Teaching Mathematicology to English Students in West Virginia

Transcription

1 UCET Travel Scholarship 2012 Report on Visit to West Virginia Wesleyan College to examine aspects of teaching mathematical methodology to children in Primary Schools. Jill Turner Senior Lecturer University of Worcester Contents 1. Introduction 2. Background 3. Context and Aims 4. Methodology 5. Findings 6. Conclusions 7. References

2 Introduction. This report summarises my findings from a week s visit to West Virginia Wesleyan College where I had the opportunity to share some teaching on the Elementary Education Major course s module in Mathematical Methods. This is a class for students in their sophomore (2nd), junior (3rd) or senior (4th) year undergraduates prior to their Clinical (school experience) the following semester. I focused on the mathematical understanding of the students themselves and the pedagogical processes in which they are involved. I was also able to visit an elementary school and see how these processes manifest themselves in the classroom. Background. It has always been my belief that to succeed in mathematics children need to have an understanding of the processes involved and the links between the various areas. I strongly feel that the key to understanding process is through the development of mental processes, dialogue, models and images and the use of practical apparatus. Throughout my career I have taught and encouraged school children and HE students to engage with mathematics as a practical subject, seizing opportunities for hands-on wherever possible and creating a learning environment beyond the didactic. I want to be able to extend my own research beyond current British experience and add an international dimension to my work. In the USA, HE providers are also challenged to provide excellent mathematical pedagogy for their trainee teachers. School pupils struggle with similar areas to their UK counterparts, especially with calculation. I am keen to examine teaching and learning methods and share some of my own experiences with colleagues in American initial teacher training. The need for children to be able to calculate effectively and accurately and to be able to confidently approach methods of calculation through understanding the processes has been recently highlighted by ministers such as Michael Gove, (September 2012) and through the development of the National Curriculum (2013). There has been much political and academic debate in England about the age at which children should master these processes as well as how much understanding matches ability to perform. Cotton (2010) emphasises the need for a range of methods appropriate to particular calculations whereas the DfE (2013) wants pupils to use written methods for short multiplication and division by a single-digit integer of two-digit then three-digit then four-digit integers, then of numbers with decimals; then use long multiplication In May 2007 I presented at the LUNA conference at the University of Oulu, Finland where delegates were keen to learn about British methods for teaching long multiplication and division. I also had the opportunity to visit an international school where mathematics was being taught through problem solving in line with the thinking of the Freudenthal Institute in Holland. It was exciting to observe children applying their mathematical skills from a real life situation, albeit a text book suggested context, delivered by staff who intervened with support on request. The current understanding is that Finnish pupils gain success in mathematics through utilising resources to overcome possible barriers to learning. (Ofsted, 2010), and yet the classroom was strikingly similar to many I have visited here in the UK.

3 It is these similarities and the differences which I wanted to explore alongside the expectations of the trainee teachers in the United States. Context and Aims West Virginia Wesleyan College itself is situated in Buckhannon, West Virginia and has 1400 undergraduate students of whom over 90% live on campus. A private institution the annual tuition fees top $22000 and accommodation a further $9000. However many of the students are on full and part scholarships which are awarded based on academic success in entry tests and by various athletic and state awards. I spent time with a group of students in their Mathematical Methods class where we had discussions about algorithms and examined both the progressions of 4th and 5th graders which helpfully equate in ages to our Year 4 and 5 children. Most of the teaching in elementary schools in West Virginia is dependent on process and written methods, there is little or no emphasis on talk for mathematics (Bagnall, 2012).The students represented years 2-4 of their degree course and could choose to follow this compulsory module at any time during their undergraduate course. That being said the majority of students within the group were seniors (in year 4 of their course). The aims of the research were to examine the pedagogy of teaching calculation in elementary schools in West Virginia and to look for parallels and possible innovations to share with colleagues in the United Kingdom. I was also hopeful of establishing a partnership where students from both HE providers could share experiences in the future through electronic collaboration such as video conferencing or web links such as face time or Skype. Methodology The data collection methods for my research are set in the interpretevist paradigm. Although you could argue that this type of research lacks rigour (Sharp, 2010), due to its failure to provide evidence based data, I still believe that through interviews and observations a genuine reflection of the situation how it is provides an interesting perspective on reality. By examining the evidence obtained through observation and interviews I was always going to obtain data which could be interpreted as biased, but through awareness and discussion of the possibilities of this, (Punch, 2009) I would always seek to minimise the effects. I made notes following my observations of the students in class and group interviews held with them afterwards. I kept a diary, in which I wrote reflections and notes about my observations on the three occasions. I also entered follow up questions to probe on my next time with the students. I had two occasions where I interviewed Dr Bush, the situation could be described as semi structured as although I had pre-set questions several other areas were discussed as befits the nature of this type of situation. Again I made notes in my diary to supplement those made during the interviews themselves. Many of the questions related to paper work and the evidence trail that students need to follow.

