from:* Computers & Education*.
Special issue on Education and the Internet. August 1995.

**Gerry Stahl, Tamara Sumner, Robert
Owen
**

Many teachers yearn to break through the confines of traditional textbook-centered
teaching to 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.

The Internet provides a medium for sharing innovative educational resources globally.
School districts and teacher organizations have already begun to post curriculum ideas on
Internet servers. However, just storing unrelated educational materials on the Internet
does not by itself solve the problem. It is too hard to find the right resources to meet
specific needs. Teachers need productivity software for *locating* sites of materials
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.

We have designed and prototyped a Teacher's Curriculum Assistant (TCA) that provides *software
support for teachers to make effective use of educational resources posted to the Internet*.
TCA 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. TCA encourages teachers to annotate and upload
successfully used curriculum to Internet servers to share their ideas with other teachers.
In this paper we motivate the need for such computer support and discuss what we have
learned from designing TCA.

The Internet has the potential to transform educational curriculum development beyond the horizons of our foresight. The process has begun, as educators across the country start to post their favorite curriculum ideas for others to share. Already, this first tentative step has revealed the difficulties inherent in using such potentially enormous, loosely structured sources of information. Teachers wandering around the Internet looking for ideas to use in their classrooms confront a set of problems that will not go away by itself as the Internet becomes a more popular medium for sharing curriculum -- on the contrary:

1. Teachers have to *locate* sites of curriculum ideas scattered across the
network; there is currently no system for announcing the locations of these sites.

2. They have to *search* through the offerings at each site for useful items.
While some sites provide search mechanisms for their databases, each has different
interfaces, tools, and indexing schemes that must be learned before the curricula can be
accessed.

3. They have to *adapt* items they find to the needs of their particular
classroom: local standards, the current curriculum, their own teaching preferences, and
the needs or learning styles of their various students.

4. They have to *organize* the new ideas in coherent curricula that build toward
long-term pedagogical goals.

5. They have to *share* their experiences using the curriculum or their own new
ideas with others who use the resources.

In many fields, professionals have turned to *productivity software* to help them
manage such tasks involving complex sources of information. We believe that teachers
should be given similar computer-based tools to meet the problems listed above. If this
software is designed to empower teachers -- perhaps in conjunction with their students --
in open-ended ways, opportunities will materialize that we cannot now imagine.

In this article, we consider how the sharing of curriculum ideas over the Internet can
be made more effective in transforming education. We motivate specific issues in the
design of productivity software for curriculum development by classroom teachers, and
introduce the Teacher's Curriculum Assistant (TCA) we are building for this purpose.
First, we discuss the nature of constructivist curriculum, contrasting it with traditional
approaches based on behaviorist theory. Then we 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. We provide a scenario of
a teacher developing curriculum using productivity software like TCA, and conclude by
discussing some issues we feel will be important in *maximizing the effectiveness of the
Internet* as a medium for the dissemination of innovative curriculum for educational
reform.

The distribution of curriculum over the Internet and the use of productivity software
for searching and adapting posted ideas could benefit any pedagogical approach. However,
it is particularly crucial for advancing *reform* in education.

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
activities and materials should be presented on a day to day basis? This concrete question
is the one that Internet sharing can best address. We generalize the term *curriculum*
to cover this question.

Consider curriculum 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 "number skills". *Behaviorist*
learning theory supported the view that one method of training could work for all
students; reformers face a much more complex challenge. There is a growing concensus among
educational theorists that different students in different situations construct their
understandings in different ways [1]. This approach is often called *constructivism*
or constructionism [2]. It implies that teachers 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.

Behaviorism and constructivism differ primarily in their views of how students build up their knowledge. Traditional, rationalist education 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 curriculum into isolated atomic propositions and feeding these predigested facts to the students. This approach to education was suited to the industrial age, in which workers on assembly lines performed well-defined, sequential tasks.

