Carnegie Mellon University and the Homewood Montessori School in Pittsburgh propose to improve basic math and language skills education primarily for Pittsburgh Public School students, but also for students anywhere in Pennsylvania and the world.

To meet this goal, we propose to develop entirely web-based, freely available interactive software based on the Montessori "manipulatives" for teaching basic math and language skills in class, in the library, and at home.

Current constraints to meeting these objectives include the limited availability of manipulatives (1 per classroom), the absence of cheap manipulatives that can be used in the home that are coordinated by the curriculum, the physical constraints of the manipulatives themselves, the lack of networked computers in school, and the lack of access to educational software developers.

By partnering with students in Carnegie Mellon University’s Human Computer Interaction Institute, and therby cost effectively creating high quality, free, web-based software based on the Montessori manipulatives, and by seeding the Homewood Montessori school with seven internet-connected multimedia PCs, one server, an ISDN line and a LAN (local area network), we can overcome these constraints.

This project aligns with Link-to-Learn goals because it establishes a partnership between a Pittsburgh Public School and Carngie Mellon University, it increases access to technology based education resources for disadvantaged groups, it effectively incorporates technology into educational curricula, it promotes collaborative development, and it provides incentives and resources to improve professional development for educators in the effective use of computer-based technologies.

Through an investment of $49,990 matched by $21,663, Homewood Montessori and Carnegie Mellon should be able to sustain this project after one year of Commonwealth funding. They will have completely self-contained software, support in place for teachers who want to create new lessons based upon this software, and a fixed cost of only $50/month to maintain ISDN access. As internet access increases, more and more students and teachers will be able to use these products with no further investment.

Homewood Montessori School is a Pittsburgh Public School located in the Homewood section of Pittsburgh, Pennsylvania. It is an urban multicultural magnet school, which maintains a 50/50 mix of students of color and other students. Enrollment is open to all students who are residents of the city. Acceptance into the program is through application and lottery when classes are oversubscribed. Current enrollment in K-6 is approximately 175 students. Seven Montessori trained and certified teachers make up the teaching staff. The curriculum is a combination of Montessori and Pittsburgh Public School.

The Montessori philosophy requires that a student’s educational experience at ages six through twelve reach out beyond the classroom environment. The immediate Homewood area has very limited or non-existent resources available for the school to meet this goal. Our fundamental educational objective is to enrich the student’s learning experience both in and especially beyond the classroom.

B. What are the specific educational objectives (not technical solutions) you will pursue to meet your goal.

1. To provide extensions of the Montessori didactic (hands-on) Mathematics and English grammar materials. More specifically, to improve the teaching of the following fundamental concepts

• number
• place value
• multiplication
• division
• fractions
• multiplication by fractions
• area
• volume
• grammar

2. To extend the learning environment beyond the classroom. More specifically, to provide internet access to Homewood students.

3. To provide greater accessibility to the Montessori materials in the classroom environment. With a limited number of Montessori materials available in the classroom, a virtual version of the materials would allow more students to access the materials at any given time.

4. To provide opportunities for students to utilize Montessori materials in their home or public environment, thereby contributing to the home/school/child linkage that is central to the Montessori philosophy. More specifically, to provide internet accessible extensions of the Montessori manipulatives that are used successfully in class. The internet is available in all Pittsburgh Public Libraries, but Montessori materials are not. The Montessori materials are fully manipulable, exploratory environments in which students learn fundamental concepts by moving from the concrete to the symbolic to the abstract. They are rooted in real objects in the student’s experience, are fully coordinated with existing curricula, encourage a love of learning, and are simple enough to use away from the classroom and a teacher’s guidance.

5. To provide opportunities for the Homewood Montessori staff to interact with other public and private Montessori school teachers nationally and worldwide over the internet.

1. The school budget does not provide adequate resources to purchase math and grammar materials to meet the Montessori program's needs.

2. Budget constraints make it almost impossible to extend the learning environment beyond the classroom. Even field trips and classroom visits by outside content experts are becoming more and more difficult to arrange with any meaningful frequency.

3. Montessori materials and enrichment extensions are not available for children to take home.

4. Homewood Montessori School does not have the technology or expertise to create or take advantage of networking opportunities.

Exercises done in class benefit substantially from concrete, manipulable teaching aids like colored blocks, beads, compass and ruler, etc. Students who need extra help in understanding simple concepts like fractions benefit tangibly from being able to manipulate devices which make the ideas concrete in an environment where they can be tutored and guided through their exercises (Brown & Campione, 1990). Incredibly, however, school budgets are almost devoid of money to purchase and upgrade these sorts of materials. What is more difficult still is providing students these sorts of tools (and the guidance to use them) for homework. Homework is predominantly pencil and paper, and done in a context in which little help can be expected from today’s overstressed and overworked parents.