4 My research was intended to be investigative, I was not looking for answers as to best way to deliver pedagogy for teacher education, however, the resulting data may well have opened my eyes to those possible innovations mentioned earlier. It was very important that I kept an open mind and that my critique would evolve once I had some findings. When interviewing it is often easy to interpret answers during the interview itself and then with reflection change interpretations completely. Although as the interviewer I am aware of this at the time my natural mindset wants me to think why at each response. Findings The students in the United States have many of the same issues as those faced by English students on an initial teacher training course; issues related to subject knowledge and their ability to support learning for all ages of elementary pupils combined with issues of confidence with teaching and behaviour management. Their mathematics element of the course consists of a combination of pedagogical and subject knowledge. The students have specific mathematical methods tuition for 3 (separate) hours per week over a semester of 18 weeks. One of these hours per week is spent in school working as tutor buddies to pairs or small groups of pupils. As a result of prepared activities regularly delivered to the same pupils the students are able to personalise the learning for their pupils. Their regular weekly input helped form professional relationships with the pupils and both (students and pupils) were eager to move learning forward. The quality of the students prepared activities varied; the school pupils commented on their opportunities as well as the students feeding back to their peers in a later class. The timing of my visit was significant. The students had had time to embed their working relationships with their buddies. The pupils eagerly anticipated their visits and engaged readily with the activities. This was evidenced from the smiling faces of the school pupils and the greetings to their buddies. During my observations, the students were reinforcing calculation methods with reference to multiplication and division: methods of calculation were similar to those used in British schools with the ultimate being an efficient method of long division to fifth graders, much the same as the method advocated by the new National Curriculum (2013). By the introduction of Do McDonalds sell Burgers? one student was supporting the children s learning by giving them an acronym (DMSB) phrase to use to remember the order of operations required. The higher ability students were quick to understand this idea and were readily applying the method with each stage relating to the burger creation. Perhaps they were relying on rote learning as suggested by Haylock (2010,) which would make access more difficult for the majority of learners. An English student in the group felt that the standards for mathematics in his USA classroom were lower than they might be in the United Kingdom (UK). Investigating this further and cross referencing with the Primary National Strategy (2006) children in the UK should be exposed to the same levels of learning as their counterparts in the USA. The student and I discussed experiences and factors such as catchment areas and range of abilities to further investigate why this might be the case. In the university class there was a discussion about teaching the long division algorithm. Many students reflected on their own experiences of learning as well as those of teaching. Hatfield et al (2008) discuss the disproportionate amount of time spent mastering this algorithm but go on to state the

5 importance of focusing on the understanding element of the division process. The English student I referred to earlier explained to his peers how repeated subtraction helped him to understand. He felt that this method had taught him the ability to become efficient and in fact had been his earliest recollection of a teacher encouraging him to refine his methods so he could do things more quickly. The idea of a tutor buddy is not a revelation; systems for its use have been set up across the globe sin places such as India, Australia and other parts of the USA.Models have been trialled but institutions currently seem to be working within their own proven parameters, such as that of Springfield College (2013). This was my first time observing practice directly. The teachers in the Elementary school were complimentary about the students, they felt that their pupils were fortunate to have the opportunity to work in such small groups and that they looked forward to the times when the students were in. They themselves often followed up the student work with discussion and pupil evaluations on how successful they felt the activity had been in supporting learning. The burger acronym was noted as memorable with the students using DMSB into the next few lessons with division and sharing it with their peers. Interestingly the class teacher from the elementary school requested the resource the student had initiated to use with more children. The students felt that preparing different activities for their buddies each week was time consuming but well spent because they could see the positives for the children. The university tutor commented that the school pupils have a certain expectation from their resources and look around to see if other pupils have more interesting things to engage with, this creates competition amongst the students to produce good and effective resources. One student commented that it became competitive as they were producing more and more elaborate games, another felt that simple easy rule activities were better because the learning was not masked and the children felt good about achievement. Examining this last comment further, the student felt that practice was paramount in accurate mathematical calculation and that using simple resources such as dice enabled the pupils to engage as much as the more complex. The pupils spoke enthusiastically about the students coming each week. They enjoyed the sessions because often they were helped by the activities to understand the work they had been covering that week. One child commented, I like the way I can use what I have learnt in a fun activity, my buddy always has something interesting for me to do. These results lead me to the question does learning have to be fun? Which is more important the learning or the fun element? In my experience pupils in the UK list boring as the uppermost mustn t be in their list of teacher qualities or learning situations, and I recall interviewing potential trainees who always talk about making lessons interactive and engaging. I wondered if boring meant the same to a pupil in West Virginia as it did back home in Worcester. Is boring the opposite of fun? I pursued this with the students asking if any of the activities they had done with the children was thought to be boring. My question was met with some embarrassed giggles; tedious and boring were terms they were not supposed to use in school as it showed a lack of respect. This echoed my own teaching experiences when I often talked with pupils about boring tasks are only felt by boring people. It was interesting to discover a cultural similarity. I asked how the pupils judged something to be fun and their response was to say that fun often meant different or unusual, one child said away from the norm, and one said when it

