# This concludes…

Now that the Discovering Mathematics module has come to an end it has allowed me time to reflect on everything that has been presented in each lecture. There has been a range of guest speakers come in and take time to share their experiences and their observations specific to their own professions or vocations.  This has been hugely beneficial as it has really hit home the extent to which maths is used in the wider society outwith the education environment,This for many of us was our taste of maths in operation outwith our placement environment,

It has changed my whole mindset concerning why maths principals are resourceful and relevant to everyday life, It forced me to broaden my horizons the way I viewed maths and I could appreciate that there are  lots more functions available within maths that we can make use of outwith the obvious old favourites. One last thing we were asked to do by our lecturer was to bring in a favourite childhood board game and prepare some notes on the maths involved within this game. I chose to challenge myself and use the knowledge from this module to form the basis of my notes.

Ordinarily, I would have chosen something as simple as monopoly and chose the easy option of discussing the use of money involved. However, I decided to stick with my favourite childhood game and delve deeper with regards to the underlining fundamental mathematical principals involved, thus being ‘Guess Who’.

Aim of guess who is:

Each player starts the game with a board that includes cartoon images of 24 people and their first names with all the images standing up. Each player selects a card of their choice from a separate pile of cards containing the same 24 images. The object of the game is to be the first to determine which card one’s opponent has selected. Players alternate asking various yes or no questions to eliminate candidates, such as “Does this person wear glasses?” The player will then eliminate candidates by flipping those images down until all but one is left. Well-crafted questions allow players to eliminate one or more possible cards

The mathematical principals what I identified were:

• Data and analysis
• Probability and chance
• Process of elimination

Picking a game with no physical numbers involved was always going to be a challenge to pinpoint mathematical principals which apply. However, just by using the knowledge that I have gained through this module it has become apparent that maths goes so much deeper than numbers and figures. The principals above all relate to basic maths concepts that at school you learn alongside the use of numbers but by having the conceptual knowledge of using these fundamental maths procedures I can then apply them to different contexts in this case individuals on the board games features. This shows the power that mathematics can hold beyond the classroom if the correct pedagogy style is carried out. Which relates to Lipping Ma’s work that PUFM is essential in carrying out ‘teaching excellence’ which will provide learners with the ‘how and why’ of maths. Being able to solve a maths problem is not always the important task in hand within the classroom, learners will benefit much more if they can explain how they got to the answer and having the conceptual knowledge of why you are adopting that strategy to solve the problem in the first place. This will understandably cement a value towards the maths being taught and learnt in schools and children will be able to take this knowledge of fundamental mathematics into their adult life and more importantly be aware of when they need to utilise it in different contexts.

Lipping, M (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. New York and London: Routledge.

# “You’re hired”

I think I speak on behalf of most students when I express my fear when I was presented with my university timetable and it showed a three-hour maths lecture……

However, this mindset was quickly changed when I found out what the lecture entailed. We were required to take part in a business stimulation game, which would involve us working in partners to act as demand planners. This would relate to the theme of the lecture by looking at supply chains of businesses and carrying out demand planning with regards to our own business.

We were provided with a stock list presenting different prices and what we could get profit wise if we were to sell this stock in different quarters of the year. Each group started with the same budget and we had to pick no more than five items from the stock list for each quarter, We were then provided with figures by the lecturer of how our business performed in terms of how much stock we had sold. This then allowed us to make informed decisions about what stock we would like to order for the following quarter of the year and so forth until the business year came to an end. We could calculate the profit of each stock item after each year quarter to add to our original budget and by the end of the year the aim was to be the group with the most money in the budget, therefore have made the most profit.

If you had asked me at the start of this module, what maths is involved in this game? I would have simply answered addition, multiplication and subtraction.

However, having completed this game it has become very clear of the principals of maths involved go so much deeper. My partner and I were having to use data and analysis to predict what stock we would have to pre-order for the following months, we were having to use patterns and trends by looking at previous months’ performances and predicting the upcoming months that may have special occasions which could affect our stock sales for example valentine’s day had a major impact on the sale of champagne. We were having to think of shelf life of products so thinking about dates and time scales that the products would stay fresh for and judge if they were going to be cost efficient or not.