According to constructivism, learners *interpret* problems in their environments
using *conceptual frameworks* that they developed in the past [3]. In challenging
cases, problems can require changes in the frameworks. Such conceptual change is the
essence of learning: one's understanding evolves in order to comprehend one's environment
[4]. To teach a student a mathematical method or a scientific theory is not to place a set
of propositional facts into her mind, but to give her a new tool that she can make her own
and use in her own ways in comprehending her world.

Constructivism does not entail the rejection of curriculum. Rather, it requires a more
complex and flexible curriculum. Traditionally, curriculum consisted of a textual
theoretical lesson, a set of drills for students to practice, and a test to evaluate if
the students could perform the desired behaviors. In contrast, *a constructivist
curriculum* might target certain cognitive skills, provide a setting of resources and
activities to serve as a catalyst for the development of these skills, and then offer
opportunities for students to articulate their evolving understandings [5]. The cognitive
skills in math might include qualitative reasoning about graphs, number lines, algorithms,
or proofs, for example.

We believe that the movement from viewing 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, *alternative
knowledge representations* [6]. As researchers in artificial intelligence, we know that
knowledge representations are key to characterizing or modelling cognition. We have also
found that professionals working in typical contemporary occupations focus much of their
effort on developing and using alternative knowledge representations that are adapted to
their tasks [7]. Curricula to prepare people for the next generation of jobs would do well
to familiarize students with the creation and use of alternative conceptual
representations.

We are interested in helping teachers to create learning environments that stimulate
the construction and evolution of understanding through student exploration using multiple
conceptual representations. *A stimulating learning environment is one with a rich
ecology, in which many elements interact in subtle ways.* In this section we present an
illustration of a rich ecology for learning mathematical thinking that includes: inductive
reasoning, recursive computation, spreadsheet representation, graphing, linear equations,
and programming languages.

*Figure 1. Regions of a circle; n = 8..*

A typical curriculum suggestion that might be posted on an educational resources
listing on the Internet is the *problem of regions of a circle*: Given **n**
points on the circumference of a circle, what is the maximum number of regions you can
divide the circle into by drawing straight lines connecting the points? (See Figure 1.)
For instance, connecting two points divides the circle into 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 thinking.

The problem with this curriculum offering as an Internet 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 instance, a discussion of inductive reasoning brings out
some of the character of this particular problem. If one counts the number of regions, **R(n),** for **n** = 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 **n**,
the series diverges completely from the powers of 2. Why? Here *inductive reasoning*
can come to the rescue of the hasty inductive assumption -- if, that is, the problem is
accompanied by a discussion of inductive reasoning.

Consider the general case of **n** points. Assume that you
know the answer for **n-1** points and think about how many new
regions are created by adding the **n**-th point and connecting
it to each of the **n-1** 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 *sigma notation* for sums of indexed terms is explained as a tool for
working on the problem. Perhaps a group effort will be needed to check each step and avoid
mistakes.

At this point, a teacher might introduce the notion of *recursion* and relate it
to induction. If the students can *program in Logo or Pascal* (programming languages
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 **n**
very quickly without the tedious and error-prone process of counting regions in drawings.
It would be nice to formalize the derivation of this result with a *deductive proof*,
if the method of formulating proofs has been explained.

Now that students are confident that they have the correct values for many **n**,
they can enter these values in a *spreadsheet* to explore them. The first
representation they might want to see is a *graph* of **R(n)**
*vs*. **n**. On the spreadsheet they could make a column
that displays the difference between each **R(n)** and its
corresponding **R(n-1)**. Copying this column several times, they
would find that the fourth column of differences is constant. This result means that **R(n)** follows a fourth order equation, that can be found by solving *simultaneous
linear equations*.

The point of this example is that sharing the isolated statement of the problem is not enough. The rich learning experience involves 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's many facets through several conceptual frameworks.

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 that constructivist reforms call for.
Computer support for curriculum development should make the kinds of resources shown in
Figure 2 readily available.

