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The Flexible Learner – Teaching and Learning

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Teaching and Learning

Since I arrived at Dundee my understanding and appreciation of the difference between instrumental and relational learning has increased exponentially. In reading the ideas from Colley et al. (2002) I feel glad to see them advocating learning as a social and relational process. Having recently attended the Scottish Mathematical Council’s (SMC) Stirling Maths Conference, I was completely blown away by an unexpected lightbulb moment that made me stop and question everything I have ever done in a classroom. It was particularly to do with teachers teaching skills, knowledge and understanding at the bottom end of Blooms’ Taxonomy in class time followed by students going home and doing homework on higher order skills, such as applying, analysing, creating and evaluating. Why, as creative, experienced, intelligent professionals are we using our precious time with our young people to teach them skills that the majority of them could pick up themselves with a basic introduction? Why are we not using our time to build on this ‘basic’ knowledge and how to apply, analyse, evaluate, experiment with and create new learning from it? What a waste of time!

Blooms

http://blog.curriculet.com/wp-content/uploads/Blooms-Taxonomy.png

I do realise that it is unwise to view things in such simplistic terms using Blooms’ Taxonomy but considering Blooms’ Taxonomy was the catalyst for realising that I have been doing the monotonous, easy transferring of knowledge from me to my pupils rather than using my skills to help them be co-constructors of their own learning in order that they take and make sense of and add relevance to THEIR own situation. What a waste of MY talent! Although I have instinctively been teaching in a relational way (Skemp, 1972), I need to help my pupils identify how one aspect of their learning relates to another and that actually teaching in this way IS better than teaching the rule for doing this and the procedure for doing that.

As Colley et al. also suggest, learning is a social process.  One of the most underused strategies for teaching mathematics is talking about it. If you walk into a school, primary or secondary, you are still more often than not likely to find children doing mathematics in silence; they are usually sitting in groups but working individually in silence. This is changing in primary classrooms, particularly in early years classes, but in secondary schools the overwhelming need to meet assessment targets in terms of ‘getting through the course’ drives the way that mathematics is taught; this is not a criticism merely a statement of the reality of the situation and no judgement is assigned to this. There are, however, some practices being trialled in some secondary mathematics departments, such as the flipped classroom, which may help to meet both the need to get through the material whilst using the face-to-face pupil-teacher interaction in a more productive way.

How can we support our students in engaging in a deeper approach to their learning?

In reflecting on myself as a learner, I have always been someone who has done what was needed to be done and therefore I would consider myself to be a strategic learner. I learn deeply the things that will be of practical use in my job, are relevant to me and my way of working and that help me to do my job more effectively. I have consequently engaged with learning more deeply since I have identified a clear purpose for learning.

To answer this question in general terms the Curriculum for Excellence (CfE)(Education Scotland, no date, no page) does a good job in this regard. Education Scotland (no date) encourage educators to consider the 7 principles of curriculum design to engage our learners in deep learning.

  • Breadth
  • Depth
  • Coherence
  • Relevance
  • Progression
  • Challenge and enjoyment
  • Personalisation and choice

From these 7 principles, what I have identified as my motivations for learning more deeply are: relevance, coherence, personalisation and choice, challenge and enjoyment and progression, in that order.

In working with the PGDE students on co-operative learning, one of the key things I have been trying to relay is that the children have to be involved in their own learning, it has to be purposeful and that the teacher’s job is as a facilitator of the learning rather than the architect of it. Shuell (1986) in Biggs and Tang (2007) illustrates what I have been saying:

It is helpful to remember that what the student does is actually more important in determining what is learned than what the teacher does.

It occurs to me that perhaps the biggest change in my attitude towards teaching is tied up in my idea of my own importance. When I first started teaching I felt I was the most important person in the classroom. When I retrained as a primary teacher, my class and I were the most important people in the school. As a Depute Head Teacher everyone in the school was important including me and then as a Head Teacher everyone in the school was important, except me. So now, when I plan for an input, the first thing I think about is what do the students need to know about the topic closely followed by, how am I going to engage the students in this learning and what will make this happen. How very interesting – ego?!

