Category Archives: 2 Prof. Knowledge & Understanding

Mathematical Health?

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One of my favourite lecture inputs from this module was surrounding the issue of mathematics in the healthcare field. I found this lecture to be very interesting as I had never given any thought to how mathematics plays an important role in other professions, after all we must be teaching mathematics for a reason, right?

Dr Ellie Hothersall described just how essential mathematics is to the healthcare profession. Its essential for calculating medicine dosages, recording and interpreting data such as blood pressure and heart rate. A solid knowledge of mathematically concepts and logical thinking is needed in order to interpret patients medical records as doctors and nurses need to assess what is needed for the next steps of care. When you continually think about what nurses and doctors have to do everyday it becomes very apparent that their jobs involve a lot a mathematical skills.

As a soon to be new mum myself, I was recently able to witness the mathematics involved in getting my first ultrasound scan. Firstly, the measurements of baby are taken and record, this information is used to assess if baby if developing at the correct rate. The Sonographer was then able to calculate how far along in my pregnancy I am to determine the due date. I then went to see the midwife, where she took my blood, a simply blood test involves measurement, volume and logical thinking. Although the tests did not involve any complicated mathematical calculations this visit I am sure that in the coming months I will encounter more and more mathematical skills and concepts that the healthcare practitioners looking after me will have to tackle. This module has certainly made me look deeper into just how essential mathematics is to the society.

I understand just how important the need for competence and confidence in mathematics is to the healthcare field, which in turn has made me question whether nurses and doctors feel happy and comfortable with the amount of mathematics involved in their job and whether they themselves feel that they have a “profound understanding of fundamental maths”. I feel like there is a huge need to ensure that all nurses, doctors and other healthcare professional are given the right amount of mathematical trainingand understanding as there job heavily relies on having the correct skills as it can be a question of life and death!20151203_102835561_iOS

Liping Ma

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By choosing the Discovery Mathematics elective I hope to gain a better understanding of what fundamental mathematics entails and further still how to develop my ideas on this to incorporate in to my practice.

I believe the fundamental aspects of mathematics are the basic concepts in which a learner needs to understand in order to progress to more complex mathematic problems and processes. These are used as the building blocks or the foundation in which all other understanding and learning can take place from. Liping Ma (2010) suggests that we need to develop a ‘profound understanding of fundamental mathematics’ in order to teach and promote effective mathematical learning. This suggests that you need to have a more coherent knowledge of the conceptual structures included in mathematics and how they are used for higher order thinking. According to Liping Ma (2010) there are four key elements that contribute to a persons profound understanding of fundamental mathematics, the four elements are:

Connectedness: ability to relate topics to one another so that you can build on prior knowledge to work through new processes and ideas.

Multiple Perspectives: ability to use a variety approaches to solve mathematical problems. the ability to see things in different ways and become flexible in your approach

Basic Ideas: ability to identify the basic mathematical ideas which are prominent throughout maths topics and use these ideas to inform future processes.

Longitudinal Coherence: what we learn from the start of our mathematical journey influences our current mathematical status regardless of how fragmented our previous knowledge may be.

In order to become a teacher with a profound understanding of fundamental mathematics, I need to ensure that I am able to interlink mathematically concepts and ideas together with other concepts and processes, this will also allow me to fully understand how the topics involved in mathematics interlink and are connected. I need to explore different methods of calculating sums, equations and problems this will allow me to model different solutions to my learners which will hopefully allow for their understanding to develop and progress easier, this will also allow my learners to gain a more flexible view on mathematical problems. I think it is crucial to ensure that basic ideas are always revisited to reinforce learning and to build a solid understanding of mathematics. I hope that my understanding of this elective will allow me to develop and create a positive mathematical classroom environment.

References:

Ma, L. (2010) Knowing and Teaching Elementary Mathematics. Abingdon, Oxon: Routledge

Instrumental Understanding V Relational Understanding?

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When it comes to thinking about how people may start to understand new ideas and concepts the best theorist to look at is Skemp. Skemp (1989) believed that there are two types of understanding when it comes to mathematics: Instrumental and Relational. Through this module and professional reading I have attempted to try and understand the two approaches.

Instrumental understanding is when you are able to use the mathematical rule or concept but do not really have the knowledge behind the concept/rule to apply it in other situations, the method is more a “habit” understanding whereas relational understanding is when you are able to use, apply and manipulate the rule or concept and you know why you use the particular method. Relational understanding allows people to have a more reflective attitude to learning and allows for more exploration to occur.

From this, I can see that relational understanding is a deeper, more complex understanding of instrumental understanding.  Although it is important to highlight that a person who lacks confidence in mathematics can benefit from having an instrumental understanding as it allows for immediate satisfaction and can boost self esteem, however it is equally important that as teachers you try to promote a more relational understanding as this will allow for a more concrete understanding of mathematics.

Mathematics in our lives.

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Before studying on the Discovery Mathematics module, I never really put any thought into just how much mathematics was in my everyday life!