This lecture was eye-opening to myself and my partner, as I think it was to the whole module group, it highlighted the way maths concepts can interlink (Ma,1999) with one another and how basic maths concepts (Ma,1999) can be used in something so far removed from the four walls of the classroom. I think it was a simple enough idea to carry out with a future upper stage class which would highlight the resourcefulness of maths in the context of wider society. I believe that it would show the relevance of how we can take these concepts that we are learning within a school and how they can be adapted for future use which will promote engagement and benefit their development of mathematic principals as opposed to ‘working from a textbook’.

Lipping, M (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. New York and London: Routledge.

# Is maths a memory game?

I decided to challenge myself with regards to the maths assessment questions, which can be accessed through the link below. Having been out of formal education now for 7-8 years I wanted to see what I had obtained from the maths classroom and what was quite frankly wasted on myself. During my schooling years there were often days where I would sit in maths and really enjoy it and then there were days where I would feel myself tensing up and thinking why do I put myself through this? I feel this is a very common attitude shared my many individuals!

If you follow the link below you will see a range of different maths problems underlining different maths principles; I worked my way through these questions and the result was a bit of a shock, considering my maths ability was never an issue. I would never say that I was ‘great’ at maths but how can a large area of my childhood that I had to endure from near enough  primary 1 right through until Higher level have become a mind blank now?

The questions that I was able to answer quickly and confidently were the ones concerning the principals of :

• Percentages
• Graphs
• Distances and converting units
• time

However, I struggled with the questions dealing with:

• Angles
• Symmetry
• terms such as ‘mean’ and ‘prime’ numbers
• Formulas
• Shapes and calculating their areas

After having completed the test and taking the time to reflect on my performance it has become very apparent that the areas that I coped well with are principles of mathematics that I am using frequently, even having been out of ‘education’ for some time.

For example;

• I use percentages when I go shopping; by working out the new price if there is a sale on or when I am using my student card and I am lucky to get ‘10%’ off the original price.
• I am using simple addition and subtraction daily when it comes to calculating money and expenses for when I travel to University or even something as simple as buying lunch each day.
• I am being exposed to graphs continuously on the news at night or even in newspapers so I am able to stay familiar with the data they are presenting and the concepts.
• Distance is not alien to myself, as a driver, I am constantly reading road signs and calculating the distance if I am driving to a new destination using google maps and quite often I am having to convert units from meters to kilometres/miles and so forth.
• Time is something that is continuously being utilised whether that is setting my alarm at night and calculating how much sleep I am going to get or calculating what time of train I need to get in the mornings to make sure I am on time for university.

I am constantly using these principles of maths, perhaps not at the same level as they were in the test, but because I am being exposed to these regularly they do not seem as daunting and I was able to approach them without feeling like I have to turn on my maths brain. This goes to show that because they hold relevance in my life with regards to past times that I enjoy for example shopping, driving or going out for lunch/dinner I have not viewed them as the maths procedures that they are. I was oblivious as to how maths really does surround us in most things we do. I think that if maths was used highlighted like this in classrooms more, especially within the secondary sector, the engagement of pupils would rocket as they could see the resourcefulness of the subject.

If you look at the principles of maths that I was a tad rusty with, it is areas that I am clearly not using now in my adult life, because I’m not required to. Such areas are calculating shapes and their volumes and working out angles. This could be a requirement for some individuals career choices, therefore, I can’t speak for everyone. All I can conclude from the findings of this test is that these areas which I can’t see relevance in (due to not having to use them with regards to my current lifestyle) I certainly found daunting and it left me with the mindset of; was this a waste of my time at school and were they just taught for my assessment purposes?

https://my.dundee.ac.uk/bbcswebdav/pid-4364108-dt-content-rid-2300278_2/courses/ED11010_CAS_D65_201314/OMA%20Workshop%20activity%20questions%202012-13.doc

# 5, 6, 7, 8!

Could we be guilty of using elements of maths on a daily basis without even realising it?

I can openly hold my hands up and admit to this, as I was using a form of mathematics every day for three years in my last area of study, this being dance. When choreographing to music I was using a system called the ‘base 8 system’. But what does this mean in simpler terms?

In our everyday number system, we use the ‘base 10 system’ or it can also be called the decimal system.

