A Cross-Curricular Approach to the Teaching of Mathematics

A Cross-Curricular Approach to the Teaching of Mathematics:

Using Video as a tool to enhance Teaching and Learning

In order to promote STEM and develop techniques to enhance pupils’ understanding and teachers’ pedagogy, staff at TownleyGrammar School embarked on the above project with funding from NCETM.

This report documents the second phase in this project.

Principal Aims of the Project

• Engage pupils through cross-curricular work with other STEM subjects, using video as a tool to encourage the pupils to reflect on their problem solving strategies and interpretation and communication of the outcomes.
• Promote the use of video across the borough via an MLE room.
• Raise the profile and awareness of STEM subjects across the borough.

Background to the Project

• The school was awarded a second specialism in Mathematics and ICT from September 2009.Since the school already had a specialism in the Performing Arts, the concept of using making films to enhance teaching and learning was a natural yet untapped progression.
• Prior to being awarded the second specialism, the school was asked to lead the borough on developing pedagogy and resources for the new Mathematics curriculum. The Year 7 curriculum was altered from a 20-topic year to a 9-unit year, with three units each term. These units were designed to give pupils more opportunity to explore the ideas within them through project work, discussion, etc. The first few units, which will feature in the discussions below, were Triangles, Statistics, Economics, Equations, Health and Mobile Phones.

Flip Video Cameras

Staff in the Maths department have continued to make good use of the video cameras. Videos have now been made demonstrating how to perform transformations (e.g. rotations, reflections and enlargements) and these have so far been used as teaching aids with Year 11 pupils during their revision programme. Lower down the school some classes have also been encouraged to make their own training videos on the same topic.

We have also used the cameras to make training videos. The Maths department has sent a team to the Team Challenge competition for several years and won its regional heat in 2006 and 2010. Knowing how much the students at these events get out of them, we decided this year to run our own event for the whole of Year 8 (about 210 pupils). Naturally there were teething errors, particularly with the number of students involved, over fifty teams of four in one room! Whereas in the actual events each team brings a teacher so that there is the same number of facilitators as teams, we had to use students from Years 10 upwards during their Maths lessons. This meant training them. We chose to describe the event and what their roles were and what should be happening, but for many this was insufficient preparation and some teachers were not as familiar with the rules as they might have been. It is certainly far easier to understand the process when you can see it taking place in front of you. So we used our current winning team to help make short training videos of the rounds (Crossword, Head-to-Head, Relay Race) for competitors and facilitators alike.

From a cost point of view, we have purchased a set of rechargeable batteries and a charger. The initial outlay has been expensive but long term this should be a cost effective way of ensuring we can use the cameras more frequently.

Other departments have not been so quick to embrace the use of video cameras and that is where Phase Three (this term) should come in.

Year 7 Mobile Phones Project (Video Diary)

The implementation of the new Year 7 curriculum, although exciting for most staff and pupils, has not been without controversy. Some parents, particularly those with older children, have attacked the course for being too hard (in terms of trigonometry [a fair point], for letting pupils work in collaborative groups, for the research (‘shouldn’t that be the teacher’s job?’) and a host of other issues. Essentially it could be said that it’s just ‘not what they are used to’, either for their older children or their own facing-the-front answering thirty identical questions from a textbook. However, in light of these criticisms, the department has felt the need collectively to focus on examination topics, leaving the Mobile Phones project until later in the term. So this project has not yet taken place.

Collaborative Planning for Year 9 Project (Maths and Physics)

As part of Phase Two the Maths and Physics departments collaborated on a unit of work for Year 9. Year 9 had met travel graphs and speed, distance and time calculations briefly in Year 8 as well as an introduction to standard form. The project was a more practical applied version of this with the opportunity for pupils to perform research and give presentations.

The first lesson involved the pupils using a stopwatch and props to perform a race for which the distances and times were recorded. The distances varied from class to class. One class which worked outside on the field had markers at 0 metres and 15 metres with another marker halfway between them. The pupils had to hop from 0 m to 7.5 m, then perform ten star jumps on the spot, then walk to the 15 m marker using pigeon steps. Pupils raced in pairs so whichever pupil was faster thus far then waited for the other pupil to catch up. They then tied their legs together with a scarf and walked three-leggedly back to the start. Five timings were taken (hop, star jump, pigeon steps, tie legs, three-legged walk).

The second lesson required the pupils to compare cards with statements and distance time graphs (some statements could apply to more than one graph and some graphs had no applicable statements so the pupils had to write something suitable. Some pupils were then chosen to come up to the interactive whiteboard to explain their choice. For the second part they constructed distance-time graphs for their own races and calculated speeds for each leg of the race.

In the third lesson the pupils played a mathematical team game involving pupils going to school by different means of transport and using speed, distance and time calculations to work out what order they arrived in and who was late. This gave the pupils the chance to work together in a different environment from the first lesson. Pupils were not given any guidance on how to tackle the problem but most were able to figure out an appropriate strategy (in this case, tabulating the information and completing the gaps).

