MATHS REVISION PAGE

I have just retired from the University of Portsmouth where in my in final few years I was tasked with teaching Foundation Maths to students from a range of backgrounds. The standard fell somewhere between GCSE and A level Maths. I might do some tutoring in the future, but not this year as I don't know the syllabus well enough to provide the level of professionalism I would want to. 

This is just a site to help parents on Hayling with some additional Maths help for their children. It is not meant to take the place of attending lessons nor of on-to-one tutors if you are looking to pay for those. Instead these are, I hope, a helpful and cheap way of encouraging children to understand Maths. I am happy to add to the site if I spot helpful videos in the future.

A good site for general revision is the Khan Academy. This provides videos for different parts of a maths course and is aimed, I think, at the American market. I seem to be able to view the videos without paying, but if this becomes a problem then a lot of their videos can be accessed by Youtube. Use the search term 'Khan academy' and then any maths topic that you want to look up. The Khan Academy also support an interesting video - Everything you need to pass GCSE Maths Exam. Just type in this as search term in Youtube and it should take you to a 2 hour video!

Another potential group of videos is Teaching GCSE Maths. There are meant to be over 500 short videos, but not sure they cover all the Maths course personally. They still provide a useful set of short video introductions for some topics. 

Pearson Edexcel also provide free videos that cover the maths course, although these videos are longer than some others.  

In addition to these courses it might also be useful to look up online calculators for formula. When  running the Foundation course the one thing that really surprised me being old, was how many online calculators for formula there were that provided workings for students. This means that they can find the answer and be provided with workings out so they can see how to do it - hopefully meaning that they won't just look at the answers and write them down or is that just me being overly naïve! One thing to watch out for with these sites, however, is that there may be a limit to the number of 'free' gos you can have on some sites before a charging page pops up. The ones below are just those I have picked out from a brief scan of the web - there will be others and they may be better! 

BIDMAS/BODMAS

 Algebra

Logs/Exponentials and calculator

Differentiation 

Integration

Geometry

Hope the above helps.

Please get in touch if you want more added, although it may a take a while for me to get around to it. 

My email is robert.inkpen@port.ac.uk 

Hazardous Events and the Haddon Matrix

Looking at hazards in different ways, through different conceptual frameworks is always useful as it tends to make you think about things, however slightly, in a different way. A framework often used in injury prevention, in road accident research and public health is the Haddon Matrix. This was devised by William Haddon back in the 1970s for use in road traffic accidents. The basic matrix is divided into 12 cells. The rows are defined by the temporal aspect of the event; pre, during and post, whilst the columns are defined as ‘host’ (you could rethink this as ‘the individual’), ‘equipment’ and two for environment; one for ‘physical’, one for ‘social’. The idea is to fill in each of the cells with key aspects that will influence or did the hazardous event. Effectively you are playing out different scenarios and filling in the cells depending on what factors you see as significant in each scenario. The framework forces you to deal systematically with the nature of the hazard and how it might play out in reality.

 

 
Figure 1 Haddon Matrix

 

The example provided is for road traffic accidents but the basis can be translated to other types of hazard. In the crash, the condition of the individual before the crash may be important for the reasons in the matrix. Each individual will have different characteristics that could be important and each can be included as appropriate. Similarly, different aspects of the equipment will be important depending on the nature of the crash and so these factors may not be clear until after the event. The environmental factors, seem to be more diffuse and provide a context, that for certain types of individual behaviour and certain equipment failings produce an environment conducive to a hazardous event. Importantly, despite the description and division of the event into these separate cells, the contents of each cell depends upon the relationships between the host, equipment and environment. For example, the social norms that permit DUI, would not be important had not the host not had a seatbelt and been drinking. The poorly designed fuel tanks only become significant when the drunk driver chase and so on.


 

Figure 2 Illustration of use of Haddon matrix

This framework does have its limitations. The recognition of important factors can be so wide ranging as to be useless in planning if extreme scenarios, with infinitesimal probabilities of occurring are considered. On the other hand, it may not be until the event happens that it becomes clear what factors are important. The matrix will probably be of most use when similar hazardous events are being considered, as similar events would be expected to have roughly similar important factors. The matrix can also be used to identify where particular factors are not relevant. In a pile-up on a foggy motorway, for example, the detailed life history of the individual in the second car in the crash may not have any significance to their survival, it is the general physical conditions that are of over-riding significance. Equipment factors, such as airbag installation, age of car, may have an impact however. In other words, the matrix might be useful to explore the topographies of different hazards or disaster; in exploring the nature or shape of the hazard and what factors dominate that landscape and which are incidental ‘bumps’ on the terrain (please excuse the landscape metaphor, but I am a physical geographer!)

The matrix framework helps to identify the factors that might be important at each stage; the Swiss cheese identifies if a particular trajectory of factors lines up to produce a disaster. The matrix helps identify the possibles, the Swiss cheese, whether these possibles are important in combination. In the case of the BP oil spill, for example, the Haddon matrix could be used to identify key pre, during and post disaster factors, such as the alleged failure in safety procedures and lack of disaster planning. The trajectory arrow of the Swiss cheese model can then be used to assess if this one failure affects the next layer, if one failure or factor then lines up with another to produce the cascade of errors that result in a disaster.