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<title>Gerry Stahl, Group Cognition, Chapter 1</title>
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<p class=3Dchapternumber>1</p>

</div>

<p class=3DChapter><a name=3D"_Toc99366417">Share Globally, Adapt Locally</=
a></p>

<p class=3DAbstractCxSpFirst>For this project, I worked with several collea=
gues
in <st1:place w:st=3D"on"><st1:City w:st=3D"on">Boulder</st1:City>, <st1:St=
ate
 w:st=3D"on">Colorado</st1:State></st1:place>, to apply what we understood =
of
educational theory and approaches to computer support of collaboration to t=
he
plight of classroom teachers. Constructivist approaches to learning were we=
ll
established as being favored by most educational researchers. The problem w=
as
to disseminate this to teachers in the actual classrooms. Even when teachers
were trained in the theory, they had no practical instructional materials to
implement the new approach on a daily basis. There were few textbooks or ot=
her
resources available; even if materials were located, the teachers would sti=
ll
have to spend vast amounts of time they did not have to integrate them into=
 the
classroom practices and the institutional requirements. </p>

<p class=3DAbstractCxSpMiddle>The Internet was just starting to reach public
schools, so we tried to devise computer-based supports for disseminating
constructivist resources and for helping teachers to practically adapt and
apply them. We prototyped a high-functionality design environment for
communities of teachers to construct innovative lesson plans together, usin=
g a
growing database of appropriately structured and annotated resources. This =
was
an experiment in designing a software system for teachers to engage in
collaborative knowledge building. </p>

<p class=3DAbstractCxSpLast>This study provides a nice example of a real-wo=
rld
problem confronting teachers. It tries to apply the power of AI and
domain-oriented design environment technologies to support collaboration at=
 a
distance. The failure of the project to go forward beyond the design phase
indicates the necessity of considering more carefully the institutional con=
text
of schooling and the intricacies of potential interaction among classroom
teachers.</p>

<h1>Introduction</h1>

<p class=3DNormalnoindent>Many teachers yearn to break through the confines=
 of
traditional textbook-centered teaching and present activities that encourage
students to explore and construct their own knowledge. But this requires
developing innovative materials and curriculum tailored to local students.
Teachers have neither the time nor the information to do much of this from
scratch.</p>

<p class=3DMsoNormal>The Internet provides a medium for globally sharing
innovative educational resources. School districts and teacher organizations
have already begun to post curriculum ideas on Internet servers. However, j=
ust
storing unrelated educational materials on the Internet does not by itself
solve the problem. It is too hard to find the resources to meet specific ne=
eds.
Teachers need software for locating material-rich sites across the network,
searching the individual curriculum sources, adapting retrieved materials to
their classrooms, organizing these resources in coherent lesson plans and
sharing their experiences across the Internet.</p>

<p class=3DMsoNormal>In response to these needs, I designed and prototyped =
a <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Teach=
er&#8217;s
Curriculum Assistant</span></span> (<span class=3DSource><span style=3D'mso=
-bidi-font-family:
"Times New Roman"'>TCA</span></span>) that provides software support for
teachers to make effective use of educational resources posted to the Inter=
net.
<span class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'=
>TCA</span></span>
maintains information for finding educational resources distributed on the
Internet. It provides query and browsing mechanisms for exploring what is
available. Tools are included for tailoring retrieved resources, creating
supplementary materials and designing innovative curriculum. <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
encourages teachers to annotate and upload successfully used curriculum to
Internet servers in order to share their ideas with other educators. In this
chapter I describe the need for such computer support and discuss what I ha=
ve
learned from designing <span class=3DSource><span style=3D'mso-bidi-font-fa=
mily:
"Times New Roman"'>TCA</span></span>.</p>

<h1>The Internet&#8217;s Potential for Collaboration Support</h1>

<p class=3DNormalnoindent>The Internet has the potential to transform educa=
tional
curriculum development beyond the horizons of our foresight. In 1994, the
process was just beginning, as educators across the country started to post
their favorite curriculum ideas for others to share. Already, this first
tentative step revealed the difficulties inherent in using such potentially
enormous, loosely structured sources of information. As the Internet become=
s a
more popular medium for sharing curricula, teachers, wandering around the
Internet looking for ideas to use in their classrooms, confront a set of
problems that will not go away on its own<span style=3D'font-family:Symbol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man";
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style=3D'mso-char=
-type:
symbol;mso-symbol-font-family:Symbol'>&frac34;</span></span>on the contrary=
:</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l0 level1 lfo1;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
1.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>Teachers
have to <i style=3D'mso-bidi-font-style:normal'>locate</i> sites of curricu=
lum
ideas scattered across the network; there is currently no system for announ=
cing
the locations of these sites.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l0 level1 lfo1;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
2.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>They
have to <i style=3D'mso-bidi-font-style:normal'>search</i> through the offe=
rings
at each site for useful items. While some sites provide search mechanisms f=
or
their databases, each has different interfaces, tools and indexing schemes =
that
must be learned before the curricula can be accessed.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l0 level1 lfo1;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
3.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>They
have to <i style=3D'mso-bidi-font-style:normal'>adapt</i> items they find t=
o the
needs of their particular classroom: to local standards, the current
curriculum, their own teaching preferences and the needs or learning styles=
 of
their various students. </p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l0 level1 lfo1;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
4.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>They
have to <i style=3D'mso-bidi-font-style:normal'>organize</i> the new ideas =
within
coherent curricula that build toward long-term pedagogical goals.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l0 level1 lfo1;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
5.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>They
have to <i style=3D'mso-bidi-font-style:normal'>share</i> their experiences=
 using
the curriculum or their own new ideas with others who use the resources.</p>

<p class=3DMsoNormal>In many fields, professionals have turned to productiv=
ity
software&#8212;like spreadsheets for accountants&#8212;to help them manage
tasks involving complex sources of information. I believe that teachers sho=
uld
be given similar computer-based tools to meet the problems listed above. If
this software is designed to empower teachers<span style=3D'font-family:Sym=
bol;
mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Ro=
man";
mso-char-type:symbol;mso-symbol-font-family:Symbol'><span style=3D'mso-char=
-type:
symbol;mso-symbol-font-family:Symbol'>&frac34;</span></span>perhaps in
conjunction with their students<span style=3D'font-family:Symbol;mso-ascii-=
font-family:
"Times New Roman";mso-hansi-font-family:"Times New Roman";mso-char-type:sym=
bol;
mso-symbol-font-family:Symbol'><span style=3D'mso-char-type:symbol;mso-symb=
ol-font-family:
Symbol'>&frac34;</span></span>in open-ended ways, opportunities will
materialize that we cannot now imagine. </p>

<p class=3DMsoNormal>In this chapter, I consider how the sharing of curricu=
lum
ideas over the Internet can be made more effective in transforming educatio=
n. I
advance the understanding of specific issues in the creation of software
designed to help classroom teachers develop curricula and increase
productivity, and introduce the Teacher&#8217;s Curriculum Assistant (<span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>)
that I built for this purpose. First, I discuss the nature of constructivist
curriculum, contrasting it with traditional approaches based on behaviorist
theory. Then I present an example of a problem-solving environment for high
school mathematics students. The example illustrates why teachers need help=
 to
construct this kind of student-centered curriculum. I provide a scenario of=
 a
teacher developing a curriculum using productivity software like <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span><span
style=3D'text-transform:uppercase'>,</span> and conclude by discussing some
issues I feel will be important in <i style=3D'mso-bidi-font-style:normal'>=
maximizing
the effectiveness of the Internet</i> as a medium for the dissemination of
innovative curricula for educational reform.</p>

<h1>The Problem of Curriculum in Educational Reform</h1>

<p class=3DNormalnoindent>The distribution of curriculum over the Internet =
and
the use of productivity software for searching and adapting posted ideas co=
uld
benefit any pedagogical approach. However, it is particularly crucial for
advancing <i style=3D'mso-bidi-font-style:normal'>reform</i> in education.<=
/p>

<p class=3DMsoNormal>The barriers to educational reform are legion, as many
people since John Dewey have found. Teachers, administrators, parents and
students must all be convinced that traditional schooling is not the most
effective way to provide an adequate foundation for life in the future. They
must be trained in the new sensitivities required. Once everyone agrees and=
 is
ready to implement the new approach there is still a problem: what activiti=
es
and materials should be presented on a day to day basis? This concrete ques=
tion
is the one that Internet sharing can best address. I generalize the term <i
style=3D'mso-bidi-font-style:normal'>curriculum</i> to cover this question.=
 </p>

