Mathematics & Statistics Blogs

Current UCD Biology, Mathematics & Education student, Emily Lewanowski-Breen, describes her experience of attending an international conference as an undergraduate student

This summer, I had the opportunity to attend the GIREP-ICPE-EPEC 2017 International Conference, which was hosted by Dublin City University from 2 July to 7 July. The theme of this conference was “bridging research and practice in physics teaching and learning”. Whilst I am studying to become a Maths and Biology teacher as part of the Science and Maths Education in UCD, I felt it would be beneficial for me to gain insight into the teaching and learning of physics since I will also be qualified to teach Junior Cert Science. Additionally, I thought it would be a great experience to discover more about the world of research as it is my dream to one day pursue a PhD in maths education.

However, I will admit that I was both nervous and excited about the idea of attending my first conference as I didn’t really know what to expect. How will the conference be structured? What if I don’t understand the presentations? Will I be the only undergraduate student there? These are a few of the questions that came to mind as I made my way to DCU on the first morning of the conference. However, despite my initial concerns, it turned out to be an incredible experience and I really enjoyed every minute of it.

So back to my first question- “how will the conference be structured?” Well, each day actually followed a similar format. The mornings began with a one-hour ‘plenary session’ in the Helix at DCU, whereby a researcher or academic spoke about their work in the field of physics and science education. I particularly enjoyed the talk by Dr Paul van Kampen from DCU on “the teacher as a young professional” as I could really relate to the points he discussed. For example, he spoke about the importance of encouraging active learning in the classroom, which is something that is central to the Science and Maths Education programme in UCD. In fact, we always strive to make our lessons as student-centred and engaging as possible through the incorporation of groupwork and questioning. We even trial or discuss our lessons with one another during our education lectures and provide constructive feedback, which I find really helpful.

This being said, I also enjoyed the talk presented by Dr Bethany R. Wilcox from Colorado School of Mines on the use of interactive techniques to encourage student participation in lectures as it was interesting to see how other students learn at third level. I was particularly fascinated by the multi-solution problems she discussed as it is something that I hope to incorporate in my own teaching.

These plenary talks were followed by the ‘parallel sessions’, which consisted of a series of 20-minute oral presentations that took place at the same time but in separate rooms. There were around eight sessions taking place at any one time so the hard part was trying to decide which one to go to! Thankfully, the conference programme had detailed descriptions of each of the sessions, which made it a lot easier to plan out my day.

This brings me to my second question – “What if I don’t understand the presentations?” Well, I am delighted to say that each of the talks and presentations were actually very accessible, which was great considering that I am not from a physics background. In fact, I learned so much over the course of the week and even got a lot of ideas and inspiration for my own teaching. I particularly enjoyed learning about multidisciplinary activities, which are essentially activities that incorporate more than one area of science, thereby developing students’ problem-solving skills. For example, they had a physics worksheet on electricity but it had a biology context, which was something I had never seen before, but now hope to incorporate in my own science lessons. I also enjoyed the presentation by Dr Shane Bergin from UCD on the impact that informal learning environments have on students’ science identity as it was a very engaging session and it was great to learn more about Irish initiatives such as ‘City of Physics’ and ‘Quavers to Quadratics’.

However, I was particularly intrigued by the flipped classroom model, whereby students watch videos of lessons at home, allowing class time to be devoted to discussions and activities. I had heard of this teaching approach before but hadn’t realised the potential impact it can have on students’ learning, so it was interesting to learn more about it during the parallel sessions. Nevertheless, I was also delighted that a lot of the ideas and concepts we learn about in the Science and Maths Education programme in UCD were actually discussed during the conference because not only did it allow me to feel more engaged in the sessions, but it made me realise how far I have already come as a pre-service teacher. The discussions on the different types of knowledge required by science teachers, for example, really resonated with me given that we constantly reflect on the development of our own knowledge for teaching as part of our degree.

So now to answer my final question- yes, I was the only undergraduate student at the conference but this didn’t bother me in the slightest because everyone was so friendly and welcoming. In fact, I have come to realise that conferences are great for networking, even for undergraduate students. It was just such an honour to meet researchers, academics, and teachers from all around the world; everywhere from Brazil and Colorado to Sweden and Australia. I was particularly fascinated to hear how the Irish education system and teacher training programmes compare to other countries and was delighted to share my own experience of the Science and Maths Education programme in UCD. Some of the people I met were actually really impressed by the level of collaboration and team-work within my degree and even asked me for advice on how they could encourage it within their own teacher training programmes…so that was pretty cool! In fact, meeting new people was perhaps one of my favourite aspects of the conference because I enjoyed hearing about their experiences and research interests and was glad that I could contribute my own ideas.

