New research from the University of Waikato shows using computers to explore maths concepts can help students understand ideas more quickly, and can also make maths more engaging.
Researcher and lecturer Nigel Calder studied a group of ten-year-olds in Tauranga schools, and another group of teachers in training, to see how using computers to investigate maths problems changed their perception of maths.
Calder monitored the way students learned as they worked with spreadsheets, graphs, charts and computer games.
Calder’s research showed students understood some concepts more easily, and they encountered some concepts they would not have normally without access to the computer, for example scientific notation, he says.
The research highlights the relationships between visual representations and abstract maths concepts, says Calder.
“Children can manage large amounts of data and get instantaneous feedback, enabling them to explore maths problems that would not be possible with pencil and paper only,” he says. “Computers make it so much easier to ask and answer ‘what if’ questions, therefore fostering mathematical thinking, so children can look at patterns, develop generalisations, and look at the relationship between different models of the same data.”
Computers also make it easier for students to create and change graph and table representations, he says.
In addition to enabling students to understand ideas more quickly, nearly all of the students said using computers made learning maths easier and more fun, says Calder.
He also found that when the children worked in pairs or small groups, they stimulated each others thinking and tested each others informal conjectures.
“This develops mathematical thinking, especially when they have to explain their ideas or justify what they did or their conclusions. Computers helped them achieve this. Discussing what was happening on screen really enhanced their thinking and stimulated their discussion and learning,” he says.
It was quieter, though, when the children had a monitor each, he adds.
“The tension created by differences in what the students expected to happen when they inputted something, and what visually happened, created rich mathematical learning opportunities as they debated and worked out why that difference occurred,” he says.
There were differences between the ten-year-olds and the teaching students group.
“The ten-year-olds were generally more confident and willing to experiment. They took risks and were more comfortable deleting stuff and starting again.”
Calder has been passionate about using computers in the teaching of mathematics for the past 20 years. He found that students were more interested when he used maths examples when he taught computer studies. “The linking of graphs so dynamically to numbers and symbolic forms also fascinated me,” he says.
Calder is part of a team from the Centre for Science and Technology Education Research, based at the University of Waikato, which is working with pupils at Tahatai Coast School in the Bay of Plenty.
Pupils at the school are using Mac computers to develop their own computer programs for solving and exploring mathematical ideas.