<p class=3DMsoNormal>Consider curricula for mathematics. Here, the reform
approach is to emphasize the qualitative understanding of mathematical ways=
 of
thinking, rather than to stress rote memorization of quantitative facts or
&#8220;number skills.&#8221; <i style=3D'mso-bidi-font-style:normal'>Behavi=
orist</i>
learning theory supported the view that one method of training could work f=
or
all students; reformers face a much more complex challenge. There is a grow=
ing
consensus among educational theorists that different students in different
situations construct their understandings in different ways <!--[if support=
Fields]><span
style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Greeno&lt;/Author&gt;&lt;Year&gt;1=
993&lt;/Year&gt;&lt;RecNum&gt;458&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TY=
PE&gt;7&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;458&lt;/REFNUM&gt;&lt;AUTHORS&g=
t;&lt;AUTHOR&gt;Greeno,
J.&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1993&lt;/YEAR&gt;&lt;TITLE&gt;=
For
research to reform education and cognitive
science&lt;/TITLE&gt;&lt;SECONDARY_AUTHORS&gt;&lt;SECONDARY_AUTHOR&gt;Penne=
r,
L., Batsche, G., Knoff, H., Nelson,
D.&lt;/SECONDARY_AUTHOR&gt;&lt;/SECONDARY_AUTHORS&gt;&lt;SECONDARY_TITLE&gt=
;The
Challenge in mathematics and science education: Psychology&amp;apos;s
response&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;New York,
NY&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;APA
Press&lt;/PUBLISHER&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Greeno, 1993)<!--=
[if supportFields]><span
style=3D'mso-element:field-end'></span><![endif]-->. This approach is often
called <i style=3D'mso-bidi-font-style:normal'>constructivism</i> or <i
style=3D'mso-bidi-font-style:normal'>constructionism</i> <!--[if supportFie=
lds]><span
style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE &lt;EndNote&gt;&lt;Ci=
te&gt;&lt;Author&gt;Papert&lt;/Author&gt;&lt;Year&gt;1993&lt;/Year&gt;&lt;R=
ecNum&gt;459&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TYPE&gt;1&lt;/REFERENCE=
_TYPE&gt;&lt;REFNUM&gt;459&lt;/REFNUM&gt;&lt;AUTHORS&gt;&lt;AUTHOR&gt;Paper=
t,
Seymour&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1993&lt;/YEAR&gt;&lt;TITL=
E&gt;The
children&amp;apos;s machine: Rethinking school in the age of the
computer&lt;/TITLE&gt;&lt;PLACE_PUBLISHED&gt;New York,
NY&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;Basic
Books&lt;/PUBLISHER&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Papert, 1993)<!--=
[if supportFields]><span
style=3D'mso-element:field-end'></span><![endif]-->. It implies that teache=
rs
must creatively structure the learning environments of their students to
provide opportunities for discovery and must guide the individual learners =
to
reach insights in their own ways. </p>

<p class=3DMsoNormal>Behaviorism and constructivism differ primarily in the=
ir
views of how students build their knowledge. Traditional, rationalist educa=
tion
assumed that there was a logical sequence of facts and standard skills that=
 had
to be learned successively. The problem was simply to transfer bits of
information to students in a logical order, with little concern for how
students acquire knowledge. Early attempts at designing educational software
took this approach to its extreme, breaking down curricula into isolated at=
omic
propositions and feeding these predigested facts to the students. This appr=
oach
to education was suited to the industrial age, in which workers on assembly
lines performed well-defined, sequential tasks.</p>

<p class=3DMsoNormal>According to constructivism, learners <i style=3D'mso-=
bidi-font-style:
normal'>interpret</i> problems in their environments using <i style=3D'mso-=
bidi-font-style:
normal'>conceptual frameworks</i> that they developed in the past <!--[if s=
upportFields]><span
style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Roschelle&lt;/Author&gt;&lt;Year&g=
t;1996&lt;/Year&gt;&lt;RecNum&gt;210&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE=
_TYPE&gt;7&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;210&lt;/REFNUM&gt;&lt;AUTHOR=
S&gt;&lt;AUTHOR&gt;Roschelle,
Jeremy&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1996&lt;/YEAR&gt;&lt;TITLE=
&gt;Learning
by collaborating: Convergent conceptual
change&lt;/TITLE&gt;&lt;SECONDARY_AUTHORS&gt;&lt;SECONDARY_AUTHOR&gt;Timothy
Koschmann&lt;/SECONDARY_AUTHOR&gt;&lt;/SECONDARY_AUTHORS&gt;&lt;SECONDARY_T=
ITLE&gt;CSCL:
Theory and Practice of an Emerging
Paradigm&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;Hillsdale,
NJ&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;Lawrence Erlbaum
Associates&lt;/PUBLISHER&gt;&lt;PAGES&gt;209-248&lt;/PAGES&gt;&lt;/MDL&gt;&=
lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Roschelle, 1996)<=
!--[if supportFields]><span
style=3D'mso-element:field-end'></span><![endif]-->. In challenging cases,
problems can require changes in the frameworks. Such conceptual change is t=
he
essence of learning: one&#8217;s understanding evolves in order to comprehe=
nd
one&#8217;s environment. To teach a student a mathematical method or a
scientific theory is not to place a set of propositional facts into her min=
d,
but to give her a new tool that she can make her own and use in her own way=
s in
comprehending her world. </p>

<p class=3DMsoNormal>Constructivism does not entail the rejection of a
curriculum. Rather, it requires a more complex and flexible curriculum.
Traditionally, a curriculum consisted of a textual theoretical lesson, a se=
t of
drills for students to practice and a test to evaluate if the students could
perform the desired behaviors. In contrast, <i style=3D'mso-bidi-font-style=
:normal'>a
constructivist curriculum</i> might target certain cognitive skills, provid=
e a
setting of resources and activities to serve as a catalyst for the developm=
ent
of these skills and then offer opportunities for students to articulate the=
ir
evolving understandings <!--[if supportFields]><span style=3D'mso-element:f=
ield-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;NCTM&lt;/Author&gt;&lt;Year&gt;198=
9&lt;/Year&gt;&lt;RecNum&gt;460&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TYPE=
&gt;1&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;460&lt;/REFNUM&gt;&lt;AUTHORS&gt;=
&lt;AUTHOR&gt;NCTM&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1989&lt;/YEAR&=
gt;&lt;TITLE&gt;Curriculum
and evaluation standards for school
mathematics&lt;/TITLE&gt;&lt;PLACE_PUBLISHED&gt;Alexandria,
VA&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;National Council of Teachers of
Mathematics&lt;/PUBLISHER&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(NCTM, 1989)<!--[i=
f supportFields]><span
style=3D'mso-element:field-end'></span><![endif]-->. The cognitive skills in
math, for example, might include qualitative reasoning about graphs, number
lines, algorithms or proofs.</p>

<p class=3DMsoNormal>My colleagues on the project and I believe that the mo=
vement
from viewing a curriculum as fact-centered to viewing it as
cognitive-tool-centered is appropriate for the post-modern (post-industrial,
post-rationalist, post-behaviorist) period. Cognitive tools include,
importantly, <i style=3D'mso-bidi-font-style:normal'>alternative knowledge
representations</i> <!--[if supportFields]><span style=3D'mso-element:field=
-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Norman&lt;/Author&gt;&lt;Year&gt;1=
993&lt;/Year&gt;&lt;RecNum&gt;106&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TY=
PE&gt;1&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;106&lt;/REFNUM&gt;&lt;AUTHORS&g=
t;&lt;AUTHOR&gt;D.A.
Norman&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1993&lt;/YEAR&gt;&lt;TITLE=
&gt;Things
That Make Us Smart&lt;/TITLE&gt;&lt;PLACE_PUBLISHED&gt;Reading, MA&lt;/PLAC=
E_PUBLISHED&gt;&lt;PUBLISHER&gt;Addison-Wesley
Publishing Company&lt;/PUBLISHER&gt;&lt;PAGES&gt;290&lt;/PAGES&gt;&lt;/MDL&=
gt;&lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Norman, 1993)<!--=
[if supportFields]><span
style=3D'mso-element:field-end'></span><![endif]-->. As researchers in arti=
ficial
intelligence, we know that knowledge representations are key to characteriz=
ing
or modeling cognition. We have also found that professionals working in typ=
ical
contemporary occupations focus much of their effort on developing and using
alternative knowledge representations that are adapted to their tasks <!--[=
if supportFields]><span
style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Sumner&lt;/Author&gt;&lt;Year&gt;1=
995&lt;/Year&gt;&lt;RecNum&gt;461&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TY=
PE&gt;3&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;461&lt;/REFNUM&gt;&lt;AUTHORS&g=
t;&lt;AUTHOR&gt;Sumner,
Tamara&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1995&lt;/YEAR&gt;&lt;TITLE=
&gt;The
high-tech toolbelt: A study of designers in the
workplace&lt;/TITLE&gt;&lt;SECONDARY_TITLE&gt;Human Factors in Computing
Systems (CHI &amp;apos;95)&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;De=
nver,
CO&lt;/PLACE_PUBLISHED&gt;&lt;PAGES&gt;178-185&lt;/PAGES&gt;&lt;/MDL&gt;&lt=
;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Sumner, 1995)<!--=
[if supportFields]><span
style=3D'mso-element:field-end'></span><![endif]-->. Curricula to prepare p=
eople
for the next generation of jobs would do well to familiarize students with =
the
creation and use of alternative conceptual representations.</p>

<h1>A Diverse Learning Ecology</h1>

<p class=3DNormalnoindent>Teachers need help to create learning environment=
s that
stimulate the construction and evolution of understanding through student
exploration using multiple conceptual representations. <i style=3D'mso-bidi=
-font-style:
normal'>A stimulating learning environment is one with a rich ecology, in w=
hich
many elements interact in subtle ways.</i> In this section I present an
illustration of a rich ecology for learning mathematical thinking that
includes: inductive reasoning, recursive computation, spreadsheet
representation, graphing, simultaneous equations and programming languages.=
 </p>

