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\insrsid12078499\charrsid12078499  Imagine}{\insrsid3225387 -d}{\insrsid12078499\charrsid12078499  Logo: applications and implications}{\insrsid8671394\charrsid14633103 
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, }{\b0\i\insrsid477331 croe}{\b0\i\insrsid1116573\charrsid1116573 @dcs.warwick.ac.uk}{\insrsid1116573\charrsid1116573 
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Centre for New Technologies Research in Education, The University of }{\insrsid1116573 桃色视频}{\insrsid1116573\charrsid4391025 , }{\insrsid1116573 Coventry, UK}{\insrsid1116573\charrsid1116573 
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University}{\insrsid2782015  of 桃色视频}{\insrsid7282863\charrsid4391025 , }{\insrsid2782015 Coventry}{\insrsid12059307 , UK}{\insrsid7282863 
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\insrsid14109054  learning is strongly suggested by \endash  amongst other things \endash }{\insrsid8603198\charrsid8603198  the wide range of applications that spreadsheets have found in education. Given the prominent role that Logo has play
ed in research into comp}{\insrsid14109054 uter support for constructionist learning}{\insrsid8603198\charrsid8603198 
, there is a natural motivation for studying the relationship between spreadsheets and Logo programming. The technical issues surrounding the implementation of dependency in Imagine }{\insrsid14109054 Logo }{\insrsid4739917 (Kalas & Blaho, 2000) }{
\insrsid14109054 have been addressed in }{\insrsid10557813 previous work of Peter }{\insrsid8603198\charrsid8603198 T}{\insrsid10557813 om}{\insrsid8603198\charrsid8603198 c}{\insrsid10557813 s}{\insrsid8603198\charrsid8603198 
anyi (2003). Tomcsanyi's research gives useful insight to the Imagine Logo programmer, but does not indicate how dependency mig}{\insrsid5980926 ht be exploited by end-users }{\insrsid8603198\charrsid8603198 the }{\insrsid5980926 high-level }{
\insrsid8603198\charrsid8603198 way that it has been in spreadsheets. This paper introduces a prototype extension of }{\insrsid14109054 Imagine Logo, informally called}{\insrsid8603198\charrsid8603198  }{\b\insrsid8603198\charrsid12059307 Imagine-d Logo}{
\insrsid8603198\charrsid12059307 ,}{\insrsid8603198\charrsid8603198  tha}{\insrsid3497930 t allows dependencie}{\insrsid8603198\charrsid8603198 s to be specified using spreadsheet-style definitions.}{\insrsid13566327\charrsid8603198 
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\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9126066 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid9126066\charrsid265031  }{\insrsid265031 
Figure 1. A slide from a presentation developed using Roe\rquote s }{\b\insrsid265031\charrsid265031 Imagine-d}{\b\insrsid265031  }{\b\insrsid265031\charrsid265031 Logo}{\insrsid265031  prototype}{\insrsid9126066 
\par }\pard\plain \s24\ql \li0\ri0\sb240\sa60\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0\itap0\pararsid12276097 \b\f1\fs24\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {
\b0\fs22\cf0\kerning0\insrsid8603198\charrsid8603198 The current scope and potential for Imagine-d Logo are discussed and illustrated with reference to practical issues encountered in using Imagine Logo to program a microwor
ld, to implement spreadsheets and to give computer support for presentations. The broader implicatio}{\b0\fs22\cf0\kerning0\insrsid5980926 ns of introducing }{\b0\i\fs22\cf0\kerning0\insrsid5980926\charrsid5980926 dependency by definition}{
\b0\fs22\cf0\kerning0\insrsid8603198\charrsid8603198  into a Logo environment in this manner are briefly discussed from}{\b0\fs22\cf0\kerning0\insrsid14109054  }{\b0\fs22\cf0\kerning0\insrsid8603198\charrsid8603198 
the perspectives of education and computing.}{\b0\fs22\cf0\kerning0\insrsid8603198 
\par }{\insrsid12276097 Keywords
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid12276097 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid8603198 Ima
gine Logo, dependency, spreadsheets, Empirical Modelling, programming paradigms}{\insrsid12276097\charrsid12276097 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa120\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0\pararsid12542392 \b\f1\fs32\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid1522239 Introduction}{
\insrsid8671394 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1522239 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid5661894 Spreadsheets and Logo \endash }{\insrsid11093037  }{\insrsid1522239 
in all}{\insrsid5661894  its rich and numerous variants \endash }{\insrsid1522239  have been amongst the most influential applications where computing support for education is concerned. By way of background, Baker and Sugden (}{\insrsid5652072 2003}{
\insrsid1522239 ) describes the wide range of educational applications for spreadsheets, and }{\i\insrsid1522239 What is Logo?}{\insrsid5652072  (Logo Foundation}{\insrsid1522239 
) gives a good account of the impact of Logo on education. It is natural to seek to integrate these two approaches to educational technology. Such an integration raises challenging issues from several different perspectives:
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid3555031 \loch\af10\dbch\af0\hich\f10 \'a7\tab}}\pard\plain \s16\qj \fi-340\li510\ri0\widctlpar
\jclisttab\tx510\aspalpha\aspnum\faauto\ls1\adjustright\rin0\lin510\itap0\pararsid5723220 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\b\insrsid3555031 P}{\b\insrsid1522239\charrsid265031 ractical programming}{\insrsid1522239 
: What motivating advantages might there be in introducing spreadsheet principles into Logo and how is this best accomplished technically?}{\insrsid1522239\charrsid5723220 
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid3555031 \loch\af10\dbch\af0\hich\f10 \'a7\tab}}{\b\insrsid3555031 P}{\b\insrsid1522239\charrsid265031 edagog}{\b\insrsid1522239 y}{\insrsid1522239 
: What is the significance of spreadsheets and Logo as vehicles for learning, and what is the relationship between them?}{\insrsid1522239\charrsid5723220 
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid3555031 \loch\af10\dbch\af0\hich\f10 \'a7\tab}}{\b\insrsid3555031 C}{\b\insrsid1522239 omputing}{\b\insrsid1522239\charrsid265031  science}{\insrsid1522239 
: How can we make unified sense of the two different computational paradigms represented in spreadsheets and Logo?}{\insrsid1522239\charrsid5723220 
\par }\pard\plain \qj \li0\ri0\sb120\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid12976183 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid2114678 Our}{\insrsid1522239  initial an}{\insrsid2114678 
d primary emphasis}{\insrsid10557813  }{\insrsid2114678 here }{\insrsid1522239 is on the practical programming perspective. We introduce a prototype extension of Imagine Logo, developed by the first author}{\insrsid7615094 , }{\insrsid1522239 that was mo
tivated by issues encountered in programming microworlds based on the throwing events of t}{\insrsid5652072 he Olympic Games (Roe et al, 2005}{\insrsid1522239 ). This prototype - to be referred to as }{\i\insrsid1522239 Imagine-d Logo}{\insrsid1522239 
 - builds on previous work by Tomcsanyi (2003), but }{\insrsid5980926 more closely resembles Geomland }{\insrsid10450047 (Sendov & Dicheva, 1988) }{\insrsid5980926 in its exploitation of}{\insrsid2114678  dependency. Another implicit}{\insrsid1522239 
 influence }{\insrsid2114678 stems from both authors\rquote }{\insrsid1522239  work}{\insrsid2114678  on}{\insrsid1522239  
the principles and tools of Empirical Modelling [EM], a general approach to computing that can be viewed as rooted upon a methodology for modelling with dependency (E}{\insrsid10557813 M }{\insrsid16544485 website; Beynon, 2007). The lat}{
\insrsid10557813 er}{\insrsid1522239  section}{\insrsid10557813 s}{\insrsid16544485  of the paper discuss}{\insrsid1522239  the Imagine-d Logo prototype from the broader pedagogical and computational perspectives associated}{\insrsid10557813 
 with EM thinking, and conclude}{\insrsid1522239  by considering the potential implications for the future development of Logo-like languages. 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa120\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0\pararsid10308416 \b\f1\fs32\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\b0\insrsid8127532 
Adding spreadsheet-style capabilities }{\b0\insrsid8127532\charrsid12919630 to }{\cs27\b0\dbch\af11\insrsid8127532\charrsid12919630 \hich\af1\dbch\af11\loch\f1 Imagine Logo}{\insrsid10308416\charrsid12919630 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid2623649 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid8127532 
The spreadsheet is the archetypal example of an application that exploits }{\i\insrsid8127532 dependenc}{\i\insrsid7475190 y maintenance}{\insrsid8127532 , the mechanism whereby changing one value propag
ates changes to other values in a predictable way. The idea of dependency is often informally invoked by programmers in a much more general context. In implementing object dependencies }{\insrsid8127532\charrsid12919630 in }{
\cs27\dbch\af11\insrsid8127532\charrsid12919630 \hich\af1\dbch\af11\loch\f1 Imagine Logo}{\insrsid8127532 , Tomcsanyi (2003) is concerned with quite general situations in which an object's attributes depend on the attributes of another.