*Figure 2. A number of multimedia resources related to the
"regions of a circle" problem. These include textual documents, drawings,
equations, spreadsheets, graphs, and computer program source code.*

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 *design*.
To support teachers in developing curriculum that achieves this, we must go beyond
databases of isolated resources to* *provide* design environments for curriculum
development*.

It may seem to be an overwhelming task to design an effective learning environment for
promoting the development of basic cognitive skills. However, dozens of reform curricula
have already been created*. The problem now is to disseminate these in ways that allow
teachers to adapt them* to their local needs and to reuse them as templates for
additional new curricula. It is instructive to look at a recent attempt to make this
curriculum available. The "MathFinder CD-ROM: a collection of resources for
mathematics reform" excerpts materials from thirty new math curricula [8]. Like the
posting of curriculum ideas at several Internet sites, this is an important early step at
electronic dissemination.

Unfortunately, MathFinder has a number of serious limitations due to its CD-ROM
(read-only) format. It relies on a fixed database of resources that allows resources to be
*located* but not expanded or revised. Its indexing is relatively simple -- primarily
oriented toward illustrating a particular set of math standards -- yet its *search
mechanism is cumbersome* for many teachers. Since its resources are stored in bitmap
images, they *cannot be adapted* in any way by teachers or students. Moreover,
MathFinder provides* no facility for organizing resources* *into curricula -- *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, MathFinder *does not allow
teachers to share* their experiences with annotations or to add their own curricular
ideas. Thus, of the five issues listed in the Introduction, MathFinder only provides a
partial solution to the issues of location and search.

An alternative approach is suggested by our work on *domain-oriented design
environments* [9-13]. 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. We have built a prototype version of a Teacher's Curriculum
Assistant (TCA) based on this approach. TCA includes a *catalog* of previously
designed curricula that can be reused and modified. It has a *gallery* of educational
resources that can be inserted into partial curriculum designs. There is a *workspace*,
into which curricula from 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. The *specifications* are used for searching the case-base of curriculum,
adapting the resources, and *critiquing* new designs.

TCA allows teachers to download curricular resources from the Internet and to create coherent classroom activities tailored to local circumstances. In particular, TCA addresses the set of problems identified in the Introduction:

1. TCA is built on a database of information about educational resources posted to the
Internet, so it provides a mechanism for teachers to *locate* sources of curriculum
ideas at scattered Internet sites.

2. The TCA database indexes each resource in a uniform way, allowing teachers to *search*
for all items meeting desired conditions.

3. TCA includes tools to help teachers *adapt* items they find to the needs of
their classroom.

4. TCA provides a design workspace for *organizing* retrieved ideas into lesson
plans that build toward long-term goals.

5. TCA lets teachers conveniently *share* their experiences back through the
Internet.

To illustrate how TCA works, each of these points will be discussed in the following sections. These sections present a scenario of a teacher using TCA to locate resources, search through them, adapt selected resources, organize them into curriculum, and share the results with other teachers.

Assume that you are a high school mathematics teacher using TCA. In the coming year you have to introduce some geometric concepts like Pythagoras' Theorem and deductive proofs. More generally, you might like to discuss the ubiquity of patterns and ways to represent them mathematically. The TCA Find menu lets you search for semester themes and their constituent weekly units and lesson plans related to these topics. TCA distinguishes four levels of curriculum available on the Internet:

* A *theme* is a major curriculum, possibly covering a
semester or a year of school and optionally integrating several subjects. A theme consists
of multiple teaching units.

* A weekly *unit* is part of a theme, typically one
week of lessons for a single subject. A unit is described by its constituent daily lesson
plans.

* A *plan* is one day's lesson for a class. A lesson
plan might include a number of resources, such as a lecture, a reading, an exercise or
project, perhaps a quiz, and a homework assignment.

* A *resource* 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 curriculum indexed by TCA.

TCA lets you locate relevant curriculum by analyzing information stored on your computer about items available on the Internet. Along with the TCA software on your computer there is a case-base of summaries (indexes) of curriculum and resources that can be downloaded. These summary records reference curriculum 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 you can decide whether or not it is of interest.