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    <p class=3DMsoNormal>Figure 1-1. Regions of a circle; <b style=3D'mso-b=
idi-font-weight:
    normal'><span style=3D'font-family:Chicago'>n</span></b> =3D 8..</p>
    <p class=3DMsoNormal><o:p>&nbsp;</o:p></p>
    </div>
    <![if !mso]></td>
   </tr>
  </table>
  <![endif]></v:textbox>
 <w:wrap type=3D"square" anchorx=3D"margin" anchory=3D"margin"/>
</v:shape><![endif]--><![if !vml]><img width=3D203 height=3D250
src=3D"ch01_files/image002.gif" align=3Dright hspace=3D12
alt=3D"Text Box:  &#13;&#10;Figure 1-1. Regions of a circle; n =3D 8..&#13;=
&#10;&#13;&#10;"
v:shapes=3D"_x0000_s1026"><![endif]>A typical curriculum suggestion that mi=
ght be
posted on an educational resources listing on the Internet is the <i
style=3D'mso-bidi-font-style:normal'>problem of regions of a circle</i>: Gi=
ven <span
class=3DSource><b><span style=3D'mso-bidi-font-family:"Times New Roman"'>n<=
/span></b></span>
points on the circumference of a circle, what is the maximum number of regi=
ons
one can divide the circle into by drawing straight lines connecting the poi=
nts?
(See figure 1-1.) For instance, connecting two points divides the circle in=
to
two regions; connecting three points with three lines creates four regions.
This is a potentially fascinating problem because its subtleties can be
explored at length using just algebra and several varieties of clear thinki=
ng.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<div style=3D'mso-element:para-border-div;border-top:solid windowtext 1.0pt;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none;
mso-border-top-alt:solid windowtext .75pt;mso-border-bottom-alt:solid windo=
wtext .75pt;
padding:1.0pt 0in 1.0pt 0in'>

<p class=3DMsoNormal style=3D'border:none;mso-border-top-alt:solid windowte=
xt .75pt;
mso-border-bottom-alt:solid windowtext .75pt;padding:0in;mso-padding-alt:1.=
0pt 0in 1.0pt 0in'>Figure
1-1 goes approximately here</p>

</div>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The problem with this curriculum offering as an Intern=
et
posting is that it has not been placed in a rich setting. To be useful, a
fuller curriculum providing a set of conceptual tools is needed. For instan=
ce,
a discussion of inductive reasoning brings out some of the character of this
particular problem. If one counts the number of regions, <span class=3DSour=
ce><b><span
style=3D'mso-bidi-font-family:"Times New Roman"'>R(n),</span></b></span> fo=
r <span
class=3DSource><b><span style=3D'mso-bidi-font-family:"Times New Roman"'>n<=
/span></b></span>
=3D 1 to 6, one obtains the doubling series: 1, 2, 4, 8, 16, 31. Almost! One
expects the last of these numbers to be 32, but that last region is nowhere=
 to
be found. For larger <span class=3DSource><b><span style=3D'mso-bidi-font-f=
amily:
"Times New Roman"'>n</span></b></span>, the series diverges completely from=
 the
powers of 2. Why? Here, <i style=3D'mso-bidi-font-style:normal'>inductive
reasoning</i> can come to the rescue of the hasty inductive
assumption&#8212;if, that is, the problem is accompanied by a discussion of
inductive reasoning. </p>

<p class=3DMsoNormal>Consider the general case of <span class=3DSource><b><=
span
style=3D'mso-bidi-font-family:"Times New Roman"'>n</span></b></span> points.
Assume that the answer is known for <span class=3DSource><b><span
style=3D'mso-bidi-font-family:"Times New Roman"'>n-1</span></b></span> poin=
ts and
think about how many new regions are created by adding the <span class=3DSo=
urce><b><span
style=3D'mso-bidi-font-family:"Times New Roman"'>n</span></b></span>-th poi=
nt and
connecting it to each of the <span class=3DSource><b><span style=3D'mso-bid=
i-font-family:
"Times New Roman"'>n-1</span></b></span> old points. There is a definite
pattern at work here. It may take a couple days of careful thought to work =
it
out. It would also help if the <i style=3D'mso-bidi-font-style:normal'>sigma
notation</i> for sums of indexed terms is explained as a representational t=
ool
for working on the problem. Perhaps a collaborative group effort will be ne=
eded
to check each step and avoid mistakes.</p>

<p class=3DMsoNormal>At this point, a teacher might introduce the notion of=
 <i
style=3D'mso-bidi-font-style:normal'>recursion</i> and relate it to inducti=
on. If
the students can program<i style=3D'mso-bidi-font-style:normal'> </i>in<i
style=3D'mso-bidi-font-style:normal'> Logo or Pascal</i> (programming langu=
ages
that can represent recursive processes), they could put the general formula
into a simple but powerful program that could generate results for hundreds=
 of
values of <span class=3DSource><b><span style=3D'mso-bidi-font-family:"Time=
s New Roman"'>n</span></b></span>
very quickly without the tedious and error-prone process of counting region=
s in
drawings. It would be nice to formalize the derivation of this result with =
a <i
style=3D'mso-bidi-font-style:normal'>deductive proof</i>, if the method of
formulating proofs has been explained.</p>

<p class=3DNormalnoindent>Now that students are confident that they have the
correct values for many <span class=3DSource><b style=3D'mso-bidi-font-weig=
ht:normal'><span
style=3D'mso-bidi-font-family:"Times New Roman"'>n</span></b></span>, they =
can
enter these values in a <i style=3D'mso-bidi-font-style:normal'>spreadsheet=
</i>
to explore them. The first representation they might want to see is a <i
style=3D'mso-bidi-font-style:normal'>graph</i> of <span class=3DSource><b><=
span
style=3D'mso-bidi-font-family:"Times New Roman"'>R(n)</span></b></span> <i
style=3D'mso-bidi-font-style:normal'>vs</i>. <span class=3DSource><b><span
style=3D'mso-bidi-font-family:"Times New Roman"'>n</span></b></span>. On the
spreadsheet they could make a column that displays the difference between e=
ach <span
class=3DSource><b><span style=3D'mso-bidi-font-family:"Times New Roman"'>R(=
n)</span></b></span>
and its corresponding <span class=3DSource><b><span style=3D'mso-bidi-font-=
family:
"Times New Roman"'>R(n-1)</span></b></span>. Copying this column several ti=
mes,
they would find that the fourth column of differences is constant. This res=
ult
means that <span class=3DSource><b><span style=3D'mso-bidi-font-family:"Tim=
es New Roman"'>R(n)</span></b></span>
follows a fourth order equation, which can be found by solving <i
style=3D'mso-bidi-font-style:normal'>simultaneous equations</i>. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DNormalnoindent><!--[if gte vml 1]><v:shape id=3D"_x0000_i1025" t=
ype=3D"#_x0000_t75"
 style=3D'width:348pt;height:261.75pt'>
 <v:imagedata src=3D"ch01_files/image003.png" o:title=3D"" cropbottom=3D"-5=
61f"
  cropright=3D"-559f"/>
 <w:bordertop type=3D"single" width=3D"12" shadow=3D"t"/>
 <w:borderleft type=3D"single" width=3D"12" shadow=3D"t"/>
 <w:borderbottom type=3D"single" width=3D"12" shadow=3D"t"/>
 <w:borderright type=3D"single" width=3D"12" shadow=3D"t"/>
</v:shape><![endif]--><![if !vml]><img width=3D472 height=3D357
src=3D"ch01_files/image004.jpg" v:shapes=3D"_x0000_i1025"><![endif]></p>

<p class=3DMsoNormal>Figure 1-2. A number of multimedia resources related t=
o the
&#8220;regions of a circle&#8221; problem. These include textual documents,
drawings, equations, spreadsheets, graphs and computer program source code.=
</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The point of this example is that sharing the isolated
statement of the problem is not enough. The rich learning experience involv=
es
being introduced to alternative representations of the problem: induction,
recursion, spreadsheet differences, graphs, computer languages, simultaneous
equations, etc. There is not one correct method for tackling a problem like
this; a mathematically literate person needs to be able to view the
problem&#8217;s many facets through several conceptual frameworks. </p>

<p class=3DMsoNormal>A curriculum in the new paradigm typically consists of
stimulating problems immersed in environments with richly interacting
ecologies, including: cognitive skills, knowledge representations,
computational tools, related problems and reference materials. Perhaps a
creative teacher with unlimited preparation time could put these materials
together. However, the reality is that teachers deserve all the support they
can get if they are to prepare and present the complex learning ecologies t=
hat
constructivist reforms call for. Computer support for curriculum development
should make the kinds of resources shown in figure 1-2 readily available.</=
p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<div style=3D'mso-element:para-border-div;border-top:solid windowtext 1.0pt;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none;
mso-border-top-alt:solid windowtext .75pt;mso-border-bottom-alt:solid windo=
wtext .75pt;
padding:1.0pt 0in 1.0pt 0in'>

<p class=3DMsoNormal style=3D'border:none;mso-border-top-alt:solid windowte=
xt .75pt;
mso-border-bottom-alt:solid windowtext .75pt;padding:0in;mso-padding-alt:1.=
0pt 0in 1.0pt 0in'>Figure
1-2 goes approximately here</p>

</div>

<h1>From Database to Design Environment</h1>

<p class=3DNormalnoindent>Curriculum planning for learning ecologies is not=
 a
simple matter of picking consecutive pages out of a standard textbook or of
working out a sequential presentation of material that builds up to fixed
learning achievements. Rather, it is a matter of <i style=3D'mso-bidi-font-=
style:
normal'>design</i>. To support teachers in developing curriculum that achie=
ves
this, we must go beyond databases of isolated resources to<i style=3D'mso-b=
idi-font-style:
normal'> </i>provide<i style=3D'mso-bidi-font-style:normal'> design environ=
ments
for curriculum development</i>.</p>