Our project will invest in internet infrastructure for the Homewood Montessori School, and it will build web-based software that addresses the particular educational objectives discussed above. On the infrastructure side, we propose to bring in an ISDN line into the Homewood School, wire the school internally with ethernet for internet connectivity in each K-6 classroom, buy a Windows NT server, and provide seven multimedia PCs for the classrooms themselves. This will allow every K-6 student in the school to have internet access from their own classroom, an outcome that would be extremely desirable for the Homewood students. But we don’t want to stop there.

We also want to develop web-based software based on Montessori manipulatives that will teach the basic concepts of place value, fractions, grammar, arithmetic, and several other fundamental skills. The software will be accessible from any computer that can run a standard web-browser like Netscape or Internet Explorer.

A wide body of educational research shows that students learn more when they become active in the learning process (Corbett and Anderson, 1992; Browne and Cambione, 1990; Garfield and Ahlgren, 1988), and especially when they can manipulate concrete representations of the concepts they are trying to master (Anderson, et. al, 1992; Garfield 1995; Lampert, 1985). "Montessori manipulatives," which are an essential part of the Montessori curriculum, embody precisely these pedagogical principles. They provide concrete and manipulable representations of crucial basic ideas, and they make the student become active in mastering these ideas. For example, the Montessori Golden Beads (Figure 1) is a classic manipulative used to teach place value, multiplication, area and volume, and other crucial basic concepts. We have identified three manipulatives as particularly well suited to be converted into a "virtual version." They are Golden Beads, Grammar Symbols, and Fraction Inserts.

Golden Beads come individually (red), in strings of two (green), in strings of three, four, etc, up to ten (gold). They also come in packets of ten strings-of-ten that form a ten by ten square, in ten grids of one hundred that form a one thousand bead cube, etc.

By physically manipulating such objects, for example by constructing a square of 3s, students move from the concrete to the symbolic to the abstract. The beads come in a compartmentalized box in the Montessori classroom, and students complete many concrete tasks before they advance to the symbolic level (3x3=9), or the abstract (e.g., the area of square is side x side, the volume of a cube is side x side x side, and A x B = B x A). We will create an extended version of Golden Beads as a "virtual manipulative," which will provide a flexibility that cannot be achieved by the physical objects. For example, in teaching that multiplication is commutative, students are asked to construct 3 x 2 and then 2 x 3 (Figure 2).

To do this, students must be in the classroom. They must first go the Golden Bead box, get three of the green 2-bead packets, get two of the purple 3-bead packets, count the beads in each, and establish that indeed, the total of both is six. On the computer, which the students can access in a variety of locations, the objects can be instantly found and displayed. They can then be regrouped, so 3x2 becomes 2x3, with the color changing automatically, but without changing position on the screen. By giving the student control of this operation, they will see that the grouping doesn’t change the set of objects, further reinforcing the idea of multiplicative commutivity.

Grammar Symbols (Figure 3) combine colored shapes with grammatical classes like noun, verb, article, etc. Verbs are given a round, red shape to connote motion and energy, while nouns are given a black pyramidal shape to connote mass and substance. Students are given a sentence, which they must then parse into the various grammatical components. Creating a virtual manipulative for Grammar Symbols will involve two pieces: an interface for the student, and a word-processing-like environment within which teachers (and parents) can construct exercises. Teachers will be able to type a sentence, select a word or phrase within the sentence, and then, instead of making them italic or boldface, make them verb phrases or noun phrases, etc. In minutes a teacher’s aid will be able to construct dozens of appropriate exercises. The software will be able to assess the students’ answers and provide help should the student need it. By tracking systematic patterns of mistakes, a computer can give feedback to the teacher, and adjust the exercises offered so that they are particularly appropriate for the individual student involved.

Fraction Insets (Figure 4) are used to teach fractions, a fundamental concept which is all too often not adequately mastered by many students.

Fraction Inserts involve a pie dish and pie pieces that are a given fraction of the whole, for example, 1/8. What cannot be done in the Montessori manipulative, at least easily, is multiplication of fractions. While the student can be asked to show that 6/16 and 3/8, for example, look the same, they cannot be asked to take 1/2 of 3/8. The computer version of Fraction Inserts allows this trivially. The student will be able to select any region of the pie with the mouse, and then divide the selected region into any size fractional segments, for example halves, quarters, eighths, etc.

These "virtual manipulatives" will coordinate with Montessori and standard public school curricula, will be exciting for the student and teacher, will begin to fulfill the real promise of the internet, and will be extremely useful as remedial aids, in and out of the classroom.

One part of the solution involves the explosive enrichment that results from internet connectivity in every classroom. We will also develop a more focussed solution, namely the "virtual manipulatives."