Why do we use base 10? is it because we have 10 fingers?

One hypothesis is that of George ifrah, a French author and historian of mathematics, his findings show that the base 10 system has traces from the central African language; ” ‘five’ and ‘ten’ are respectively moro and mbouna. Moro is actually the word for ‘hand’ and mbouna is a contraction of moro (‘five’) and bouna, meaning ‘two’ (thus ‘ten’ = two hands)”. (Ifrah, 2000; 21-22) He was a firm believer in ‘finger counting’ playing a powerful role in the influence of the base ten system.

So why do some teachers shy away from the pedagogical style of finger counting?!

In my last area of study, I was using the Base 8 system due to the time signature of the music I was continuously using. Which understandably had eight beats to a bar, which meant that I was able to choreograph a certain move to each beat of the song to ensure I was keeping in sync and keeping the rhythm. When I would reach the end of the first count of eight I would start again and it would be recorded as the second count of eight and so forth. Having this sound knowledge of the base 8 system (or in other words counting to eight repeatedly!) I was able to choreograph and perform with support and confidence.

The ‘Base 8 system’ helped form the format of my dance routines when teaching, as you can see in the example above. Some of the counts were ‘half time’ which just means that the move is performed at double the speed.

I am now over half way through the Discovering Mathematics module and  it is apparent there is definitely a lack of knowledge in today’s society as to the extent and impact that maths has on our everyday lives.We have to ask the question what can we do as future educators to bring this awareness and understanding to our classrooms and pupils.

Ifrah, G (2000). The Universal History of Numbers: from Prehistory to the invention of computers. :Wiley. 21-22.

# As a nation do we need to have ‘PUHC’?

Every day there seems to be a new health warning regarding what you should and shouldn’t eat or certain products you should or shouldn’t use. Gone are the days where you can switch on the news or pick up a newspaper and be faced with success stories or even positive headlines in general.

How are these health warnings presented to us?

Long-winded sentences comprising of facts encrypted with medical terms or short snappy phrases, which can more often than not contradict the main point of the whole article. Yes, it goes without saying it is the second option. As a nation, we are continuously exposed to a number of short snappy statistics.

Statistic – “The practice or science of collecting and analysing numerical data in large quantities”. (Oxford dictionary)

The danger with this process of advertisement is statistics can be very deceiving and people do not pay attention to the context, just the numbers (tvtropes). (But is the carefully calculated number figure being presented the only maths principal?) For example in order for a statistic to hold any accountability, data has to be collected concerning different variables, take yoghurt advertising as a perfect example. We are constantly exposed to adverts raving about the latest yoghurt consisting of “0% fat and only 99 calories” so you are immediately under the illusion it is a healthier option as a snack. So we jump on the bandwagon as we can snack on this product ‘guilt free’, however over time, start to get frustrated that you are not losing the weight like you would assume now that you are ‘leading a healthier lifestyle’. Perhaps because the statistic which drew you in to buy the product failed to mention that the yoghurt is still laden with sugar, hence why it still tastes so good. It completely contradicts the words that were once used to describe this product i.e healthy. Consumers were instantly drawn in with the clever use of numbers and perhaps are not knowledgeable about the remaining contents, which will prevent them from enjoying a ‘healthy snack.’

In simpler terms, do we need to have a ‘Profound Understanding of Health Care?

With regards to what we are eating, feeling and actively doing to keep fit. In order to stay remotely with what we perceive as ‘healthy’, we need to take statistics with a pinch of salt, until we have the conceptual knowledge and evidence of the data gathered to establish the statistic in the first place. So we can understand and process the real message behind the product advertisement.

You could relate this to Lipping Ma’s research of having a ‘Profound Understanding of Fundamental Mathematics’ by having

• “multiple perspectives” (Ma,1999:122)-  Being aware of the different approaches to establishing this statistic in the first place and take into consideration of the different variables that would have had to be tested to come to the final figure that is being promoted.
• “Basic Ideas” (Ma,1999:122) – Knowing the components of the statistic or in simpler terms the ingredients essential to making this product so you can make an informed judgement before you rush out to buy what you think is a ‘healthy snack’.

“I never believe in statistics unless I’ve forged them myself!”- Winston Churchill.