After you have selected a set of interesting items based on the information in the case-base, TCA downloads the items to your computer. This happens without you having to know where they were located or how to download them. The items are then available for modification, printing, or distribution to your students. If Internet traffic is slow, you may opt to download batches of curriculum and resources over night and then work with them the next day.

TCA provides a combination of query and browsing mechanisms to help you select curriculum of interest and to find resources that go with it. You can start by specifying that you want curriculum for ninth grade mathematics. Then you can browse through a list of themes that meet the specification. If the list is too long, narrow down your search criteria.

The *theme* named "A Look at the Greek Mind" is summarized as:
"This is an integrated curriculum that explores myth, patterns and abstract
reasoning." It emphasizes patterns and is likely to include Pythagoras' theorem.
Click on this theme in the list. Your computer now displays summaries of the *units*
that make up the curriculum for that theme. This list shows three weekly units. Select
week 1, described as "Abstract thinking: number theory and deductive reasoning."

*Figure 3. Screen image of the lesson plan workspace. A number of
resources (lectures, exercises, group activities, and homework) related to the regions of
a circle problem are assembled for a day's class. Note that total class time and homework
time are computed and teacher preparations for the resources are listed below the
workspace.
*

You now see summaries of that week's five daily *lesson plans*. Look at the
geometry example for day 3, "Inductive reasoning example: regions of a circle."
Select that one and the screen changes to show the lesson plan in Figure 3. It lists
several *resources* to choose from for that period: lecture topics, class exercises,
activities for small groups and homework assignments.

Notice resource #2 where students create a spreadsheet chart: "chart of ratios on
a circle." Select it by clicking the mouse on the summary of that resource. The
Editor window (see Figure 4) shows the detail for that resource, including its index
values.

*Figure 4. Screen image of a TCA display of the indexing for a
resource. The resource is a spreadsheet, which is also shown in the window.
*

The description contained in the case-base for each posted 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. TCA includes search mechanisms that allow you to specify your curriculum needs using combinations of these indexes. Resources are also cross-referenced so that you can retrieve many different resources that are related to a given one. Thus, once you have found the "problem of regions of a circle", you can easily locate discussions of inductive reasoning, formal proofs, recursion, simultaneous linear equations, sample programs in Logo or Pascal, spreadsheet templates for analyzing successive differences, and graphing tools. You can also find week-long units that build on geometric problems like this one, with variations for students with different backgrounds, learning styles, or interests. TCA allows you to search both top-down from themes to resources and bottom-up from resources to curriculum.

Adaptation tools are available in TCA for resources that have been downloaded from the
Internet. The TCA system can often *make automated suggestions* for adapting a
resource to the specification given in the search process. For instance, if you retrieve a
resource that was targeted for 11th grade when you are looking for 10th grade material,
then TCA might suggest allowing your students more time to do the tasks or might provide
more supporting and explanatory materials for them. In general, you will need to make the
adaptations; even where the software comes up with suggestions, you must use your judgment
to make the final decision.

While TCA can automate some adaptation, most tailoring of curriculum requires hands-on
control by experienced teachers. Sometimes TCA can support your efforts by *displaying
useful information*. For instance, if you are adapting resources organized by national
standards to local standards you might like your computer to display both sets of
standards and to associate each local standard with corresponding national standards. In
other situations, perhaps involving students whose first language is not English, TCA
might link a resource requiring a high level of language understanding to a supplementary
visual presentation.

The adaptation process relies on alternative *versions* of individual resources
being posted. TCA helps you adjust to different student groups, teaching methods, and time
constraints by retrieving alternative versions of resources that provide different
motivations, use different formats, or go into more depth. You can substitute these
alternative resources into lesson plans; they can then be modified with multimedia editing
software from within TCA.

Included in Figure 4 was a reduced image of the spreadsheet itself. If you click on
this image, TCA brings up the commercial software application in which the document was
produced. So you can now *edit and modify* the copy of this document which appears on
your screen. You need not leave TCA to do this. Then you can print out your revised
version for your students or distribute it directly to their computers. In this way, you
can use your own ideas or those of your students to modify and enhance curricular units
found on the Internet.

