Why Maths Matters

On Friday 8th of March I attended the ‘Why Maths Matters‘ conference in University of Limerick.  The day was about ‘taking stock, examining practice and developing policy’. At the start of the conference Sean Sherlock TD reminded us of the Thomas Davis quote “educate that you may be free”.  There were a few threads which were begun by Sean and picked up by many speakers throughout the day.  My take away messages from the conference were the importance of having a population who recognise the importance of Maths in the world around them and the need for a coordinated conversation about Maths.

Professor Bill Barton from Auckland University spoke at length about the ‘Maths problem’.  The main thrust of his presentation was that there is no easy fix to the problem but that an emphasis on problem solving, abstraction, generalisation and logical reasoning is a step in the right direction.  He also spoke about the importance of students confidence around Maths and suggested that at certain times this might be more important than Maths competence.  Bill emphasised how it is ‘no longer acceptable for people to say I can’t do Maths’ and the  importance of ‘a population who understands the power and recognises the opportunities provided by mathematical analysis’.  As a mathematician and educator I also see these two areas as of critical importance.  The social acceptability that people are ‘not good’ at Maths, and the disconnection that people feel from the Maths they learn and the Maths they use in the world around them, prompted me to write a blog post over a year ago, one of my most popular posts and the post that prompted the most discussion.

During the day we heard from many speakers about the importance of starting early to engage students in Mathematical thinking, the gender divide in Irish education, the importance of empowering teachers,  recent developments in Maths Education in Ireland and the Mallow community initiative to research and pilot initiatives and developments in the teaching of mathematics and science.

Bill Lynch from the NCCA spoke about the rollout of the new Project Maths sylabus.  The early indications are good notwithstanding some issues that need to be ironed out.  Evidence from the pilot schools suggests an increase in student engagement with Maths and a changing role for the teacher in the classroom.  Challenges include the time needed to cover the syllabus and difficulties around solving unfamiliar problems.  There has been a lot of discussion around the introduction of Project Maths over the past few years.  As with any significant change like this there will be issues but I personally think that it is a step in the right direction.  I know that’s easy for me to say because I’m not dealing directly with the impact of the curriculum but I think that with some adjustment Project Maths can deliver what was intended.

The conference concluded with a very entertaining and engaging presentation by Elizabeth Oldham from Trinity followed by a panel discussion.  Elizabeth took us through curricula changes over the past 50 years both in Ireland and elsewhere.  She distinguished between the intended, implemented and attained curricula and urged caution when comparing the intentions of one curriculum with the implementation of a previous one.  Again the issue of lack of sufficient time to cover the syllabus came up in relation to Project Maths.  On a related topic Elizabeth drew our attention to the fact that as a nation our recommended minimum time for Maths in schools is less than most other European countries.  As with all things we must live with the consequences of our actions in this regard.

Both Bill Barton and Elizabeth Oldham spoke about cross national studies like PISA and TIMSS.  I’ll leave you with Elizabeth’s views ‘these studies not only compare the incomparable, they rationalise the irrational!’.

What makes a good Maths teacher?

I have been pondering the characteristics of a good Maths teacher a lot over the past two years. Along with a number of my colleagues in LIT Tipperary I have been working on a concurrent teacher Education degree for future Maths and Geography teachers. As the co-ordinator of the Maths stream of the degree, I have spent many an hour over that time, pondering and discussing with many of my own colleagues, and academics in other institutions, the characteristics of a good Maths teacher. My own very strongly held view is that the most important quality is a love or a passion for the subject. With this as the starting point, then everything else is possible.  Another quality that is crucial in my view, is an ability to nurture an inquisitiveness about Maths.  Often, when you speak to people with a love of Maths, or even those who don’t hate the subject!, they will refer to a specific teacher.  We should never underestimate the impact that we as Maths teachers have on our students both positively and negatively.  For me this was certainly the case with my secondary school Maths teacher.  She helped to send me on a path that has provided me with a variety of very satisfying careers, which has culminated so far in allowing me to do a job that I love.