Stevenson, A (2003). Oxford Dictionary of English. London : Oxford University Press

Lipping, M (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. New York and London: Routledge. 122.

# Going back to the basics …..

The general feeling expressed towards mathematics is an anxious/negative one (Chinn,2012) whether that is expressed at school age or even among adults.

But why is this?

Is it because there is too much emphasis on maths being very formula/number based. This could be a result of the process of rote learning which I’m sure we have all endured throughout our school years. Having to  memorise endless formulas until they hopefully become automatic and then having to apply them to numerous mind-numbing sums/problems. Hearing yourself say “when will I ever have to use this when I am older?!”

Understandably, it is clear to see why maths can leave children unmotivated and disconnected with regards to the learning involved. Luckily for myself, I was one of the few in my class who strangely enjoyed maths. Being an individual who craves immediate feedback, maths always fulfilled this need by having only the one answer, you knew if you had got it right or wrong and could break down where you went wrong, but not always why you went wrong. This contrasts with the likes of the literature side of the curriculum, where there are multiple answers/ways of thinking about a scenario which I could never fully divulge in.

The other common stigma which is attached to maths when at school, especially present within the secondary sector, is the focus being predominately on “pushing for excellence….passing tests” (Skemp,1986:123). It is very grade related and assessment driven with the way in which the curriculum is taught. The importance of how and why you have used a certain formula or procedure is often overlooked. Therefore, the learning becomes very procedural and not conceptual which former teacher and principal in China, Lipping Ma agrees with (1999).

Have we forgotten about the why and the how in maths?

Upon leaving school it is very apparent that I have not used a great deal of maths (that i am aware of) and I am left feeling a great disconnection and confidence with the mathematical side of the curriculum, this was highlighted when I was out on my previous placement. I feel that any sort of relevance within the maths material that was being proposed to myself at school was never properly highlighted in terms of how I could use the skills in the future.Therefore, my attitude towards the subject has remained very stagnant, I think that by choosing to study ‘Discovering Mathematics’ i will hopefully have my eyes opened to the wonders and power that maths holds and how important it is and can be utilized within everyday life. Hopefully, from this understanding,  my appreciation will grow and I will be able to reflect this mindset to future generations.

Chinn, S (2012). More trouble with maths: A complete manual to identifying and diagnosing mathematical difficulties. London and New York: Routledge

Skemp, R (1986). Psychology of learning mathematics. London: Routledge. 123.

Lipping, M (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. New York and London: Routledge.

# Preparation is Key…….

Now that our first placement is looming and apprehension is creeping in more and more each day it is important that I am on the ball with all the areas within my control. After having some experience within a Primary School prior to coming to University in terms of volunteering one afternoon a week I have a very rough idea of how challenging it will be especially now that I will be in charge of group and whole class lessons.

Growing up one phrase that I always heard, regardless of my surroundings was ‘preparation is key’ and that could not be more true for placement. Planning every aspect in the hope to ensure the whole process runs smoothly. As much as every student wants it to run smoothly and be a success in some shape or form the main key of placement is to get an initial taste of professional life as a teacher.

Aside from the placement ROTR tasks, completing prescribed evaluations and being observed and finally assessed, one thing that is important to focus on right from the word go is personal and professional goals. This is something that I am thinking about now and something that I may have to re-evaluate once I meet my class and become aware of the different needs of every individual within the class. There might come the need to base one of my goals around an individual or group that I am responsible for, this will be something that I will have to monitor each week and use my initiative when out on practice.

It is important that I make my goals:

Specific

Measurable

Attainable

Relevant

Timely

SMART goals for MA1 placement:

(Behaviour) MANAGEMENT

• I want to make sure that I go in from day one as a teacher figure and not as someone who the children view as a friend or a ‘soft touch’. You hear tips from professionals in the profession saying “Don’t crack a smile for the first few months” as the pupils need to know that you are in charge and that you have complete control of the class. In my last smaller scale placement at a primary school the children only saw me for a couple of hours an afternoon and I got the sense that they viewed me as not very authoritative and would try and push the boundaries in terms of their behaviour.

I will make sure that I am familiar with the Behaviour Management Policy and the different procedures that the class teacher has in place regarding discipline and equally appraisal. This will ensure there is consistency and hopefully respect from the pupils.

