Skill Development

The final part of this chapter concentrates on the skills that the children have developed over the course of video conferences. As was stated at the beginning of this chapter, it is the micro-strategies associated with skill development that are being considered here and the best place to begin is to discuss the skills that the children have developed throughout their involvement in this study. It should also be made clear here that this discussion about the development of skills encapsulates my observations and as such are from my perspective.

The skills being referred to here can be broken down into two distinct areas. The first is mathematical skills and concepts, for example mental arithmetic, properties of shape and the use of logic. The second is interpersonal skills, for example communication, leadership and team working. There will also be some discussion about the children’s use of mathematical language and, in particular, consideration will be given to how this has developed over time.

I will first consider the mathematical terminology that was used by the children when they were presenting their solutions to the camera or asking questions through the technology. There may be many interpretations of what is meant by ‘mathematical terminology’, but in the context of this study this broadly refers to words that the children would not normally use in a non-mathematical context. For example, words such as factor, prime, perimeter, quotient, conjecture and Cartesian

would be considered mathematical terminology, but numbers were not. A complete list of the mathematical terminology used by the children is included in appendix two.

In some instances, I provided the children with a definition during the instruction phase of a mathematical task. On other occasions, I asked the children to tell me the definition of a particular word. The video data shows that if a word was new to the children or if previous activities had

already known the word and there was plenty of time left, then I asked the children for a definition. The children often made use of any new mathematical words when presenting their solutions and they did sometimes ask about the meaning of words that had not been explained. A good example of this was the wordquotient,which appeared in video conference 11. Although I defined the word quotient in the first video conference that day, the children still asked me to explain it as they were not sure of the meaning. In the second video conference that day, I provided a slightly more detailed definition to the children and this was included as part of the instruction phase. This time the children understood immediately what the word meant and no further clarification was needed.

Video Conference 11a – “Thequotientis the answer you get when you divide two numbers.” Video Conference 11b – “Just like the productis the answer you get when you multiply two

numbers together, the quotient is the answer you get when you divide two numbers.”

In order to describe and analyse the mathematical terminology being used by the children, a tally chart was constructed from observing the video data. The chart recorded any mathematical words that the children used and the results are presented below in the form of a bar chart. Initially, there was some discussion about whether or not the number of schools participating in the video conference should be taken into consideration, since it could be argued that more endpoints might use more mathematical terminology. However, the video data showed this was not the case as when there were fewer schools participating, the children had more time to participate.

Fig. 23 – Bar chart of the frequency of mathematical terminology used per video conference

On the bar chart above, bars that are the same colour are based on the same lesson plan delivered to the two separate groups of children. It can be seen from the chart that the frequency of mathematical terminology being used might be related to the topic of the video conference, since similar conferences had similar frequencies. This is, of course, purely speculative and further research would be required to establish whether any such connection exists. However, given that this data suggests that there may be a link, I will take a moment to briefly look at this in more detail. In particular, I would like to order the sessions in a list from those with a high frequency of mathematical terminology being used by the children down to those with a low frequency. To achieve this I will take the mean average frequency of any sessions that were repeated (i.e. the same colour on the bar chart) and then list them in order in the table below.

Table 3 – Mean average frequency of mathematical terminology used per video conference

Whilst there may be a link between the frequency of mathematical terminology being used by the children and the focus of the session, the two video conferences related to strategy games would be evidence to the contrary. The first pair of video conferences on strategy games had a mean average frequency that was almost three times as large as the second pair of video conferences on strategy games. The table and the graph also show that there is no obvious increase or decrease in the frequency of mathematical language being used over time. As such, it would appear from looking at this data that such a connection does not exist, but as explained earlier, further research in this area would be necessary to draw any firm conclusions.

Another avenue for further research might be to establish whether there is any link between the mood of the teacher and the quality of learning experienced by the children. Looking in my diary reveals that on the day of video conference eight it was Comic Relief and the children were dressed up in their own clothes and wearing red noses. There were some children off-task, perhaps due to the excitement of the day, but overall they performed well in tackling the mathematics. There were also some technical minor issues with controlling the camera at Angelford School due to an apparent problem with batteries in the remote control. Video conference five had only Benefactors School during the first conference and all schools during the second conference. This was the first pair of video conferences that had been successfully recorded following the technical issues of video

Video Conference Mean Average

Frequency Topic of Video Conference

8 75 Squares and Rectangles

5 70.5 Factors and Multiples

6 42.5 Strategy Games

12 40 Problem Solving

11 36 Number Magic

7 31 Milk and Chess

13 14.5 Strategy Games

conferences one, two and three. At the end of the conferences, I wrote in my diary that I was “really pleased” and happy that both video conferences were “recorded successfully”. This could indeed suggest that my mood was better than usual during video conferences five and eight, both of which incidentally had the highest frequencies of mathematical terminology from the children.