<p class=3DMsoNormal>It may seem to be an overwhelming task to design an
effective learning environment for promoting the development of basic cogni=
tive
skills. However, dozens of reform curricula have already been created<i
style=3D'mso-bidi-font-style:normal'>. The problem now is to disseminate th=
ese in
ways that allow teachers to adapt them</i> to their local needs and to reuse
them as templates for additional new curricula. It is instructive to look a=
t a
recent attempt to make this type of curriculum available. The &#8220;MathFi=
nder
CD-ROM: a collection of resources for mathematics reform&#8221; excerpts
materials from thirty new math curricula <!--[if supportFields]><span
style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Kreindler&lt;/Author&gt;&lt;Year&g=
t;1992&lt;/Year&gt;&lt;RecNum&gt;462&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE=
_TYPE&gt;1&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;462&lt;/REFNUM&gt;&lt;AUTHOR=
S&gt;&lt;AUTHOR&gt;Kreindler,
L.&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Zahm,
B.&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1992&lt;/YEAR&gt;&lt;TITLE&gt;=
MathFinder
sourcebook: A collection of resources for mathematics
reform&lt;/TITLE&gt;&lt;PLACE_PUBLISHED&gt;New York,
NY&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;The Learning
Team&lt;/PUBLISHER&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Kreindler &amp; Z=
ahm,
1992)<!--[if supportFields]><span style=3D'mso-element:field-end'></span><!=
[endif]-->.
Like the posting of curriculum ideas at several Internet sites, this is an
important early step at electronic dissemination. </p>

<p class=3DMsoNormal>Unfortunately, MathFinder has a number of serious
limitations due to its CD-ROM (read-only) format. It relies on a fixed data=
base
of resources that allows resources to be <i style=3D'mso-bidi-font-style:no=
rmal'>located</i>
but not expanded or revised. Its indexing is relatively simple<span
style=3D'font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman";mso-char-type:symbol;mso-symbol-font-family:Symbol'><span
style=3D'mso-char-type:symbol;mso-symbol-font-family:Symbol'>&frac34;</span=
></span>primarily
oriented toward illustrating a particular set of math standards<span
style=3D'font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman";mso-char-type:symbol;mso-symbol-font-family:Symbol'><span
style=3D'mso-char-type:symbol;mso-symbol-font-family:Symbol'>&frac34;</span=
></span>yet
its <i style=3D'mso-bidi-font-style:normal'>search mechanism is cumbersome<=
/i>
for many teachers. Because its resources are stored in bitmap images, they =
<i
style=3D'mso-bidi-font-style:normal'>cannot be adapted</i> in any way by te=
achers
or students. Moreover, MathFinder provides<i style=3D'mso-bidi-font-style:n=
ormal'>
no facility for organizing resources</i> <i style=3D'mso-bidi-font-style:no=
rmal'>into
curricula</i><span style=3D'font-family:Symbol;mso-ascii-font-family:"Times=
 New Roman";
mso-hansi-font-family:"Times New Roman";mso-char-type:symbol;mso-symbol-fon=
t-family:
Symbol'><span style=3D'mso-char-type:symbol;mso-symbol-font-family:Symbol'>=
&frac34;</span></span>despite
the fact that most of the resources it includes are excerpted from carefully
constructed curricula. Because it is sold as a read-only commodity, MathFin=
der <i
style=3D'mso-bidi-font-style:normal'>does not allow teachers to share</i> t=
heir
experiences with annotations or to add their own curricular ideas. Thus, of=
 the
five issues listed in the Introduction of this study, MathFinder only provi=
des
a partial solution to the issues of location and search.</p>

<p class=3DMsoNormal>An alternative approach is suggested by our work on <i
style=3D'mso-bidi-font-style:normal'>domain-oriented design environments</i=
> <!--[if supportFields]><span
style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Stahl&lt;/Author&gt;&lt;Year&gt;19=
92&lt;/Year&gt;&lt;RecNum&gt;14&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TYPE=
&gt;3&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;14&lt;/REFNUM&gt;&lt;AUTHORS&gt;&=
lt;AUTHOR&gt;Stahl,
Gerry&lt;/AUTHOR&gt;&lt;AUTHOR&gt;McCall, Raymond&lt;/AUTHOR&gt;&lt;AUTHOR&=
gt;Peper,
Gerri&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1992&lt;/YEAR&gt;&lt;TITLE&=
gt;Extending
hypermedia with an inference language:<span style=3D'mso-spacerun:yes'>&nbs=
p;
</span>An alternative to rule-based expert systems&lt;/TITLE&gt;&lt;SECONDA=
RY_TITLE&gt;IBM
ITL Conference:<span style=3D'mso-spacerun:yes'>&nbsp; </span>Expert
Systems&lt;/SECONDARY_TITLE&gt;&lt;PAGES&gt;160-167&lt;/PAGES&gt;&lt;URL&gt=
;http://www.cis.drexel.edu/faculty/gerry/publications/conferences/1990-1997=
/ibm92/ExtHyper.html&lt;/URL&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;Cite&gt;&lt;Au=
thor&gt;Stahl&lt;/Author&gt;&lt;Year&gt;1993&lt;/Year&gt;&lt;RecNum&gt;12&l=
t;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TYPE&gt;2&lt;/REFERENCE_TYPE&gt;&lt;R=
EFNUM&gt;12&lt;/REFNUM&gt;&lt;AUTHORS&gt;&lt;AUTHOR&gt;Stahl,
Gerry&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1993&lt;/YEAR&gt;&lt;TITLE&=
gt;Interpretation
in Design: The Problem of Tacit and Explicit Understanding in Computer Supp=
ort
of Cooperative Design&lt;/TITLE&gt;&lt;SECONDARY_TITLE&gt;Department of
Computer Science&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;Boulder,
CO&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;University of
Colorado&lt;/PUBLISHER&gt;&lt;PAGES&gt;451 +
xiv&lt;/PAGES&gt;&lt;TYPE_OF_WORK&gt;Ph.D.
Dissertation&lt;/TYPE_OF_WORK&gt;&lt;ISBN&gt;CU-CS-688-93&lt;/ISBN&gt;&lt;L=
ABEL&gt;Stahl1993a&lt;/LABEL&gt;&lt;KEYWORDS&gt;&lt;KEYWORD&gt;Stahl&lt;/KE=
YWORD&gt;&lt;/KEYWORDS&gt;&lt;URL&gt;http://www.cis.drexel.edu/faculty/gerr=
y/publications/dissertations/computer&lt;/URL&gt;&lt;/MDL&gt;&lt;/Cite&gt;&=
lt;Cite&gt;&lt;Author&gt;Fischer&lt;/Author&gt;&lt;Year&gt;1993&lt;/Year&gt=
;&lt;RecNum&gt;9&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TYPE&gt;3&lt;/REFER=
ENCE_TYPE&gt;&lt;REFNUM&gt;9&lt;/REFNUM&gt;&lt;AUTHORS&gt;&lt;AUTHOR&gt;Fis=
cher,
Gerhard&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Nakakoji,
Kumiyo&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Ostwald,
Jonathan&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Stahl,
Gerry&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Sumner,
Tamara&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1993&lt;/YEAR&gt;&lt;TITLE=
&gt;Embedding
computer-based critics in the contexts of
design&lt;/TITLE&gt;&lt;SECONDARY_TITLE&gt;Conference on Human Factors in
Computing Systems (INTERChi
&amp;apos;93)&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;Amsterdam,
NL&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;Addison
Wesley&lt;/PUBLISHER&gt;&lt;PAGES&gt;157-164&lt;/PAGES&gt;&lt;KEYWORDS&gt;&=
lt;KEYWORD&gt;Generic
critics, specific critics, interpretive critics, design environments,
specification, construction, domain
orientation,&lt;/KEYWORD&gt;&lt;KEYWORD&gt;perspectives, critiquing
systems.&lt;/KEYWORD&gt;&lt;/KEYWORDS&gt;&lt;URL&gt;http://www.cis.drexel.e=
du/faculty/gerry/publications/conferences/1990-1997/chi93/CHI93.html&lt;/UR=
L&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;Cite&gt;&lt;Author&gt;Repenning&lt;/Autho=
r&gt;&lt;Year&gt;1995&lt;/Year&gt;&lt;RecNum&gt;463&lt;/RecNum&gt;&lt;MDL&g=
t;&lt;REFERENCE_TYPE&gt;0&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;463&lt;/REFNU=
M&gt;&lt;AUTHORS&gt;&lt;AUTHOR&gt;Repenning,
Alexander&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Sumner,
Tamara&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1995&lt;/YEAR&gt;&lt;TITLE=
&gt;Agentsheets:
A medium for creating domain-oriented visual programming
languages&lt;/TITLE&gt;&lt;SECONDARY_TITLE&gt;IEEE Computer. Special issue =
on
visual
programming&lt;/SECONDARY_TITLE&gt;&lt;VOLUME&gt;March&lt;/VOLUME&gt;&lt;/M=
DL&gt;&lt;/Cite&gt;&lt;Cite&gt;&lt;Author&gt;Fischer&lt;/Author&gt;&lt;Year=
&gt;1998&lt;/Year&gt;&lt;RecNum&gt;224&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFEREN=
CE_TYPE&gt;7&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;224&lt;/REFNUM&gt;&lt;AUTH=
ORS&gt;&lt;AUTHOR&gt;G.
Fischer&lt;/AUTHOR&gt;&lt;AUTHOR&gt;K. Nakakoji&lt;/AUTHOR&gt;&lt;AUTHOR&gt=
;J.
Ostwald&lt;/AUTHOR&gt;&lt;AUTHOR&gt;G. Stahl&lt;/AUTHOR&gt;&lt;AUTHOR&gt;T.
Sumner&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1998&lt;/YEAR&gt;&lt;TITLE=
&gt;Embedding
critics in design
environments.&lt;/TITLE&gt;&lt;SECONDARY_AUTHORS&gt;&lt;SECONDARY_AUTHOR&gt=
;Maybury,
M. T&lt;/SECONDARY_AUTHOR&gt;&lt;SECONDARY_AUTHOR&gt;Wahlster,
W.&lt;/SECONDARY_AUTHOR&gt;&lt;/SECONDARY_AUTHORS&gt;&lt;SECONDARY_TITLE&gt=
;Readings
in Intelligent User Interfaces&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&g=
t;New
York&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;Morgan
Kaufman&lt;/PUBLISHER&gt;&lt;PAGES&gt;537-561&lt;/PAGES&gt;&lt;URL&gt;http:=
//www.cis.drexel.edu/faculty/gerry/publications/journals/ker/index.html&lt;=
/URL&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Fischer<i
style=3D'mso-bidi-font-style:normal'> et al.</i>, 1993; Fischer<i
style=3D'mso-bidi-font-style:normal'> et al.</i>, 1998; Repenning &amp; Sum=
ner,
1995; Stahl, McCall, &amp; Peper, 1992; Stahl, 1993)<!--[if supportFields]>=
<span
style=3D'mso-element:field-end'></span><![endif]-->. A software design
environment provides a flexible workspace for the construction of artifacts,
and places useful design tools and materials close at hand. A design
environment for curriculum development goes substantially beyond a database=
 of
individual resources. Based on this approach, we built a prototype version =
of a
Teacher&#8217;s Curriculum Assistant (<span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</span></span>). <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
includes a <i style=3D'mso-bidi-font-style:normal'>catalog</i> of previously
designed curricula that can be reused and modified. It has a <i
style=3D'mso-bidi-font-style:normal'>gallery</i> of educational resources t=
hat
can be inserted into partial curriculum designs. There is a <i
style=3D'mso-bidi-font-style:normal'>workspace</i>, into which curricula fr=
om the
catalog can be loaded and resources from the gallery inserted. It is also
possible for a teacher to specify criteria for the desired curriculum. <i
style=3D'mso-bidi-font-style:normal'>Specifications</i> are used for search=
ing
the case-base of curricula, adapting the resources and <i style=3D'mso-bidi=
-font-style:
normal'>critiquing</i> new designs.</p>

