1.1 Conceptualization Towards the Development of a Mathematics-Based Teaching Aid
Many schools are gaining interest in maker-centred teaching and learning practices aimed at promoting student interest in STEM (Science, Technology, Engineering & Mathematics). While there have been articles highlighting interdisciplinary practices between Design & Technology (D&T), science and mathematics through design-and-make projects, very few articles have described how students can be guided to demonstrate their creative use of scientific principles through design-and-make projects that exhibit specific mathematical concepts. Guiding students to design and make such projects can help them deepen their understanding of mathematical concepts in a hands-on-minds-on-hearts-on manner, as well as providing them with an avenue to demonstrate their creativity by coming up with designs that utilize a variety of scientific principles.
In this regard, the author, who teaches science and D&T in a secondary school in Singapore, worked with a group of three students to develop a simple hand-held kit that demonstrates the mathematical concept of Pythagoras Theorem. The inspiration for this kit came about during a visit to the Singapore Science Centre where the author and his three students (who are in secondary two - equivalent to Grade 8 students, averaging 14 years of age) viewed an exhibit demonstrating Pythagoras Theorem as shown in Figure 1.
Figure 1. Pythagoras Theorem exhibit
The students commented that while they appreciate being able to see a visual proof of the theorem through the exhibit, they felt that it would have been better if their mathematics teacher had a portable version of the exhibit as a teaching aid to introduce the concept (at the time of teaching) in the classroom. The visual scaffold could have helped them in grasping the concept. This led to the author and his three students to come up with an idea to conceptualise a smaller and portable version of the exhibit that can be used as a teaching aid for mathematics teachers to teach students the concept at the secondary two level. It seemed apt that the author and his three students reached out to mathematics teachers in the school to gather their views. Mathematics teachers welcomed this idea, which then led to a pilot study of the three students coming up with a prototype in the D&T workshop.
In the process of designing and making a hand-held prototype, the students communicated regularly with their mathematics teacher to gather ergonomics data, such as where the prototype would be used in a classroom, as well as anthropometry data, such as the average palm size of teachers who would be using the prototype. The prototype, shown in Figure 2, makes use of a 3cm-4cm-5cm Pythagorean triple combination (which formed the right-angled triangle) and tiny Styrofoam beads (found in a ‘bean bag’ doll) to demonstrate the concept. Apart from designing skills, students learnt plastic processing skills and took about three hours to develop the prototype.
Figure 2. The hand-held prototype developed by the three students
The three students presented the prototype to their mathematics teacher who was happy and satisfied with the design. This prototype, referred to as the Pythagoras Demo Kit, gained attention from the mathematics community in the school. Mathematics teachers thanked the students for developing a prototype that is valued in teaching and learning of mathematics.