Category Archives: 1 Prof. Values & Personal Commitment

Discovering mathematics reflection- Have I discovered it?

www.google.co.uk/mathslove

I’m not quite sure I have the same love for mathematics as the numbers above….however, I can say that my fear of maths has reduced dramatically over the course of this Discovering Mathematics elective!

I have just finished my assignment about having a ‘Profound Understanding of Fundamental Mathematics’ and I have Liping Ma to thank for making those four elements of PUFM torment me every night for the last 3 weeks whilst trying to get to sleep – CONNECTEDNESS, BASIC IDEAS,MULTIPLE PERSPECTIVES and LONGITUDINAL COHERENCE. It has taken me the length of the elective to get my head round these 4 elements and be able to apply them to my own mathematics experiences and to our lectures. I am grateful to Ma as It has been very beneficial being able to view maths as a coherent whole. I feel through my engagement with the lectures and wider reading, I have started to repair my fragmented view of mathematics as I begin to open up the underlying network between different mathematical concepts.

ENJOYMENT

Looking back over the discovering mathematics elective, I wanted to pick out a particular lecture that I enjoyed and show how it helped develop my understanding of how mathematics can be used in wider society.

Maths – Data & Statistics (Dr Elanor Hothersall)

During this lecture we had a guest speaker, Dr Hotersall, who works for NHS Tayside as a consultant in public health. Dr Hotersall was quick to identify one of the main barriers for individuals working in the health profession – a lack of understanding of the basic mathematical concepts. This was in regard to nurses and doctors calculating drug dosages, fluid prescriptions, concentrations of medications, interpreting research and probabilities which leads to treatment decisions, biomechanics and in particular pharmacodynamics (what happens to your body when you swallow medicine). To be honest, before this talk, I never really considered the underpinning mathematical literacy that was required to work in the health field, yet I would want to be fully confident that my nurse/doctor was competent enough in mathematics to prescribe me the correct drug dose and be able to calculate the correct reduced dose if they were treating my son. Dr Hothersall also went on to discuss how in her job she regularly has to compare health information and statistics, identify patterns and anomalies in results and decide acceptable levels of variation. Overall it was a fascinating lecture and really made me think deeply about how basic mathematical ideas and concepts can be crucial when working in such an important profession.

Where do I go from here?

Although my maths anxiety has reduced from the start of this elective it is still clear in my mind that I need to participate in professional development by continuing to engage with mathematics topics, courses and training opportunities. I need to work hard to develop my confidence and understanding of basic mathematical concepts if I am going to be able to explain them well to my pupils and encourage them to explore them with confidence. It is really important to me that I do not allow my pupils to experience any negativity when it comes to maths. I want mistakes to be welcomed as long as we can work back from them, see why it went wrong and then discuss, debate and predict how we could get to the right answer. Collaboration and discussion is going to be vital to achieving success in my maths classroom! I like to talk things through and feel that children will benefit from dialogue when working through mathematical processes. I am happy with the wide variety or research I have done for this elective and I feel that my blogs show a high level of engagement with my professional development.

I want to thank Richard and Tara for all their lectures and hard work throughout the module – especially for putting up with my puzzled face and silly little questions. Also a big thanks to all the guest lecturers who provided us with a good insight into how fundamental mathematics can be applied in wider society and to other professions beyond educational applications.

Breaking down the idea of ‘Longitudinal coherence’ in mathematics

Leave a reply

Ma (2010) identified ‘Longitudinal Coherence’ as the final property of having a profound understanding of mathematics. If I am totally honest, this is the one that baffles me. I think this is because of my own fragmented experience of mathematics. When I was at primary school, I was never encouraged to link topics of learning, or reflect on more advanced learning, thinking about which concepts I had developed in order to get where I am now in my mathematics understanding.

I think I must have read the below definition of Longitudinal Coherence about 100 times:

‘Fundamental understanding of the whole mathematics curriculum and no limitation to the knowledge that should be taught in a certain grade. The ability to exploit an opportunity to review crucial concepts that students have studied previously and know what students are going to learn later and building the foundations for this future learning.’ (Ma, 2010, p.121)

After reading it 101 times and still feeling perplexed, I knew that I would have to do further reading to try and get different examples of what longitudinal coherence was in order to fully understand this property. Again, I found this difficult as every time I felt I was starting to get to grips with the concept, it began to feel like I was talking more about ‘connectedness’ than longitudinal coherence. I guess that it’s okay to have slightly different takes on the 4 crucial concepts of PUFM developed by Ma. I would say that connectedness and longitudinal coherence could have been combined as they do have very strong links with one another.