\par Tomcsanyi's approach to implementing dependencies within an object-oriented programming framework is similar in spirit to that of Perry (}{\insrsid5652072 2001}{\insrsid8127532 ). Dependencies are introduced by the pr
ogrammer through embellishing the underlying classes in ways that demand considerable technical skill. By contrast, making computer models using spreadsheets is an activity that can be carried out by non-specialists, and can been viewed as a form of end-u
ser }{\insrsid5652072 programming (see e.g. Nardi, 1993)}{\insrsid8127532 . In order to introduce dependency }{\insrsid8127532\charrsid12919630 into }{\cs27\dbch\af11\insrsid8127532\charrsid12919630 \hich\af1\dbch\af11\loch\f1 Imagine Logo}{
\insrsid8127532\charrsid12919630  in a way that gives similar scope for the non-expert programmer, certain key requirements must}{\insrsid8011985  be met. The programmer:}{\insrsid8127532 
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid8127532 \loch\af10\dbch\af0\hich\f10 \'a7\tab}}\pard\plain \s16\qj \fi-340\li510\ri0\widctlpar
\jclisttab\tx510\aspalpha\aspnum\faauto\ls1\adjustright\rin0\lin510\itap0\pararsid14168001 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid8127532 should not be concerned with the way in which 
the underlying system maintains the dependencies}{\insrsid8011985  between objects in the program;}{\insrsid8127532 
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid8127532 \loch\af10\dbch\af0\hich\f10 \'a7\tab}should be able to ascertain the definition of an attribute/object/variable by inspection.
\par }\pard\plain \qj \li0\ri0\sb120\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid14168001 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid8127532 
To achieve the kind of expressive power that Tomcsanyi (2003) realis
es in his implementation of object-dependencies, it is also desirable to support a wider range of dependency relations than is supported by a traditional spreadsheet. For instance, whereas the spreadsheet is best suited to maintaining scalar relationships
 
recorded in a tabular format, it is natural to consider maintaining relationships between geometric objects in the Imagine Logo environment. By way of illustration, Figure 2 displays what Tomcsanyi (2003) identifies as "a kind of canonical construction of
 dynamic geometry" - a triangle together with the common point of intersection of the perpendiculars dropped from its vertices onto the opposite side.
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\lang1040\langfe1033\langnp1040\insrsid9899460\charrsid265031 
\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9899460 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid9899460\charrsid265031  }{\insrsid9899460 
Figure 2. A simple dynamic geometry construction}{\insrsid15471102 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8522222 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid8522222 In this c
onstruction, the geometric relationships are maintained by dependency when the position of any of the red vertices p1, p3 and p4 is changed.
\par }{\insrsid1116573 Neither }{\insrsid14168001 of the above }{\insrsid1116573 requirement}{\insrsid14168001 s}{\insrsid8522222  is met in Tomcsanyi's implementatio
n of dependency in Imagine Logo. The Imagine-d Logo prototype addresses these requirements by making it possible to specify and revise the dependencies between attributes of objects in much the same way that this is done in a spreadsheet: by formulating a
nd editing explicit definitions for attributes. This has the advantage of making dependency relationships much easier to understand and to trace.
\par From a technical programming perspective, Roe's extension of Imagine Logo is similar to that described by Tomcs
anyi (2003). The same underlying principles are used to maintain dependency, but the details of the implementation are hidden from the programmer. This potentially means that end-user programmers can make effective use of dependency. It also promotes qual
ities that can be found in modelling with spreadsheets, making models simpler to specify, quicker to build, and more readily open to extension.}{\insrsid8127532 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa120\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0\pararsid8522222 \b\f1\fs32\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid8522222 
A dependency layer for Imagine Logo
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8522222 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid8522222 The Imagine-d}{\insrsid2114678  Logo prototype }{\insrsid13065232 was
 developed without access to the Imagine Logo source code: it accordingly }{\insrsid2114678 adds}{\insrsid8522222  a dependency layer }{\insrsid2114678 at the dialogue-box level }{\insrsid8522222 to Imagine }{\insrsid13065232 Logo. }{\insrsid2114678 
This layer supplies}{\insrsid8522222  a 'front-end' in which attributes can be given values using definitions that can be specified and edited dynamically in much the same way as the cells of spreadsheet. This involves developing a language within which
 to specify dependencies between many}{\insrsid5652072  different kinds of attributes \endash }{\insrsid8522222 
 ideally, a language sufficiently rich to support all aspects of programming activity afforded by Imagine Logo. A further important consideration is that the extension of the interface sh
ould respect the look and feel of the Imagine Logo programming environment.
\par The full technical details of the implementation are beyond the scope of this paper. The features of the prototype will be motivated and illustrated with reference to }{\insrsid5261189 practical programming issues }{\insrsid8522222 
that were encountered in the process of building the Olympic Games microworlds.
\par A simple example of the kind of dependency to be specified is that between the positions of two turtles that is discussed in Tomcsanyi (2003). The relationship 
between the position of the cat and the mouse in Figure 1 illustrates the general idea. In the pane on the right-hand side of this figure dragging movements of the cat result in left-right movements of the mouse that maintain a fixed horizontal dist}{
\insrsid5261189 ance between the two. The way}{\insrsid8522222  in which }{\insrsid5261189 the model-builder specifies this dependency }{\insrsid8522222 differs between the top and bottom cat-mouse pairs, }{\insrsid12919630 though the effect is the same.}
{\insrsid8522222 
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8600352 {\insrsid8600352 The specification of the dependency between the positions of the cat and the mouse in the top cat
-mouse pair in Figure 1 typifies the way in which a }{\insrsid8600352\charrsid12919630 relationship between attributes is expressed in an }{\cs27\dbch\af11\insrsid8600352\charrsid12919630 \hich\af1\dbch\af11\loch\f1 Imagine Logo}{
\insrsid8600352\charrsid12919630  program. As displayed in Figure 3, the specification takes }{\insrsid16544485 the form of a triggered action \endash }{\insrsid8600352\charrsid12919630  located in the }{\cs27\dbch\af11\insrsid8600352\charrsid12919630 
\hich\af1\dbch\af11\loch\f1 Events}{\insrsid16544485  field \endash }{\insrsid8600352\charrsid12919630  that is invoked whenever the cat (here implemented by the turtle }{\cs27\dbch\af11\insrsid8600352\charrsid12919630 \hich\af1\dbch\af11\loch\f1 x1}{
\insrsid8600352\charrsid12919630 ) is dragged about the screen. The effect of this triggered action is to update the x coordinate of the mouse (here represented by the turtle }{\cs27\dbch\af11\insrsid8600352\charrsid12919630 \hich\af1\dbch\af11\loch\f1 x2
}{\insrsid8600352\charrsid12919630 ).}{\insrsid8600352 
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\lang1040\langfe1033\langnp1040\insrsid5261189\charrsid265031 
\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid5261189 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid5261189\charrsid265031  }{\insrsid5261189 
Figure 3. A triggered action associated with \'93dragging the cat\'94 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10910201 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid8600352 
In contrast, the specification of the dependency between the positions of the cat and the mouse in the bottom cat-mouse pair in Figure 1 exploits a spreadsheet-style definition feature that is implemented in Imagine-d
 Logo. For this purpose, the Basics field in the specification for the mouse at the bottom right (here implemented by the tu}{\insrsid5652072 rtle x4) is adapted \endash  without any significant change to its layout and format \endash  as}{
\insrsid8600352  displayed in Figure 4. The x and y coordinates of the turtle x4 can be specified in this context }{\insrsid5652072 not only as explicit }{\insrsid396782 values }{\insrsid5652072 but }{\i\insrsid8600352\charrsid5652072 by definitions}{
\insrsid8600352 , so that the x coordinate of turtle x4 is defined to be the x coordinate of turtle x3 incremented by a constant number of pixels. This definition, like a spreads
heet definition, can be directly edited by the model-builder. Figure 1 shows the result of changing the value of the constant increment from 150 to 100 pixels.