Over the course of the development of the degree I have had many empassioned arguments (or discussions as I prefer to call them) as to what the focus of the Maths stream of a Teacher Education degree should be – Maths content vs. methodology.  For me, it goes without saying that Maths teachers should be comfortable with the topics that they are teaching, and I also believe that Maths teachers should be pushed in their own Maths ability as they study to become a Maths teacher.   But where the disagreement has often occurred has been the level of the Maths content that should or shouldn’t be included.  Over the years I have come across many people who have been very comfortable in their own Maths ability but who, in my humble opinion, haven’t been particularly good at imparting that knowledge.   Having an understanding of the topics is not enough – you really need to de-construct the topic and look beyond it to investigate connections between topics and different ways to approach the topics when you are teaching them.  For me, having an understanding of where people struggle with topics is very important, as is approaching topics from different angles, to allow more people to connect with the subject matter.   What do you think?

ACM Irish Collegiate Programming Competition

Saturday 24th March saw 2 teams from LIT Tipperary travel to UCC for the ACM Irish Collegiate Programming Competition.   “ACM, the world’s largest educational and scientific computing society, delivers resources that advance computing as a science and a profession. ACM provides the computing field’s premier Digital Library and serves its members and the computing profession with leading-edge publications, conferences, and career resources.”  (http://www.acm.org/)   I saw a link to the event a couple of months ago (probably on Twitter) and decided it would be worthwhile for some of our students to get involved.   Teams of up to 3 undergraduate students can enter the competition and on the day teams are given 8 programming problems which they must write code to implement within a four hour timeline.  This year there were approximately 30 teams from Dublin Institute of Technology, University of Limerick, Trinity College Dublin, Dublin City University, NUI Maynooth, University college Cork, Institute of Technology Blanchardstown, Robert Gordon University Aberdeen and Limerick Institute of Technology.  We didn’t feature in the prizes but both teams came out smiling after the 4 hours and seemed to enjoy the competition.  Now that we know what’s involved I’m looking forward to going back next year.  For more details check out http://acm.ucc.ie/.

To PhD or not to PhD …

image from http://paworldclassmath.webs.com/mathhumor.htm

Over the past few years I have toyed around with the idea of entering a PhD programme.  I didn’t tell anyone about my aspirations but it was something I was mulling over in my head.  The thoughts of starting a body of work, that will realistically last for 5-6 years, and, which will really take me out of my comfort zone, is absolutely terrifying but I think I’m finally ready to start the ball rolling.  I’m not sure of the exact area or topic but I do know that it will be on some aspect of Mathematics Education.  As I look into the abyss, the only thing that will make me jump in, is a topic that I feel passionate about and that I will hopefully still feel passionate about at the end of the PhD process.   Am I being unrealistic?  Probably, but I’m an optimist by nature so hopefully that will carry me through the dark days ahead when I wonder why I took this step.  Wish me luck as I take my first tentative steps on this journey

Mam, I’m starting to think mathematically

When I collected my 12 year old today, he told me that that he thought that he was starting to think mathematically.  I was intrigued as to what brought about this statement so I asked him why he thought this.  He said that in school today, he was throwing a ball to his friend at the back of the class, and started to think about the angle at which he would have to throw the ball to connect with his friend.  I was so excited at the unexpected enthusiasm about Maths from him that I didn’t really get into the discussion about whether or not he should have been throwing balls in class!!  That conversation will happen tomorrow.  Anyway back to angles, he talked about how he went through various angles that would or wouldn’t work before throwing the ball.  For me this is a breakthrough – despite the positive attitude towards Maths in our house and the passion that I have for the subject, I have always been very aware that this passion and enthusiasm is not shared by us all.  I have always been very conscious of not forcing Maths on my children and in some ways may have pulled back too much because of this.  I have often had discussions with both my son and daughter about where they use Maths in what they do, but I suppose my son particularly would have struggled with seeing it in what he does.  He takes a lot of it for granted, for example money etc. and so would not see a direct link between the Maths he studies and how he uses it in what he does.  Playing American football with some of his friends after school, prior to my collecting him, again got him thinking about the angle at which he should throw the ball.  Now that he has made a connection between the Maths that he is studying in school and the automatic calculations we all make when throwing something, I’m hoping that it is just the start of the conversations about Maths instigated by him and not me.