Now let us consider the two pairs of video conferences with the lowest frequencies. Video conference ten was the first session after the Easter holidays. A number of changes to the regular structure of the video conferences occurred during this session. The theme tune was changed from

BBC Athleticsto The Crystal maze; Countdownwas replaced withWho wants to be a Millionaire; a request was made for the ICT technician to change the screen layout using the JVCS booking service. An indication of my mood on this day could be taken from my diary again about the probability of the much needed technical modifications occurring, “I don’t hold out much hope for any change”. Although the children did well in tackling the mathematics, it took them some time to get used to using the equipment again. One student commented that I was wearing a nice shirt. In both conferences on this day, I ran out of time and was not able to deliver the full lesson as planned. In video conference 13, my diary shows that I am unhappy about two specific issues. The first was that the screen layout changed unexpectedly and I was not happy with how it looked. The second was that I had facilitated a swap between Angelford School and Benefactors School to help with timetabling issues at Angelford School. This was difficult to arrange and I had to call in a favour at Benefactors School to make this possible. As such, I was not particularly pleased when Angelford School failed to join the video conference. In my diary I wrote, “I was slightly annoyed that I had arranged for Angelford to swap with Benefactors”.

Again, there is not enough data or evidence in the scope of this study to make any claims. Furthermore, the data was not coded to consider the mood of the teacher and this would be crucial

a link between the mood of the teacher and the learning experience that the children have, this claim would only be strengthened or weakened through further research.

The mathematical concepts that the children were working with during the video conferences were wide ranging. Sometimes, these concepts were introduced by me for the children to think about and other times, the concepts came about by me correcting misconceptions that the children had. For example, there were two misconceptions during video conference five; all odd numbers only have two factors; all numbers that are consecutive to multiples of six are prime. When such misconceptions occurred, my usual method for dealing with them was to give the children a counter- example to consider. This was a useful approach, since it backed up the concept that only one counter-example is needed to show that a statement is false, whilst proof is required to show that a statement is true. This concept of proof and counter-examples was then formally used in video conference 11 when the children had five mathematical statements and had to decide whether these were true or false.

Sometimes, the mathematical concepts formed a fundamental part of the problem. For example, one of the activities in video conference eight asked the children to decide “Is a square a rectangle?”. One or two children had already grasped the idea that a square is a special case of a rectangle, with one child saying “a rectangle is a family of shapes and a square is a member of that family”. The majority of the children had not considered this before and it took them some time to grasp this concept. However, once they understood the concept, it was clear that some of them felt a sense of achievement. Other mathematical concepts covered within these video conferences are included in the list below, although this is not an exhaustive list.

the correct use of brackets in calculations

the difference between combinations and permutations maximisation of area using a fixed perimeter

properties of odd and even numbers logical thinking for developing strategy

the difference between rotation symmetry and reflection symmetry properties of prime numbers

the idea that problems can have multiple solutions

trial and improvement (although the children referred to this as trial and error)

In relation to the children’s mental arithmetic,Countdownis perhaps the best mechanism I have for considering whether this has improved or not. This shows that over time the children’s solutions generally contained fewer mistakes. However, even if it was possible to demonstrate an improvement in mental arithmetic using this data, it would be impossible to say whether this was a result of the mathematics they were using in the video conferences or a result of their natural progression as they move through school, prepare for their key stage two SATs and academically and personally mature.

5.4 Discussion

I would like to begin this discussion by reflecting on the cyclic model for video conferencing presented towards the beginning of this chapter and to consider how this compares to teachers providing guidance in the traditional classroom environment. In order to make this comparison, we must consider the features of a mathematical problem solving lesson. Such a lesson would normally involve children ‘specialising’ and ‘generalising’ (Mason, 1985, p109). That is, the children would

and they would then set about proving that it holds for a wider set of circumstances. Specialising and generalising is represented in the above model in that the children’s initial explanation of a solution was usually a specialised solution and then the extension task represented a move towards generalising their solution. The traditional classroom model also involves three stages of the children justifying their solutions; ‘convince yourself, convince a friend, convince an enemy’ (Mason, 1985 p48). This is again represented in the video conferencing model. The key difference, however, is that the initial two stages of convincing yourself and convincing a friend take place away from the camera, whilst the final stage of convincing an ‘enemy’ (i.e. Adam the teacher) takes place in front of the camera.

