Category Archives: 1.4 Prof. Commitment

Discovering mathematics reflection- Have I discovered it?

www.google.co.uk/mathslove

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

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

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

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

 

 

Who I am and why I’m here!

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.