After a lot of research, I finally found some work which has helped me have a better understanding of what I believe to be longitudinal coherence from a teachers perspective:

“We produce many students who do not think globally – or to use a more common word these days, holistically- about mathematics. In the present context, teachers who come through such a training program may know the individual pieces of the school curriculum, but they are less adapt at seeing the interrelationships among topics of different grades. (Wu, 2002,p.19)

The above quote came with an example of helping students see the connections and coherent development of whole numbers all the way through to algebra:

Whole numbers ———> fractions —————> finite decimals, ratio, rates, percent, algebra (p.20)

Maybe Wu (2002) provided a simpler definition of longitudinal coherence than Ma (2010), or maybe because his description was accompanied by examples I was able to follow it better and have a clearer understanding. My role as a teacher is to continually encourage pupils to identify recurring themes and mathematical concepts when approaching new topics. Pupils should be able to see and draw on previous learning to help them develop new understanding. This should happen throughout the whole-school mathematics curriculum to enable students to see why previous learning was relevant and how it is supporting them in their current and future experiences.

Although this property initially baffled me, it is now the property which I connect with the most as I don’t feel I was given the opportunity to develop this at school. If anything, this places me in better stead for my future teaching pedagogies. I will always be able to look back on my own mathematics journey and ensure that I do the opposite to what I experienced at school.

Reflecting on my engagement with this module so far, I have found it extremely beneficial to breakdown the four properties of PUFM, (connectedness, multiple perspectives, basic ideas and longitudinal coherence), in order to develop my understanding of them. I feel that I can now engage with upcoming lectures with a different perspective and approach to mathematics. I want to be able to connect with the different topics we cover on a deeper level. I want to see how I can apply the 4 properties to help develop my own mathematics confidence and also my competence in developing positive teaching strategies.

Sources

Ma, L. (2010) Knowing and Teaching Elementary Mathematics – Teachers’ Understanding of Fundamental Mathematics in China and The United States. London: Routledge

Wu, H. (2002) “Longitudinal coherence of the curriculum” in What is so difficult about the preparation of mathematics teachers?. University of California: Berkley. Available at: https://math.berkeley.edu/~wu/pspd3d.pdf Accessed 31/10/15

Learn for Life – Our new curriculum!

Leave a reply

Mind-map of our new curriculum

In our education studies lectures, we have been have been looking at the education policies of the different political parties. We were then posed the question “If you could scrap curriculum for excellence and make up an entirely new curriculum, what would it be?” and additionally “Why have you come up with the curriculum you have chosen? What are the incentives, the morals and the underpinning values and missions behind it?”

During our discussion, a main point that was widely agreed on was the introduction of ‘Life Skills’ into the curriculum. By this we mean: Cooking, Health and Safety, First Aid, Animal care, Environmental care and Parenting Skills. Now I know the latter point is a contentious one. We understand that this is a delicate issue however, we educate our children about sexual health, alcohol and drug abuse and in doing so, we are not encouraging the behaviour associated with these things. We are exposing the dangers and the negative effects being involved in these activities could cause. With the teenage birth rate in the UK at 37.7% per 1000 population in (NHS, Information Services Division, 2013) there is a need to make teenagers and young people aware of the demands and skills required for parenting. The emphasis on sexual health and family planning will of course be a priority in the delivery of health and wellbeing section of the curriculum.

Another element that we were all keen to introduce was ‘Moral Skills’. We think it is extremely important to instill respect, kindness and generosity in our pupils. We want pupils to have firm and respectful relationships built within the community and work together to provide good public services to support people who are in less-fortunate positions. It was suggested that children could be regularly involved in volunteering with local charities and homeless shelters within the community. Classes and year groups could work on projects throughout the year to help raise money or awareness for things they feel strongly about in the community. The idea is that these projects would be student initiated and student led. They should feel a strong sense of independence and have the majority of control in order to work together to achieve something great.