A second difference between the classroom model and the video conferencing model is the point at which teacher intervention takes place. In the classroom, teachers can more easily monitor the progress of the children and intervene at key moments, which they deem to be the most appropriate times to provide some guidance for the children. In the video conferencing environment, the teacher cannot monitor the progress of the children as easily and it is the children themselves who effectively decide when such teacher interventions take place.

The final difference between the two models is the pressure of time. In the classroom, it is fair to say that the pace of problem solving lessons is generally slow since it is about exploring new ideas and mathematical concepts. However, in this study, the pace was quicker in the video conferencing environment. That is, the activities changed more frequently and this was perhaps reflective of my inherent concerns about remotely maintaining control of the children’s behaviour.

Below is an extract from a video conference, which shows how the cyclic model can look in practice. Additional commentary is provided to make the links between the extract and the flowchart as clear as possible.

Extract from video conference 6 (traffic lights)

Fieldhaven: We think it’s best to go in the middle because all the opponent can do is change it to orange.

Adam: So you think that you should place a red counter in the middle? Fieldhaven: Yes.

Adam: Why do you say they can only change it into an orange? Fieldhaven: If they put it [a counter] anywhere else then you’ve won. Adam: Okay. Does that mean it’s better to go first or second? Fieldhaven: First.

Adam: Is there anything else that you’ve discovered?

Fieldhaven: If you start with red in the corner, and they swap to orange, you can swap to green.

Adam: So is this a winning strategy is it? Fieldhaven: Yes.

Adam: Have you tried it out? Fieldhaven: Yes.

Adam: And does it work? Fieldhaven: Yes.

Adam: Try the winning strategy you have developed on somebody else [in your school] to see if they can beat you.

Fieldhaven: Okay

Adam: Also think about whether it is easier to get three red, three orange or three green counters.

The children explain their solution... Closed questions are asked to clarify the solution... The teacher asks questions to help the children refine their current solution. These should ideally be open questions, but often they are closed as with the second question here. The teacher asks about further solutions

The cycle begins again with the children explaining another solution. The teacher asks questions to help the children refine their current solution. It should be noted here that the confirmation stage of the model has been omitted because it is clear that the children and the teacher are already in agreement about the interpretation of the solution being discussed.

The teacher sets an extension task for the children to work on and gives them more time to think about their existing solutions.

It should be noted here that ‘Fieldhaven’ represents the words of more than one of the children in this school and the flowchart was produced by considering all of the recorded video conferences. As such, individual interactions, such as this one, will not always follow the flowchart exactly.

The use of PowerPoint slides was a key factor in the delivery of the video conferences in this study, yet little thought was given to the impact that these slides would have on teaching and learning. Qvist (2007, p1) makes the point that PowerPoint slides are used in thousands of classrooms all over the world every day, which raises the question, “Do PowerPoint slides support learning?”. It is true that PowerPoint slides can help presenters to organise themselves (Qvist, 2007, p4), but it is argued by Tufte (2003, p4) that this can also bring with it much unnecessary “PowerPoint Phluff”, such as automatic hierarchy and inappropriate data presentation. In particular, Tufte disagrees with reading aloud from PowerPoint slides and suggests that they should only be used to display images / graphics that cannot be reproduced as printed handouts (Tufte, 2003, p24). He further argues that the core ideas of teaching are explanation, reasoning, finding things out, questioning, content and credible authority, which he claims are contrary to the “market-pitch approach” of PowerPoint (Tufte, 2003, p13). In response to Tufte’s criticisms, supporters of the software would argue that whilst it is often misused, it should be recognised that PowerPoint is a medium rather than a method and that it can be used effectively with effective instructional methods (Atkinson, 2004, p2). This allows us to draw an interesting analogy with video conferencing, which itself can be considered as either a medium or a method. Given that the answer to the earlier question about whether PowerPoint supports learning is arguably that it can if the correct teaching strategies are used, then it could further be argued that the same is true for video conferencing.

In this study, PowerPoint was used to display both textual and graphical information and made use of built in features such as sound effects and motion paths to emphasise key points. Some have argued that using graphics supported by brief text can enhance learning (Fox et. al., 2004, p6) and we know