To be honest I’m not sure what has brought about this change in attitude but I’m just going with the enthusiasm.  In the car we had a chat about trajectories and quadratic equations, not in any formal way, but just to introduce the ideas, so that when they both come to cover these topics in Maths over the next few years, they’ll have a reference point.  Over the past few weeks we have discussed how the different birds in Angry Birds have different trajectories and how you need to change the angle at which you launch the various types of birds.  We’ve also been looking at some of Vi Hart’s doodling on Youtube (see my previous post here).  This has led to us looking for Fibonacci spirals in lots of different places.  Maybe this has given him a different view of Maths.  Whatever has brought about the change I’m just grateful of the chance to talk to my own children in a fun way about Maths

Connecting students with Maths

As Maths teachers we are constantly telling students that Maths is all around us but do we really show them? Yesterday I read a blog post by Ira Socol titled ‘Changing Gears 2012: maths are creative, maths are not arithmetic‘. This blog post gets at the crux of the problem and has given me plenty to think about as a Maths lecturer first and a Mathematician secondly. For me this order is really crucial – I have come across some amazing mathematicians in my years in the Maths sphere. Many were Maths geniuses but sometimes these people were so comfortable in the Maths zone that they found it difficult to pass on these often complex concepts to others. I will always be a Mathematician by trade but over the years I have become a Maths lecturer first and foremost. I am very aware that it’s not enough for me to understand the concepts, for my students it’s all about whether or not I can help them to understand topics which they will need as Computer Scientists.  I am very conscious that concepts that I just get leave others completely baffled.

A simple example is that I have been dealing with functions with my students over the past few days. I have discovered over a number of years that students often just don’t get functions – they can take a function definition such as f(x) = -4x + 9 and calculate f(3) and f(-2) etc. but when asked to deal with a real application many struggle. Because of the success of my Java coding in Maths class last term I have decided to teach functions through coding this term. We dealt with the above example by writing the Java code to implement it using x and y as variables, reading in x as the input and calculating the output y = -4 * x + 9 and printing out the y values. We then used the test data (f(3) and f(-2)) to make sure that our program worked as it should. We then worked through some basic pay calculations such as ‘A person gets paid €8.50 an hour. They get paid time and a half for any hours worked over 40 hours and double time for any hours over 60. Calculate their pay.’. If we ignore the complication of overtime this is a basic function y = 8.5x. Adding in the overtime complexity is often where students struggle. Seeing the different ways that students see this problem and work through their way of performing the calculation is fascinating. I’m not sure that us Maths teachers do enough of this allowing students to find their own way – there isn’t only one way of doing things and the discussions that follow when exploring these different ways often throw up issues with the approach taken or performance issues associated with a certain approach.

In Ira’s blog post he mentioned Fibonnacci and coincidentally I came across a Youtube clip by Vi Hart about Maths doodling which also referenced Fibonnacci.

I love this clip and it has provided me with an opportunity to talk to my own children about Maths in a way that they can connect with.  We’re going out to buy cauliflower and pineapple at the weekend to count the Fibonnacci spirals contained therein I came across another great clip by Vi Hart called infinity elephants which I’ll be using when I’m teaching infinite sequences in future.

I feel that as a Maths  lecturer I do a good job.  I’ve helped many students to overcome the  genuine terror that they feel towards Maths.  But can I honestly say that I do enough to connect my students with Maths?  I’m not sure that I do but that can change!

I was never good at Maths

I have loved Maths all my life and this led me to undertake an undergraduate degree in Applied Mathematics and subsequently a Masters in Financial Mathematics.  What has always amazed me is the reaction of people when I mention that Maths is what I have studied and/or lectured.  Generally the reaction is either “I loved Maths at school” or more normally “I was never good at Maths”.  Maybe it’s the same for other subjects but I don’t think so.  It’s almost like it’s a badge of honour for people which I find very disheartening.  There are a lot of people who struggle with English but I don’t think it’s the first thing that they lead with in a conversation.  I know that I am biased, in that Maths is where I’m at, so I’m keenly aware of others perceptions of it, but what I find most difficult is the social acceptability that people are ‘not good’ at Maths.