In reading Teaching Learners to be Self-Directed http://longleaf.net/wp/articles-teaching/teaching-learners-text/ the above relates to initially me being the teacher of Stage 1 learners, not necessarily that they wanted to be Stage 1 learners but that I treated them in that way. Then I moved on to be a teacher of Stage 2 learners in that I tried to inspire and work with them. I would say that learning about co-operative learning strategies and gaining in experience and confidence has enabled me to move my learners towards becoming Stage 3 learners but I don’t know if I will ever be able to take learners to the next stage because I don’t want ‘to become unnecessary’ (Grow, 1991/1996, no page).

Grow suggests that the role of the Stage 4 teacher is ‘not to teach subject matter but to cultivate the student’s ability to learn’ (Grow, 1991/1996, no page).  This brings to mind the old adage that secondary teachers are seen as teachers of their subject whereas primary teachers are teachers of children. This is completely unfair but secondary teachers do think differently about their jobs because they have very different pressures to their primary colleagues. Being a primary teacher and a secondary teacher are two very different things as is being an early years’ teacher in comparison to an upper primary school teacher.

Phil Race’s model of learning:

  1. Wanting to learn
  2. Learning by doing
  3. Learning through feedback
  4. Making sense of what has been learned

In reading what Knowles has to say about the way adults learn I think that this reflects what I was hinting at earlier in regard to how I learn. As an adult learner I do need to know why something is relevant; that I am able to make decisions about what I am learning; that what has come before is important but what comes next is valuable and useful in a practical way. An interesting observation is that adults are life-centred rather than subject-centred.

I need to think about how I facilitate small group teaching. I know the theory and how to it works with children but I have not really applied these strategies to working with my students this year. I need to use more co-operative learning strategies. Perhaps that is what I do need to learn on this course is how to shift from being a teacher to becoming a facilitator of my students’ learning.

The Flexible Learner – Blended Learning

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Blended learning

What is it?

This term is generally applied to learning and teaching that occurs both face-to-face and through an online interface. The majority of the courses on which I teach have this blend of approaches to a greater or lesser degree. Most of the PGDE and MA modules are face-to-face with materials collated onto the University’s virtual learning environment (VLE) My Dundee to provide further exemplification of ideas and concepts discussed in lectures and workshops or to provide a place to share and store helpful resources and suggestions for practice.

The M.Ed modules use the online environment more extensively, providing opportunities for the students to communicate with each other and their tutor in a collaborative way and to engage in the majority of their learning online.

According to TeachThought (2013, no page) using technology in blended learning should ‘not just supplement, but transform and improve the learning process’. It could therefore be argued that the ‘taught’ Education programmes do not blend learning as technology is often used to supplement not transform learning and indeed the M.Ed ‘distance learning’ programmes probably do not fit TeachThought’s definition either in that there is a lack of face-to-face contact and therefore limited opportunities to develop strong, purposeful communities of learning. How my colleagues and I use the VLE is effective and utilises the majority of its functionality, however, it cannot really be described as blended learning, yet!

Why blend learning?

According to the U.S. Department of Education (2010) studies contrasting blended learning (online and face-to-face instruction) with face-to-face instruction have shown blended learning to be more effective, whilst using online learning or face-to-face instruction singly are no more or less effective than each other. Torrisi-Steele and Drew (2013), however, identify that whilst some studies did agree with the U.S. Department of Education’s contentions, there were no comprehensive explorations of the reasons for the noted effectiveness; for example, the teaching strategies employed or the quality of resources. The U.S. Department of Education’s meta-analysis and review of online learning goes on to identify that online learning which has a collaborative aspect, whether that be with other students or with a tutor, is more effective than independent online learning (U.S. Department of Education, 2010).  The above arguments provide a reason for blending learning but not necessarily a clear picture as to whether the main reason for the effectiveness of blended learning is the ‘blend’ of the learning or whether there are other issues at play.