Engage Learners from the start

• Regardless of what stage you have at school it is vital to engage the pupils from the offset. I know myself when I was at school you could almost gauge how your teacher was going to deliver a lesson or introduce a new topic, this became slightly tiresome and the ability to stay focused on what was being taught became tedious. I believe if you fail to capture pupils from the start of the lesson you are doing them an injustice regarding their development as learners as they will want to participate and contribute more if they are interested in what is in front of them.

I intend to use my initiative and make a conscious effort to think of creative ways to introduce any lesson that I will be responsible for. Whether this is thinking of new ways to deliver specific areas of the curriculum or getting the children involved as much as I can so that they can become independent learners.

Getting to know each individual

• It is a teachers’ responsibility to cater to every individual in their class whether that is something as simple as knowing their names to more extensive aspects such as knowing the best way they learn regarding their learning style. I found one of the most frustrating things growing up was when your teacher simply didn’t know you as a person.

I want to make sure that I know the children’s’ names from the first few days so that it will make my teaching practices run more smoothly and ensures that I am engaging with a range of pupils when posing questions to the class as opposed to sticking with the same children repeatedly. I want to be aware of any additional needs or children that need extra support within my class so that I can cater to their needs or if I need to go away and read up on any extra resources so that I can fully benefit each and every individual I am responsible for.

# Tackle Inequality to Achieve Better Outcomes for Individuals

Colin Miller. Head of Essential Skills and Progression at West Lothian Council says: “We’re finding that girls who are good at maths and science at school tend to go into the care side of things (doctors and nurses) rather than engineering and construction”. ….This could be due to the fact that engineering and construction occupations in this day and age are seen as a male environment as sites and workshops are predominately male.

This was certainly the case when I was at Primary School and even throughout my time at Secondary school. There was a divide present amongst genders and very much so with the subjects in which we studied. After reading an article in the latest ‘Education Scotland’ it was great to see that this issue is being recognised very publicly and that there have been efforts to overcome this stereotypical feeling. West Lothian College which is near to my home town have brought in attempts to get girls more involved and interested in the ‘STEM’ subjects – Science, Technology, Engineering and Maths and show them that they have a place in this ‘masculine world’. When I was at school I absolutely loved Physical Education this was due to my passion for being active and keeping fit as well as being involved with a dance club from a very young age. However, this was dampened by the members of my class being predominantly male, I was one of three girls who carried it on until Higher level. However this did not put me off, it made me more determined to show them that there is a place for girls amongst these ‘types’ of subjects.

West Lothian Council have taken it upon themselves to recruit a number of female workers specialising in Engineering and Mathematics to come and teach workshops at the College. This attempt was to highlight to young girls that woman can succeed into such careers and make their mark just as equally as male workers. However, this attempt did not show a large shift in the number of girls entering such career paths it merely showed that it had got more girls talking about it and showing only verbal interest as opposed to fully committing and making that final leap into one of the professions. Another slightly more effective effort adopted by the college has been appointing ambassadors of the ‘STEM’ subjects. These ambassadors continuously undergo talks and lectures about how the teachings of each subject can then be applied in certain professions for example, the use of maths in daily engineering procedures. So just by putting context and relevance behind the teaching of these subjects, that the girls are showing passion for in the first place, has got them thinking of how they could succeed into a career that they once thought was not made for them. These professions suddenly now have purpose and have become very appealing. These efforts have shown great success in the number of girls enrolling in the HNC engineering course as well as open days for such ‘masculine’ subjects being populated mainly by females.

I personally think that the way the curriculum has be set there is no intention for certain areas to be directed at a specific gender. However, due to the old fashioned view which has transported into this day and age, that girls are still very much the stay at home domesticated sex and men are the ‘bread winners’ if you like. I think that this is why there is a great feeling of inequality amongst certain subjects. The effects it can have on young people growing up if they are made to feel like they aren’t intended for a certain subject could be devastating not only for their personal wellbeing but their future career as they could have an unknown niche or talent that will never be discovered.

After reading the efforts of West Lothian College I think there needs to be similar actions taken by other institutions including Primary School as this is when children are most influenced. This ensures that we are supporting every individual in whatever they wish to study or progress into.

‘Let’s get it right for every child’!