Overall, the GIREP-ICPE-EPEC Conference was a very enriching and worthwhile experience and I would like to thank Dr Shane Bergin for inviting me to attend the event. I was truly inspired by the people I met and their dedication to improving the teaching and learning of physics and science across all levels of education. I definitely gained a lot from the experience and feel more prepared to teach physics at Junior Cert level as part of my upcoming fourth-year placement. In fact, I would highly recommend other undergraduate students to attend conferences because not only do they provide you with the opportunity to meet researchers at the forefront of their fields, but they also allow you to discover what a career in research might entail. You never know, maybe you will be just as inspired as I was - after all, undergraduates are the researchers of the future.

Third year student Emily Lewanowski-Breen shares her experience of the Science and Mathematics Education pathway in UCD. 

THE DECISION TO GO INTO TEACHING

One of the most common questions that I am asked as a Science and Maths Education student is “did you always know that you wanted to go into teaching?” and the answer is “no, I really didn’t”. In fact, when I first came to UCD, I didn’t even know what area of science I wanted to specialise in, let alone what career path I wanted to follow! The flexibility of the Common Entry Science course therefore really appealed to me as it allowed me to take a wide range of modules in first year to see where my interests lie. I did everything from Linear Algebra and Environmental Biology to Organic Chemistry and Astronomy despite the fact that I didn’t do physics or chemistry for the Leaving Cert!

However, it was the first year maths education module that made me realise that my passion lies in teaching. I always enjoyed maths in school and this module encouraged me to reflect on my own learning of maths whilst also providing me with insight into both teaching and research. I found the lectures really engaging and I loved the class discussions and activities (we even used mini whiteboards, clear dry erase paint and Lego!). Fortunately, this module is not just for those who are interested in continuing with the Education pathway. Many students, for example, took the module as a way of developing their communication and teamwork skills and some simply took it out of interest. In fact, I would highly recommend the module as it was a very different yet enjoyable way of learning. It definitely inspired me to continue with the Science and Maths Education pathway in second year and ultimately, I knew I would end up specialising in this stream because I would have been heartbroken if I decided otherwise (I’m not kidding!). So now here I am, a third year Biology and Maths Education student, on my way to become a post-primary teacher and I honestly think it is the best decision I ever made. Yes, teaching can be challenging at times but I find it nonetheless rewarding and I love the idea of being able to share my passion for biology and maths with post-primary students.

SCHOOL PLACEMENTS AND TEACHING EXPERIENCE

What I particularly love about my degree is that the undergraduate education modules not only introduce us to different concepts and theories related to teaching, but they also incorporate a number of placements which help to build our skills (and they are also a lot of fun!). During semester one of third year, for example, I was a peer tutor for a first year undergraduate maths module in UCD. Whilst this tutoring was mainly one-to-one, I often took a small group of students up to the whiteboard to explain a particular concept or to help them with their worksheet questions. This was actually my first experience of teaching maths, which I was initially quite nervous about, but it turned out to be really enjoyable! There was even a senior tutor in the classroom with me who answered any questions I had, and my lecturer also provided me with a lot of tips and advice in advance of the tutorials, so there really was no need to worry! However, I will admit that it was challenging at times because I had to learn how to adapt myself to different situations, but that is what motivated me to improve my skills and I really enjoyed the experience.

That semester, I also worked together with two of my classmates to design a maths lesson as part of a model of teacher collaboration known as Lesson Study. I really liked that we could be creative and design our own activities and worksheets for the students rather than using the textbook examples. Once we finished planning the lesson, we actually went to a school near UCD to teach it to a transition year class and it was amazing to see our first ever lesson come to life in the classroom! Not only did it make the project feel more meaningful but it was also a great learning experience because we could see what worked well and what we needed to change.

In the second semester of third year, we also have an eight-week placement in a post-primary school, which consists of three classes a week. This placement is a great experience because not only do we get to help out in the classroom, but we also get the opportunity to teach our own lessons. It’s nice because we each have our own mentor teacher who is with us in the classroom at all times and they very kindly provide us with a lot of support and advice.