From the moment I wake up to the moment I go to sleep I will have encountered mathematics several times throughout the day. Waking up, the first thing I do is check outside the window to see what the weather is like, okay so most of you are saying “Where is the maths there?” logical thinking falls under the category of mathematics. You assess the weather in order to dress appropriately. Making a cup of tea in order to function for the rest of the day involves mathematical concepts such as volume, measurements and temperature. Making sure there is enough water in the kettle to fill your gigantic mug, pouring just the right of milk for it to be the right temperature to drink straight away for the limited time on offer a you slept in!

Driving to University involves using logical thinking, direction, journey time and speed, all of these involve having mathematical skills in order to get to university on time. Another factor involved in driving is making sure you have enough fuel to get you from A – B. This involves knowing how many miles to the tank you get and knowing how far you need to travel! Mathematics is everywhere!!!!

Cooking tea or making a meal is full of mathematically ideas and concepts. Measuring the water out correctly for boiling pasta, knowing the volume needed in order for the pasta to cook perfectly. Cooking times for chicken, salmon etc … knowing the temperature to cook the food at. Timing each part of the meal in order for it all to come together on the plate at the same time and at the same temperature.

Going shopping is possibly one of the daily jobs most of us to and it is the one that is probably full of the most mathematically concepts. Who thought needing a bottle of shampoo could be so mathematically challenging. You want to make sure you are getting your moneys worth so you need to check the volume of shampoo you are getting and for what price. You need to check whether there are any deals on and check if the deal price is better than the standard price. How many washes will the shampoo cover? All these questions involve having the mathematically knowledge in order to save you money and this can apply to most products in a supermarket.

Lastly, going to bed is quite the maths challenge, you need to set your alarm the next day so you do not sleep in for university/work/life this involves know what time you need to leave to get to your destination on time, once you know that then you need to know how long it takes you to get ready in the morning and then once you know that, you need to work out how long it actually takes you to crawl out your bed in the morning, after all these factors have been accounted for you can then set your alarm for the correct time!!

Mathematics is really everywhere in our lives, there is no escaping it! Therefore it is vital that society understand its importance and value the place for it in our national curriculum. So many people, including myself before this unit and so unaware of how much mathematics they actually carry out on a daily basis, its amazing!

It’s the most wonderful time of the year!!!

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I absolutely love this time of year! Christmas has always been my very favourite time and surprisingly, my love of Christmas has only grown since I have become a little older! Yes of course Christmas is so exciting as a child and getting up on Christmas morning and running downstairs to see if Father Christmas has been is such a magical moment but nothing can beat driving home for Christmas to my mum and dads house to see my sisters, nieces, brother in laws and the rest of the motley crew! The appreciation of what Christmas is really about is much more apparent when you have become that much older, but mathematics is something I would never have linked with my beloved festive holiday!

When you think of hosting Christmas dinner, there is a whole host of mathematically concepts that spring out to me, maybe this is down to the sheer fact that ever since studying on the Discovering Mathematics elective my brain is processing in maths alone! Firstly, you need to know how many guests of coming to join in the festivities, once you know how many people are coming you then need to think of the table logistics!! Do you have enough room? Will Gran be on that wonky little table at the end?? How many crackers to we need? Knives, Forks and Spoons? Glasses – what will provide the most fluid? After the serious business or table planning has been sufficiently sorted then it is on the the quantity!!

Christmas Dinner List:

Turkey, Stuffing, Roast Potatoes, Carrots, Parsnips, SPROUTS!!! & Chestnuts, Pigs in Blankets, Red Cabbage and Apple, Cranberry Sauce, Bread Sauce, Gravy – so much to handle!

Dessert:

Christmas Pudding, Brandy Snaps and Ice Cream, Cheesecake and Trifle – you have to have a variation otherwise someone is missing out!

Drink:

Beer, Wine, Prosecco, Champagne, Sherry, Baileys and of course the soft drinks for the little ones!

Okay so you’ve rationed out the food to make sure everyone has their festive fill and made sure there is plenty over for the 7 pm Leftover Sandwich Special. It is now on to the main event, cooking the Christmas dinner, logical thinking needs to take place about how long certain foods need to be cooked according to size and weight, how long things take to defrost and when they need to be ready for, if you need to get the chestnuts peeled on Christmas Eve and when you will have to peel the spuds by, when Dad is heading home from the pub in order for the Turkey to be carved and the best stuffing and gravy to be created! and lastly if you have guests coming, you need the arrival times to fit in which the cooking of the food!!! It’s a tough job juggling with meat, veg and desserts! Making sure that when that gravy hits the plate the best Christmas dinner is produced with all products served at just the right temperatures! My mum and dad are amazing at getting this right every Christmas they deserve a medal!

So there you have it I have managed to link an understanding of mathematically concepts to the deliverance of Christmas dinner! I hope I’ve not made you too hungry but I do hope you have taken away the importance of understanding the basic ideas or mathematics!

Merry Christmas, hope you have a wonderful time!