Meanwhile, the pupils were given two homeworks, the first to research numerical data about the planets (including orbits, length of a year on that planet, etc) and the second to invent a journey in space and produce a presentation upon it. Because the numbers involved were very large the pupils were required to use standard form (as featured in the next lesson).The journey had to be described in words and shown on a distance-time graph. For differentiation purposes, more able groups were encouraged to produce a speed-time graph with calculations for acceleration.

In the fourth lesson, pupils revised work covered on Standard Form in Year 8 (converting between numbers in standard form and ordinary form) and extended this to multiplying and dividing standard form numbers by each other and by ordinary numbers and addition and subtraction of standard form numbers. The worksheet used examples from Physics (e.g. masses of neutrons and electrons, radii of planets, etc).

Pupils presented to each other in the fifth lesson, using feedback sheets to comment on each other.

Feedback on Collaborative Planning for Year 9 Project (Maths and Physics)

Questions for Collaborative Feedback – collected by HoD and members of staff

• How did this unit of work differ from what they are used to in Maths? The unit was more practical and gave the pupils the opportunity to perform research. As a result the pupils found that it reflected the real world better. It also gave them the chance to see that Mathematics is not isolated and does relate to other subjects. Some said that it felt more like a project than a series of Maths lessons, particularly with the research and presentation aspects, and hence more like an activity they would expect to meet in ICT or a Humanities subject. However, the pupils found it difficult to find time to work on their presentation outside of class because they were from different forms.They liked the fact that they were able to actually run around and measure their own races rather than sitting in rows performing calculations and drawing travel graphs of other theoretical races. Some also commented that they liked using space to practise standard form. Often standard form can be used artificially (is there really any benefit in writing 300 as 3  102?) but by using space and information about planets the data lent itself to standard form.
• Which approach do they prefer and why? Most pupils preferred the approach because of the teamwork element – they enjoyed, in their words, ‘cooperating with other people’ – however, some felt that although the project was ‘more fun’ than their usual Mathematics lessons, they would probably have learnt more using standard classroom methods. Generally pupils felt that they would like to use the new approach occasionally with the standard approach most of the time. For some, it improved their understanding of graphs – these students tended to be able to draw graphs in Physics without any trouble but did not see the relation to graphs in Maths until a ‘scientific graph’ had been plotted in a Maths lesson!
• How could the unit have been better? Pupils felt that doing all the work in five lessons was a little rushed (possibly because homework also required collaboration which meant it took longer and they felt more overwhelmed). Certainly there was a lot of material to cover in the allotted time. Some pupils also felt that they had not received enough explanation. This would have differed from class to class so may or may not be true, although, for example, no guidance is supposed to be given for the mathematical game and pupils used to being spoonfed may well expect to be told how to start such an activity or given some examples and answers. They also raised the issue of being expected to draw a travel graph when they had not covered them for eight months (since the end of Year 8). Our pupils often lack the nous to think for themselves, look things up or do research so that is not a surprising issue for them to raise. One stated that she liked the ‘comfort of notes’ and that she felt she learnt more the normal way but she did at least enjoy doing something different. However, other pupils made the valid point that as a result of not being given ‘enough information’ they actually had the opportunity to think for themselves. Some pupils would have preferred not to have been made to present at the end but that is a confidence issue and we feel that our pupils need to try these types of activities.
• Did the link with Physics (e.g. planets, measuring an actual race) help them understand the science and/or the mathematics better? Most felt that they had a better understanding of both the Maths and the Physics as a result although many felt they had learnt a lot more about one than the other (about a 50/50 split as to which subject they had learnt more about). Bizarrely a (fortunately small) minority did not realise until they were asked the question during feedback that there had been a link between Maths and Physics!
• General points? Pupils generally pleased to have been given the opportunity to try something new and would like to do something similar again.

Feedback from NCETM portal

The first report was posted on 23rd February and no one replied. A second post on 29th March called ‘Making Videos in Maths’ gave a brief summary and almost pleaded for feedback. To date, two people have posted comments. Some information about the new Year 7 curriculum was also posted on 21st April to a forum topic called ‘Thematic or Project based KS3’.

STEM in the Year 7 curriculum

In addition to the Mobiles Phones unit which has been postponed, Year 7 have, since the last report, worked on a Health unit, an obvious link with Biology and PE. Pupils calculated BMI to practise substitution and metric/imperial conversions, analysed growth charts for height and weight leading into cumulative frequency, completed food diaries to analyse five a day and gave each other advice roleplaying as doctors and patients. Additionally, fitness data acquired during PE lessons was analysed using averages, quartiles and ranges.

Collaboration with other departments

Since the last post we have planned and delivered the project discussed previously with the Physics department. We are still intending to use video cameras in Science and Technology lessons in the next phase. However, the Technology Department has thus far been affected by staffing issues which have made it difficult to collaborate. We are hoping to have joint CPD with Science. Year 7 ICT lessons have included work on MovieMaker to enhance the pupil’s use of video.

The four STEM departments have continued to work together on the STEM Careers Fair mentioned in the previous report.Many companies are interested in using a hands-on approach rather than a lecture-based approach.

Plans for Phase Three

• CPD
• Prompting other STEM departments and borough to think about video through sharing of materials from Phases Two and Three
• STEM Careers Fair