Just as it is important for teachers to adapt curriculum 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 Exploratorium described in this issue [14].

The lesson plan is a popular representation for curriculum. It provides a system for
organizing classroom activities. TCA uses the *lesson plan metaphor* as the basis for
its design workspace. You can start your planning by looking at downloaded lesson plans
and then modifying them to meet your local needs.

The TCA workspace for designing lesson plans was shown in Figure 3. In addition to summaries of each resource, the workspace lists the time required by each resource, both in class and at home. These times are totaled at the bottom of the list. This provides an indication of whether there is too much or too little instructional material to fill the period. You can then decide to add or eliminate resources, or adjust their time allowances. The total homework time can be compared to local requirements concerning homework amounts.

TCA incorporates computational *critics* [11, 12]. Critics are software rules that
monitor the curriculum being constructed and verify that specified conditions are
maintained. For instance, critics might inform you if the time required for a one-day
curriculum exceeds or falls short of the time available.

Once you have developed curricula and used them successfully in the classroom, you may
want to share your creations with other teachers. This way*, the pool of ideas on the
Internet will grow and mature*. TCA has facilities for you to annotate individual
resources and curricular units at all levels with descriptions of how they worked in your
classroom. This is part of the indexing of the resource or unit.

Assume that you downloaded and used the "regions of a circle" resource and modified it based on your classroom experience. Now you want to upload your version back to the Internet. TCA 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 your revision would be similar to that of the original version of the resource, other teachers looking at the "regions of a circle" resource would also find your version with your 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 we hope the use of the Internet for curriculum development will go far beyond today's first steps.

We conceptualize the understanding we have reached through our work on TCA in five principles:

1. Most resources should be *located* at distributed sites across the Internet,
but carefully structured summaries (indexes) of them should be maintained on teachers'
local computers.

2. The *search* process should be supported through a combination of query and
browsing tools that help teachers explore what is available.

3. *Adaptation* of tools and resources to teachers and students is critical for
developing and benefiting from constructivist curriculum.

4. Resources must be *organized* into carefully designed curriculum units to
provide effective learning environments.

5. The Internet should become a medium for *sharing* curriculum ideas, not just
accessing them.

We have designed and prototyped a system to assist teachers in developing curriculum for educational reform. We must now refine all aspects of the system by working further with classroom teachers and curriculum developers. While the approach of TCA appeals to teachers who have participated in its design, its implementation must still be tuned to the realities of the classroom.

The distribution of resources and indexes prototyped in TCA has attractive advantages. Because the actual multimedia resources (text, pictures, video clips, spreadsheet templates, HyperCard stacks, software applications) are distributed across the Internet, there is no limit to the quantity or size of these resources and no need for teachers to have large computers. Resources 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.

However, the approach we advocate 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 TCA. This involves (a) implementing a distribution and updating system for the case-base index records and (b) establishing the TCA indexing scheme as a standard.

The distribution and updating of indexes can be handled by tools within TCA and support software for major curriculum contributors. However, the standardization requires coordination among interested parties. Before any teachers can use TCA there must be useful indexed resources available on the network, with comprehensive suggested lesson plans. We hope to initiate cooperation among federally-funded curriculum development efforts, textbook publishers, software publishers, and school districts. If successful, this will establish a critical mass of curriculum on the Internet accessible by TCA. Then the Internet can begin to be an effective medium for the global sharing of locally adaptable curriculum.

This paper describes work done at Owen Research with support by DOE grant
DE-FG03-93ER81588 and NSF grant III-9360544. We wish to acknowledge encouragement from Len
Scrogan, Technology Specialist in the Curriculum and Instruction Division of Boulder
Valley Public Schools, and Jim Spohrer of Apple Computers. Our design environment approach
grows out of research at the Center for LifeLong Learning and Design, University of
Colorado.

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