Torrisi-Steele and Drew (2013, p. 378) suggest that blended learning needs to ‘exploit the attributes of technology and face-to-face teaching… to achieve enriched learning experiences or perhaps create better learning experiences not possible through the use of face-to-face teaching or technology alone’. Whilst their research clearly emphasises how transformational blended learning can be they raise some important issues regarding the ability of staff to use technology to enhance learning and teaching not just supplement it. Hew and Cheung (2014) agree, saying ‘It is not sufficient to merely put course contents on a web site for students to download for a blended-learning course to be successful’ (Hew and Cheung, 2014, p. 5). One of the main issues Torrisi-Steele and Drew (2013) highlight surrounds academics having to expand their knowledge of the technological tools and appreciate the advantages and disadvantages of these tools. Alongside this the introduction of technological tools often requires a complete overhaul of teaching strategies and course design to take account of different modes of delivery and assessment and this is no easy task.

So how could I use blended learning and what benefits would it bring?

In terms of blending learning I have already started to integrate aspects of online learning into my learning activities. The next step is to structure this learning to provide meaningful, integrated activities which use technology for a purpose rather than just a fancy way of collecting information or sharing course content. In considering key activity 3 (see appendix 4), the use of technology has to also incorporate students taking an active role in their own learning and being co-creators of it. For this to be manageable and relevant for everyone then using technology to facilitate tutor-directed tasks (TDTs) in the form of a Glow blog seems a sensible place to begin and for my guinea pigs to be my secondary mathematics students. My reasons for choosing my secondary mathematics students are three-fold: they will be a small group that I can support and monitor more easily; I see them regularly throughout the academic year and therefore this can be become an iterative process of change and improvement; and anything they do using an online learning space contained in Glow can be used as evidence towards their Standards for Provisional Registration (SPR) and continued when they leave university to be used for their professional update.

References

Assessment Reform Group (1999) Assessment for Learning: Beyond the Black Box. Cambridge: University of Cambridge School of Education.

Education Scotland (no date) Curriculum for Excellence: Principles for curriculum design. Available at: http://www.educationscotland.gov.uk/learningandteaching/thecurriculum/howisthecurriculumorganised/principles/index.asp (Accessed: 13 June 2016).

General Teaching Council for Scotland (GTCS) (2012) Standards for Registration [Online]. Available at: http://www.gtcs.org.uk/web/FILES/the-standards/standards-for-registration-1212.pdf (Accessed: 14 June 2016).

Grow, Gerald O. (1991/1996) ‘Teaching Learners to be Self-Directed’, Adult Education Quarterly, 41 (3), pp.125-149. Expanded version available online at: <http://www.longleaf.net>.

Hannan, A. (2001) ‘Changing Higher Education: teaching, learning and institutional cultures’, Annual Conference of the British Educational Research Association, Leeds, 13 September. University of Leeds. Available at: http://www.leeds.ac.uk/educol/documents/00001855.htm (Accessed: 13 June 2016).

Healey, M., Bovill, C. and Jenkins, A. (2015) ‘Students as partners in learning’, in Lea, J. (ed.) (2015) Enhancing Learning and Teaching in Higher Education. Maidenhead: OUP.

Hew, K.F. and Cheung, W. S. (2014) Using Blended Learning: Evidenced-Based Practices. Singapore: Springer.

TeachThought (2013) The Definition of Blended Learning. Available at: http://www.teachthought.com/learning/blended-flipped-learning/the-definition-of-blended-learning/ (Accessed: 16 June 2016).

Torrisi-Steele, G. and Drew, S. (2013) ‘The Literature Landscape of Blended Learning in Higher Education: the Need for Better Understanding of Academic Blended Practice’, International Journal for Academic Development, 18(4), pp. 371-383.

