The clock project: gears as visual-tangible representations for mathematical concepts

As we have noticed from our own classroom experiences, children often find it difficult to identify the adequate operations learned in mathematics class when they are solving mechanical-operators problems in Technology class. We wanted to design a project that exploits the idea of a hands-on relationship between mathematics and technology to teach students the concept of 'transmission coefficient' in schools. Our purpose was to bridge mathematical knowledge and mechanical parts in technological devices. Our belief was that visual-tangible representations enhance human cognition by scaffolding the information process. We supplied a kit with rubber foam (Fomi) and balsa wood parts to construct an analogical clock. This included a series of gears to work with three different ratios. The project was conducted in 2007 and 2008, with 38 students ranging from 10 to 14 years of age. The students were from the 5th and 7th grades in two different schools. The project included six stages of both theory and hands-on work. In a final stage, the students were given a written test. All students were able to make workable systems of their design for a time-measuring device. This proved important for technological education. On the other hand, manipulating gears along with visual reasoning strategies allowed all students to achieve an understanding of operations with fractions. We think this is a major achievement in mathematical education.