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\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid5261189 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid5261189\charrsid265031  }{\insrsid5261189 
Figure 4. Defining the x position of the mouse via the modified interface
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10910201 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid10910201 The Imagine-d Logo prototype introduces a conceptually n}{
\insrsid3555031 ew feature into the programming }{\insrsid10910201 environment. Where the event-driven paradigm of Imagine Logo requires that relationships are specified by means of triggered actions, the definition of an a
ttribute does not readily admit a simple interpretation as a state-changing action. The implications of this are complex and subtle. It is significant for instance, that defining the x coordinate of turtle x4 with reference to the coordinate of turtle x3 
e
nsures that the value of x4'xcor changes whenever the value of x3'xcor changes, no matter what the nature of the agency that is operating. This contrasts with the discriminating way in which a position update may be associated with a specific event, as in
 dragging the cat around the screen (cf. Figure 3).
\par In general, it may be said that definitions afford clearer and more explicit descri}{\insrsid5652072 ptions of relationships though \endash }{\insrsid10910201  a }{\insrsid5652072 superficial analysis suggests \endash  }{\insrsid10910201 
at the expense of some operational simplification. Even
t-driven sequences of actions can support cyclic patterns of update for instance, whereas the value of an attribute cannot be meaningfully defined in terms of itself. The potential benefits of expressing a dependency through a definition are best apprecia
t
ed where more complicated patterns of dependency are present. Where a value is defined in terms of many different values, each of which is subject to change through a range of different agencies, the task of analysing the implicit relationships amongst fa
milies of attributes can become exceedingly complex, and specifying and maintaining the program structure becomes accordingly more difficult.
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa120\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0\pararsid5711382 \b\f1\fs32\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid6366639\charrsid6366639 
Further illustrations}{\insrsid10910201\charrsid6366639 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8522222 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid6366639\charrsid6366639 
Some additional examples serve to illustrate some of the key issues regarding the introduction of }{\insrsid8520265 spreadsheet-style definitions to}{\insrsid6366639\charrsid6366639  the Imagine Logo environment.}{\insrsid6366639 
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid6366639 {\insrsid6366639\charrsid6366639 The distinction between the event-driven and definition-based approaches to specifying dependen
cies is relevant even to simple scenarios, such as maintaining the relationship between the value in a box and the position of a slider (cf. Figure 5). The principal advantage of using a definition is that the model-builder need only inspect the specifica
t
ion of the box object in order to determine why it has its current value. This may not pose a serious problem where the dependency that determines the value in the box relates to the position of a single slider and is kept up to date by a single triggered
 action. It can become much more problematic when the dependency relations are complex. }{\insrsid6366639 
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\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10354830 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid10354830\charrsid265031  }{\insrsid10354830 
Figure 5. Alternative ways to link the value of a box to a slider
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10354830 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid9646303\charrsid9646303 Figure 6 shows a co}{\insrsid14749854 
ntrol mechanism drawn from the S}{\insrsid9646303\charrsid9646303 hotput microworld (Roe}{\insrsid9521222  et al}{\insrsid9646303\charrsid9646303 , }{\insrsid9521222 2005}{\insrsid9646303\charrsid9646303 
). In this figure, the angle of elevation of the green arrow is determined by the lower slider, and the angle of elevation of the purple arrow relative to the green arrow by the }{\insrsid9521222 upper slider. T}{\insrsid9646303\charrsid9646303 
he textbox values and the headings of the turtles are then dependent on a combination of the positions of the two sliders. }{\insrsid4803205 Within the Imagine-d Logo prototype, the heading for the purple arrow can be defined directly by the formula \'93
angleslider\rquote value + attackslider\rquote value\'94. When the}{\insrsid9646303\charrsid9646303  dependency is implement}{\insrsid4803205 ed in the traditional way, this formula appears on the right hand side of assignments in}{
\insrsid9646303\charrsid9646303  two separate triggering events associated with the two sliders}{\insrsid4803205 . T}{\insrsid9646303\charrsid9646303 o understan}{\insrsid4803205 d how the heading of the purple arrow is}{\insrsid9646303\charrsid9646303 
 determined the model-builder has to search for the events that might have an impact upon them. If it becomes necessary to updat}{\insrsid4803205 e the relationship, this formula has}{\insrsid9646303\charrsid9646303 
 to be updated in identical ways in two places.}{\insrsid10354830 
\par }\pard \qc \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10354830 {\insrsid8521564 {\*\shppict{\pict{\*\picprop\shplid1031{\sp{\sn shapeType}{\sv 75}}{\sp{\sn fFlipH}{\sv 0}}
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\lang1040\langfe1033\langnp1040\insrsid10354830\charrsid265031 
\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10354830 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid10354830\charrsid265031  }{\insrsid10354830 
Figure 6. A more complex dependency relationship involving two sliders
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8522222 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid12262856 Another feature of the S}{\insrsid12262856\charrsid12262856 
hotput microworld in which complex dependencies are 
involved is the dynamic graph used to display the x and y coordinates of the shotput trajectory. Because of the wide variety of possible trajectories, it is important to be able to adjust the range of values displayed on the axes, and the granularity of t
h
e xy-grid dynamically (see Figure 7). This involves setting up dependencies in which multiple turtles and several textboxes are involved. In this example, dragging the purple point triggers the recalculation of the maximum x and y coordinates that need to
 
be displayed. These positions of the grid lines are dependent on these maximum values, and grid lines are only displayed if they are within the range of the graph. The dependency relationships required to specify the positions and visibility of grid lines
 are here expressed by definitions.}{\insrsid12262856 
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Figure 7. Dynamic graphs implemented using dependencies expressed by definitions
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9137150 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid9137150 
A very rich family of relationships can be programmed by introducing generic dependency maintenance to the
 Imagine Logo environment. This is evident from the range of applications that can be readily implemented using the Imagine-d Logo prototype. Figure 8 displays another slide from the same presentation from which Figure 1 was drawn. Dependencies framed as 
definitions have been used in this presentation in several ways:
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid9137150 \loch\af10\dbch\af0\hich\f10 \'a7\tab}}\pard\plain \s16\qj \fi-340\li510\ri0\widctlpar
\jclisttab\tx510\aspalpha\aspnum\faauto\ls1\adjustright\rin0\lin510\itap0\pararsid5723220 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid9137150 To implement}{\insrsid9137150\charrsid9137150  a generalised spreadsheet}{
\insrsid9137150 : A simple spreadsheet has been embedded within the displayed slide. In addition to the normal dependencies between values, there is scope to make the p
resentation of data depend on its content, to exploit slider positions as if they were cell values and to attach names to "floating cells" that do not have to be located within the grid.