We highlighted team building and school trips as a brilliant opportunity to introduce more outdoor and active learning experiences. No matter the weather, we want children to have hands-on educational experiences outside, working together to problem-solve, overcome challenges and develop real-life skills. I discussed the benefits of outdoor learning in a previous blog post about education in Sweden, and I feel passionate about bringing the attitudes and values towards outdoor learning into the Scottish curriculum. Children rarely get the opportunity within school to go to outdoor learning facilities and take part in air obstacle courses, abseiling, water sports and team building challenges and if they do, it is once and year and considered to be a luxury or reward. Why should it be like this? The learning experiences that children leave with after trips like this are rich, varied and can be applied in their day to day lives.

We decided that we would maintain all of the curricular areas, however there would be major adjustment to the topics being taught and the relevance of learning. We want children to be educated about things that will help them to live their lives when they leave school. I believe we are still teaching children topics that were being taught in the 1970’s. Although the introduction of technology changes the way children are taught, the basis and reasoning behind these topics being taught is still the same. We discussed Maths as being a topic which is essential to daily life. However, in schools we do not use maths in a way which helps children develop the mathematics skills needed once they leave school. Children are not educated in budgeting, mortgages, loans and interest and even if they are, it is out of a textbook,not from real-life examples. Children are not encouraged to make the connection between the importance of school maths and the maths they deal with in their personal lives. This is a gap that our curriculum would aim to focus on.

The final area we discussed was ‘Work Experience’. One member of the group brought up a very important point. At 17/18, the majority of students apply to go to university to specialise in a subject or profession. This is a massive decision to make and most students only receive a 2- week work placement opportunity from their school to help them make their decision. We don’t believe this is enough. We want pupils to have the opportunity to take part in regular and varied work experience to introduce them to a variety of professions which they might be interested in. We want to build good connections and relationships with employers, apprenticeships and businesses in order to provide these opportunities. We thought that a morning or afternoon a week from 14 years of age would be extremely beneficial for students. It would build confidence, self-esteem, motivation and it would help many students who are unsure of the profession or subject they wish to study at university. Additionally, students who didn’t want to go on to further education would have a wealth of experience in difference areas which would help them to make an informed decision about which career they wished to pursue.

After the discussion we reflected on what we had written and we could see that the connecting and underlying theme between all of our points was the notion of ‘learning for life’. We are educating our children so that they are prepared and ready to leave school and live successfully in the world. What they learn at school is relevant and helpful to what they will experience and need to know in the future. Our Learning for Life curriculum provides the foundation of knowledge that children and young people will need to flourish and be successful. There is no taboo about this curriculum, everything we do!! 🙂

Souces

NHS, (2013) Information Services Devision. Available at: ahttps://isdscotland.scot.nhs.uk/Health-Topics/Sexual-Health/Publications/2015-07-07/2015-07-07-TeenPreg-Summary.pdf?21798342467 Accessed 30/10/2015

Code cracker for the NSA to code cracker of the financial industry!

Leave a reply

What an incredible man, devoting his life to maths research and using his knowledge to identify and prove patterns, trends and connections in different fields.

This video on TED talks caught my attention when I saw ‘Mathematician who cracked wall street.’ I am fascinated by the work the NSA does in cracking codes to diffuse security threats. To be honest, I had never thought about the mathematics behind something like this. The identification of patterns, trends and anomalies are all involved in the process of cracking security codes. For Simons to go on and be able to apply these strategies to the financial industry really supports the notion of Mathematics being linked to multiple disciplines. Maybe I will enjoy developing a profound understanding of mathematics after all!

I was interested when the interview went on to talk about Simon’s involvement in supporting and encouraging maths research and development within education. The ‘Simons Foundation’ discussed in the TED video was cofounded in New York by Jim and Marilyn Simons in 1994.

“The Simons Foundation at its core exists to support basic — or discovery-driven — scientific research, undertaken in pursuit of understanding the phenomena of our world without specific application in mind.”

The foundation has a great focus on collaborating with scientists in the progression of fundamental scientific questions within major topics such as mathematics, computer science and physics. The Education Outreach sector of the foundation drives to encourage a deeper understanding of science and mathematics amongst pupils, teachers and members of the public.

