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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
|| **Comments** || [|THE PALAVA PROJECT – A METHOD OF ASSESSINGMODELLING CAPABILITY] The survey work is well described in this article. || **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]
 * **Topic** || **HPS**
 * Introduction to modelling at macroscopic and sub-microscopic levels: pressure in syringes (see PALAVA experiment below)

[|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.

[|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. Biography of Democritus Biography of Toricelli 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] 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. || **Avoidance of whiggishness:** 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][|]] 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][|]] [|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) 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]. [|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)]. Nature of representation [|Stanford - Mental Representation]
 * Philosophy**
 * Learner material:**
 * Teacher material (other than that provided for learners):** ||
 * Clues about compounds: law of constant composition as an indicator of atoms
 * Philosophy**:
 * Learner material:**
 * Teacher material (other than that provided for learners):**
 * Chemical change and its representation in equations. Chemical equations v mathematical equations || **History**
 * Philosophy**

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. || **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. Beguin and Cullen's early attempts to write chemical equations. [|John Dalton's symbols (see Wikipedia]) Mental modelling || History of + sign in chemical equations History of chemical arrows [|Braille chemical signs and symbols] [|Semiotics for beginners - nature of signs] || **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. History of signs in chemical equations, focusing on + and = signs, as opposed to arrows, based on Oversby papers. [|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] 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. || **Avoidance of whiggishness:** This topic is modern and whiggishness is not a problem. Nature of representation 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] || [|JSSS paper (from KS3 Strategy) on using models in science teaching] [|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].
 * Learner material:**
 * Teacher material (other than that provided for learners):**
 * Signs in chemical equations; origin and use || **History**
 * Philosophy**
 * Learner material:**
 * Teacher material (other than that provided for learners):**
 * Computer animations of chemical processes - a step in representation || **History**
 * Philosophy**
 * Learner material:**
 * [|ChemSense]**
 * Teacher material (other than that provided for learners):**
 * [|ChemSense]** were initiators in tackling student produced animations using bespoke software