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid9137150 \loch\af10\dbch\af0\hich\f10 \'a7\tab}To manage}{\insrsid9137150\charrsid9137150  the screen layout}{\insrsid9137150 : The dimensions, organisation and attri
butes of windows on the screen can be determined using dependency relationships. The position of bullets in the text can be determined relative to a reference point.
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid9137150 \loch\af10\dbch\af0\hich\f10 \'a7\tab}To animate}{\insrsid9137150\charrsid9137150  the presentation}{\insrsid9137150 
: By dragging the dog icon at the foot of the slide from left to right across the screen different right hand panes can be slotted into the slide to illustrate each of the bullet points in turn. This animation effect i}{\insrsid8197085 
s obtained by creating}{\insrsid9137150  a series of frames that display a different variant of the dog icon according to its horizontal position, and defining the choice and location of the right hand pane in terms of this position.}{
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01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100101
010d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d010101010130011001300110013001100130
01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130
0110010100ff27281030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030100110300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
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10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
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10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d3010011001103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
1030103010301030103010301030103010301030103010301030100100ff0e410110011001103010011001100110301001100110011030100110011001103010
011001100110301001100110011030100110011001103010011001100110301001100110011030100110011001103001010d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
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300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d01010101011001103010011001100110301001100110011030100110011001103010
0110011001103010011001100110301001100110011030100110011001103010011001100110301001100110011030100110010100ff43271030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
103010301030100110300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
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0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d011001010110301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030100100ff0e28011001300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
0110013001100110011001300110011001100130011001100110013001100101010d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d0101010101300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
01100130011001100110013001100110011001300110011001100130011001100110010100ff4328103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100101300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d301001010110301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100ff0e41
01100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001010130300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d0101
01010110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001100110010100ff432710301030103010301030103010301030103010301030103010301030103010301030103010301030
1030103010301030103010301030103010301030103010301030103010301030103010301030100110300d300e300d3010300d300e300d3010300d300e300d30
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10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e30300110010101103010301030103010301030103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100ff0e2801100130011001300110013001100130
01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100101
010d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d010101010130011001300110013001100130
01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130
0110010100cc27281030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030100110300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
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10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d3010011001103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
1030103010301030103010301030103010301030103010301030100100ff0e410110011001103010011001100110301001100110011030100110011001103010
011001100110301001100110011030100110011001103010011001100110301001100110011030100110011001103001010d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d01010101011001103010011001100110301001100110011030100110011001103010
0110011001103010011001100110301001100110011030100110011001103010011001100110301001100110011030100110010100ff43271030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
103010301030100110300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
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0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d011001010110301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030100100ff0e28011001300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
0110013001100110011001300110011001100130011001100110013001100101010d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d0101010101300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
01100130011001100110013001100110011001300110011001100130011001100110010100ff4328103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100101300e300d300e30
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0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d301001010110301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100ff0e41
01100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001010130300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
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300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d0101
01010110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
01100110011001100110011001100110011001010099432710301030103010301030103010301030103010301030103010301030103010301030103010301030
1030103010301030103010301030103010301030103010301030103010301030103010301030100110300d300e300d3010300d300e300d3010300d300e300d30
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10300d300e300d3010300d300e300d3010300d300e30300110010101103010301030103010301030103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100990e2801100130011001300110013001100130
01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100101
010d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d010101010130011001300110013001100130
01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130
0110010100ff27281030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030100110300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
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10300e300d3010011001103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
1030103010301030103010301030103010301030103010301030100100660e410110011001103010011001100110301001100110011030100110011001103010
011001100110301001100110011030100110011001103010011001100110301001100110011030100110011001103001010d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
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300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d01010101011001103010011001100110301001100110011030100110011001103010
0110011001103010011001100110301001100110011030100110011001103010011001100110301001100110011030100110010100ff43271030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
103010301030100110300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
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0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d011001010110301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030100100ff0e28011001300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
0110013001100110011001300110011001100130011001100110013001100101010d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030303001010101010101010101
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300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d0101010101300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
01100130011001100110013001100110011001300110011001100130011001100110010100ff4328103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100101300e300d300e30
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0d300e300d300e300d300e300d301001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d301001010110301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100ff0e41
01100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001010130300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d30300101010101010101010101010101010101010101010101010101
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300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d0101
01010110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001100110010100ff432710301030103010301030103010301030103010301030103010301030103010301030103010301030
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10010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101
10010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101
10010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101
10010101100101011001010110010101100101011001010110010101100101011001303010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d011001010110301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030100100cc0e28011001300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
0110013001100110011001300110011001100130011001100110013001100101010d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030303001010101010101010101
01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010130300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d0101010101300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
01100130011001100110013001100110011001300110011001100130011001100110010100ff4328103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100101300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d301001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001010110010101100101011001
01011001010110010101100101011001010110300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d301001010110301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100ff0e41
01100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001010130300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d0101
01010110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001100110010100ff432710301030103010301030103010301030103010301030103010301030103010301030103010301030
1030103010301030103010301030103010301030103010301030103010301030103010301030100110300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d30
10300d300e300d3010300d300e300d3010300d300e30300110010101103010301030103010301030103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100ff0e2801100130011001300110013001100130
01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100101
010d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030
300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d3030300d010101010130011001300110013001100130
01100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130011001300110013001100130
0110010100cc27281030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030100110300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e3010300e300d300e30
10300e300d3010011001103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
1030103010301030103010301030103010301030103010301030100100ff0e410110011001103010011001100110301001100110011030100110011001103010
