Developing Teacher Competencies Through Videos for Facilitation of Mathematical Modelling in Singapore Primary Schools

Abstract

Mathematical modelling tasks which are situated in real-world contexts encourage students to draw connections between school-based mathematics and the real world, enhancing their engagement in learning. Such tasks often require varied interpretations of the real-world problem context resulting in multiple pathways of solutions. Although mathematical modelling has been introduced in the Singapore mathematics curriculum since 2007, its incorporation in schools has been limited. One reason for this could be that teachers are challenged by how best to facilitate for rich student mathematisation processes during such tasks. This chapter reports how a multitiered teaching experiment using design research methodology was conducted to build teachers’ capacity in designing, facilitating, and evaluating student mathematisation during mathematical modelling tasks with an intact class of Primary 5 students (aged 10–11). The use of videos was critical because grounded images helped capture the dynamics and complexity of authentic classroom interactions. This chapter highlights how video recordings of teacher-student interactions during a modelling task were harnessed during design methodology cycles, particularly during the retrospective analysis phase, to activate critical moments of learning for the teacher towards developing her competencies in facilitating students’ mathematisation processes.

Appendix

Determining the Most Efficient Bus Route

Ms. Chang recently moved to Block 297C Punggol Road. She is going to start teaching at Punggol Primary School next week and needs to know how to travel to the school. However, the MRT is always too crowded for her to take, and it also requires her to take a feeder bus which results in inconvenience. Ms. Chang realises that there are three bus services that ply different routes to her school. Help her to find the most efficient route to travel by bus from her home to the school. The location of her home is marked in the map. Currently, the three bus services that are available for Ms. Chang to choose are Service 124, Service 62, and Service 89. The routes for Service 124, Service 62, and Service 89 are marked as blue, yellow, and pink lines, respectively, on the map. The bus stops along each bus route are marked with stickers with corresponding colours.

Your task is to give Ms. Chang a proposal consisting of the following:

• 1. How your group determines what is meant by the “most efficient” bus route

• 2. Assumptions about the problem your group made in order to help Ms. Chang

• 3. The mathematics used to decide which route is the most efficient

• 4. How your group justifies that the selected route is the most efficient

• 5. The final recommended route for Ms. Chang

For us to better understand your work, you can attach the following to your proposal:

• (a) A map containing the chosen bus route

• (b) The information you found useful for this task

Bus Fares

Distance range	Bus fare (cash)
First 1 km	$1.10
Up to every 0.7 km increase	30 cents increase

Note: The student groups were given a map in which the three different routes for selection were marked using pink, blue, and yellow colours. Bus stops were indicated along the routes using coloured stickers. In Singapore, bus fares are calculated according to the distance travelled.