For years, educators have been debating that use of technology in the classroom could radically change not just how we teach our children, but what we teach them, and when. The University of Tasmania in Australia set out to prove it. Because of their commitment to embracing the Digital Education Revolution, and to showcasing how big a transformation the use of computers can make in students’ learning, the University decided to take on the challenge of teaching integral calculus to 11-year-olds. While this age group is traditionally considered far too young for this topic, which is usually introduced at age 17 at the very earliest, the University wanted to see if computer software would make a difference in their learning. If students become comfortable with this complex topic at a young age, perhaps learning could become easier and more of them will gravitate to the scientific and technical fields as they get older.
The researchers used Maple as the software of choice for this project. They used Maple to teach fifth graders the Calculus curriculum used in the first year engineering program in Australian universities. The project team trained five classroom teachers who then worked with their students for two hours a week for six weeks. During this time, the students were introduced to a series of real-world problems and mathematical concepts, and learned how to solve these problems in Maple. Students used Maple to set up the solutions to word problems, calculate results, and graph functions.
Maple is well-known for the Clickable Math interface that focuses on the concept and not the software. While using traditional math notation, the user interface is natural, intuitive and very easy to use. The students become instantly productive and engaged. Maple’s ability to manipulate mathematical equations algebraically, perform calculus operations such as differentiation and integration, solve equations, and graph and visualize functions and solutions help remove the need for students to memorize dozens of different integration techniques and struggle with the mechanics of calculating definite integrals. Instead, they can focus on the higher level concepts and develop a deep understanding of integration and its applications.
One class was selected from each of five different schools in cities across Australia, for a total of over 100 students. These schools had average or lower-than-average socio-economic advantages and the students were not selected based on academic abilities. Emphasis was put on using examples and applications that students could relate to. For example, in one problem, students chose a curve to act as a boundary for a mural in their room, and then, with the help of Maple, calculated how much paint they would need.
At the end of the program, students wrote a test based on questions taken from first year university engineering exam papers. They used Maple to answer the questions and graph their results. Ninety seven out of the 108 students achieved a passing mark on this test. Thirty eight students scored over 80%, showing their skill at solving complex problems using computers.
“Using Maple made a huge difference to these students, and helped showcase the kind of radical changes we can bring about,” said Dr. Andrew Fluck, lead researcher of the project and Senior Lecturer in Information Technology. “Many students perceive calculus to be ‘too hard’, which can make them reluctant to even try it. And when they do try it, their attitude can actually interfere with their learning. But based on the comments these students made after the course was over, it is clear that Maple helped spark their interest in Calculus, and made them justifiably confident in their ability to handle it. Technology can be a great enabler even for students this young.”
It is clear that Maple helped spark their interest in Calculus, and made them justifiably confident in their ability to handle it.”
One of the 11-year-old students remarked how Maple had changed her perception: “Maple is wonderful to outwit Mum & Dad!” One of the girls’ fathers was amazed at the difference Maple made to his child’s learning. She said, “My dad's an architect, so I showed him Maple. He had a go with it. He said he wished he'd had it when he was studying!”
“Maple is so easy to use, its Clickable Math interface has features that make common mathematical operations as simple as pointing and clicking”, said Dr. Christopher Chin, a fellow researcher on the project and Senior Lecturer at the Australian Maritime College. “This also makes it a very easy-to-teach program. And young students effortlessly learn the fundamentals of mathematics at a very early age. Students should use the same tools that the industry is using, and this early introduction will help them in the long run.”
A paper that presented this project was awarded the prestigious ‘Best Paper’ award at the International Society for Information Technology & Teacher Education conference in Nashville. Pleased with their results, the researchers intend to conduct further studies in this area, including expanding their project to teach other advanced topics in a larger number of schools. With team members - Associate Professor Dev Ranmuthugala and Dr. Irene Penesis - the researchers have applied for a bigger grant from the Australian Research Council to expand the scope and reach of the project.
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