Empowering Young Mathematicians and Scientists

Increased access to microcomputers and the availability of sophisticated software tools enable children to learn math and science through the types experiences previously reserved for adult experts.

It’s been said that if you know the result of an experiment before you begin, it’s not an experiment, but a demonstration. This notion also applies to math. When you know the answer to the problem before you begin or have solved the same problem countless times before, you’re not thinking mathematically. You’re doing school math.

"For the most part, school math and science becomes the acquisition of facts that have been found by people who call themselves scientists." (Goldenberg, 1993)

Computers offer unprecedented opportunities for children to learn math and science through the active process of becoming a scientist or thinking mathematically. In the hands of an imaginative teacher, the computer becomes a powerful object to think with. The computer mediates a conversation with the individual user - providing feedback in the form of errors, surprises or new questions to ponder. With sufficient access, constructive software and supportive adults, the computer gives students the confidence that they can solve the problem at-hand, even if they don’t yet know the path to that solution. In other words, kids view themselves as scientists and mathematicians.

Computers can help learners concretize previously abstract concepts, visualize complex relationships, collect large quantities of data and check hypotheses quickly and easily. Sophisticated habits of mind develop in children who possess the fluency necessary to build computational models, debug their thinking and express their new understanding.

Perhaps no subject of study bears as little resemblance to the discipline it intends to teach as mathematics education. Most mathematicians would be horrified by how many pieces of educational software confuse the drill of isolated techniques with mathematical understanding. The incongruity between pedagogy, content and purposeful application occurs at a time when mathematics is changing rapidly. Mathematicians and scientists are alert to the blurring boundaries between different branches of mathematics and other disciplines, new problem solving approaches and the importance of mathematics in the social and behavioral sciences. The increasing demands of the behavioral and social sciences for reliable quantitative measurement and analysis of new types of problems not only relies on mathematics, but influences its development. Curriculum and pedagogy must keep pace with this evolution.

...most educational software powerfully reinforces the poorest sides of pre-computer education while losing the opportunity to powerfully strengthen the best sides. (Papert, 1996)

Much has been written about the societal demands for a mathematically literate population. We live in a world awash in data. Good citizenship is dependent on an ability to process often confusing and conflicting information. Economic, political and social trends require students to have a much deeper understanding and appreciation for mathematical thinking now more than ever before. The pace of technological innovation spurs the rapid evolution of mathematics.

The NCTM Standards state that fifty percent of all mathematics has been invented since World War II. (National Council of Teachers of Mathematics, 1989) Few if any of these branches of mathematical inquiry have found a home in the K-12 curriculum. Topics such as number theory, chaos, topology, cellular automata and fractal geometry may appeal to students unsuccessful in traditional math classes. These new areas of mathematics tend to be more contextual, visual, playful, experimental and fascinating than the traditional emphasis on paper and pencil-based algebra and geometry. Technology provides an opportunity for more children to view mathematics as a powerful part of their own learning and to embrace the process of mathematical inquiry. Even young children may learn powerful concepts of number, space, probability and geometry through the use of MicroWorlds, Turtle Math (http://www.microworlds.com) and other versions of Logo.

A dignified mathematics for children cannot be something we permit ourselves to inflict on children, like unpleasant medicine, although we see no reason to take it ourselves. (Papert, 1980)

Students and teachers can and should explore these new mathematical domains. Prior to the availability of personal computing it was tedious or impossible for children to explore complex mathematical phenomena or make sense of large collections of data. Paul Goldenberg, Senior Scientist at the Education Development Center, suggests that it is difficult to test out ideas unless one has a slave stupid enough not to help. (Goldenberg, 1993) The computer is a splendid lab assistant, yet the student still must do all of the thinking. Open-ended software makes it possible to manage large bodies of data by running tedious experimental trials millions of times if necessary, collecting data and displaying it in numerical or graphical form. Small changes may be made to an experiment without having to start from scratch.

Software such as The Geometer’s Sketchpad (http://www.keypress.com/) and NuCalc (http://www.nucalc.com) provide learners with open-ended tools for visualizing an enormous range of mathematical problems. Teachers may use the same software in dynamic presentations in which hypotheses may be tested and variables changed without spending half the period writing and erasing the chalkboard. SureMath (http://www2.hawaii.edu/suremath/) even helps students solve multi-step word problems. Business applications like ClarisWorks and Microsoft Office may be used to collect data, experiment with numerical conjectures and present results on paper, the screen or World Wide Web.

Mathematical thinking and the scientific method become commonplace when children have adequate access to computers and software like the programs mentioned above. This type of learning is interdisciplinary in nature. When a student builds their own virtual pet, collects acid rain data, creates a program to solve linear equations after a Mozart sonata is played, constructs a LEGO robot to solve a problem in Sub-Saharan Africa or analyzes the impact of gerrymandering on representative democracy they have blurred the artificial boundaries between subject areas and made important intellectual connections. The work of students is of real consequence and often of a higher standard than required by the curriculum. More importantly, the student is free to acquire and exhibit this new knowledge in their own voice. Problem solving is embedded in a personally meaningful context.

Simulations, commercially prepared or student-designed, allow the learner to perform experiments that would be either too expensive, dangerous, costly or time consuming if performed in other ways. Interactive Physics by Knowledge Revolution (http://www.krev.com) is a sophisticated simulation and modeling environment. Widget Workshop (http://www.maxis.com) lets kids construct imaginative inventions complete with logic gates, input/output devices, switches and whimsy. Ever wonder about the cause of traffic jams or why birds flock? StarLogo (http://starlogo.www.media.mit.edu/people/starlogo/) is an incredibly powerful environment for exploring artificial life, emergence and decentralized thinking. Best of all, it’s free.

Part of the lure, mystery and fun of science is that it is messy. Science lives in beakers, wires, petri dishes and machines. Education is just beginning to embrace ways in which computers can enhance scientific inquiry outside of the computer. Thousands of children have "done real science" by participating in the National Geographic Kid’s Network. Kids all over the world collect data and conduct local experiments and then share their information with fellow scientists and adult experts who may be engaged in important research. The Concord Consortium’s Hazenet (http://www.concord.org/haze/) project asks children to build a specialized instrument and collect data about particulates in the atmosphere. The Internet provides children with a vehicle for collaboration, data dissemination, and interaction with experts and publishing. Learners of all ages can share their experimental results, simulations and conclusions with others online and make significant contributions to the world of ideas.

Engineering is an extremely tactile branch of science, yet overlooked traditionally by school. LEGO’s Control Lab (http://www.lego.com/dacta/) invites kids to build machines and conduct physical experiments with a construction kit comprised of LEGO, a computer interface, motors, lights and sensors. The Personal Science Laboratory (http://www.teamlabs.com) is a collection of robust microcomputer-based lab probes designed to collect experimental data in chemistry, biology, physics, life and earth science. The probes measure temperature, light, pH, and motion. Data collected by the sensors is communicated to Excel for analysis and interpretation.

At a recent conference, Dr. Robert Tinker, Director of the Concord Consortium and one of the pioneers in micro-based lab science discussed the need for smart probes. Such probes would eliminate the need for a computer and interface box because advances in computer technology makes it possible to have the computing power in the probe itself. Students can take the probe out in the field to conduct experiments beyond the walls of the laboratory. Such probes are happy to sit outside in the rain for several weeks. Tinker went on to demonstrate a prototype of a motion sensor and computer housed in a lantern flashlight. The flashlight/probe can be carried wherever it is needed and data later uploaded to a Palm Pilot or other low-cost computer for analysis.

There are numerous web sites full of collaborative science and math projects. Such sites offer project ideas, opportunities for teacher collaboration, software tools, reference materials or online experts. The Concord Consortium (http://www.concord.org) and TERC (http://www.terc.edu) offer web sites full of collaborative projects, teacher development opportunities and research reports for progressive educators interested in math/science education. The Math Forum (http://forum.swarthmore.edu) offers an amazing assortment of services, projects and materials for students and teachers. A list of books recommended for teachers interested in constructionist approaches to learning math and science is available at http://www.stager.org/books.html.