<p class=3DMsoNormal><span class=3DSource><span style=3D'mso-bidi-font-fami=
ly:"Times New Roman"'>TCA</span></span>
allows teachers to download curricular resources from the Internet and to
create coherent classroom activities tailored to local circumstances. In
particular, <span class=3DSource><span style=3D'mso-bidi-font-family:"Times=
 New Roman"'>TCA</span></span><span
style=3D'text-transform:uppercase'> </span>addresses the set of five issues
identified in the Introduction:</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l3 level1 lfo2;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
1.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]><span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
is built on a database of information about educational resources posted to=
 the
Internet, so it provides a mechanism for teachers to <i style=3D'mso-bidi-f=
ont-style:
normal'>locate</i> sources of curriculum ideas at scattered Internet sites.=
</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l3 level1 lfo2;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
2.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>The
<span class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'=
>TCA</span></span>
database indexes each resource in a uniform way, allowing teachers to <i
style=3D'mso-bidi-font-style:normal'>search</i> for all items meeting desir=
ed
conditions.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l3 level1 lfo2;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
3.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]><span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
includes tools to help teachers <i style=3D'mso-bidi-font-style:normal'>ada=
pt</i>
items they find to the needs of their classroom. </p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l3 level1 lfo2;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
4.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]><span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
provides a design workspace for <i style=3D'mso-bidi-font-style:normal'>org=
anizing</i>
retrieved ideas into lesson plans that build toward long-term goals.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l3 level1 lfo2;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
5.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]><span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
lets teachers conveniently <i style=3D'mso-bidi-font-style:normal'>share</i>
their experiences back through the Internet.</p>

<h1>The <span class=3DSource><span style=3D'mso-bidi-font-family:Arial'>TCA=
</span></span>
Prototype</h1>

<p class=3DNormalnoindent>Based on preliminary study of these issues, a <sp=
an
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span><span
style=3D'text-transform:uppercase'> </span>prototype has been developed. Six
interface screens have been designed for teacher support: <span class=3DSou=
rce><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Profiler, Explorer, Versio=
ns,
Editor, Planner, and Networker</span></span>. </p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DNormalnoindent><!--[if gte vml 1]><v:shape id=3D"_x0000_i1026" t=
ype=3D"#_x0000_t75"
 style=3D'width:348pt;height:306pt' o:bordertopcolor=3D"this" o:borderleftc=
olor=3D"this"
 o:borderbottomcolor=3D"this" o:borderrightcolor=3D"this">
 <v:imagedata src=3D"ch01_files/image005.wmz" o:title=3D""/>
 <w:bordertop type=3D"single" width=3D"12"/>
 <w:borderleft type=3D"single" width=3D"12"/>
 <w:borderbottom type=3D"single" width=3D"12"/>
 <w:borderright type=3D"single" width=3D"12"/>
</v:shape><![endif]--><![if !vml]><img width=3D468 height=3D412
src=3D"ch01_files/image006.gif" v:shapes=3D"_x0000_i1026"><![endif]></p>

<p class=3DNormalnoindent>Figure 1-3. The teacher-client software interface=
 for
locating, searching and selecting resources and curricula: the <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Profi=
ler</span></span>,
<span class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'=
>Explorer</span></span>
and <span class=3DSource><span style=3D'mso-bidi-font-family:"Times New Rom=
an"'>Versions</span></span>.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The <span class=3DSource><span style=3D'mso-bidi-font-=
family:
"Times New Roman"'>Profiler</span></span>, <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Explorer</span></span> and=
 <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Versi=
ons</span></span>
interfaces work together for information retrieval (figure 1-3). The <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Profi=
ler</span></span>
helps teachers define classroom profiles and locates curricula and resources
that match the profile. The <span class=3DSource><span style=3D'mso-bidi-fo=
nt-family:
"Times New Roman"'>Explorer</span></span> displays these items and allows t=
he
teacher to search through them to find related items. <span class=3DSource>=
<span
style=3D'mso-bidi-font-family:"Times New Roman"'>Versions</span></span> then
helps the teacher select from alternative versions that have been adapted by
other teachers. Through these interfaces, teachers can locate the available
materials that most closely match their personal needs; this makes it easie=
r to
tailor the materials to individual requirements.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<div style=3D'mso-element:para-border-div;border-top:solid windowtext 1.0pt;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none;
mso-border-top-alt:solid windowtext .75pt;mso-border-bottom-alt:solid windo=
wtext .75pt;
padding:1.0pt 0in 1.0pt 0in'>

<p class=3DMsoNormal style=3D'border:none;mso-border-top-alt:solid windowte=
xt .75pt;
mso-border-bottom-alt:solid windowtext .75pt;padding:0in;mso-padding-alt:1.=
0pt 0in 1.0pt 0in'>Figure
1-3 goes approximately here</p>

</div>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DMsoNormal>The <span class=3DSource><span style=3D'mso-bidi-font-=
family:
"Times New Roman"'>Planner</span></span>, <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Editor</span></span> and <=
span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Netwo=
rker</span></span>
help the teacher to prepare resources and curricula, and to share the resul=
ts
of classroom use (figure 1-4). The <span class=3DSource><span style=3D'mso-=
bidi-font-family:
"Times New Roman"'>Planner</span></span> is a design environment for reusing
and reorganizing lesson plans. The Editor allows the teacher to modify and =
adapt
resources. This is a primary means of personalizing a curriculum to individ=
ual
classroom circumstances. Finally, the <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Networker</span></span> su=
pports
interactions with the Internet, providing a two-way medium of communication
with a global community of teachers. Using the <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Networker</span></span>, a
teacher can share personalized versions of standard curricula with other
teachers who might have similar needs.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<p class=3DNormalnoindent><!--[if gte vml 1]><v:shape id=3D"_x0000_i1027" t=
ype=3D"#_x0000_t75"
 style=3D'width:363pt;height:249pt' o:bordertopcolor=3D"this" o:borderleftc=
olor=3D"this"
 o:borderbottomcolor=3D"this" o:borderrightcolor=3D"this">
 <v:imagedata src=3D"ch01_files/image007.wmz" o:title=3D""/>
 <w:bordertop type=3D"single" width=3D"12"/>
 <w:borderleft type=3D"single" width=3D"12"/>
 <w:borderbottom type=3D"single" width=3D"12"/>
 <w:borderright type=3D"single" width=3D"12"/>
</v:shape><![endif]--><![if !vml]><img width=3D488 height=3D336
src=3D"ch01_files/image008.gif" v:shapes=3D"_x0000_i1027"><![endif]></p>

<p class=3DNormalnoindent>Figure 1-4. The teacher-client interface for adap=
ting,
organizing and sharing resources and curricula: the <span class=3DSource><s=
pan
style=3D'mso-bidi-font-family:"Times New Roman"'>Planner</span></span>, <sp=
an
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Edito=
r</span></span>
and <span class=3DSource><span style=3D'mso-bidi-font-family:"Times New Rom=
an"'>Networker</span></span>.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

<div style=3D'mso-element:para-border-div;border-top:solid windowtext 1.0pt;
border-left:none;border-bottom:solid windowtext 1.0pt;border-right:none;
mso-border-top-alt:solid windowtext .75pt;mso-border-bottom-alt:solid windo=
wtext .75pt;
padding:1.0pt 0in 1.0pt 0in'>