011001100110301001100110011030100110011001103010011001100110301001100110011030100110011001103001010d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d01010101011001103010011001100110301001100110011030100110011001103010
0110011001103010011001100110301001100110011030100110011001103010011001100110301001100110011030100110010100ff43271030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
103010301030100110300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d30
0e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d300e300d3010300d011001010110301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030
10301030103010301030100100cc0e28011001300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
0110013001100110011001300110011001100130011001100110013001100101010d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d300d3030300d300d
300d3030300d300d300d3030300d0101010101300110011001100130011001100110013001100110011001300110011001100130011001100110013001100110
01100130011001100110013001100110011001300110011001100130011001100110010100ff4328103010301030103010301030103010301030103010301030
103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100101300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e30
0d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d300e300d301001010110301030103010301030103010301030103010301030
10301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030103010301030100100ff0e41
01100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001010130300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d
300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d300d0101
01010110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110011001100110
011001100110011001100110011001100110010100ff432710301030103010301030103010301030103010301030103010301030103010301030103010301030
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\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid5711382 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid9137150\charrsid10557813  }{\insrsid5711382\charrsid5711382 
Figure 8}{\insrsid9137150\charrsid5711382 .}{\insrsid5711382\charrsid5711382  }{\insrsid5711382 Illustrating dependency in specifying slide content, layout and animation}{\insrsid9137150\charrsid5711382 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa120\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0\pararsid11102723 \b\f1\fs32\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid11102723 Discussion}{
\insrsid9137150\charrsid5711382 
\par }\pard\plain \s3\qj \li0\ri0\sb180\sa60\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0\itap0\pararsid3235239 \f1\fs24\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\fs22\cf0\kerning0\insrsid16021350 
Introducing}{\fs22\cf0\kerning0\insrsid11102723\charrsid11102723 
 dependency-by-definition to Imagine Logo has a significant practical impact on model construction. In implementing features such as dynamic graphs, the convenience of being able to formulate dependencies as definitions without needing to explic
itly set up the underlying maintenance mechanisms is liberating, and promotes the speed and flexibility of development that is associated with the use of sprea}{\fs22\cf0\kerning0\insrsid16021350 dsheets. Extending}{
\fs22\cf0\kerning0\insrsid11102723\charrsid11102723  Imagine Logo }{\fs22\cf0\kerning0\insrsid16021350 in this way }{\fs22\cf0\kerning0\insrsid11102723\charrsid11102723 seems to be particularly topical when we consider the
 prominent role that dependency plays in many successful educational pro}{\fs22\cf0\kerning0\insrsid16021350 ducts, such as }{\i\fs22\cf0\kerning0\insrsid16021350\charrsid16021350 Cabri Geometry}{\fs22\cf0\kerning0\insrsid11102723\charrsid11102723  }{
\fs22\cf0\kerning0\insrsid16021350 and }{\i\fs22\cf0\kerning0\insrsid16021350\charrsid16021350 Visual Fractions}{\fs22\cf0\kerning0\insrsid16021350 . However, i}{\fs22\cf0\kerning0\insrsid11102723\charrsid11102723 
n this context, it is worth noting (Kalas, personal communication, 2005) that the designers of Imagine Logo have long been aware of the expressive q}{\fs22\cf0\kerning0\insrsid12790176 ualities of dependencies, ye}{\fs22\cf0\kerning0\insrsid5779558 
t have }{\fs22\cf0\kerning0\insrsid11102723\charrsid11102723 been uncertain about how these can be effectively and coherently exploited}{\fs22\cf0\kerning0\insrsid16529906 . }{\fs22\cf0\kerning0\insrsid16529906\charrsid16529906 
This is consistent with the fact that understanding the relationship between modelling with dependency and programming has been a central theme of the Empirical Modelling project (EM Web) since its inception}{\fs22\cf0\kerning0\insrsid11102342 
 more than twenty years ago}{\fs22\cf0\kerning0\insrsid13777322 . Over this period,}{\fs22\cf0\kerning0\insrsid16529906\charrsid16529906  resear}{\fs22\cf0\kerning0\insrsid16529906 ch on this theme has generated:}{
\fs22\cf0\kerning0\insrsid16529906\charrsid16529906 
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid16529906\charrsid16529906 \loch\af10\dbch\af0\hich\f10 \'a7\tab}}\pard\plain \s16\qj \fi-340\li510\ri0\widctlpar
\jclisttab\tx510\aspalpha\aspnum\faauto\ls1\adjustright\rin0\lin510\itap0\pararsid16529906 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid16529906\charrsid16529906 practical tools and models to demonstrate that modelling }{
\i\insrsid16529906\charrsid16529906 purely}{\insrsid16529906\charrsid16529906  with definitions in principle has expressive power and range encompassin}{\insrsid16529906 g what has been illustrated using}{\insrsid16529906\charrsid16529906  Ima}{
\insrsid16529906 gine-d Logo above}{\insrsid16529906\charrsid16529906  (see for instance the presentation graphicspresHarfield2007}{\insrsid5208051  (EM Web}{\insrsid16529906 )}{\insrsid16529906\charrsid16529906 , }{\insrsid16529906 
in which definitions support}{\insrsid11102342  geometric modelling and}{\insrsid16529906\charrsid16529906  i}{\insrsid16529906 nterface management}{\insrsid11102342 ,}{\insrsid16529906  and implement}{\insrsid16529906\charrsid16529906 
 notations for formulating definitions that are themselves defined within the modelling tool).
\par {\listtext\pard\plain\s16 \f10\fs22\lang2057\langfe1033\langfenp1033\insrsid16529906\charrsid16529906 \loch\af10\dbch\af0\hich\f10 \'a7\tab}a methodology for modelling with dependency that is associated with a radical reappraisal of thinking about compu}{
\insrsid16529906 ting (Beynon, 2007}{\insrsid9185368 ; King, 2007}{\insrsid16529906 ).}{\insrsid16529906\charrsid16529906 
\par }\pard\plain \s3\qj \li0\ri0\sb180\sa60\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0\itap0\pararsid3235239 \f1\fs24\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\fs22\cf0\kerning0\insrsid12790176 R}{
\fs22\cf0\kerning0\insrsid11102723\charrsid11102723 elevant issues }{\fs22\cf0\kerning0\insrsid1604573 can be exposed by reviewing \'93programming with dependency\'94}{\fs22\cf0\kerning0\insrsid16021350  }{
\fs22\cf0\kerning0\insrsid11102723\charrsid11102723 from each of the three perspectives identified in the introduction: programming practice, pedagogy, and computing science.}{\fs22\cf0\kerning0\insrsid11102723 
\par }\pard \s3\ql \li0\ri0\sb180\sa60\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0\itap0\pararsid8671394 {\insrsid10443687 Programming practice}{\insrsid8671394\charrsid11102723 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8671394 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid16021350 It is}{\insrsid10443687 
 a conceptual mistake to suppose that adding features to a programming language that contribute to ease-of-development and ease-of-use necessarily thereby enhance}{\insrsid16021350 s}{\insrsid10443687 
 its value as a vehicle for constructivist learning. Learning and 'optimisation to achieve a specific programming goal' are activities that engage the mind in quite different ways, and develop in entirely divergent di}{\insrsid12790176 rections. I}{
\insrsid10443687 n learning, it is vital to pay as much attention to the environment}{\insrsid12790176  as possible and to explore}{\insrsid10443687  every discrepancy between expectat}{\insrsid12790176 
ion and observation, whereas optimisation involves specialising the task and engineering the context so as to minimise}{\insrsid10443687  the information we need to know abou}{\insrsid12790176 
t the environment and eliminate all observation and action that can be made superfluous}{\insrsid10443687 . The 
distinction drawn between virtuosity and musicality in performance is one indication that the speed with which we can accomplish specific tasks is not a good measure of how much we have learnt about a domain}{\insrsid9448508\charrsid10443687 .}{
\insrsid10443687 
\par It is also well-recognised that adding features to a programming environment does not necessarily lead to a coherent conceptual enhancement. The challenge to conceptual integrity }{\insrsid12790176 in Imagine-d Logo }{\insrsid10443687 
can be gauged from comparing the code developed by Tomcsanyi (2003) to implement the dynamic geometry depicted in Figure 2 with the following listing, which specifies the same configuration using the EDEN}{\insrsid10101494  interpreter \endash }{
\insrsid10443687  the principal tool for Empirical Modelling: 
\par }\pard\plain \s28\ql \li0\ri0\widctlpar\tx916\tx1832\tx2748\tx3664\tx4580\tx5496\tx6412\tx7328\tx8244\tx9160\tx10076\tx10992\tx11908\tx12824\tx13740\tx14656\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10443687 
\fs20\lang2057\langfe1041\loch\af2\hich\af2\dbch\af11\cgrid\langnp2057\langfenp1041 {\fs22\insrsid10443687\charrsid9834195 \hich\af2\dbch\af11\loch\f2 line AB, BC, AC
\par \hich\af2\dbch\af11\loch\f2 point A, B, C
\par \hich\af2\dbch\af11\loch\f2 AB=[A,B]\tab \tab // the line joining points A and B
\par \hich\af2\dbch\af11\loch\f2 BC=[B,C]
\par \hich\af2\dbch\af11\loch\f2 AC=[C,A]
\par \hich\af2\dbch\af11\loch\f2 A = \{\hich\af2\dbch\af11\loch\f2 20, 180\}\tab \tab \tab // the point p4
\par }{\fs22\insrsid5779558 \hich\af2\dbch\af11\loch\f2 B = \{260, 490\}\tab \tab }{\fs22\insrsid10443687\charrsid9834195 \hich\af2\dbch\af11\loch\f2 // the point p1
\par \hich\af2\dbch\af11\loch\f2 C = \{285, 50\}\tab \tab \tab // the point p3
\par \hich\af2\dbch\af11\loch\f2 line perpA, perpB, perpC
\par }{\fs22\insrsid5779558 \hich\af2\dbch\af11\loch\f2 perpC = perpend(C, AB)     }{\fs22\insrsid10443687\charrsid9834195 \hich\af2\dbch\af11\loch\f2 // the perpendicular dropped from C on to AB
\par \hich\af2\dbch\af11\loch\f2 perpB = perpend(B, AC)
\par \hich\af2\dbch\af11\loch\f2 perpA = perpend(A, BC)
\par \hich\af2\dbch\af11\loch\f2 point D
\par \hich\af2\dbch\af11\loch\f2 D = intersect(\hich\af2\dbch\af11\loch\f2 perpA, perpB)
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8671394 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid10443687 
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10443687 {\insrsid663493 In b}{\insrsid10443687 oth EDEN and the Imagine-d Logo}{\insrsid663493  prototype, }{\insrsid10443687 the programmer }{\insrsid663493 
can }{\i\insrsid10443687 either}{\insrsid663493  }{\insrsid10443687 specify the explicit procedural actions that maintain the geometric dependencies in Figure 2, }{\i\insrsid10443687 or}{\insrsid663493  }{\insrsid10443687 
embody them in a set of definitions}{\insrsid663493 . But by what criterion should }{\insrsid10443687 one approach }{\insrsid663493 be adopted }{\insrsid10443687 
rather than the other, and is the distinction between these two approaches more than a matter of individual taste?