My personal philosophy of teaching

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My personal philosophy of teaching…I want to make a difference!

This might be making a difference to a young person’s understanding of a school subject or making a young person believe in their ability to do something better or just making sure that a young person knows that someone is listening but ultimately I want to make a difference.

I prefer to think about ‘learning and teaching’ rather than ‘teaching and learning’. This may seem a little pedantic, however, I always start with the learning…what are the learners going to be learning or what do they need and want to learn? There has to be a reason for learning, a purpose, or else what is the point? This does not mean that learning has to be practical and useful all of the time, and what one person learns will not be the same as someone else, but it must be meaningful to that individual. Therefore it is no coincidence that the principles of curriculum design in Curriculum for Excellence (CfE) (Education Scotland, no date) include relevance, challenge and enjoyment and personalisation and choice. Learning must be relevant to the lives that children, young people and adults are living now and will be living in the future and help them to get the best out of themselves.

Only once the learning has been identified do I think about how I am going to teach. How I teach depends on my audience, on what I am teaching and the purpose of that teaching. There are times when you have to lecture to transfer knowledge. There are times when it is important for the learners to investigate and learn through their own experience. There are times where it is vital that learners learn together and other times for them to work on their own. Consequently, in my teaching I use a variety of teaching strategies, organisational strategies and modes of delivery.

I believe that a CPD session is a successful one if I can take one thing away from that session and implement it immediately in my practice the next day. This does not need to be a strategy or a worksheet but it could be a thought that provokes me to reconsider a way of thinking or being. When I am planning and preparing teaching inputs I consider how useful the learning will be and how I would use it, in order to understand the potential impact it will have for my learners.

My justification for teaching using different strategies and varying how I teach different groups is that ultimately it is my responsibility to enthuse, motivate and teach my learners by adjusting how I work.

I want to give my learners the best possible start on their learning journey and to encourage them to become self-motivated seekers of how to make things different and better.

 

References

Education Scotland (no date) Principles of Curriculum Design. Available at: http://www.educationscotland.gov.uk/learningandteaching/thecurriculum/howisthecurriculumorganised/principles/index.asp (Accessed: 3 May 2016).

Lecture observation

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Now that took me back…having someone sitting in my ‘class’ watching me teach. That has not happened for a good few years (accept when I was observed working with the PGDE(S) maths students just before Christmas). It was different though being observed by someone who does not know me on a personal or professional level.

I spent an inordinate amount of time preparing for the input making sure that the lecture flowed, made sense, did what I wanted it to do plus incorporated the use of resources to keep the students motivated and engaged. They probably did not know what had hit them!

Comfortingly though as soon as the students walked into the lecture theatre they made lots of ‘ooow’ noises when asked to take multiple choice cards plus a whiteboard and pen – know thy audience – they have always reacted well to the whiteboards in particular and today was no exception – a good start.

The initial YouTube clip seemed to have the desired effect and there was a buzz around the room when the majority of the group ended up on the smiley face. Perhaps on reflection though it may have been an ideal opportunity to delve into some of the mathematics behind the clip rather than taking a superficial look at the activity being related to probability – something to consider for next year; alternatively maybe come back to it at the end once the students have had an opportunity to consider the progression/skills of chance and uncertainty and be able to appreciate how to use it as a stimulus. I have already re-titled the slide ‘Chance or Certainty?’ which I think adds another dimension to what the clips represent. So doubly good start!

Admission time…I totally forgot to print off the multiple choice card slide, which I had wanted to display on the visualiser so that I did not have to keep reminding the students what each letter represented – note to self, go back to putting a resources slide on the PowerPoint to keep track of things I need!