 

Tesco for a day!

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In a recent lecture delivered to us by Richard Holme, we were introduced to the idea of logistics and demand planning. This is something that I have a little knowledge on by being a colleague of Tesco but it also opened my eyes to how much time and effort that is needed in order to stay afloat in the world of retail.

I work on the Beers, Wines and Spirits department in my local Tesco supermarket and I have recently started working on the back door which involved taking in the delivery lorries full of produce and goods. I have experienced the sheer volume of products that need to be ordered and delivered over the Christmas period in order for Tesco’s to provide the perfect Christmas that so many of it’s customers are wanting. Many things need to be taken into consideration when thinking of the journey food and products go on before they reach the shelves for the customer. Thought needs to go in to the shape and weight of the product, how far it has to travel before it gets to the depot, the sell by dates and out of code dates, what temperature the products needs to be kept at and just how much the shop is needing and lastly, the distance of the depot to store!!! This just highlights the amount of mathematical thinking that occurs when thinking about the logistics of food and product journeys!

Demand planning is where most of these thoughts turn into action! I have gained a new respect for all my stock control colleagues as they are the ones in charge of monitoring stock levels and making sure more products are due to come into store of the busy periods such as Christmas. It can be a very tough job trying to work out just how many turkeys are needed to feed the families of the local area!  Factors such as damages, waste and demand stock all play a part in affecting the outcome of the quantity of products being delivered. The amount of mathematically concepts that occur when determining what products to bring in and how many is huge. Estimation and probability, money and budgeting all come into consideration.

After having a go at being Tesco for a day, it is easy to state that there is a huge amount of mathematics that is involved and the people that work within the field of logistics and demand planning need a sound understanding of fundamental mathematics in order to be successful in the world of retail and sales.

Maths – Creative and Beautiful?

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Throughout the Discovering Mathematics module, there has been a lot of discussion between the creativity and beauty that mathematics can offer. Before this module I would not have given this much thought, I have never looked into the way in which buildings are created or the way in which an artist’s masterpiece is formed. I have always been in the mindset that people are creative and you either have the creative flare or not, I am now considering the fact that maybe people have been clever by using a mathematically concept to produce aesthetically pleasing objects.

Fibonacci is probably the first name that springs to mind when talking about mathematics holding some form of beauty and creativity.  It was Fibonacci that devised a set of numbers after studying the mating habits of rabbits!!!! These numbers have been used across the world for centuries to create aesthetically pleasing buildings, statues, artwork, logos and so much more. Not only this but mathematics can be found inbuilt in nature, the spiral of a pine cone or the amount of petals on a flower all follow the Fibonacci sequence.

The Golden ratio was devised by dividing the Fibonacci number by themselves in sequence – the answer is 1.618 – or PHI. By using this ratio, people are able to select appropriate proportions which allows people to produce attractive looking and appealing products, objects or artwork. In one or our recent inputs we were given the opportunity to measure the lengths of various different parts of our bodies and use the measurements to assess how aesthetically pleasing we appear according to the Golden Ratio. It’s safe to say I’m lucky to have found my Mr. Right already as my measurements would not have satisfied Mr Fibonacci!!!!

Image result for fibonacci sequence

By looking into the work of Fibonacci and the Golden Ratio it is clear to see that mathematics surrounds us and our daily lives, it has been instilled within nature for such a long time that it suggests to me that Mathematics may have been formed from studying nature all those years ago and mathematics has been used as a tool to understand the world we live in. I believe that so many of us walk around today totally oblivious to how much mathematics has contributed to our world. I wonder is mathematics such a huge part of our life that we subconsciously forget that we are using mathematically concepts on an everyday basis?

Mathematics – A mixed view.

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Throughout my school life I have always found mathematics enjoyable and interesting, I enjoy the challenge of maths, I like logical thinking and problem solving. I was quite confident in my abilities throughout my primary school years. In the infant classes I used Heinemann workbooks and really enjoyed working through the booklets and I always felt a sense of achievement when I moved up a level. When I progressed further up the school a lasting memory of mathematics was chanting times tables out as a class and having times table tests resulting in achieving bronze, silver and gold certificates. On leaving primary school I took my SATs exams, this was the first time that we were tested and assessed based on levels and my SATs scored determined where I was placed in my secondary school. I was placed in a low set for maths and this really knocked my confidence in the subject area, something that I was always so positive about turned into something that I had little interest in. I found myself being less challenged, I was missing my drive, the work just wasn’t engaging me. My teachers notice this and decided to move me to a higher set, I believe this action allowed my passion for mathematics to ignite again as I was being challenged in interesting ways, I didn’t always get the correct answers and I didn’t always understand the learning first time around but my teachers always came up with ways of simplifying the workings behind the answers. I left high school with an A grade GCSE in mathematics and I am so proud of how I achieved that grade. I believe that after experiencing both positive and negative experiences of mathematics myself allows me to create an environment within the classroom that will reduce maths anxiety for learners who may not share the same passion and enjoyment as I do.