\par }\pard\plain \s3\ql \li0\ri0\sb180\sa60\keepn\widctlpar\tx4185\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0\itap0\pararsid3702636 \f1\fs24\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid10443687 Pedagogy}{
\insrsid3702636 \tab }{\insrsid10443687 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid10443687 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid10443687 
In comparing Logo with Boxer, diSessa (1997) stresses the importance of criteria other than abstract expressive power in relation to learning. His concern is as much}{\insrsid11998358  with the physical form that programs take}{\insrsid10443687 
 as with the underlying p}{\insrsid11998358 rogramming constructs}{\insrsid10443687 . This is consistent with his observation (diSessa, 20}{\insrsid11744931 00) that "}{\i\insrsid11744931\charrsid11744931 make it experiential}{\insrsid10443687 
 is perhaps the single most powerful educational heuristi}{\insrsid9185368 c I know". diSessa also seeks}{\insrsid10443687 
 to challenge the assumption that educational software "comes in large units that are so slick and complex as to require many person-years of effort to create them, usually by highly technically competent software engineers". 
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11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111110111111111111
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21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211011111111111111111111111111111111111111111111
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11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111
11112111111121111111211111112111111121111111211111101111111111111111111111111111111111111111111111111111111111111111111111111111
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21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111211111112111111121111111
21111111211111112110111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111011111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111110111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110040000002701ffff030000000000}}}{\insrsid1971028 
\par }\pard\plain \s26\qc \li0\ri0\sb240\sa240\keepn\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1971028 \i\f1\fs20\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid1971028\charrsid10443687  }{
\insrsid1971028\charrsid16544485 Figure }{\insrsid9834195\charrsid16544485 9}{\insrsid1971028\charrsid16544485 . }{\insrsid10443687\charrsid10443687 The }{\b\insrsid10443687\charrsid10443687 tick model}{\insrsid10443687\charrsid10443687 
 that defines uniform motion\~(diSessa}{\insrsid10443687 , 2000)}{\insrsid1971028\charrsid10443687 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid2623649 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid9834195 
diSessa's "tick model" of uniform motion, as depicted in Figure 9, reflects his desire to shift the emphasis from programs as complex bodies of code for professional analysis towards visual artefacts that are intelligible to the learner. It also highlight
s his concern for a close correspondence between the interpretation of the program in the domain and the components of a visual representation.}{\insrsid9834195\charrsid9834195  }{\insrsid9834195 Similar concerns for }{\i\insrsid9834195\charrsid7889835 
experiential}{\insrsid9834195  rather than symbolic representations of programs were influential in the design of Imagine Logo (Kalas et al, 2000).
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3702636 {\insrsid9834195 
Beynon and Roe (2006) raise a deeper concern about the suitability of programming languages as a means to realise constructionist ideals. The traditional and fundamental understanding of }{\i\insrsid9834195 what a program is}{\insrsid7889835 
 casts the programmer in}{\insrsid9834195  the role of a specialist with r}{\insrsid11744931 econdite knowledge whose job }{\insrsid9834195 
is to ensure that a program carries out specific functional tasks that conform to explicit user requirements. Under this interpretation, neither the programmer nor the user interacts with the program as an artefact in a way that is well-matched to the }{
\insrsid10101494 agenda}{\insrsid9834195  of the active learner. The kind of conflation of pupil, teacher, developer roles that constructionist learning }{\insrsid7889835 ideally demands }{\insrsid9834195 
is much better mapped on to the collaborative moulding of a spreadsheet model to situation by human agents with different levels of domain knowledge and computational literacy discussed by Nardi (1993). Empirical Modelling}{\insrsid3699376  }{
\insrsid9834195 endorses this idea, privileging the use of sets of definitions to express the latent dependency in situations over the use of conventional procedural constructs and data abstractions to describe processes and behaviours. }{\insrsid3702636 

\par }\pard\plain \s3\ql \li0\ri0\sb180\sa60\keepn\widctlpar\tx4185\aspalpha\aspnum\faauto\outlinelevel2\adjustright\rin0\lin0\itap0\pararsid3702636 \f1\fs24\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid3702636 Computing Science
\tab 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3702636 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid3702636 The besetting problem
s of large-scale complex software development are closely connected with the need 
to develop domain knowledge in an incremental and systematic fashion whilst making computer models in a constructivist spirit. This highlights a strong connection between pedagogical aspirations for software and fundamental concerns in computing science. 
Empirical Modelling identifies the primitive learning that must underpin software development with a particular way of gaining familiarity and understanding in a domain. This activity }{\insrsid14055451 has a primary orientation closer to}{
\insrsid5324223  Papert\rquote s}{\insrsid14055451  }{\i\insrsid14055451\charrsid14055451 bricolage}{\insrsid14055451  than}{\insrsid3702636  conventional programming}{\insrsid5324223  }{\insrsid7628639 (cf. }{\insrsid5324223 R}{\insrsid7628639 oe}{
\insrsid5324223  }{\insrsid7628639 (2003), pages }{\insrsid5324223 109}{\insrsid7628639 -1}{\insrsid5324223 16)}{\insrsid3702636 , in that its emphasis is upon modelling }{\insrsid5324223 concrete }{\insrsid3702636 situations rather than prescribing }{
\insrsid5324223 abstract }{\insrsid3702636 behaviours. As discussed in Beynon (2007), this is achieved through making artefacts that are appropriately characterised as }{\i\insrsid3702636 construals}{\insrsid3702636  rather than programs. A construal
 offers interactive experience to the model-maker in which empirically validated patterns of observation, dependency and agency in the domain are faithfully reflected.