I really enjoyed each of these placements and experiences and love that they are incorporated into our undergraduate degree because it allows us to gradually build our skills and knowledge for teaching. My lecturers are also really supportive and they are always there to answer our (many!!) questions. I also get on really well with my class (there are only seven of us) and we regularly meet up for coffee or go out for dinner which is nice. We even meet with the education students in the years above and below us to see how they are getting on so there really is a wonderful sense of community.

What other modules do I have?

Along with my education modules, I also have maths and biology modules which help to build my knowledge of these subjects for teaching. However, there is also the option to take physics, chemistry or applied maths instead of biology- it simply depends on your interests! I, for one, think it is great that we have a variety of modules because I really enjoy learning about different topics and I often get inspiration from these modules for my teaching. I particularly like the fact that our maths modules not only build on the topics we covered in school, but also introduce us to other areas of maths such a group theory and even the history of maths! The seven of us actually work together on our maths problem sheets (which usually involves a few coffees and hot chocolates too!) and the Maths Support Centre in UCD is a great resource for those trickier topics.

What advice would I give to students?

There is one door into the Common Entry Science course but 26 different routes you can take once inside so it really is okay if you don’t know what area you want to specialise in straight away – believe me, that’s normal! In fact, you will have plenty of time to make the decision. My advice would therefore be to try out a variety of different modules in first year and to do whatever interests you because that’s what makes university so enjoyable. Also, if you think you may be interested in teaching or research in education, or if you are just curious to see what it is like, then I would definitely recommend Introduction to Maths Pedagogy. I mean look at me- I took the module out of interest and now here I am!

TO SUM IT ALL UP

The Science and Mathematics Education degree has already provided me with so many amazing experiences and opportunities and has really motivated me to reach my full potential as a beginning teacher of maths and biology. Not only have my skills greatly developed over the past few years, but I have also gained a lot more confidence in myself and made some amazing friends! I definitely look forward to pursuing a career in this field but, in the meantime, I am simply enjoying every minute of my time in UCD.

Recent graduate Caitríona Byrne has just completed her BSc Mathematics and gives an insight into her experiences during her undergraduate degree…

WHAT CAN I STUDY?

It is really amazing how many different areas there are in mathematics that you never see or hear about in secondary school! The maths courses that I have done in UCD have covered a wide range of topics. The courses I did in the earlier years of my degree set the groundwork for later years. They built on the mathematical knowledge I had from the leaving cert, and expanded greatly on topics like calculus and linear algebra that I had learnt the basics of in secondary school. As I progressed through the degree, and my knowledge of maths expanded, I was able to study more challenging courses like Galois theory, Group theory, Combinatorics and Differential Geometry to name but a few. These were topics I knew nothing about before I began my mathematics degree. Of course, I also got to study some more well know mathematical topics such as Cryptography, Coding theory and Financial Mathematics.

HOW DO I LEARN?

Maths modules are usually taught via a mixture of lectures and tutorials. At lectures, the main topics of the course are presented – we get to see the main theorems and ideas in the area as well as the proofs of many of the theorems. Lecturers often also explain how the topic at hand links to other topics that we studied in previous modules, or give examples of how the topic has applications elsewhere. In this way, due to their expertise in the area, the lecturer can guide us through the main ideas of the topic we are studying, so that students can learn much more quickly and with greater understanding than if we were to try to teach ourselves from a book.

At tutorials we are usually given an exercise sheet with questions that were relevant to the content taught in the recent lectures. The tutorial is spent going through the exercises. The best way to learn maths is to try to solve problems, so tutorials (and spending time working on the tutorial sheet before and after) are very important. The questions are often challenging, and I certainly spent many a night trying to solve one question or other – let us just say that maths students need to have a well-sized paper recycling bin in their room! I found university maths a lot more interesting and stimulating than maths in secondary school. There, you work on short questions – and lots of them – in order to be comfortable with different skills. However, at university since the questions can be quite difficult, I found it so much more interesting (and fun) to spend a good bit of time on one question to try to work it out.

WHAT SKILLS WILL I LEARN?