<p class=3DMsoNormal style=3D'border:none;mso-border-top-alt:solid windowte=
xt .75pt;
mso-border-bottom-alt:solid windowtext .75pt;padding:0in;mso-padding-alt:1.=
0pt 0in 1.0pt 0in'>Figure
1-4 goes approximately here</p>

</div>

<p class=3DMsoNormal>To illustrate how <span class=3DSource><span style=3D'=
mso-bidi-font-family:
"Times New Roman"'>TCA</span></span> works, each of the five issues will be
discussed in the following sections. These sections present a scenario of a
teacher using <span class=3DSource><span style=3D'mso-bidi-font-family:"Tim=
es New Roman"'>TCA</span></span>
to locate resources, search through them, adapt selected resources, organize
them into a curriculum and share the results with other teachers.</p>

<h1>Scenario Step 1: Locating Curriculum</h1>

<p class=3DNormalnoindent>Imagine a high school mathematics teacher using <=
span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>.
In the coming year she has to introduce some geometric concepts like Pythag=
oras&#8217;
Theorem and deductive proofs. More generally, she might want to discuss the
ubiquity of patterns and ways to represent them mathematically. <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
lets her browse for semester themes and their constituent weekly units and
lesson plans related to these topics. </p>

<p class=3DMsoNormal><span class=3DSource><span style=3D'mso-bidi-font-fami=
ly:"Times New Roman"'>TCA</span></span>
distinguishes four levels of curricula available on the Internet:</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l1 level1 lfo3;
tab-stops:list .25in'><![if !supportLists]><span style=3D'font-family:Symbo=
l;
mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>A <i style=3D'mso-bidi-font-style:normal'>th=
eme</i>
is a major curriculum, possibly covering a semester or a year of school and
optionally integrating several subjects. A theme consists of multiple teach=
ing
units.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l1 level1 lfo3;
tab-stops:list .25in'><![if !supportLists]><span style=3D'font-family:Symbo=
l;
mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>A weekly <i style=3D'mso-bidi-font-style:nor=
mal'>unit</i>
is part of a theme, typically one week of lessons for a single subject. A u=
nit
is described by its constituent daily lesson plans.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l1 level1 lfo3;
tab-stops:list .25in'><![if !supportLists]><span style=3D'font-family:Symbo=
l;
mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>A <i style=3D'mso-bidi-font-style:normal'>pl=
an</i>
is one day&#8217;s lesson for a class. A lesson plan might include a number=
 of
resources, such as a lecture, a reading, an exercise or project, and perhap=
s a
quiz and a homework assignment. </p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l1 level1 lfo3;
tab-stops:list .25in'><![if !supportLists]><span style=3D'font-family:Symbo=
l;
mso-fareast-font-family:Symbol;mso-bidi-font-family:Symbol'><span
style=3D'mso-list:Ignore'>&middot;<span style=3D'font:7.0pt "Times New Roma=
n"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span></span></span><![endif]>A <i style=3D'mso-bidi-font-style:normal'>re=
source</i>
is an element of a lesson plan. It might be a text, available as a word
processing document. It could also be a video clip, a spreadsheet worksheet=
, a
graphic design or a software simulation. Resources are the smallest units of
curricula indexed by <span class=3DSource><span style=3D'mso-bidi-font-fami=
ly:"Times New Roman"'>TCA</span></span>.<span
style=3D'text-transform:uppercase'> </span></p>

<p class=3DMsoNormal><span class=3DSource><span style=3D'mso-bidi-font-fami=
ly:"Times New Roman"'>TCA</span></span>
lets the teacher locate relevant curricula by analyzing information stored =
on
her computer about items available on the Internet. Along with the <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
software on her computer there is a case-base of summaries (indexes) of
curricula and resources that can be downloaded. These summary records refer=
ence
curricula and resources that have been posted to Internet nodes around the
world. In addition to containing the Internet address information needed for
downloading an item, a record contains a description of the item, so that t=
he
teacher can decide whether or not it is of interest. </p>

<p class=3DMsoNormal>After a set of interesting items has been selected bas=
ed on
the information in the case-base, <span class=3DSource><span style=3D'mso-b=
idi-font-family:
"Times New Roman"'>TCA</span></span> downloads the items to the teacher&#82=
17;s
computer. This happens without her having to know where they were located or
how to download them. The items are then available for modification, printi=
ng
or distribution to her students. If Internet traffic is slow, she may opt to
download batches of curriculum and resources overnight and then work with t=
hem
the next day.<a style=3D'mso-footnote-id:ftn1' href=3D"#_ftn1" name=3D"_ftn=
ref1"
title=3D""><span class=3DMsoFootnoteReference><span style=3D'mso-special-ch=
aracter:
footnote'><![if !supportFootnotes]><span class=3DMsoFootnoteReference><span
style=3D'font-size:12.0pt;font-family:"Times New Roman";mso-fareast-font-fa=
mily:
"Times New Roman";mso-ansi-language:EN-US;mso-fareast-language:EN-US;
mso-bidi-language:AR-SA'>[1]</span></span><![endif]></span></span></a></p>

<h1>Scenario Step 2: Searching for Resources</h1>

<p class=3DNormalnoindent><span class=3DSource><span style=3D'mso-bidi-font=
-family:
"Times New Roman"'>TCA</span></span> provides a combination of query and
browsing mechanisms to help a teacher select curricula of interest and to f=
ind
resources that go with it. She can start in the <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Profiler</span></span> (Fi=
gure
3) by specifying that she wants a curriculum for ninth grade mathematics. T=
hen
she can browse through a list of themes in the <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Explorer</span></span> tha=
t meet
the specification. If the list is too long, she can narrow down her search
criteria.</p>

<p class=3DMsoNormal>The <i style=3D'mso-bidi-font-style:normal'>theme</i> =
named
&#8220;A Look at the Greek Mind&#8221; is summarized as: &#8220;This is an
integrated curriculum that explores myth, patterns and abstract
reasoning.&#8221; It emphasizes patterns and is likely to include Pythagora=
s&#8217;
theorem. The teacher can click on this theme in the list. Her computer now
displays summaries of the <i style=3D'mso-bidi-font-style:normal'>units</i>=
 that
make up the curriculum for that theme. This list shows three weekly units.
Select week 1, described as &#8220;Abstract thinking: number theory and
deductive reasoning.&#8221;</p>

<p class=3DMsoNormal>She now sees summaries of that week&#8217;s five daily=
 <i
style=3D'mso-bidi-font-style:normal'>lesson plans</i>. She looks at the geo=
metry
example for day 3, &#8220;Inductive reasoning example: regions of a
circle.&#8221; She select that one and the screen changes to show the lesson
plan in the <span class=3DSource><span style=3D'mso-bidi-font-family:"Times=
 New Roman"'>Planner</span></span>
(Figure 4). It lists all the <i style=3D'mso-bidi-font-style:normal'>resour=
ces</i>
suggested for that period: two lecture topics, a class exercise, several
alternative activities for small groups and a homework assignment.</p>

<p class=3DMsoNormal>The screenshot of <span class=3DSource><span style=3D'=
mso-bidi-font-family:
"Times New Roman"'>Explorer</span></span> illustrates how a teacher can bro=
wse
from a given resource, like &#8220;chart of regions on a circle&#8221; up to
all the lesson plans, units and themes that include that resource and then =
back
down to all the associated units, plans and resources. This is one way to
locate related resources within curricular contexts. The teacher can also t=
urn
to the <span class=3DSource><span style=3D'mso-bidi-font-family:"Times New =
Roman"'>Versions</span></span>
component to find variations on a particular resource and comments about the
resource and its different versions by teachers who have used it.</p>

<p class=3DMsoNormal>Notice resource #2 in the <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Planner</span></span>, whe=
re
students create a spreadsheet chart: &#8220;Group activity: Chart of ratios=
 on
a circle.&#8221; When the teacher selects it with the mouse, the <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Edito=
r</span></span>
shows the detail for that resource, including its index values. </p>

<p class=3DMsoNormal>The description contained in the case-base for each po=
sted
resource is organized as a set of 24 indexes and annotations, such as:
recommended grade level, content area, pedagogical goal, instructional mode,
prerequisites, materials used, required time and the like. Note that total
class time and homework time are computed and teacher preparations for the
resources are listed below the workspace.</p>

<p class=3DMsoNormal><span style=3D'mso-spacerun:yes'>&nbsp;</span>The <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
<span class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'=
>Profiler</span></span>
allows a teacher to specify her curricular needs using combinations of these
indexes. Resources are also cross referenced so that she can retrieve many
different resources that are related to a given one. Thus, once she has fou=
nd
the &#8220;problem of regions of a circle&#8221;, she can easily locate
discussions of inductive reasoning, formal proofs, recursion, simultaneous
equations, sample programs in Logo or Pascal, spreadsheet templates for
analyzing successive differences and graphing tools. She can also find
week-long units that build on geometric problems like this one, with variat=
ions
for students with different backgrounds, learning styles or interests. <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span><span
style=3D'text-transform:uppercase'> </span>allows her to search both top-do=
wn
from themes to resources and bottom-up from resources to curricula.</p>