Maths is a subject that is studied by students in Ireland from preschool right up through school.  You would imagine, that a subject that forms a very strong basis of the school curriculum, would be something that people would be very proficient in by the time they leave school.  I am often shocked as a lecturer by the lack of understanding of what really are the basics of Maths topics.   Manipulations of basic algebraic formulae such as solving for x in 2(x+3) = -4x – 5 and performing calculations with fractions seem to cause students huge difficulties.  Even students who don’t have issues with these types of operations often struggle with being able to apply the concepts in straightforward applications.  And the ‘get out of jail’ card for many of these students is ‘I was never good at Maths’.

Of course then there are the students who are absolutely petrified of Maths.  In my ten years lecturing Maths, I have had more than a few students who are like rabbits in the headlights in Maths class.  The first few weeks are always touch and go as to whether they will stay or bolt. In discussions with many of these students over the years, I have been shocked to discover that Maths is one of the subjects that they most fear in their Computer Science courses.  This never makes sense to me, as for many of these students, Maths is one of the few subjects that they will have seen before.  This should be the subject that gives them comfort as they struggle with topics such as programming, networking etc.  What gives me a great sense of personal satisfaction is when these same students tell me that they will miss Maths.

There has been a lot of discussion about the issues with Maths education in Ireland over the past few years.  The new Project Maths syllabus has been introduced which is being rolled out on a phased basis. I’m really looking forward to the rollout of Project Maths over the next few years – before I looked into the changes which are proposed in the new Maths syllabus I was concerned about what was being removed from the syllabus.  Since then, I have had a look at the changes and while some topics are being removed and others are being pared back I think that the emphasis on applications is a very positive step forward.  It is absolutely crucial that students can place Maths in context.  Hearing students say that they will never use Maths, as they use Maths concepts without even thinking about it, shows how disconnected Maths as a subject has become from everyday life.  Anything that reverses this must be good.

While I welcome the change in emphasis in the Maths curriculum in second level, I personally don’t think it should happen in isolation.  I think we need to address the elephant in the room, which is the social acceptability of the lack of ease with Maths.  This often manifests itself in the home.  Parents who themselves are not confident in their Maths ability often pass on these insecurities about Maths to their children without even being aware of it.  Many parents, whose children are in primary school, often feel ill equipped to help their children with their Maths homework as they move up the classes.  If the child feels insecure in their own ability in Maths by the time they leave primary school, then ‘not being good’ at Maths becomes a self fulfilling prophecy as they tackle more abstract Maths concepts.  I would love to see a real engagement with parents over the coming years. Supporting parents to conquer their own Maths demons, will surely only help to overcome the Maths demons of the upcoming generation before they manifest themselves.

As always thoughts etc. gratefully accepted.

New Year’s resolutions revisited

2011 was a year where I have really begun to integrate technology into how I do what I do. As someone with a background in technology I didn’t, and don’t, have a fear of technology but I don’t think I really ever used it as I should. Like all of my colleagues in LIT Tipperary I’ve used Moodle etc. over a number of years and as a Maths lecturer I’ve always been aware of the potential for using technology in my class, but I’m not sure that I’ve leveraged the potential of technology as much as I could, or should have. Due to a number of seemingly insignificant changes during 2011, I really feel like I’m now beginning to exploit the real potential of technology.

I didn’t sign up for Twitter in 2011 but really started using it in anger in 2011. Now that I’ve connected with so many people on Twitter, and am learning so much in the process, I’m really looking forward to where 2012 takes us all Through my interactions with educators on Twitter, I’ve become involved in initiatives like #edchatie, #coderdojo and #ccGlobal. These initiatives have pushed me out of my own comfort zone but have enriched my interactions with students in many ways. I’ve also used Twitter to source presenters for the ICT in Education conference,  http://www.lit.ie/Tipperary/Schools/default.aspx, which I believe has really strengthened the breadth of sharing that happens in Thurles in May every year.