In the video above, Simons states that the charity has a vision to invest in maths teachers around America.

“Instead of beating up the bad teachers, which has caused morale problems within the educational community, we focus on the good ones, giving them status and extra funding for their own professional research.”

This approach and support has had a positive effect on teacher’s morale, confidence and their desire to remain in the teaching profession. Take a look at the following link to the Simons Foundation website to see the positive work being done in Education, Life Sciences, Autism Research and Data Analysis. They also have great links with and support the development of MoMath (National Mathematics Museum, NY) in demonstrating the capacity Mathematics has to impact the world in unique and unexpected ways.

Simons Foundation – Education and Outreach

Websites:

https://www.simonsfoundation.org/about-us/

https://www.ted.com

Inspections – purposeful or painful?

Leave a reply

Personal opinion – Painful!

Whilst I was working abroad as a Learning Support Assistant, our school received the dreaded phone call that we were to undergo an inspection within the next two weeks. I was familiar with inspections after seeing them take place when I was a student but I wasn’t nearly aware of the impact that the “It’s inspection time” phone call had on teachers, support staff, and most of all the school management team.

I think we received over 50 emails from management in the two weeks prior to the inspection.

“Make sure every display board is fully complete and displays the best work from the class.”

“Make sure your resources are fully stocked and that each table has the correct amount of stationary per child.”

“Teachers, please make sure that you are using your LSA effectively during inspection time and not for classroom administrative tasks.”

“Teachers, please make sure you are not found sitting at you desk on your computers during class lessons and are moving around, interacting with all the children during activities.” (Ironically, due to the constant pings from my teacher’s email inbox, she was on her computer reading the barking orders during lessons more than she was at her computer normally.)

We all felt the pressure from management for the inspection to go perfectly. However, the response from teachers was very negative to say the least.

http://static.guim.co.uk/sys-images/Guardian/Pix/pictures/2008/08/30/Stressed-teacher-460×276.jpg

‘After years of training, why do I need to be reminded to move around my classroom? I’m in a classroom more often than the management team are so I think I know how to do my job!!’

‘Do you think that I would let my classroom resources and stationary decrease enough that it would start to impact on the learning experiences that my students are getting?’ An few examples of the conversations you would overhear in the staffroom over lunch!

You could see the divide widening between teachers and the management team. A divide that you feared would be recognised by the inspectorate team as soon as they set foot in reception.

What effect did the management’s emails have on the relationships between members of staff? A negative one! What effect did they have on teachers’ self-esteem? A negative one! Did this have a knock on effect on stress levels of staff prior and during the inspection? Definitely! Was this a pleasant environment to be working in during those two weeks? Absolutely not!!

My underlying thought is as follows; if it was an extremely unpleasant environment to be working in during that time, filled with stress, tension and overall chaos, what effect did this process have on the learning experiences of our students during this time? I can only imagine it was a negative one. AND surely the learning experience of the child is what is being inspected.

I leave you with this last thought. I remember being asked by my deputy-head to take down one of the student’s work from a display board because it “looked unfinished”. I knew that the piece of work was complete. In fact, it was the only piece of work that child had completed in 2 months. This child had been having difficulties at home and this had affected his work in school. My class teacher had finally found a book that he was engrossed in and he had asked if he could write his own blurb for the book to try encourage his peers to read it. He had a great sense of pride and feeling of achievement when we put it on display. I don’t want to even imagine how he felt when he walked into the classroom the next day to see it had been stripped from the wall.

Is it worth stripping a child of their pride and achievement in order to get a glowing review from an inspectorate?

Absolutely not.

Incidentally, our school received ‘outstanding’ in every sector of the inspectorate. All members of staff were given a certificate in their cubby holes, congratulating us on our achievement.

It didn’t feel like an achievement nor did it feel like something to be celebrated. It was a horrible two weeks and I don’t feel that the division between ‘us’ and ‘them’ (staff and management) ever healed.

Who I am and why I’m here!

Leave a reply

I am Sara Chalmers in the University of Dundee studying for a MA in Education.