In the Montessori curriculum, which is fully integrated with the public school and which has always been performance-based, presentations are made with the manipulatives every week, and students are asked to complete exercises on the manipulatives during independent work time at school. With virtual manipulatives, teachers will be able to make more sophisticated presentations, students will be able to complete more sophisticated exercises in class, and they will also be able to complete standard or sophisticated exercises in the library (on school computers), or even at home. Computers at the school’s library, and at any location where publicly accessible internet-connected computers are available will make available fun, interesting exercises on skills that are too basic to ignore.

The virtual manipulatives will be added to the Homewood Montessori curriculum, but will also be available for remedial help in basic skills at any school in the city, state, country, and world. For the cost of implementing the virtual manipulatives for one school, we will provide remedial tools and enrichment extensions for teachers and students at any school.

F. How will you evaluate the results?

We will evaluate the results of the project in several ways. First, we will carefully survey the teachers in the Homewood Montessori school to assess whether the intervention successfully aids in teaching basic skills. Second, we will survey the students to assess whether they subjectively find the software helpful. Third, we will collect data on usage. Part of the advantage of building web-based software is that it is easy to build in automatic usage tracking, both on a coarse and more fine-grained level. On a coarse-grained level, we can track how many times the software is actually used, and how long it is used in each session. On a more fine-grained level, we can track how much time is spent on each exercise, the overall difficulty of each exercise as a function of time spent on it and the frequency of a correct solution, and systematic patterns in the mistakes made.

A large part of a student’s training in the Human Computer Interaction (HCI) major at Carnegie Mellon involves designing and executing evaluations. After two decades of experience with software that often delivers far less than promised, both in usability and in pedagogical effectiveness, HCI researchers focussed on education (Koedinger and Anderson, 1993). They have learned that evaluation before, during and after design is crucial to the development process (Newman & Lamming, 1995).

G. How will you implement the project?

The project will take place in three "stages" corresponding to the 1998 academic college calendar: the spring semester, 8 weeks of summer, and the fall semester. The team of developers will include graphic and communication design specialists, programmer specialists, web-site designers, and evaluator specialists.

We will begin the project with a Contextual Inquiry and Design (Holtzblatt and Jones, 1993; Newman and Lamming, 1995), build and evaluate prototypes, redesign and implement the software and web-site in the summer, and deploy and evaluate it in the fall.

The Contextual Inquiry and Design process, which is taught as a standard part of the HCI major, brings together the users (students and teachers), the developers (designers and programmers), and the evaluators. The team will visit the Homewood Montessori school in the early spring, observe how manipulatives are actually used by the students and teachers, elicit from the teachers and students those features of the intervention that would be the most educationally useful, and construct several candidate designs for prototyping.

The early designs would then be prototyped in software that supports extremely fast mock-ups and revisions (Macromind Director or Visual Basic), a skill the HCI students are also required to master. The software would then be put through a series of prototype-test-revise iterations, a stage which is crucial to good educational software, and an approximation of the final design would be finished by May, 1998.

In the summer of 1998, we will construct the web-site to house the software, implement the virtual manipulatives in Java (the programming language that allows interactive applications to be run from any standard web-browser, for example Netscape or Internet Explorer) and install the computers and network in the Homewood Montessori School.

In the fall of 1998, we will deploy the software in the Homewood Montessori School, evaluate it, and write up our results for presentation. Below is a schedule of work.

1. Do a contextual inquiry in Homewood Montessori School involving K-6th grade students and their teachers w.r.t. to virtual manipulatives and how they might best be augmented.
1. Complete an initial design for the manipulatives and for the web-site to house them.
1. Design a detailed evaluation for the software.
1. Build-test-revise prototypes.

1. Complete a re-design based on the evaluations of the prototype.
1. Build a web-site with Java applets that implement the final design.
1. Install computers, network, and server in the Homewood Montessori School.

1. Introduce the software into the Homewood Montessori School.
1. Train the Montessori teachers.
1. Evaluate the software in context.
1. Write up the results.
1. Disseminate the software

Dr. Richard Scheines, a professor of Philosophy at Carnegie Mellon will manage the project. Dr. Scheines has supervised the development of several large programs (Scheines, et al., 1994; Scheines & Sieg, 1994), one of which is an award winning educational tutor for teaching proof construction in formal logic (Scheines & Sieg, 1993).

Scheines will supervise the HCI students during the spring, summer, and fall. Ms. O’Brien, a 4th and 5th grade teacher at the Homewood Montessori School, will serve as the primary liason at the Montessori School for the manipulative designs. Beverly McKee, the librarian at Homewood Montessori School, who is trained in HTML and supervises the computing facilites at Homewood, will supervise the maintenance and updating of the web-site, and will aid in training new teachers in how to use the "virtual manipulatives" we will develop.