2011 was also the year where Google+ came on stream. I couldn’t wait to sign up during the summer, frantically trying to get an invitation and waiting for the window of opportunity to use the invitation. I must admit however that I haven’t been bowled over by G+. I find I’m overwhelmed by the sheer volume of information that is to be found there. I think this is partly my own fault, because I haven’t really organised my connections into coherent circles, but for me twitter reigns supreme. I know that there is a huge volume of information etc. also to be found on Twitter, but I seem to have found a way of working with Twitter that works well for me. I suppose the beauty of Twitter for me is that, the brevity of the message focusses my own and other peoples thoughts. What I do love G+ for are the hangouts, which allow you to connect via webcam with others on G+. I have used hangouts to connect with others to discuss various #ccGlobal projects and to connect my daughters class with Michael Thornton’s (@mthornton78) class in Virginia USA.

2011 was also the year when I started this blog – I was shocked to be both nominated and shortlisted for the Edublog Awards in the best new blog category. What has really surprised me though is how much I enjoy writing the blog posts. I suppose what finally persuaded me to start the blog in 2011 is the fact that I’m hoping to start a PhD in 2012. The write up holds a particular terror for me, not to mention the rest!, so I decided to start blogging to get me into the writing habit. Hopefully I’ll be writing about the start of my PhD journey during 2012 .

My first blog post was my academic New Year resolutions http://pamobriensblog.wordpress.com/2011/08/24/new-years-resolutions/. The resolution I made, was to do what I do differently, and, as a way of focussing my mind I made a list of three ways I was going to do this – start the blog, use a wiki with my class and create podcasts to supplement my notes for my students. Unfortunately I’ve really only stuck to one of these, this blog which I’ve kept reasonably well updated. The other two haven’t worked out as I’d hoped thy would. To be honest, I think it’s more a discussion forum than a wiki that I wanted to use with my students. The aim of the discussion forum, is to encourage a greater understanding of the importance of Maths concepts in various areas of Computer Science, so this is where I’m going to focus my attention as I start a new academic term. Regarding the podcasts, it didn’t really happen for various reasons last term, but I will right that wrong in the forthcoming term. The equipment I was using, a Logitech webcam, really wasn’t fit for purpose so I acquired a Livescribe pen during last term. Once I complete the end of term corrections during the coming week, I will focus my attention on producing pen casts which will include audio with my notes. I hope these will be of benefit for my students. While I didn’t produce my own podcasts during the last term, I did source podcasts on YouTube for various topics, which seemed to benefit the students. The other use of technology I used in class, which worked very well last term, was Java programming. The feedback from the students was very positive, so I will continue to reinforce the very strong connections between Maths and programming by including more programming in my tutorials.

My final resolution is to submit a proposal to present at the CESI conference (http://www.cesi.ie/conference-2012) which is to be held in Portlaoise on the 24th and 25th February. As an organiser of the ICT in Education conference I’m quick to ask others to present but have always shied away from presenting myself. 2012 is the year where I push myself out of my comfort zone and share what I find useful from a technology perspective. I’m very aware that a lot of teachers can find technology very intimidating simply because of the sheer volume of tools and different technologies out there. I’m thinking of proposing a workshop on Twitter and Google+ hangouts, not as an expert but as an ordinary user of these technologies. As always, any thoughts etc. gratefully accepted.

Update on New Year’s resolutions

Now that I’m six weeks into the first semester, and therefore half way through, I decided to give an update on where I’m at with my New Year’s resolutions.  If you haven’t read about my resolutions check them out here.  The main plan when I set out my resolutions was to change how I do what I do.  While I haven’t used the technologies that I set out at the start I think I have made some progress in changing what we do in class.  My three main resolutions were

1. start a blog
2. use a wiki, specifically a discussion forum
3. create podcasts to support my course notes

The blog has been started, and continues to be updated, and I must say I am really enjoying writing these blog posts.  I had hoped to have used a wiki and podcasts at this stage but unfortunately I can’t give an update on these technologies in this post.  Regarding using the wiki, I haven’t used a discussion forum yet but the plan is to get this started next week.  I had planned to use it from the start, but decided to let the students settle in before I brought this in to the mix.  Having taught Maths to 1st year computing students for the past 4 years and to 2nd year computing students for the past 8 years, I often find that the students ease with Maths ranges from being very comfortable with the topics, right across the spectrum to sheer terror at the mention of an ‘x’ or a ‘y’.  This year with my first years seems to be following the same pattern.  The challenge for me, is to move on with those who are comfortable, and show them where and how they might use the Maths topics as future Computer Science graduates, while building the confidence of those who are terrified at the very thought of Maths.  I think the time is now right, to bring in the discussion forum, so here’s hoping it gets the students thinking about how Maths might be useful to them in their chosen field of study.