In mathematics at third level, I really enjoyed the emphasis on logic and understanding. We saw so many theorems with proofs, and a huge amount of time is spent on proofs. By carefully going through the proofs we were shown during lectures, slowly but surely I improved at being able to construct proofs by myself. When I was in secondary school, theorems and proofs were considered a dull but necessary part of mathematics that just needed to be learnt off (much like a learning your scales on a musical instrument). However, in college you learn how to prove theorems. Learning to prove or disprove mathematical statements forms a large part of any mathematics degree. For instance, for the majority of my exams in final year, I didn’t need to use a calculator at all! A typical exam question would be a mathematical statement which you need to prove (or disprove). This is certainly one of the main mathematical skills that I feel that I have come out of my degree with: knowing how to go about trying to prove (or disprove) mathematical statements. In a more general setting, this training enables maths graduates to be highly analytical and excellent problem solvers – skills that are prized in the workplace.

WHAT IF I GET STUCK?

Every maths student runs into problems that they find difficult or confusing – at least I know that I often did! There is a lot of support for mathematics students in UCD. There is a maths support centre where you can drop in and ask questions. Also, lecturers are really helpful. For instance, when I get really stuck on something, I can ask the lecturer about it at the end of the lecture or email them. I have found the lecturers to be really helpful and keen to make sure that I understand their answer. They really want you to understand their courses and they are willing to take the time to explain the answer to your question to you- which is really great!

  Physics student Lána Salmon describes how she overcame problems with Maths in first year.

On the first day of first year I found my way to my first lecture having only gotten lost twice along the way. The class was called  ‘Applied Maths: Mechanics and Methods’. It was a whole new experience for me – I had to get to know the 60 strangers around me, but also get to know this new kind of maths I had never experienced before. It was exciting and daunting. Our lecturer, Dr Conor Sweeney, had so much enthusiasm and energy it was hard not to feel excited about what was to come!

A NEW WAY OF LEARNING

After the first few lectures of Applied Maths we had our first tutorial. A tutorial is like a problem solving class – we found ourselves sitting around tables in groups of 8-10, solving problems and asking questions. It was a completely new way of learning maths – interactive, applied, real. I had high hopes for this new way of  problem solving.

In this tutorial I began to notice something – people around me were catching onto the maths quicker than me, able to answer questions with ease. I began to get worried – I thought I wasn’t able for this level of maths, that I would fall behind. 

Maths and Physics were my worst subjects in the Leaving Cert. So entering UCD Science focusing on Maths and Physics may seem like a strange choice. But they were the subjects I enjoyed most, and the ones I was determined to work hard on. I wanted to know more about the world, the Universe and how it all works. To do that I needed to know the maths behind it all. I was enthusiastic to learn these things and that’s what drove me.

HELP IS AT HAND – UCD MATHS SUPPORT CENTRE

But now I was surrounded by people who were catching onto the maths quicker. My confidence sunk. I found myself re-learning my Leaving Cert maths, writing pages upon pages of notes. I spent hours more on assignments than others.

I found out that Applied Maths was a Leaving Cert subject that most people in the class had taken. My school didn’t offer Applied Maths and to be honest I’d never heard of it.

A bit of weight had been taken off my shoulders – these people were more practiced in this kind of maths than me, it makes sense that they were more able for it. I didn’t feel any less pressure though – I still had to work harder to keep up. I think it was then that I realised that I could ask for help – a lesson that has stuck with me to this day.

UCD has a Maths Support Centre – a place where you can go to clear up any problems you may be having with certain topics or sections of your classwork. Between the Maths Support Centre, our tutor and our lecturer, I got some extra help and things slowly began to make more sense.

I think in those few weeks I began to learn how I study best, and also how my learning strategy is different to other peoples. I found out that I’m a slow learner and it may take a while for a subject to make complete sense to me. Making detailed notes and step by step problem solving guides is the best way for me to study.

PRACTICE MAKES PERFECT!

In many ways the Applied Maths class lay the groundwork for my future maths learning. I’m not the best at maths and I can’t say that I’m entirely confident with it, but I know that with hard work and the support that UCD has given me I can continually work on my maths ability. It is a skill to be practiced, and I find myself falling in and out of practice sometimes but always trying my best.

A lot of people find maths daunting and want to avoid it. But like learning a language, it is a skill to be practiced and used. While some may catch onto maths quicker than others, with continued practice you improve and begin to unlock the tools you need –  to explore the Universe,  understand the stock markets,  predict the weather, analyse statistics, engineer the next technologies and much much more.