<h1>Scenario Step 3: Adapting to Local Needs</h1>

<p class=3DNormalnoindent>Adaptation tools are available in <span class=3DS=
ource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</span></span><span
style=3D'text-transform:uppercase'> </span>for resources that have been
downloaded from the Internet. The <span class=3DSource><span style=3D'mso-b=
idi-font-family:
"Times New Roman"'>Planner</span></span> component provides a design worksp=
ace
for assembling a custom lesson plan and the <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>Editor</span></span> helps=
 a
teacher to adapt individual resources to her local needs. The <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span><span
style=3D'text-transform:uppercase'> </span>system can often <i style=3D'mso=
-bidi-font-style:
normal'>make automated suggestions</i> for adapting a resource to the
specification given in the search process. For instance, if she retrieves a
resource that was targeted for 11th grade when she is looking for 10th grade
material, then <span class=3DSource><span style=3D'mso-bidi-font-family:"Ti=
mes New Roman"'>TCA</span></span><span
style=3D'text-transform:uppercase'> </span>might suggest allowing her stude=
nts
more time to do the tasks or might provide more supporting and explanatory =
materials
for them. In general, she will need to make the adaptations; even where the
software comes up with suggestions, she must use her judgment to make the f=
inal
decision. </p>

<p class=3DMsoNormal>While <span class=3DSource><span style=3D'mso-bidi-fon=
t-family:
"Times New Roman"'>TCA</span></span> can automate some adaptation, most
tailoring of curricula requires hands-on control by an experienced teacher.
Sometimes <span class=3DSource><span style=3D'mso-bidi-font-family:"Times N=
ew Roman"'>TCA</span></span>
can support her efforts by <i style=3D'mso-bidi-font-style:normal'>displayi=
ng
useful information</i>. For instance, if she is adapting resources organize=
d by
national standards to local standards she might like her computer to display
both sets of standards and to associate each local standard with correspond=
ing
national standards. In other situations, perhaps involving students whose f=
irst
language is not English, <span class=3DSource><span style=3D'mso-bidi-font-=
family:
"Times New Roman"'>TCA</span></span> might link a resource requiring a high
level of language understanding to a supplementary visual presentation.</p>

<p class=3DMsoNormal>The adaptation process relies on alternative <i
style=3D'mso-bidi-font-style:normal'>versions</i> of individual resources b=
eing
posted. The <span class=3DSource><span style=3D'mso-bidi-font-family:"Times=
 New Roman"'>TCA
VERSIONS</span></span> component helps a teacher adjust to different student
groups, teaching methods and time constraints by retrieving alternative
versions of resources that provide different motivations, use different for=
mats
or go into more depth. She can substitute these alternative resources into
lesson plans; they can then be modified with multimedia editing software fr=
om
within <span class=3DSource><span style=3D'mso-bidi-font-family:"Times New =
Roman"'>TCA</span></span>.</p>

<p class=3DMsoNormal>Included in the <span class=3DSource><span style=3D'ms=
o-bidi-font-family:
"Times New Roman"'>Editor</span></span> is a reduced image of the spreadshe=
et
itself. If a teacher click on this image, <span class=3DSource><span
style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</span></span> brings u=
p the
commercial software application in which the document was produced. So she =
can
now <i style=3D'mso-bidi-font-style:normal'>edit and modify</i> the copy of=
 this
document which appears on her screen. She need not leave <span class=3DSour=
ce><span
style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</span></span> to do th=
is.
Then she can print out her revised version for her students or distribute it
directly to their computers. In this way, she can use her own ideas or thos=
e of
her students to modify and enhance curricular units found on the Internet. =
</p>

<p class=3DMsoNormal>Just as it is important for teachers to adapt curricul=
a to
their needs, it is desirable to have resources that students can tailor.
Current software technology makes this possible, as illustrated by a number=
 of
simulations in the <span class=3DSource><span style=3D'mso-bidi-font-family=
:"Times New Roman"'>Agentsheets</span></span>
Exploratorium <!--[if supportFields]><span style=3D'mso-element:field-begin=
'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Ambach&lt;/Author&gt;&lt;Year&gt;1=
995&lt;/Year&gt;&lt;RecNum&gt;464&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TY=
PE&gt;0&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;464&lt;/REFNUM&gt;&lt;AUTHORS&g=
t;&lt;AUTHOR&gt;Ambach,
P.&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Perrone, C.&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Repp=
ening,
A.&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1995&lt;/YEAR&gt;&lt;TITLE&gt;=
Remote
exploratoriums: Combining networking media and design environments to suppo=
rt
engaged learning&lt;/TITLE&gt;&lt;SECONDARY_TITLE&gt;Computers &amp;amp;
Education&lt;/SECONDARY_TITLE&gt;&lt;VOLUME&gt;24&lt;/VOLUME&gt;&lt;NUMBER&=
gt;3&lt;/NUMBER&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;Cite&gt;&lt;Author&gt;Stahl=
&lt;/Author&gt;&lt;Year&gt;1995&lt;/Year&gt;&lt;RecNum&gt;5&lt;/RecNum&gt;&=
lt;MDL&gt;&lt;REFERENCE_TYPE&gt;3&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;5&lt;=
/REFNUM&gt;&lt;AUTHORS&gt;&lt;AUTHOR&gt;Stahl,
Gerry&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Sumner, Tamara
&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Repenning,
Alexander&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1995&lt;/YEAR&gt;&lt;TI=
TLE&gt;Internet
repositories for collaborative learning: Supporting both students and
teachers&lt;/TITLE&gt;&lt;SECONDARY_TITLE&gt;International Conference on
Computer Support for Collaborative Learning (CSCL &amp;apos;95)&lt;/SECONDA=
RY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;Bloomington,
Indiana&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;ACM
Press&lt;/PUBLISHER&gt;&lt;PAGES&gt;321-328&lt;/PAGES&gt;&lt;KEYWORDS&gt;&l=
t;KEYWORD&gt;Computers,
networks and other technological developments relevant to CSCL; educational
distance groupware; design and interface issues.&lt;/KEYWORD&gt;&lt;/KEYWOR=
DS&gt;&lt;URL&gt;http://www.cis.drexel.edu/faculty/gerry/cscl/papers/ch06.p=
df&lt;/URL&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Ambach, Perrone, =
&amp;
Reppening, 1995; Stahl, Sumner, &amp; Repenning, 1995)<!--[if supportFields=
]><span
style=3D'mso-element:field-end'></span><![endif]-->.</p>

<h1>Scenario Step 4: Organizing Resources into Lesson Plans</h1>

<p class=3DNormalnoindent>The lesson plan is a popular representation for a
curriculum. It provides teachers a system for organizing classroom activiti=
es. <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
uses the <i style=3D'mso-bidi-font-style:normal'>lesson plan metaphor</i> a=
s the
basis for its design workspace. A teacher can start her planning by looking=
 at
downloaded lesson plans and then modifying them to meet her local needs.</p>

<p class=3DMsoNormal>The <span class=3DSource><span style=3D'mso-bidi-font-=
family:
"Times New Roman"'>TCA Planner</span></span> workspace for designing lesson
plans was shown in Figure 4. In addition to summaries of each resource, the
workspace lists the time required by each resource, both in class and at ho=
me.
These times are totaled at the bottom of the list of resources in the <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>Plann=
er</span></span>.
This provides an indication of whether there is too much or too little
instructional material to fill the period. The teacher can then decide to a=
dd
or eliminate resources or adjust their time allowances. The total homework =
time
can be compared to local requirements concerning homework amounts. </p>