I left school in 2010 having secured the conditions required to start my BA in Sport and Active Lifestyles Promotion at Glasgow Caledonian University. Shortly after starting my course, I realised that I wasn’t yet ready for the ‘university experience’ and felt that I was struggling to settle in. Luckily, I was able to transfer to my local college back home, and there I completed my HNC in Fitness, Health and Exercise.

Teaching had always been in the back of my mind as a career choice but it was extremely important to me that I gained some practical experience within a school setting before embarking on a degree at university. I thought this would be a good opportunity to combine working with traveling and gain further life experience. I managed to secure a job as a Teaching Assistant (TA) at the British School of Bahrain. It was my two years working there that confirmed that teaching the only career I wanted to pursue. As a TA, I was able to observe and support extremely talented individuals within the profession, and experience different teaching styles and the effects these had on learners.I was able to get involved in coaching extra-curricular activities and really get to know the students and how best they learned as individuals. During my second year, I decided it was the right time to apply to the University of Dundee to study education. I remember being so motivated and inspired by the course lecturers on the day of my interview and I was absolutely thrilled when I received an unconditional offer for the following academic year.

My primary goal is to become a successful student teacher at the University of Dundee. Over the next four years I want to take full advantage of the breadth of knowledge and experience that my tutors, lecturers and fellow students have to offer. I am excited to work alongside those doing Social Work and Community Learning and Development, and building a good inter-agency partnership with them as this will be vital in the future. I have identified that to become a ‘successful student’, I need to maintain my good organisational skills and a high level of self-discipline with regard to time management and punctuality. An area of my learning that I need to develop is my ability to be perceptive and not be afraid to challenge and explore in-depth the reasoning behind teaching techniques, theories and what evidence there is to support them. In order to achieve this, I will need to familiarise myself with the university library and do extensive reading and research. This in turn, will increase my subject knowledge and may even highlight an area within education that I may like to specialise in further down the line.

Looking ahead to my career after my time at Dundee University, my goal is to become a teacher who regularly sets targets. I want to constantly reflect on my teaching and identify areas that require further development so that I am continually striving to support my learners in the best possible way. I believe that I will be able to do this by attending regular professional development training courses, increasing my subject knowledge through research and reading and maintaining good professional relationships with all those involved in a child’s learning journey. I support the progressions currently happening within education and welcome the changes still to come. Children and young people are being encouraged to take ownership of their own learning. They are no longer consumers of education, they are co-producers, and it wouldn’t surprise me if children are the directors of their own education by the time I retire.

For me, there is no end goal for my teaching as it is a life-long learning experience. There will always be an area that I can develop, another book I can read or the latest tablet device to get to grips with. Most importantly, every year there will be a fresh set of faces bustling through my classroom door, all desperate to teach me something new, and I cannot wait.

My Educational Philosophy

Leave a reply

I value education as it has the opportunity to support and guide children through their learning and development with the aim of producing confident, independent individuals who are able to contribute effectively to society and the economy.

Many people have differing views on the purpose of education. My belief is that its primary role is to provide an equal and active learning experience for all children and young people regardless of gender, race, religion or social classification. It is important that schools adopt an ethos which encourages pupils to have a sense of belonging to a community; with children feeling united and part of something great. Through achieving this, schools and education will be able to combine academic learning experiences and the transmission of morals and values with the intention of creating a fair and more egalitarian society.

It is absolutely critical that children are at the heart of the education process. They deserve to have a voice and play an active role in their learning. This differs from the idea that education is consumed and that it involves the creation of accepting minds rather than creative individuals. Having looked at practices such as Montessori schooling, I can see the benefits of children having the freedom to engage in activities which interest them and how this can support their development. I also like how the focus is on the process of learning and not the end result. Children are rewarded on effort and not by test results or grades. I believe that this approach is a crucial aspect of intrinsic motivation and one that will result in confident, independent thinkers who are not afraid of facing challenges.

In summary, education plays a vital role in creating ethical, independent and successful individuals. It is a teachers role to provide an engaging and stimulating learning environment which allows children to grow and explore through social and environmental interactions. It is absolutely critical that this opportunity is provided to all children and young people.

Share this:

Share this:

Share this:

Share this:

Share this:

Share this:

Share this: