Five Lessons: A Taste of the Future, Today

Interactive lessons allow students to learn more science and math, earlier and deeper.

By Robert Tinker

This issue of @Concord features five ready-to-use “Lessons” that illustrate how interactive models and tools can fit into real classrooms today. Each of these lessons addresses important content that can be found in all the standards and frameworks, and does it by giving students tools with which to explore and interact. The lessons illustrate how sophisticated math and science content can be taught earlier and how generative the resulting understanding can be.

There is a world of difference between watching how a graph is constructed and creating it yourself, watching pre-recorded sound waves and capturing your own, or hearing about evolution and setting up a situation in which animals will evolve.

Why these lessons?

For years, the Concord Consortium included a “Monday’s Lesson” feature in our @Concord newsletter, which was quite popular. Each was an innovative, classroom-ready learning activity that you could use on Monday morning. We responded last year to this popularity by including five lessons in our fall issue, one for each day of the school week. That was so well received, we are doing it again in this issue. But just writing about this great interactive software fails to convey its educational potential. You have to use it and try it with your students. To make this as easy as possible, we have included the software on a free CD. Just pop the CD into your Mac, Windows, or Linux computer and you and your students can run all the activities.

The lessons and CD are intended just to whet your appetite. Much more is available at our website. Best of all, it’s all free. U.S. taxpayers have already purchased these innovative computer-based learning activities by making it possible for us to win grants, so we invite you to download and use them.

Enhancing inquiry with probeware

Whenever possible, students should interact with part of the real world. That’s why we have been on a 25-year campaign to use probes and sensors with computers. What we first named “Microcomputer-Based Labs,” and now goes by the more modern “Probeware,” gives students unprecedented ability to explore the world, capture and analyze data, and understand fleeting effects.

Adoption of probeware has been slowed because it usually requires special equipment—probes or sensors and some interface electronics. The costs of these, the incompatibility of available systems, and the need to keep all student materials, documentation, software, and equipment together and functioning has proven to be too much trouble for many teachers. So we are developing probe-based learning activities that run on almost any computer, including handhelds, with almost any probe hardware.

Monday’s Lesson, “Investigating Sound,” is drawn from this project. Rather than requiring special hardware to detect sound, it uses the microphone now built into almost every computer. The software tool is streamlined, with few options, because it is designed for students as early as grade three. But it does not lack sophistication: a tremendous amount of computation is used to deduce the frequencies present in the sound. Students don’t need to understand the computations, just how to interpret the results.

Beyond calculation

Too much of mathematics is about learning facts and procedures. One of the reasons calculators are resisted in math education is that calculators already know all the calculation facts and procedures, so students don’t have to think about them. But what happens if the calculator fails?

Tuesday’s Lesson, “What Can You Do with a Broken Calculator?,” shows how a broken calculator can stimulate student thinking. This software simulates a calculator with inoperative buttons and even allows the user to determine which keys do not work. The challenge is to come up with the right answer in spite of these hindrances—to design a work-around.

For instance, one student might solve a multiplication problem without a multiply key by thinking of multiplication as repeated additions. Another student might guess the answer, check by dividing, and then use the result to make a more accurate guess. Both approaches require understanding, not mechanical application of rules. Like most real-world problems, there is more than one right answer. A perceptive teacher will encourage different solutions and stimulate a discussion about why one might be better than another.

Elementary calculus

Calculus is the gateway to much of mathematics and science, but its beauty and utility is often obscured with derivations and proofs. Calculus comes late in the curriculum, not because it is difficult to comprehend, but because its formal derivation is. Few students think calculus is easy and fun.

A better approach is to design a strand of materials that build the concepts early. Students who never take a calculus course will still be able to use calculus ideas, and those who go on to formal calculus will build on a deep conceptual understanding.

Wednesday’s Lesson, “The Trickster Squirrel,” uses the Qualitative Grapher, which introduces calculus concepts in early grades. Unlike most graphers, it does not have numeric values on its axes, so students have to focus on the shape of curves and their meaning.

Figure 2 shows a graph that is easily constructed and explored. A student has attempted to show how a basketball might bounce, and while the graph does capture some of the general features, it is also wrong in several respects. By running the model, the student would soon notice that the ball should not slow down before hitting and that it will not rise steadily as shown. These are calculus ideas that couple slope and speed as well as curvature and acceleration.

Population experiments

It is almost impossible to do hands-on experiments with genetic drift and evolution, because many generations and large populations are required. The underlying situation involves sophisticated statistics, so a mathematical approach cannot be used with beginning students. This is a perfect case for a computational model.

Thursday’s Lesson, “Budgie Populations,” gives students hands-on experience with genetics, using our Population Explorer. This model traces the fates of individuals that obey basic genetic rules and react to the environment. Students can create a large population that reproduces according to standard Mendelian genetics. Any individual in this population can be examined to see not only its outward characteristics, but its genes and the molecules in these genes. Genes can be made to mutate. Students can alter the environmental impact on the health and survival of individuals with certain characteristics and see what happens over many generations.

Of course, under the right conditions and over long times, the population can show genetic drift, speciation, and evolution. These are emergent phenomena that do not have to be programmed into the model; they are inherent in the assumptions of genetics, mutations, and environmental pressure. Experiments with such a system establish the basis of evolution.

Science from the atoms up

Perhaps one of the most important ideas of science is nowhere in any of the standards: atoms stick together because of inter-atomic forces. Without these forces, there would be no liquids or solids; there would be no hemoglobin, viruses, or fingernails; and cloth would fall apart. Many biological molecules are active only when two or more stick together with inter-atomic force. It is almost impossible to understand the world without reference to inter-atomic forces.

Conversely, an understanding of these forces provides a deep unification of physics, chemistry, biology, and engineering. Students who understand the atomic basis of phenomena can apply their understanding to topics that would otherwise seem unrelated. This helps students see the organizing power of an atomic viewpoint and reduces the amount of science students have to memorize.

Self-assembly is a potent idea that dominates biology and is being examined as a potential way to assemble nano-sized particles and machines. If you understand that disorder (or entropy) generally increases, then self-assembly seems impossible.

Friday’s Lesson, “Molecular Self-Assembly,” is one of almost 200 that use our Molecular Workbench software based on inter-atomic forces. Not only can students observe molecular self-assembly, they can create their own molecules and see how their properties determine the ability to self-assemble and the shape of the resulting structure. Thinking about how the forces they have previously encountered can be used to create a particular shape makes the process feasible and comprehensible.

The future

In the future, computer-based models and tools will transform education by expanding the world that can be experienced and learned. The five examples in this issue give a taste of what that future looks like. Interaction is the key. There is a world of difference between watching how a graph is constructed and creating it yourself, watching pre-recorded sound waves and capturing your own, or hearing about evolution and setting up a situation in which animals will evolve. The lessons in this issue engage students in interactions and explorations.

The lessons also make concepts accessible to much younger learners. No abstract mathematics is required in the science lessons, not even beginning algebra. The only mathematical skill required is graph interpretation, and that skill can be acquired early using the Qualitative Grapher, or even the Sound Grapher. This is the promise of technology: it will allow the creation of lessons that allow students to learn more science and mathematics, more deeply, and far sooner.

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Robert Tinker (bob@concord.org) is President of the Concord Consortium.