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Understanding Fundamental Mathematics

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In the Discovering Mathematics model I was introduced to the idea of fundamental mathematics. My understanding of this was that it was the skills that we use within maths such as multiplication, division, addition and subtraction. However, after reading Liping Ma I have realised it is so much more than this.

According to Ma (2010) there are four main principles that teachers need to know to have a reached a profound understanding of mathematics Connectedness,. Connectedness is one of these and teachers should be able to make connections among mathematical concepts and procedures. This was something I had not thought about before and led to me realise that there are some mathematical procedures I can carry put but have no idea of the reason why. An example would be when dividing fractions I have been taught to flip the second fraction and then multiply the top numbers and multiply the bottom numbers. I decided to try source the reasons for this and if I am honest some books and web pages confused me further and I could to relate why this is not taught as it may confuse the procedure further. I came across an explanation which instantly made sense to me by Raymond Johnson. He starts with the problem:

beg

and explains that it is easier to explain when it is written as a compound fraction:

compounf
He says that that dividing by a fraction is difficult but dividing by one is easy. To turn a fraction into 1 you multiply it by its recirprocal. Which would be the fraction divided by its inverse. 1 is the only number that can be multiplied with without changing the value and therefore the original fraction should be multiplied by:
invers
Therefore,

end

by doing this the bottom fractions become 1 which do not make an impact and therefore this is why the original factor becomes multiplies by the inverse.

Ma (2010) states that multiple perspectives is also a principle that is require within a profound understanding of fundamental mathematics. this requires teacher to be able to provide explanations of approaches as this leads to the students having a flexible understanding of mathematics. Now knowing the reasons for why you divide fractions in this way I can connect this idea to other areas of mathematics such as equivalent fractions.  Through investigating this I am begging to understand Ma’s four principles and their importance.

 

Johnson, R (2011) http://blog.mathed.net/2011/07/pretty-short-explanation-of-invert-and.html

Demand Planning

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Demand planning is not something I knew anything about before learning about it in the Discovering Mathematics elective module, and if I am truly honest the thought of a three hour workshop on this topic did not exactly excite me. However, I was completely proved wrong and in fact the demand planning workshop has been my favourite by far!

Rose (undated) describes ‘Demand planning is a multi-step operational supply chain management (SCM) process used to create reliable forecasts.  Effective demand planning can guide users to improve the accuracy of revenue forecasts, align inventory levels with peaks and troughs in demand, and enhance profitability for a given channel or product’.

With this in mind we participated in a game which involved us ordering products whilst considering the demand for this due to the time or year or the selling price of the item.  For example it is less likely you are going to buy a Christmas selection box in April – unless you’re highly organised! Not only did the game involve us making simple calculations such us multiplying the number ordered by the price we then had to work out how many were sold using percentages. The profit margin on items also had to be considered as we were trying to make as much money as possible. Whilst working through the activity all purchases, stock, profit and loss was recorded on a printed spreadsheet. Working in pairs made this activity really exciting and I think for a split second I’d spent my share of £69,00! Throughout this activity I kept thinking if adults could be so absorbed by this activity imagine how engaged children would be.

In my future teaching I will definitely incorporate this task as it can be adapted to different ages. It provides opportunity to introduce business like language such as profit and loss, starting budget and mark up on products. I like the fact the activity included thinking of a company name as I feel children like to personalise and have ownership of their work. The activity can include other aspects of the curriculum as the children could produce formulas to include in the spreadsheets to work out calculations. Overall the activity is a way of showing how mathematics is used in the wider world whilst being a highly engaging and enjoyable experience.

 

 

Rose, M (undated) http://searchmanufacturingerp.techtarget.com/definition/demand-planning

Op Art – A Mathematical Art Lesson

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When I was on my first year placement I was faced with the challenge of choosing which curricular area I would like to teach for my first lesson. After a discussion with my class teacher we decided that I would deliver an art lesson as this is subject I have a personal interest in. However, I decided I would like to incorporate another curricular area to the lesson to cover interdisciplinary learning. This lead me to the work of Victor Vasarely and Op Art.

Op Art is an art form which is a mix between abstract art and optical illusions.

Vega – Victor Vasarely 1957 Acrylic on canvas 195x130cm http://www.op-art.co.uk/victor-vasar

 

 

 

 

 

 

Cassiopee II – Victor Vasarely 1958 Acrylic on canvas 195×130 http://www.op-art.co.uk/victor-vasarely/

Vega (1957) was the inspiration behind my lesson because it is striking and interesting in my opinion . I also felt it had the potential to allow me to include mathematics into my lesson due to the various shapes and sequential pattern. I took myself to Pinterest to research Vasarely further and discovered art lessons which were based upon recreating his work. I took some ideas from this and adapted this to meet the needs of my class. Whilst researching the lesson I came across a blog www.artfulartsyamy.com which was very helpful on explaining how to recreate the spheres and this set the foundation for my lesson.

I began the lesson with a Powerpoint about Vasarely and discussed the images with the class and asked them what they found interesting relating to shape, colour and composition. The art work was completed on squared paper to ensure all the background squares were of equal size. Various sized circles from the flat shapes in the classroom were made available and the children chose how many they would like to use and which sizes. The children were asked to place the circles on the paper, draw around them and then divide them into quarters. Next they were asked to draw the lines that would help transform them into sphere like shapes.

http://www.artfulartsyamy.com/2012/01/lesson-plan-op-art-spheres-easy-way.html

Once completed the children were asked to choose one or two colours and alternate these with each square and repeat this over the whole piece. These were the results…

 

IMG_3374 IMG_3377 IMG_3375

 

Overall I feel that this lesson was very successful and the mathematical elements made it more accessible for the children who did not feel that art was their strongest subject. Not only do the finished pieces look great the children were very proud of them as it took patience and effort to ensure the finished product had the magnified effect!