ASI Exchange 2002 in Vancouver, BC, Canada
... thanks JC
To stimulate and accelerate connections and opportunities
in BC's advanced technology community

PrimeClimb: Mounting the Mosaic of Collaborative Interactions

Jonathan Cohen, James Dai, Michael Wu, Troy Wu
UBC EGEMS Research



Click here for our brief work-in-progress report to the exhibit (PDF format).

About EGEMS

EGEMS, Electronic Games for Education in Mathematics and Science, is an interdisciplinary group from the University of British Columbia. Directed by Dr. Maria Klawe, EGEMS is interested in researching the role of educational computer games in the classroom environment in supporting and reinforcing mathematical concepts learned in class. A parallel focus is on the gender issues involved. EGEMS works with a multitude of people ranging from elementary school teachers, professors, and industrial companies.

What is PrimeClimb?

'PrimeClimb rules!'
Screenshot of PrimeClimb game

PrimeClimb, created by EGEMS, is an educational computer game that supports introductory classroom teachings of prime factorization for grade six and seven students. The game is played by two players, and success can be achieved through collaborative play. Pairs of students climb a treacherous mountain together with only their hint-giving tool and wits. The climbers are limited in the distance they may travel because a safety rope constrains their movement. This mountain is made up of numbers which climbers may climb on. When a climber climbs onto a number that has a shared common factor with his or her partner's number, that climber falls. The safety rope helps the fallen climber recover. This rope acts as a constraint at times and encourages climbers to work together. The magnifying glass is the hint-giving tool in the game. It can break down any number and display its factorisation in the PalmPilot.

Our Current Research

In the classroom, traditional learning involves students communicating to learn from one another. Shared hint-giving tools facilitate this in the educational computer environment. Such a tool have been integrated into PrimeClimb: the magnifying glass. It is capable of displaying factor breakdowns, which often prove useful in finding shared common factors between numbers. Several factors that define a "shared" tool are: resource limitation, visual effect permanence, distributed nature of feedback (do both players see the result, or just the tool user, or just the partner?), and their effects.

The Magnifying Glass tool presents factorization information visually as a factor tree. It is limited in number of uses, and the factor tree remains visible so long as the user does not apply the magnifying glass onto another number (in which the factor breakdown of the new number is displayed). Only the user of this tool will see its results.

... idling
The magnifying glass tool

Currently, we are interested in exploring whether or not limiting the number of shared hint-giving tools improves mathematical and collaborative learning through encouragement of individual accountability and communication between peers. One way of promoting accountability on the individual level is to allow both members of the team to use a tool and then place a team limit on the number of tool usages. For example, we may find that students teach one another through the use of their shared tools. In order to draw conclusions about patterns of behaviour and learning, we need to record and document both a student's game inputs and a student's off-screen interactions while playing PrimeClimb.

Research Setup

We are primarily interested in analyzing design factors of hint-giving tools that promote collaboration in educational systems. Toward this end we have conducted a study in a local elementary school with two versions of the game to analyze the pedagogical effects of limiting a valuable shared resource - the number of magnifying glasses given to the players per level. The two versions used are in shown in Table 1.

Tool AllocationSample Size
Version ALimited (6 per level)22 children
Version BRelatively unrestricted22 children
Table 1: Sample allocation

Methodology

The main contribution of this presentation is in the methodology of data capture and analysis of our study. The sessions of the study proceeded as follows: the pairs of children were first given a pre-questionnaire to access their mathematic factorization skills and general attitudes toward collaboration in math and computer games. They then played PrimeClimb together for 20 minutes and the session ended with a post-questionnaire that reassessed their math skills and attitudes. Each play session was computer-logged and video-recorded. In order to correlate the digital events in the computer log with social discussion and interactions, an absolute clock was displayed on the game screen at all times. Each video captured a player's upper body along with his or her game screen; thus two tapes were produced from each session (Figure 2, the image has been blurred to preserve the subject's identity).

Captured audio transcripts have proved successful in correlating digital events to facilitate design analysis in ethnography and math education research. We hope to use our captured video data to correlate the social interactions with the PrimeClimb game events. By plotting both sets of events on the same absolute timeline (which is made easier through the displayed absolute clock on the bottom left corner of Figure 2), correlations between the digital and social worlds can be analyzed. The mixed video data capture the sessions more completely than audio transcripts and will allow us to supplement the social discussion with physical interactions, such as the exchange of glances or gesture encouragement.

To record the former, game play logs generated by the application can be used. For the latter, we can video tape the playing sessions of a student. This can be done by recording (with the use of two cameras): what is happening on the computer screen, and what physical actions are being performed. Note that these video feeds should ultimately be synchronized to make annotations easier. It is important to recognize that we must overcome some underlying challenges of documenting social interactions. For example, when annotating video, what criteria constitute a "student explanation" or a "hand gesture"?

...
Synchronizing the game screen with social interations


Brief Discussion

After a brief glance at the collected data, we have seen that in the version of the game that restricts the number of uses allowed for the hint-giving tool, the tool played a much larger part in the discussion between the players in their strategizing to beat the levels. For example, in this version of the game the players reminded each other of the presence of the tool and the remaining number of tool uses much more frequently than the version with much less restrictive numbers of tool allocation.

It is also worth noting that different categories of social interactions of children playing PrimeClimb are becoming increasingly clear. As in past research from mathematics education, the categorization of peer-to-peer discussion in a mathematical context must take place first before analyses of pedagogical values of those categories can be carried out. A few possible emerging patterns of interaction include: a player explaining to the other player why a move is not allowed using mathematical language, a player explaining the reason for an unsuccessful move using mathematical knowledge, and a player carefully strategizing and logically planning a series of moves. An example of the latter is when a player states that she is on a prime number and encourages her partner to move as high as possible (this is an easy strategy but could prove faulty as multiples of prime numbers share common factors). We hope to apply this categorization and consequent analysis of peer-to-peer discussion about math to our computer supported collaborative environment.

Future and Beyond

We have also noted that all the children had very little difficulty grasping the interface to the game - a result of multiple prototype sessions that have shaped the game interface. This means PrimeClimb can act as a stable foundation upon which other research questions about collaboration can be launched. For example, by changing the mountain of numbers to a mountain of different geometric shapes, we can analyze how younger children interact in a collaborative pattern recognition setting.