<p class=3DMsoNormal><span class=3DSource><span style=3D'mso-bidi-font-fami=
ly:"Times New Roman"'>TCA</span></span>
incorporates computational <i style=3D'mso-bidi-font-style:normal'>critics<=
/i> <!--[if supportFields]><span
style=3D'mso-element:field-begin'></span><span
style=3D'mso-spacerun:yes'>&nbsp;</span>ADDIN EN.CITE
&lt;EndNote&gt;&lt;Cite&gt;&lt;Author&gt;Fischer&lt;/Author&gt;&lt;Year&gt;=
1993&lt;/Year&gt;&lt;RecNum&gt;9&lt;/RecNum&gt;&lt;MDL&gt;&lt;REFERENCE_TYP=
E&gt;3&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;9&lt;/REFNUM&gt;&lt;AUTHORS&gt;&=
lt;AUTHOR&gt;Fischer,
Gerhard&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Nakakoji,
Kumiyo&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Ostwald,
Jonathan&lt;/AUTHOR&gt;&lt;AUTHOR&gt;Stahl, Gerry&lt;/AUTHOR&gt;&lt;AUTHOR&=
gt;Sumner,
Tamara&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1993&lt;/YEAR&gt;&lt;TITLE=
&gt;Embedding
computer-based critics in the contexts of
design&lt;/TITLE&gt;&lt;SECONDARY_TITLE&gt;Conference on Human Factors in
Computing Systems (INTERChi
&amp;apos;93)&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;Amsterdam,
NL&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;Addison
Wesley&lt;/PUBLISHER&gt;&lt;PAGES&gt;157-164&lt;/PAGES&gt;&lt;KEYWORDS&gt;&=
lt;KEYWORD&gt;Generic
critics, specific critics, interpretive critics, design environments,
specification, construction, domain
orientation,&lt;/KEYWORD&gt;&lt;KEYWORD&gt;perspectives, critiquing
systems.&lt;/KEYWORD&gt;&lt;/KEYWORDS&gt;&lt;URL&gt;http://www.cis.drexel.e=
du/faculty/gerry/publications/conferences/1990-1997/chi93/CHI93.html&lt;/UR=
L&gt;&lt;/MDL&gt;&lt;/Cite&gt;&lt;Cite&gt;&lt;Author&gt;Fischer&lt;/Author&=
gt;&lt;Year&gt;1998&lt;/Year&gt;&lt;RecNum&gt;224&lt;/RecNum&gt;&lt;MDL&gt;=
&lt;REFERENCE_TYPE&gt;7&lt;/REFERENCE_TYPE&gt;&lt;REFNUM&gt;224&lt;/REFNUM&=
gt;&lt;AUTHORS&gt;&lt;AUTHOR&gt;G.
Fischer&lt;/AUTHOR&gt;&lt;AUTHOR&gt;K. Nakakoji&lt;/AUTHOR&gt;&lt;AUTHOR&gt=
;J.
Ostwald&lt;/AUTHOR&gt;&lt;AUTHOR&gt;G. Stahl&lt;/AUTHOR&gt;&lt;AUTHOR&gt;T.
Sumner&lt;/AUTHOR&gt;&lt;/AUTHORS&gt;&lt;YEAR&gt;1998&lt;/YEAR&gt;&lt;TITLE=
&gt;Embedding
critics in design environments.&lt;/TITLE&gt;&lt;SECONDARY_AUTHORS&gt;&lt;S=
ECONDARY_AUTHOR&gt;Maybury,
M. T&lt;/SECONDARY_AUTHOR&gt;&lt;SECONDARY_AUTHOR&gt;Wahlster,
W.&lt;/SECONDARY_AUTHOR&gt;&lt;/SECONDARY_AUTHORS&gt;&lt;SECONDARY_TITLE&gt=
;Readings
in Intelligent User
Interfaces&lt;/SECONDARY_TITLE&gt;&lt;PLACE_PUBLISHED&gt;New
York&lt;/PLACE_PUBLISHED&gt;&lt;PUBLISHER&gt;Morgan Kaufman&lt;/PUBLISHER&g=
t;&lt;PAGES&gt;537-561&lt;/PAGES&gt;&lt;URL&gt;http://www.cis.drexel.edu/fa=
culty/gerry/publications/journals/ker/index.html&lt;/URL&gt;&lt;/MDL&gt;&lt=
;/Cite&gt;&lt;/EndNote&gt;<span
style=3D'mso-element:field-separator'></span><![endif]-->(Fischer<i
style=3D'mso-bidi-font-style:normal'> et al.</i>, 1993; Fischer<i
style=3D'mso-bidi-font-style:normal'> et al.</i>, 1998)<!--[if supportField=
s]><span
style=3D'mso-element:field-end'></span><![endif]-->. Critics are software r=
ules
that monitor the curriculum being constructed and verify that specified
conditions are maintained. For instance, critics might automatically alert =
the
teacher if the time required for a one-day curriculum exceeds or falls shor=
t of
the time available.</p>

<h1>Scenario Step 5: Sharing New Experiences</h1>

<p class=3DNormalnoindent>Once a teacher has developed curricula and used t=
hem successfully
in the classroom, she may want to share her creations with other teachers. =
This
way<i style=3D'mso-bidi-font-style:normal'>, the pool of ideas on the Inter=
net
will grow and mature</i>. <span class=3DSource><span style=3D'mso-bidi-font=
-family:
"Times New Roman"'>TCA</span></span> has facilities for her to annotate
individual resources and curricular units at all levels with descriptions of
how they worked in her classroom. This is part of the indexing of the resou=
rce
or unit. </p>

<p class=3DMsoNormal>Assume that a teacher downloaded and used the &#8220;r=
egions
of a circle&#8221; resource and modified it based on her classroom experien=
ce.
Now she wants to upload her version back to the Internet. The <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA N=
etworker</span></span>
component automates that process, posting the new resource to an available
server and adding the indexes for it to the server used for distributing new
indexes. Because the indexing of her revision would be similar to that of t=
he
original version of the resource, other teachers looking at the &#8220;regi=
ons
of a circle&#8221; resource would also find her version with her comments. =
In
this way, the Internet pool of resources serves as a medium of communication
among teachers about the specific resources. It is in such ways that I hope=
 the
use of the Internet for curriculum development will go far beyond today&#82=
17;s
first steps. </p>

<h1>What I Have Learned</h1>

<p class=3DNormalnoindent>I conceptualize the understanding I have reached
through my work on <span class=3DSource><span style=3D'mso-bidi-font-family=
:"Times New Roman"'>TCA</span></span>
in five principles:</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l2 level1 lfo4;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
1.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>Most
resources should be <i style=3D'mso-bidi-font-style:normal'>located</i> at
distributed sites across the Internet, but carefully structured summaries
(indexes) of them should be maintained on teachers&#8217; local computers o=
r in
centralized catalogs.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l2 level1 lfo4;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
2.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>The
<i style=3D'mso-bidi-font-style:normal'>search</i> process should be suppor=
ted
through a combination of query and browsing tools that help teachers explore
what is available.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l2 level1 lfo4;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
3.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]><i
style=3D'mso-bidi-font-style:normal'>Adaptation</i> of tools and resources =
to
teachers and students is critical for developing and benefiting from
constructivist curriculum.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l2 level1 lfo4;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
4.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>Resources
must be <i style=3D'mso-bidi-font-style:normal'>organized</i> into carefully
designed curriculum units to provide effective learning environments.</p>

<p class=3DMsoNormal style=3D'margin-left:.25in;text-indent:-.25in;mso-list=
:l2 level1 lfo4;
tab-stops:list .25in'><![if !supportLists]><span style=3D'mso-list:Ignore'>=
5.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </spa=
n></span><![endif]>The
Internet should become a medium for <i style=3D'mso-bidi-font-style:normal'=
>sharing</i>
curriculum ideas, not just accessing them.</p>

<p class=3DMsoNormal>A system to assist teachers in developing curricula for
educational reform has been designed and prototyped. All aspects of the sys=
tem
must now be refined by working further with classroom teachers and curricul=
um
developers. While the approach of <span class=3DSource><span style=3D'mso-b=
idi-font-family:
"Times New Roman"'>TCA</span></span> appeals to teachers who have participa=
ted
in its design, its implementation must still be tuned to the realities of t=
he
classroom.</p>

<p class=3DMsoNormal>The distribution of resources and indexes prototyped i=
n <span
class=3DSource><span style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</=
span></span>
has attractive advantages. Because the actual multimedia resources (text,
pictures, video clips, spreadsheet templates, HyperCard stacks, software ap=
plications)
are distributed across the Internet, there is no limit to the quantity or s=
ize
of these resources and no need for teachers to have large computers. Resour=
ces
can be posted on network servers maintained by school districts, regional
educational organizations, textbook manufacturers and other agencies. Then =
the
originating agency can maintain and revise the resources as necessary.</p>

<p class=3DMsoNormal>However, the approach advocated here faces a major
institutional challenge: the standardization of resource indexing. The
difficulty with this approach is the need to index every resource and to
distribute these indexes to every computer that runs <span class=3DSource><=
span
style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</span></span>. This in=
volves
(a) implementing a distribution and updating system for the case-base index
records and (b) establishing the <span class=3DSource><span style=3D'mso-bi=
di-font-family:
"Times New Roman"'>TCA</span></span> indexing scheme as a standard. </p>

<p class=3DMsoNormal>The distribution and updating of indexes can be handle=
d by
tools within <span class=3DSource><span style=3D'mso-bidi-font-family:"Time=
s New Roman"'>TCA</span></span>
and support software for major curriculum contributors. However, the
standardization requires coordination among interested parties. Before any
teachers can use <span class=3DSource><span style=3D'mso-bidi-font-family:"=
Times New Roman"'>TCA</span></span>
there must be useful indexed resources available on the network, with
comprehensive suggested lesson plans. It is necessary to establish cooperat=
ion
among federally-funded curriculum development efforts, textbook publishers,
software publishers and school districts. If successful, this will establis=
h a
critical mass of curriculum on the Internet accessible by <span class=3DSou=
rce><span
style=3D'mso-bidi-font-family:"Times New Roman"'>TCA</span></span>. Then the
Internet can begin to be an effective medium for the global sharing of loca=
lly
adaptable curriculum.</p>

<p class=3DMsoNormal><o:p>&nbsp;</o:p></p>

</div>

<div style=3D'mso-element:footnote-list'><![if !supportFootnotes]><br clear=
=3Dall>

<hr align=3Dleft size=3D1 width=3D"33%">

<![endif]>

<div style=3D'mso-element:footnote' id=3Dftn1>

<p class=3DMsoFootnoteText><a style=3D'mso-footnote-id:ftn1' href=3D"#_ftnr=
ef1"
name=3D"_ftn1" title=3D""><span class=3DMsoFootnoteReference><span style=3D=
'mso-special-character:
footnote'><![if !supportFootnotes]><span class=3DMsoFootnoteReference><span
style=3D'font-size:12.0pt;mso-bidi-font-size:10.0pt;font-family:"Times New =
Roman";
mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US;mso-farea=
st-language:
EN-US;mso-bidi-language:AR-SA'>[1]</span></span><![endif]></span></span></a>
Note that this paper was written in 1995, when the Internet was available b=
ut
the WorldWideWeb was not yet popular and browsers like Netscape and Internet
Explorer did not exist. The technical implementation of TCA and the
distribution of resources on servers and desktops would be designed differe=
ntly
ten years later. Although digital libraries of educational resources have b=
een
created meanwhile &#8212; such as <a href=3D"http://www.mathforum.org/">www=
.mathforum.org</a>
&#8212; they lack several of <span class=3DSource><span style=3D'mso-bidi-f=
ont-family:
"Times New Roman"'>TCA</span></span>&#8217;s affordances.</p>

</div>

</div>

</body>

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