With the podcasts, or more correctly the videocasts, I have made very little progress so far.  This is mainly due to not having the correct equipment and work generally getting in the way of work!!  I have used a Logitech webcam to make an initial videocast, but the results were far from ideal.  I have since been told that a Livescribe Pen is what I really need, to do what I want to do, so the order is in and I can’t wait to get started with that!!  As always, the update will be here at some stage in the future  While I haven’t created my own podcasts, I have provided Youtube clips to support the topics that I have been covering in class.  These seem to be proving popular with students, particularly those who are less confident with Maths.

Enough about what I haven’t done yet, and on to what I have done and what seems to be working.  One of the problems we often find with students who study on Computer Science courses, is that they have very little idea of what they are getting themselves into, and are often very disillusioned when they realise what is actually involved.  With the availability of so many applications and various technologies, the perception is often that a computing course will involve just using these applications and technologies.  What a lot of people don’t realise is that, on computing courses, students are creating content rather than consuming it.  Writing applications and testing them is a very important aspect for a lot of our courses so that’s what I have been focussing on in class.  We have coded in Java in Maths class, check out the blog post on how we got on here.  We’ve used Java again this week, coding loops to calculate the terms and the sum of the terms in an arithmetic sequence.  I’ve been able to stress the importance of being able to calculate test data to make sure that their programs are working as they should.  We’ve also discussed why it’s important that the students can work through the various calculations themselves, as this understanding is crucial if they want to be able to code applications which perform these calculations.  In previous years I have spoken about the importance of understanding calculations and being able to create test data but I haven’t taken the next step of actually coding.  This year, I decided to take that step and the feedback so far seems positive.

So, the plan for the next 6 weeks of the semester is to use the discussion forum and to create podcasts and make those available for students.  I’m also hoping to bring in guest lecturers from industry to speak to the students about where Maths is used, to give a context to what they are covering in class.

A woman who inspired me to become who I am

Last Wednesday, 5th October 2011, was World Teachers Day and today, Friday 7th October 2011, is Ada Lovelace Day.  Ada Lovelace was a mathematician in the 19th century who is often referred to as the First Computer Programmer.  Both of these days, highlighting the contributions of teachers, in the case of World Teachers Day, and the contributions of women to the Science, Technology, Engineering and Maths areas, in the case of Ada Lovelace Day, have made me think about a teacher and a mathematician who has inspired me to become who I am.

While in secondary school, I loved studying Maths.  During Transition Year we began studying the Leaving Cert Honours Maths syllabus and we were lucky enough to be assigned Mary Haugh as our teacher.  Over the next three years my love of Maths continued and if anything got stronger.  I loved Maths class and really enjoyed the problem solving aspect of the syllabus.  This is in no small part due to Mary Haugh.  Her guiding principle in class was that there was no such thing as a stupid question.  This allowed us, as a class, to tease out the many nuances of the various Maths topics.   When filling in my CAO choices in school I found it difficult to choose between an Applied Maths course and an Industrial Chemistry course.  I sought the advice of Mary and while she was careful not to influence me, the chat helped me to clarify what I wanted to study.   I followed my heart and put Applied Maths first, which I believe was the best decision of my life.

This gave me an opportunity to have careers as a computer analyst/programmer, a statistician and now as a lecturer.  Since starting to lecture I often find myself thinking of how enjoyable my Maths classes in school were and how comfortable we all felt being able to ask questions.  This is something I have tried to incorporate into my own classes – I do appreciate how difficult it can be for people to ask questions in a class of more than 70 people but I still encourage participation in lectures and also in my smaller tutorial sessions.  I’m not sure how successful I have been in this endeavour, but I do strive to put people at ease and try to help them to overcome the genuine terror and lack of understanding that a lot of people feel when faced with a Maths class.

So thank you Mary Haugh for inspiring me both while I was studying Honours Maths in school and also in my current career as a lecturer of Maths.