The next few slides with their activities and interactive and discursive opportunities worked well but the main strategy which helped enormously at this point in the input was that I have started to learn more of the students’ names providing me with the opportunity to engage more specifically with them. I tried not to use this in a threatening way but boy did it make everyone sit up a little more! As I see the MA2 students for a significant number of inputs this is going to be a priority for me for next year and in fact I am already making in-roads to learning the names of the MA1s. This hadn’t actually been a priority for Semester 1 as with teaching the 180 PGDE(P) students there was no way I could remember everyone’s name. Also there had been no need to learn names up until this semester as I had not really taught an entire cohort of students in a lecture situation and was able to use my table names and number cards to ensure participation in the workshops. Working in a lecture theatre environment has been a steep learning curve as it is so unlike a classroom teaching environment. Saying this it has really spurred me on to think about and investigate ways to ‘make’ people interact with me, although this is still a work in progress.

So, returning to why today was different from my observation before Christmas. It was potentially because there were more students today and I have not built up as close a relationship with them as I have with my PGDE(S) mathematicians and therefore am not as relaxed working with them? As hinted at earlier perhaps it is the difference in my relationship with the two observers. I was more nervous today and perhaps need to reflect a little bit more about why that was. However, it is amazing how once you get started your instincts and experience kick in and eventually you forget that there is someone there, watching.

The one thing that I have really loved about coming to the University is that I am again experiencing that buzz you get from planning interesting activities and seeing them work (or not!) and taking chances and trying things out. Although my job as a senior leader in a school was rewarding and challenging I came into teaching to teach and that is what I am doing again and I love it!

Every day is a learning day, folks! Every day!

Architecture and tessellation

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I was reminded recently of an innovative house building design called a Hivehaus. I first came across this building on the Channel 4 programme “George Clarke’s Amazing Small Spaces” presented by George Clarke. The first time I saw the programme I remember thinking it was a brilliant design and how versatile yet simple it was. However, having now taught a couple of inputs on the Discovering Mathematics module it has occurred to me that not only is the Hivehaus design mathematically pleasing – well to me anyway, it is all based in the fundamental properties of mathematics as a result of its use of tessellation of shapes.

The pictures below are of the Hivehaus prototype and also the 3D plan view from the website planning tool, which you can use to design your own Hivehaus!Hivehaus prototype picture

Hivehaus 3D plan view

It is immediately obvious from picture above that the house is built by connecting (or tessellating) hexagonal units. What is not obvious from this particular picture is that you can add rhomboid or trapezoidal shaped rooms. These rooms are generally studies or bathrooms and fit into the gaps between the larger hexagonal rooms. I suspect that the gentleman who developed this innovative approach to house building used his vast experience of physically building things to ensure rooms of different shapes fit together well although it could be argued that without a fundamental understanding of shape and how shapes fit together, he would not have been able to make this work.

I will have to remember to use this example next time I teach on the Discovering Mathematics module.

 

Student roles and mathematical competence

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Just been reading an article from the Mathematics Education Research Journal about student roles and mathematical competence. I’m not quite sure what to make of it and what the article was ultimately trying to conclude. It describes how mathematics is taught in two different ways in a first grade and second grade class in an American school. The children who were part of the study had been taught one way in the first grade class and were now experiencing a different way of being taught in the second grade class. I suppose I was expecting to read that the more discursive, investigative way of teaching in first grade was going to come out as a better way of teaching and that the children would not enjoy being taught in a more traditional manner in second grade. It doesn’t seem to be that way. However, it has made me wonder if the children had been taught in the traditional way in first grade and then in a more problem solving based way in second grade if this would have made a difference to their feelings of security and success.

I think the one message that does, however, come clearly through is that the attitude of the teacher towards the children and their answers is similar in that both teachers treat incorrect solutions as learning opportunities and don’t discount the children’s answers, right or wrong.

 

Inspiring use of blogs by new MA1 UoD students

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I’ve just been reading through some of the blogs created by the new MA1 students here at UoD and have been blown away by their insightful, honest entries. If this is the face of professional learning together and sharing our highs and lows, then bring it on. Absolutely inspirational stuff; these young people are going to be our teachers of the future – brilliant!