# Out with the old in with the new……..

For someone who hasn’t had a lot of experience regarding ‘formal reflection’ in the past I found this whole idea of online blogging a bit daunting. The process of vocalising my thoughts and personal feelings towards a certain subject for all to see was seen as a challenge. I am definitely someone who gathers thoughts in my head and when it comes to putting it down into words I find it slightly uncomfortable. My past blogs on my Eportfolio have seen me sit on the fence and you could say I have adopted a democratic standpoint and went with the general consensus beliefs. However, after reading some of my peers blogs for inspiration I see that they are starting to form very strong independent views which I can only guess will benefit them hugely in their future professional career. They are able to question professional viewpoints and question the world of teaching in terms of why there are certain teaching methods and why some areas of the Curriculum are not as valued as others. It was nice to see the contrast in the posts blogged by peers from topics they liked to ones that they feared. It was reassuring to see that my peers were blogging about topics that they do not feel confident with equally as much as the ones that they feel passionate about as opposed to shying away and becoming complacent.

It was interesting amongst these blogs to also read about topics that go beyond our course, for example one blog I came across was about an issue which is happening down in England regarding children and obesity which is a very common problem all over the United Kingdom. This has spurred me on to really start to engage in reflecting on areas outwith the course for example I love to watch documentaries which could easily relate to problems occurring in the Primary School. I have decided that I am going to make more of an effort to go beyond what is prescribed (TDT tasks and reading tasks) and really make a conscious effort to start forming my own opinion and most importantly writing and reflecting on them afterwards. I have taken it upon myself to buy a notepad which I am going to keep purely for personal reflection. I am going to make an effort to reflect after each input on what were the key points in that lecture/workshop and how do I feel about them. This will hopefully spark more questions in my head and I will be focussed on finding out more by engaging in extra reading and hopefully it will help me come to more of a standpoint which will really mature me as a student.

# An Enquiring Practitioner

An Enquiring Practitioner is someone who takes on the responsibility of carrying out practice based research, in order to enhance their own learning, as an individual or collaboratively with others. Looking more specifically into the teaching profession, this idea of ongoing research enables them to be more engaged with their own learning which as a result enhances a child’s development through their practices.Outlined within the Donaldson report, it is now a vital procedure of good practice for individuals to adopt even as early as student teachers like myself.

The benefits of being an enquiry practitioner are endless; it should become a daily aspect in order to promote reflection and critical evaluation within and outside the classroom. First and foremost it allows teachers to monitor their own practices and highlights areas where they can build and develop on. This should as a result empower them as professionals as they can investigate new strategies to adopt and allows them to expand on their knowledge and widen their horizons. Just by taking this time to reflect back and critique their own methods should enhance their pupil’s development and attainment level in the long run.

Working collaboratively as enquiry practitioners can be effective also, again this idea of carrying out research and reflecting back on practices although this time with the eyes and ears of others can trigger whole new perspectives.

Although this procedure is seen as an integral part of the teaching profession like anything there are challenges present. It can be seen as very time consuming, as professionals, teachers are renowned for having many responsibilities so this added pressure of continuously carrying out research and expanding on their own methods and practices can be rushed and not as thorough as required. For this reason alone it is essential that as a new teacher I try to adopt this approach early so that it becomes very natural and therefore attainable. Like anything individuals tend to feel more at ease when they have a routine, teachers are no different they can sometimes find themselves set in their ways concerning their lessons and teaching styles. As a result this idea of critiquing their strategies on a regular basis can become a very uncomfortable experience and a little overwhelming.

Carrying out enquiry practice as a group can pose equally many challenges, more so with the way in which they work together. Reflection can be such a personal skill, that it will then be inevitable for dispute to occur regarding a difference of opinions. Within a group dynamic there is also often a contrast of characters so some individuals may try to take more of a dominant role which will affect the overall group atmosphere. As a result the motivation will be hindered due to there not being an equal social responsibility amongst all members.

I feel it is important that I come to terms with being an enquiring practitioner if I am to succeed as a student teacher. It will be beneficial to reflect on a personal level of how my initial practices go and I can use them as a benchmark to build from for my future teaching career. It will also inspire my practices as I work with experienced teachers and gather advice to start to build up my own repertoire.