivity of about 1 in 14000)
Jon Berzelius' fundamental work is written in Wikipedia, including his symbolic forms that represent elements and atoms. Chemical Heritage Foundation on Lavoisier Philosophy:
Induction is the process by which ideas about atoms were proposed to explain constant composition of compounds. Explanation from Intute web site
Given incompleteness of chemical reactions, can equations be balanced? A major problem in traditional quantitative analytical chemistry was to ensure firstly that the materials used were pure, and secondly, that the reaction used for calculations proceeded 100% as written.
What is the nature of the distinction between chemical and physical change? Is it helpful, powerful or simply plain wrong? Some of the history of its introduction may be a good start.
Avoidance of whiggishness:
Development of systems of chemical representation took place over a long period of time. The challenge was to infer sub-microscopic explanations from macroscopic phenomena. Learner material:
Beguin and Cullen's early attempts to write chemical equations. John Dalton's symbols (see Wikipedia) Teacher material (other than that provided for learners):
Mental modelling
Avoidance of whiggishness:
The impact of external influences such as printing technology on conventions for printing chemical equations demonstrates the complex interchange between the rationality of chemists making decisions about their discipline and others. Learner material:
History of signs in chemical equations, focusing on + and = signs, as opposed to arrows, based on Oversby papers. Teacher material (other than that provided for learners): Semiotics for beginners - nature of signs
All of the web sites visited on 2 Dec 08, by Googling Chemical Notation, focused only on expressions of formuae, and not on the signs, such as arrows, and +. The Braille site is mainly concerned with arrows. there are many computer sites concerned with mark up of chemical formulae but not signs.
Computer animations of chemical processes - a step in representation
Avoidance of whiggishness:
This topic is modern and whiggishness is not a problem. Learner material: ChemSense
Nature of representation Teacher material (other than that provided for learners): ChemSense were initiators in tackling student produced animations using bespoke software
Rob Toplis from UK carried out some work with pre-service teacher education students using ChemSense published by the RSC
Maija Aksela and Jan Lundell from Finland have published work using Spartan in CERP
Overview
The theme of modelling is pervasive through the whole of science education. I have chosen to restrict the topic to chemical equations, largely because I have a lot of material on it both historical and philosophical, and it is central theme in school chemistry in all countries, but also because it exemplifies ideas about representation that are common across all the sciences. It also bridges the tension between conceptual understanding and quantitative calculations that are present in chemical education and chemistry.
Modelling through chemical equations
THE PALAVA PROJECT – A METHOD OF ASSESSINGMODELLING CAPABILITY
The survey work is well described in this article.
Article on The Era of Alchemy by Greg Goebel, in the public domain; do read the section on The Rise of Scientific Ideas for comments about the challenges of studying gases when they can not be contained. The article suggests that 'the long-lost atomic ideas of Democritus, who had correctly envisioned air as particles bouncing around in a vacuum' 'had resurfaced in the 15th century, and made a convert in the form of the French philosopher Pierre Gassendi (1592:1655), who spread the word'.
A biography of Democritus is in Wikipedia
Another biography of Democritus (Stanford Encyclopedia of Philosophy).
Whether Democritus understood a vacuum (void) in the same way that we do now is debatable.
Both Boyle and Toricelli in the 17th century created models of air based on quantitative data about air, e.g. the effect of pressure on air volume at a fixed temperature. Bernoulli developed these in 1738.
Philosophy
Democritus' views on epistemology, and whether senses can discover truth are discussed in the Wikipedia biography . This is further discussed in the Stanford text. The Stanford text contains an excellent discussion of ancient Greek philosophy in a reasonably accessible tone, for teachers. The ideas of the Greeks came from thinking, i.e. philosophy, not empirical and practical investigation.
A Wikipedia biography of Pierre Gassendi is available but is tough reading, in line with the ideas of the time!
Looking at whether Democritus' ideas about a void and atoms are the same as today.
Learner material:
Biography of Democritus
Biography of Toricelli
Teacher material (other than that provided for learners):
Clues about law of conservation of mass: efforts to represent atoms.Third level of representation ie symbolic. Issues about balancing equations.
Law of constant composition (definite proportions) from Wikipedia
See pictures of balances from Science and Society picture library. Note Ramsden's balance from late 18th century, and the 'self-indicating balances designed by Da Vinci, 1452-1519'.
Lavoisier computed masses, using an accountant's expertise (he did work as in the Ferme Generale collecting taxes for the French government, for which he was beheaded in 1794 on the guillotine) and his tables (reproduced here) look very similar to financial tables.
'The oldest surviving balance used for a published series of chemical experiments is said to be that used by ... Joseph Black', described in his doctoral thesis of 1754 (quoted here). Black's balance had a sensitivity of about 1 in 14000)
Jon Berzelius' fundamental work is written in Wikipedia, including his symbolic forms that represent elements and atoms.
Chemical Heritage Foundation on Lavoisier
Philosophy:
Induction is the process by which ideas about atoms were proposed to explain constant composition of compounds.
