People Maths: A Dramatic Approach – George Hardy

This project seeks to extend the boundaries of Kinaesthetic and Visual learning styles by involving students in explanations and explorations of Mathematics at Key Stage 3 and Key Stage 4 in active, creative and dramatic ways.

Northampton Academy was opened in 2006, specialising in both sport and business enterprise. I was appointed as an AST (Mathematics) at this time, having previously been a Head of Faculty and a Head of Year. The number of students on roll at the Academy is 1330, with 12% of students on roll receiving school meals. The Academy serves the Eastern District of Northampton and works closely with parents, industry and other schools.

The aim of this project is to stretch the limits of creativity within Mathematics lessons with a view to engaging students and deepening their learning experience by utilising drama, body maths and a host of outlandish props. The project was formalised a year ago as my main theme for Lead Practitioner work with the SSAT.

The motivation to experiment with kinaesthetic approaches came from my re-discovery of Bloomfield and Vertes’ ‘People Maths, Hidden Depths’. Their definition of People Mathematics is that of ‘using people to form the moving pieces of a mathematical activity, be it a puzzle, a sum, a diagram or a demonstration . . . with the emphasis heavily on discussion within the group taking part’ (Bloomfield and Vertes, 2005 p.7). These discussions within participant groups then leads to the discovery of the hidden mathematical depths to which the title refers.

This, of course, I found desirable as a goal, yet on a more superficial level I wanted to involve the students in a kinaesthetic way that was entertaining and therefore a visual stimulus to those students who elected to watch instead of participate. This way the kinaesthetic learners could engage and benefit from various levels of discussion, and the visual learners could observe and be brought into discussion by the teacher at appropriate times.

I selected one teaching group (Year 10, GCSE Higher Tier entry) to whom I issued diaries in which to record their experiences and thoughts after a ‘People Maths’ lesson. The majority of newly designed lessons were trialled with this group, making them a logical and convenient choice to be the research sample.

This diary-structured research case study was simple in design, running for 6 months with sample size 29. The diaries were open format, allowing diarists to record activities and events in their own words, as opposed to being highly structured in which all activities are pre-categorised (Brown and Dowling,1998 p.65). The advantage of using the free format diary is that there is greater opportunity to recode and analyse the collected data than with a more structured diary (Corti 1993, p3).

The lessons in which I employ this People Maths strategy can be broadly categorised under the following headings:

People / Body Maths (Demonstration)
In this category, students are used as props or dynamic parts of a topic introduction or explanation. For example, students form ‘living’ straight line graphs, with the floor as axes, and using individual whiteboards expand two brackets using the box method.

People / Body Maths (Team)
Here, students also role play, yet design the dramatic input and choreography themselves. Examples of this include manipulating equations with a chorus line stepping forward for each stage of the equation’s development, and writing and performing songs to aid memory retention.

Creative Display
With students in their established People Maths groups, a brief is issued to them to display a concept with an ‘anything goes’ attitude to the items used. For a recent 3-D exercise, students were required to construct a 3-D child’s toy and calculate its volume. Possible items to employ included carrots, parsnips, ice-cream cornets, traffic cones and hoops (from the PE department), beach balls and polystyrene spheres.

The diary-structured research yielded many positive comments which, in the context of as localised case study, can be considered as evidence of the project’s success. A selection of quotes follows:

‘I like watching rather than taking part’

‘The chairs I like because we were having fun’ (6-square problem, Sam Loyd’s 15 puzzle)

‘You could either get involved or the people could watch . . . it was helpful to different types of learners’ (1 metre cubed converted to cubic centimetres: demonstration with 12 one metre rulers)

I enjoyed doing these (anything goes) displays because it was creative. I learned how the circle theorems work by doing it instead of just reading it’

‘The bit I liked best was actually doing it and then after looking at the pictures and finding the F-angles and Z-angles. I think it will help me understand it more and it will stick in my memory. I think it’s good because it is something different and I like getting involved.’

‘The (measuring of the) staffroom (with composite shape floor-space) was fun because we got to measure the (volumes of the) rooms in the school, and we got to do room F3. It was great.’

‘I think that People Maths is beneficial for us because it makes people remember more.’

There was no available control group with which to compare learning progress. The majority of students are now on or above target grades; it is inconclusive statistically as to whether People Maths is an element contributing to this development. However the diary quotes from the case study make it difficult to dismiss People Maths as a factor in the group’s improvement.

During the past year I have presented this People Maths approach to a variety of teachers and educationalists. Evaluation forms have included the following feedback:

‘. . . great ideas and suggestions for active learning’

‘. . . inventive and useful for many topics’

‘I will try more practical ‘People Maths’ activities in my classroom and encourage others to do the same’.

Most things work when the experimental culture is established within the group. Some teaching groups take longer than others to adapt to this different environment in which students can be the props. One group took much coaxing to get three students to model angles in triangles, and retreated to their seats as soon as possible. A similar group were much more enthusiastic given that the initial experience used all students and, significantly, used them outside in the school yard. [Loci: line (of students) bisecting an angle, line (of students) equidistant from two points].

Not all areas of mathematics are readily adaptable to a People Maths approach. In some cases the ‘anything goes’ team displays and mind-maps were a useful alternative (e.g. fraction addition, circle theorems). In other situations the group was taught in a more traditional manner.

This project is being developed, with a view to extending the types of activity that can involve a stimulating combination of kinaesthetics and visuals. I am planning to focus on Auditory learning as a preferred style during my second year as a Lead Practitioner. Within the present categories of this study, I aim to cultivate an ever-expanding resource base, converting the mundane into the unusual for the purpose of engagement and deep learning in the classroom.

Bibliography

1 ‘Alan Bloomfield, A. and Vertes, R. (2005), People Maths, Hidden Depths’, ATM.

Brown, A.J. and Dowling, P.C. (1998), Doing Research / Reading Research: A Mode Of Interrogation For Education, London, Falmer Press.

Corti, L. (1993), Social Research Update, issue no. 2, http://www.soc.surrey.ac.uk/sru/SRU2.html