\par The notion of giving computer-support to making construals fits in well with diSessa's conception of }{\i\insrsid3702636 material intelligence}{\insrsid3702636 
 as "an intelligence achieved cooperatively with external materials". The close correspondence between the components of the Boxer program in Figure 9 and their physical counterparts in the domain is well-matched to an ana
lysis of domain observables, dependencies and agents. Generalising such a correspondence to typical computer programs is altogether more problematic. The fundamental historical rationale for the program concept has been that of automating human agency out
-
of-the-loop. The sharp mathematically defined abstractions that pervade the theory of programming are its legacy. The difficulty of maintaining a credible correspondence between objects as experienced in the domain and objects as they emerge in the design
 of programs is but one indication of the tension between automated action and reflective thinking.}{\insrsid2570450 
 It is clear for instance that the object-oriented programming activity associated with implementing the dynamic geometry of Figure 6 in Tomcsanyi (2003) does
 not admit the same direct interpretation in geometric terms as the family of EDEN definitions above. }{\insrsid3702636 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa120\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0\pararsid3702636 \b\f1\fs32\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid3702636 Conclusion
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid3702636 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid13965258 The above discussion highlights the}{\insrsid8676707  crucial}{
\insrsid13965258  importance in constructionist use of the computer of the experiential aspects of the modeller\rquote s interaction.}{\insrsid8676707  For learning to be effective, there must be a close and \endash  in some sense \endash 
 directly perceptible relationship between situations, objects and concepts in the domain}{\insrsid13965258  }{\insrsid8676707 and the interactive experience of the model-making. In establishing this relationship, what is \endash  or comes to be \endash 
 hidden and implicit in the interaction is quite as important as what is explicit. Arguably, much learning is associated with acquiring such familiarity with relationships between }{\insrsid9119855 significant observables that the procedur
es for identifying these relationships that at first must be laboriously followed become routine and internalised. }{\insrsid2451962 But where the polished products of professional software}{\insrsid9119855  }{\insrsid2451962 development }{
\insrsid13203041 strive to anticipate what kind of functionality and familiarisation is appropriate and attainable and optimise the user\rquote s interaction}{\insrsid9119855  }{\insrsid13203041 accordingly, the }{\insrsid12336929 
essence of educational software is that it should expose the }{\insrsid30320 raw }{\insrsid12336929 activities that are associated with identifying functionality and gaining familiarity with procedures.}{\insrsid3702636 
\par }{\insrsid16012140 Dependencies are archetypal examples of relati}{\insrsid14839759 onships that underpin learning. The merits of spreadsheets for educational applications can plausibly be attributed to the fact that \endash  unlike conventional programs 
\endash  they carry out dependency maintenance activity in a way that is both hidden and intentionally }{\i\insrsid14839759\charrsid14839759 uninterpreted}{\insrsid14839759 
. Programming environments such as Imagine-d Logo and EDEN in principle support similar sense-making conventions that allow some \'93program code\'94 to be explicitly interpreted and some to be as-if-internalised by the model-maker.}{\insrsid14044445 
 The problematic issue is that such a policy of blended interpretation and uninterpretation is not consistent with the orthodox}{\insrsid14113926  abstract}{\insrsid14044445  conception of computational semantics.}{\insrsid16012140 
\par }{\insrsid14113926 Modern variants of Logo, such as Imagine Logo and Boxer, have taken significant steps towards the concretisation that is essential in supporting a new practice of computing better attuned to the demands of constructionist learning. }{
\insrsid10188013 The sense-making theories needed to enfranchise such practice and }{\insrsid8209150 to promote its mature use have yet to be identified. }{\insrsid14113926 As Albirini, citing G\'e4rdenfors and Johansson, remarks: \'93}{\insrsid4522178 
educational technolog}{\insrsid14113926\charrsid14113926 y still lacks a unifying theory of learning that would serve as a foundation for its use in the classroom"}{\insrsid14113926  (Albirini, 2007).}{\insrsid8209150 
 The motivating thesis behind Empirical Modelling is that }{\insrsid4522178 such a theory of learning has to be developed in conjunction with}{\insrsid8209150  }{\insrsid4522178 a }{\insrsid8209150 radical}{\insrsid4522178 ly}{\insrsid8209150  }{
\insrsid4522178 new }{\insrsid8209150 conception }{\insrsid4522178 of computing (Beynon, 2007). }{\insrsid14044445 
\par }{\insrsid30320 As diSessa\rquote s \'93tick model\'94 of uniform motion illustrates}{\insrsid4734895  (see Figure 9)}{\insrsid30320 , there are contexts in which there is an excellent match between }{\insrsid13378906 
experience of a domain and of its representation in a computer-based artefact. }{\insrsid4734895 It is evident that the quality of the \'93tick model\'94 is linked to the fact that the }{\insrsid3417472 \'93}{\insrsid4734895 turtle}{\insrsid3417472 \'94}{
\insrsid4734895  metaphor }{\insrsid4081430 for change }{\insrsid4734895 is ideally suited to representing the dynamics of physical motion and time. }{\insrsid5779558 
One of the problematic aspects of our current conception of computing is that the professional programmer aspires to a world-view that is equally w
ell-attuned to the very same turtle metaphor. Under this view, software should ideally fit into a world where the processes of change are effected }{\insrsid4742807 through the continuous action of}{\insrsid5779558 
 tamed agents operating under the stable gaze of a benign objective}{\insrsid2577491  external 
observer. In this world, constructing software is uncovering the theory that governs the mind as machine and all change as ultimately explicable with reference to eternal absolute physical laws.}{\insrsid5779558 
\par }{\insrsid14634047 Papert\rquote s vision for constructionist learning is not well-served by this limited understanding of computation. Such }{\insrsid4081430 an objectified}{\insrsid11674952  concept}{\insrsid14634047\charrsid14634047 
ion of change needs to make r}{\insrsid11674952 oom for an altogether wilder percept}{\insrsid14634047\charrsid14634047 ion of the perspectives and vectors that are associated with learning: their subjectivity, potential incoherence, a
nd the absence of well-rehearsed and practiced trajectories}{\insrsid11674952 . }{\insrsid12392269 The primary emphasis in computing for this purpose is }{\insrsid11674952\charrsid11674952 not }{\insrsid12392269 on }{\insrsid11674952 processes and }{
\insrsid11674952\charrsid11674952 behaviours, but }{\insrsid12392269 on }{\insrsid11674952\charrsid11674952 situations in which human interpretation operates in flux, uncer}{\insrsid12392269 tainty and potential confusion,}{\insrsid7158572  and}{
\insrsid12392269  on construals rather than}{\insrsid11674952\charrsid11674952  programs}{\insrsid12392269 .}{\insrsid11491588 
\par }{\insrsid4081430 The above reflections suggest}{\insrsid788923  two different ways}{\insrsid14778031  in which the Imagine-d Logo prototype }{\insrsid788923 might}{\insrsid9856878  cont}{\insrsid11998358 ribute to future research. With}{\insrsid9856878 
 a sufficiently robust and comprehensive implementation, the dependency front-end could become a standard feature of the Imagine Logo environment, to be used in a discretionary manner as users see fit. The examples in this paper have illustrated the poten
tial for using such a front-end in several different ways: to link the contents of a screen display to internal values, to set up dependencies between turtle positions, or to define simple dynamic geometry configurations.}{\insrsid5989449 
 There is scope for school-based empirical testing to explore the merits of such a mixed-paradigm approach. }{\insrsid788923 
A more radical research direction would involve trying to blend the fine qualities of tools such as Imagine Logo and Boxer where accessibility is concerned}{\insrsid10552799  with }{\insrsid9587130 existing }{\insrsid10552799 Empirical Mode
lling tools such as the EDEN interpreter}{\insrsid3500807  (as discussed in King, 2007)}{\insrsid9587130 . The extensive Empirical Modelling project}{\insrsid10552799  }{\insrsid9587130 
archive (EM web) already demonstrates proof-of-concept for dependency-by-definition in a wide range of applications}{\insrsid4474619 , but as yet has had}{\insrsid9587130  little exposure }{\insrsid4474619 
where users without specialist computer science knowledge are}{\insrsid4081430  concerned. Given}{\insrsid4474619  the Jamesian philosophical }{\insrsid3500807 stance}{\insrsid4474619  of Empirical }{\insrsid3500807 Modelling, a better }{\insrsid11998358 
metaphor for mental activity in that context \endash  rather than a turtle}{\insrsid4474619  }{\insrsid3500807 in motion }{\insrsid4474619 \endash  }{\insrsid3500807 might be that}{\insrsid4474619  proposed by Naur (}{\insrsid13108459 2001}{
\insrsid4474619 ): }{\i\insrsid4474619\charrsid4474619 an octopus jumping in a pile of rags}{\insrsid4474619 .}{\insrsid6629514 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa120\keepn\widctlpar\aspalpha\aspnum\faauto\outlinelevel1\adjustright\rin0\lin0\itap0\pararsid5661557 \b\f1\fs32\cf9\lang2057\langfe1033\kerning32\cgrid\langnp2057\langfenp1033 {\insrsid3702636 References}{
\insrsid8671394 
\par }\pard\plain \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid7223485 \f1\fs22\lang2057\langfe1033\cgrid\langnp2057\langfenp1033 {\insrsid5838273 Albirini, A. }{\insrsid14113926 (2007) }{
\i\insrsid5838273\charrsid16131190 The Crisis in Educational Technology, and the Prospect of Reinventing Education}{\insrsid5838273 , }{\insrsid5838273\charrsid13833543 E}{\insrsid5838273 ducational Technology & Society. 10(1), 227-236
\par }{\insrsid7940418 Baker, J.E. & Sugden, S.J. (2003)}{\insrsid133434  }{\i\insrsid7940418\charrsid7940418 Spreadsheets in Education - the First 25 Years}{\insrsid13108459 . }{\insrsid7940418 e-Journal: Spreadsheets in Education 1(1): 18-43}{
\insrsid7223485\charrsid7223485  }{\insrsid7223485 
\par }{\insrsid13833543\charrsid13833543 Beynon, M. (2007). }{\i\insrsid13833543\charrsid13833543 Computing technology for learning - in need of a radical new conception}{\insrsid13833543\charrsid13833543 . E}{\insrsid13833543 ducational Technology & Society. 