Explanation from Intute web site
Given incompleteness of chemical reactions, can equations be balanced? A major problem in traditional quantitative analytical chemistry was to ensure firstly that the materials used were pure, and secondly, that the reaction used for calculations proceeded 100% as written.
From Wikipedia - ' The law of definite proportions might seem obvious to the modern chemist, inherent in the very definition of a chemical compound. At the end of the 18th century, however, when the concept of a chemical compound had not yet been fully developed, the law was novel. In fact, when first proposed, it was a controversial statement and was opposed by other chemists, most notably Proust's fellow Frenchman Claude Louis Berthollet, who argued that the elements could combine in any proportion.[3[[http://en.wikipedia.org/wiki/Law_of_definite_proportions#cite_note-2|]]] The very existence of this debate underscores that at the time, the distinction between pure chemical compounds and mixtures had not yet been fully developed.[4[[http://en.wikipedia.org/wiki/Law_of_definite_proportions#cite_note-3|]]]
This part of chemistry marked progress in manufacture of chemical balances) (Lavoisier had his balances made in the Netherlands by (biography Nicolas Fortin)and Pierre Bernard Megnie)
Learner material:
Law of constant composition
Nature of philosophical induction
Chemical Heritage practical on fermentation. It is aimed at early undergraduate level.
Chemical Heritage practical on magnesium burning.
A Chemical Heritage paper on Lavoisier's instruments as Objet's D'Art.
Teacher material (other than that provided for learners):
Non-stoichiometric compounds from Wikipedia
First chemical equation (1615) by Beguin
Biography of Cullen (1710-1790) (used diagrams as chemical equations)
Biography of Lemery (1645-1715).
Philosophy
Nature of representation
Stanford - Mental Representation
Nature of scientific modelling
What is the nature of the distinction between chemical and physical change? Is it helpful, powerful or simply plain wrong? Some of the history of its introduction may be a good start.
Development of systems of chemical representation took place over a long period of time. The challenge was to infer sub-microscopic explanations from macroscopic phenomena.
Learner material:
Beguin and Cullen's early attempts to write chemical equations.
John Dalton's symbols (see Wikipedia)
Teacher material (other than that provided for learners):
Mental modelling
History of + sign in chemical equations
History of chemical arrows
Braille chemical signs and symbols
Philosophy
Semiotics for beginners - nature of signs
The impact of external influences such as printing technology on conventions for printing chemical equations demonstrates the complex interchange between the rationality of chemists making decisions about their discipline and others.
Learner material:
History of signs in chemical equations, focusing on + and = signs, as opposed to arrows, based on Oversby papers.
Teacher material (other than that provided for learners):
Semiotics for beginners - nature of signs
All of the web sites visited on 2 Dec 08, by Googling Chemical Notation, focused only on expressions of formuae, and not on the signs, such as arrows, and +. The Braille site is mainly concerned with arrows. there are many computer sites concerned with mark up of chemical formulae but not signs.
First of an article on the history of animating.
Wikipedia full article on history of animation
Philosophy
I wonder what there is about philosophy of animating.
The Art and Science of Computer Animation by Stuart Mealing (1998) here.
Daily Stanford article (2005) on Cartoons Simplify Chemistry with (largely) dismissive) comments by academics
How cartoons Work: The Cartoon Code by Randall P Harrison (1981) focussing on simplifying that relates to animating
This is an area that needs further thinking. Most of the papers I have unearthed are on mechanics of animation production.
This topic is modern and whiggishness is not a problem.
Learner material:
ChemSense
Nature of representation
Teacher material (other than that provided for learners):
ChemSense were initiators in tackling student produced animations using bespoke software
Rob Toplis from UK carried out some work with pre-service teacher education students using ChemSense published by the RSC
Maija Aksela and Jan Lundell from Finland have published work using Spartan in CERP
Theodore CHRISTOFILIS & Margarita KOUSATHANA abstract paper on models in science education
REALITY, TRUTH and THE LOGIC of SCIENCE: EXPLORING STUDENTS’ VIEWS ABOUT SCIENTIFIC KNOWLEDGE by Abhijeet BARDAPURKAR, Mumbai, India
We, teachers of chemistry, have become teachers of the history of chemistry… but which type of history must we teach? by José A. Chamizo
NZ teaching with models
Research on models in teaching chemistry (RSC)
JCE Chemical affinity diagram of 18th century (a kind of chemical equation)
David Knight includes a little on chemical equations in his Hyle article
The role of submicroscopic and symbolic representations in chemical explanations Treagust, Chittleborough & Mamiala
PALAVA project: submicroscopic representations for gases in syringes by Oversby
Gail Chittleborough's thesis Chapter 1
Mental models web site
Wikipedia mental models
Promoting understanding of chemical representations: Students' use of a visualization tool in the classroom Authors: Wu, Hsin-Kai; Krajcik, Joseph S.; Soloway, Elliot
Philosophy for Children site.