6 makes me smile. None of these would enter the dictionary as descriptions of the word fun. We discussed making it interesting and playing to learn and the pupils also said they enjoyed the attention of the teacher made possible by working in such small groups. The students talked about engagement and learning without actually knowing they are learning. In these days of tailor made resources being so available in our primary school classrooms and publishers keen to fabricate to match the teachers requests trainee teachers do not necessarily have to spend the hours making suitable resources for their classes of children. However here in the USA were trainees doing just that; coming up with resources which would match the children s learning and encourage engagement. I wonder if the emphasis is on entertainment as well as learning? This is beyond the realms of my research but would be interesting to explore further with emerging teachers. The university tutor responsible for these students maintained she watched the students grow into teachers during these school visits. She added that they became responsible, professional, caring and realised that it was more about the children than themselves. Recent research presented at the LICE conference (McKerr and Turner, 2012) suggest that student teacher s emerge into professionals during the final year of their courses as the develop a readiness to take on the professional aspects of their future roles, responsibility, accountability and a willingness to contribute to the wider picture. Back at university the students reflected on the successes of their weekly activities with a couple of students sharing their findings with the group each week. The support for each other and learning from each other which took place during this experience was far and above carrying out a simple activity with a small group and this was a real advantage of the teaching buddy system. I would really like to be able to incorporate this system within one of my future modules and will definitely find a way of incorporating it into initial teacher training. An unexpected finding from my research was the differences in culture between our two countries. My expectations of a land where its people speak the same language as ours having a similar culture to ours were rapidly altered. Stereotypical expectations of everything American being big and brash, loud and proud were almost immediately misproven. The students were delightful, welcoming and keen to learn about English student life as you might expect. My planned short interviews and group discussions were rapidly lengthened by students turning up early so they could ask me questions and tell me about their experiences. People all over the town and the university on hearing my accent were keen to enquire about my background and reasons for visiting their area. Not so very unusual but the hospitality and openness that went with this was amazing, and genuine. I was fortunate in being able to attend some of the University s sporting events; a football game which lasted three hours and consisted of teams of up to a hundred players, a girls softball game which again lasted for a few of hours and a couple of soccer (our football) games. For the second soccer game we travelled away with the team to another local (40 miles away) university. The travelling spectators were keen to introduce themselves and all desperately wanted to talk about English football, fortunately my knowledge allowed me to answer most of their questions which on

7 reflection were mostly connected with cultural differences such as ticketing availability, individual famous players, Americans playing in England and the league system. I also managed to explore some of West Virginia, a state which is about the same land area size as mainland Britain, with a population of 1.4million. The students thought nothing to travelling miles to go to the cinema, dine, shop or attend functions. The vast majority of the students came from West Virginia or the neighbouring states of Virginia, Pennsylvania and Maryland. One student told me he had only been out of WV twice in his life, once for a holiday to Florida and the other time to see a Medical specialist in New York. I found this surprising and would have loved the time to pursue this further to investigate if travel helps to broaden the mind. Conclusions What have I learnt? How will my research impact on the future? There are many similarities in the provision of training for students teachers in the United States to those of the United Kingdom. The National Curriculum dominates subject delivery in the United Kingdom whilst currently this is not the case in the United States although there are pending moves to make it so. Currently the schools boards decide on curriculum content and it is generally historic in content, hence the heavy emphasis on book led materials with little use of the internet being observed during my visit. However this could be seen as a good or bad thing when opened to interpretation. The impact of my visit will remain with me, I have already quoted several anecdotal aspects during my teaching here. I would really love to take the research further and observe how a National Curriculum will evolve overseas, the Americans appear keen to model their curriculum on certain aspects of the British one but which aspects will the perceive as an excellent model? References Bagnall, B. (2012) What s all the talking about? accessed March 30th 2013 Cotton, T. (2010) Understanding and Teaching Primary Mathematics. Harlow, Pearson. DfES (2006) Primary National Strategy, Primary framework for literacy and mathematics. London :DfES Department for Education: Draft National Curriculum until /mathematics/ks2/ma2 accessed on April 3rd 2013 Haylock, D. (2010) Maths Explained for Primary Teachers 4th Edition. London, Sage Publications

8 Ofsted, (2010) Finnish pupils success in mathematics: Factors that contribute to Finnish pupils success in Mathematics. Punch, K. (2009) Introduction to Research Methods in Education, London,Sage Sharp, J. (2010) Success with your Education Research Project, 2nd edition. Exeter,Learning matters 2010 Hatfield, M., Edwards, N. Bitter, G. and Morrow, J.(2008) Mathematics Methods for Elementary Teachers, USA.Wiley and Sons