}{\insrsid857415 10(1), 94-106}{\insrsid13833543\charrsid13833543 
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid15215159 {\insrsid133434 Beynon, W.M., Roe, C.P. (2006)}{\insrsid7223485\charrsid7223485  }{\i\insrsid7223485\charrsid7223485 
Enriching Computer Support for Constructionism}{\insrsid7223485 . I}{\insrsid7223485\charrsid7223485 n Alkhalifa, E. (ed.) Cognitively Informed Systems, 209-233}{\insrsid15215159 
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid9529048 {\insrsid8670237\charrsid8670237 Cabri geometry:}{\insrsid13108459  }{\insrsid8670237\charrsid8670237 http://www.cabri.com/v2/pa}{\insrsid5324223 
ges/en/index.php (}{\insrsid8670237 27}{\super\insrsid8670237\charrsid8670237 th}{\insrsid8670237  March 2007)}{\insrsid9529048\charrsid9529048  }{\insrsid9529048\charrsid14242352 
\par }{\insrsid9529048 diSessa, A.A. (1997) }{\i\insrsid9529048\charrsid9529048 Twenty reasons why you should use Boxer (ins}{\i\insrsid9529048 tead of Logo) }{\insrsid9529048 In M. Turcs\'e1nyi-Szab\'f3
 (Ed.), Learning & Exploring with Logo: Proceedings of the Sixth European Logo Conference. Budapest Hungary, 7-27}{\insrsid9529048\charrsid9529048  }{\insrsid9529048\charrsid14242352 
\par }{\insrsid9529048 diSessa, A.A. (2000) }{\i\insrsid9529048\charrsid2888281 Changing Minds: Computers, Learning and Literacy}{\insrsid9529048\charrsid2888281 . Boston: MIT Pres}{\insrsid9529048 s}{\insrsid7940418 
\par }{\insrsid13108459\charrsid13108459 EM  Web: }{\field{\*\fldinst {\insrsid13108459\charrsid13108459  HYPERLINK "http://www.dcs.warwick.ac.uk/modelling" }{\lang1046\langfe1033\langnp1046\insrsid8521564\charrsid3949603 {\*\datafield 
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68007400740070003a002f002f007700770077002e006400630073002e007700610072007700690063006b002e00610063002e0075006b002f006d006f00640065006c006c0069006e0067000000795881f43b1d7f48af2c825dc485276300000000a5ab000000000000000000}}}{\fldrslt {
\cs21\ul\cf2\insrsid13108459\charrsid13108459 http://www.dcs.warwick.ac.uk/modelling}}}{\insrsid5324223  (}{\insrsid13108459\charrsid13108459 28}{\super\insrsid13108459\charrsid13108459 th}{\insrsid13108459\charrsid13108459  March 2007)
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid1338402 {\insrsid13833543\charrsid13833543 Kalas, I. & Blaho, A. (2000) }{\i\insrsid13833543 Imagine\'85}{\i\insrsid13833543\charrsid13833543 
New generation of Logo: Programmable pictures}{\i\insrsid13833543 .}{\insrsid13833543\charrsid13833543  In Proceedings of WCC2000, 427-430}{\insrsid16529906 
\par }{\insrsid9185368 King, K. }{\insrsid7628639 (2007).}{\insrsid7952836  }{\i\insrsid9185368\charrsid9185368 Uncovering}{\insrsid9185368  }{\i\insrsid9185368\charrsid9185368 Empirical Modelling}{\insrsid7628639 , MSc, Computer Science, 桃色视频 University}{
\insrsid9185368 
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid7223485 {\insrsid1338402 Logo Foundation. }{\i\insrsid1338402\charrsid1338402 What is Logo?}{\insrsid1338402  }{\field\flddirty{\*\fldinst {\insrsid1338402  H
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\par }{\insrsid133434 Nardi, B. A. (1993).}{\insrsid16131190  }{\i\insrsid16131190 A small matter of pr}{\i\insrsid5324223 ogramming}{\insrsid5324223 .}{\insrsid7223485\charrsid7223485  MIT Press}{\insrsid7223485 
\par }{\insrsid13108459 Naur, P. (2001) }{\i\insrsid13108459\charrsid13108459 Anti-philosophical Dictionary}{\insrsid13108459 . naur.com publishing}{\insrsid13108459\charrsid13108459 
\par }{\insrsid14242352 Perry, M. (2001)}{\insrsid14242352\charrsid14242352  }{\i\insrsid14242352\charrsid14242352 Automate Dependency Tracking}{\insrsid14242352\charrsid14242352 , Parts 1, 2 & 3, JavaWorld.com, Aug-Oct 2001, }{\field{\*\fldinst {
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\par }{\insrsid5324223 Roe, C.P. (}{\insrsid7628639 2003}{\insrsid5324223 ). }{\i\insrsid5324223\charrsid5324223 Computers for Learning: An Empirical Modelling perspective}{\insrsid5324223 .}{\insrsid5324223\charrsid5324223  }{\insrsid5324223 PhD}{
\insrsid7628639  thesis}{\insrsid5324223 , Computer Science, The University of 桃色视频}{\insrsid5324223\charrsid5324223 
\par }{\insrsid6691226\charrsid6691226 Roe, C.P., Pratt, D., Jones, I.}{\insrsid6691226  (}{\insrsid13265462 2005}{\insrsid6691226 )}{\insrsid6691226\charrsid6691226  }{\i\insrsid6691226\charrsid6691226 Putting the }{\b\i\insrsid6691226\charrsid6691226 
learning}{\i\insrsid6691226\charrsid6691226  back into e-learning}{\insrsid6691226\charrsid6691226 .}{\insrsid6691226  }{\insrsid1392725 In Proceedings}{\insrsid6691226\charrsid6691226  }{\insrsid1392725 of CERME4, Sant Felix de Guixols, Spain}{
\insrsid6691226 
\par }{\insrsid16131190 Sendov B., Dicheva D. (1988). }{\i\insrsid16131190\charrsid16131190 Mathematics Laboratory in Logo Style}{\insrsid16131190 , In Fr. Lovis & E. Tagg (eds.), }{\i\insrsid16131190 Computers in Education}{\insrsid16131190 
, IFIP, ECCE'88, North Holland, 213-217}{\insrsid16131190\charrsid6691226 
\par }\pard \qj \li0\ri0\sa120\widctlpar\aspalpha\aspnum\faauto\adjustright\rin0\lin0\itap0\pararsid8670237 {\insrsid133434 Tomcsanyi, P. (2003) }{\i\insrsid133434\charrsid1055888 Implementing object depend}{\i\insrsid1392725\charrsid1055888 
encies in Imagine Logo}{\insrsid1392725 , In Proceedings of}{\insrsid133434  EuroLogo 2003}{\insrsid9519091 , 27-30 August, Porto, Portugal}{\insrsid8670237\charrsid8670237  
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