“In many schools today, the phrase “computer-aided instruction” means making the computer teach the child. One might say the computer is being used to program the child. In my vision, the child programs the computer and, in doing so, both acquires a sense of mastery over a piece of the most modern and powerful technology and establishes an intimate contact with some of the deepest ideas from science, for mathematics, and from the art of intellectual model building.” (Papert, 1980; p. 5)
“Info-Vis” is short for Information Visualization and refers to the concept that student learning is enhanced when they are given the opportunity to see or create visual representations of abstract concepts. The variety of online applications and simulations available that offer this capability are staggering. One could spend hours upon hours just previewing and practicing with different simulation sites. This lesson was an opportunity to look more closely at one of those sites and to interact with a few others through our classmates’ contributions. My partner and I chose NetLogo as our information visualisation activity.
NetLogo is a simulation software that was developed by Uri Wilensky and was designed to help students understand difficult concepts in science and social sciences by allowing them to manipulate variables at a micro level and see how this results in changes at a macro level (Stieff & Wilensky, 2003). NegLogo can be used to promote higher order thinking and to encourage students to construct their own understandings of how systems interact. Stieff and Wilensky (2003) found that students thinking shifted from relying on rote procedures to “more thorough attempts at conceptual reasoning and logical justification of answers” (p. 293).
The activity, Graphing Linear Functions and Quadratics with NetLogo, that my partner and I designed with NetLogo for high school math students involved students using the simulation Pursuit (Wilensky, 1998) to investigate linear functions. The students used the simulation to investigate what different types of functions looked like and then went into the code to change the slope and y-intercept. The activity was constructivist in nature and incorporated peer collaboration and class discussions. Although NetLogo gave a very visual representation of the interaction between slope and the direction of the line, I feel that using graphing calculators would have been simpler and easier for the students to navigate in, while being equally visual. A second activity that we developed involved using Pursuit as a mathematics 12 review of graphing functions. The nature of the Pursuit (Wilensky, 1998) program leant itself to this activity.
In general, I had difficulty relating NetLogo to authentic mathematics experiences. While it could work, as they activities we created suggest, there are other, simpler simulations that would work equally well. Graphing calculators, Illuminations, and Model It are just a few of the other options. With graphing calculators it is easier to alter variables and concentrate on what you are investigating without getting lost in the programming aspect. However, I thought that the simulations for science were very visual, interactive and allowed for more predictions and knowledge construction that the math activities.
Part of my lack of enthusiasm for the mathematical uses of NetLogo probably stems from the potential I see in the original LOGO program and how it was intended to be used. The original intent of LOGO was to use the affordances of the easy programming language for children to learn how to speak math – a type of mathematical immersion program. Seymour Papert, one of the original creators of LOGO, said that, “The idea of “talking mathematics” to a computer can be generalized to a view of learning mathematics in “Mathland”; that is to say, in a context which is to learning mathematics what living in France is to learning French.” (p. 6). He saw the use of LOGO to develop mathematical concepts as an opportunity for children to explore how mathematics works by teaching it to the computer; by making them think about what they are trying to get the computer to do, they are made to think about mathematics in a new way. For Papert, the heart of the exercise was the programming, not using simulations and just altering the programming here and there to see what effect it had. Truly understanding how to explain the math to the computer was what created the deeper learning and understanding of mathematics. “And in teaching the computer how to think, children embark on an exploration about how them themselves think … Thinking about thinking turns the child into an epistemologist, an experience not even shared by most adults.” (Papert, 1980; p. 19)
Information visualization is an important aspect of students’ education. Being able to picture abstract concepts can make them more concrete and understandable. This is particularly true for visual learners, but is important for all of us. In my classroom, it has reinforced and renewed my efforts to integrate applets and exploration with graphing calculators. Unfortunately, the issue availability of technology limits how often, if at all, I can put the online simulations into the hands of my students, but they can still be powerful tools for class exploration as a whole.
References:
Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books.
Stieff, M. & Wilensky, U. (2003). Connect chemistry – Incorporating interactive simulations into the chemistry classroom. Journal of Science Education and Technology, 12(3), 285-302.
Wilensky, U. (1998). NetLogo Pursuit model. http://ccl.northwestern.edu/netlogo/models/Pursuit. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.