South West Spoke

Final Case Study Report Template

IMPORTANT: The SW final report guidance document must be consulted before completing this report template. Please complete all sections.

Project Title: School Mathematics to University - A Research Study

Project Leader: Garrod Musto

Department/School: N/A

Institution: Kingswood School, Bath

Other institutions/organisations involved in the project: University of Bath

Abstract:

The project was designed to develop an understanding of the transitional experiences of mathematics and other STEM undergraduates. Having met the project’s key objectives, recommendations have resulted that will hopefully prove useful for HEI staff in developing their practice in STEM subjects, drawing upon the project lead's unique perspective within the secondary sector.

The  development of the teaching and learning of first year students within their respective courses is an important feature of retention and the recommendations developed through this project will aid lecturers meet this aspiration, or at least be aware of some of the issues that have been identified through the 2 main strands of the project; examining and addressing transitional issues (from staff and student perspectives), and also enhancing engagement and CPD opportunities for HE staff within secondary schools.

The grounded theory approach adopted, enabled a number of key themes to emerge through the student interview transcriptions, which helped inform further research into transitional issues and aided the success of the subsequent online survey to over 3000 Further Maths Support Programme (FMSP) students nationwide.

An investigation of the FMSP survey data indicated that not only had engagement with FMSP aided the students’ mathematical understanding, but an unexpected consequence was that the methodology aided their transition to undergraduate study as they developed essential study skills and adopted learning styles akin to those required within HE. It was also of interest to note that, in the past 12 months, the University of Bath’s Mathematics Department has begun to use FMSP resources to help support their first year students, whilst the University’s Computer Science department has also decided to support future cohorts of Maths and Comp Science students with similar material.

As a chartered Maths teacher with experience of developing continuous professional development (CPD) models within secondary mathematics, the project leader has a commitment to the CPD of others within mathematics education. One of the major legacies of the project has been the development of links between undergraduate course leaders and secondary schools. The opportunity to discuss current A-level syllabus content has proven invaluable to HEI staff and has informed the

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restructuring of course material in a variety of STEM-related courses at the University of Bath. Also, the opportunity for school visits for HE staff and reciprocal lecture observations within HEI's enabled the Project Lead (pl)to identify features of delivery which may be considered good practice within the secondary sector. These are listed below within the outputs section.

List of Outputs:

(1) STUDENTS – investigating transition issues

(a) raw data and transcripts

Student transcript initial issuesFMSP survey and responses

(b) summaries and evaluation / recommendations.

Staff transcript initial issuesSummary of initial thoughts and themes to explore with lit reviewEvaluation of the student transcript lecturer interview [transcript]FMSP summary of responsesEvaluation of efficacy of FMSP, also anecdotal evidence from Maths and CompSci, in addition to sound bite from Tom Button; Student Support Manager; FMSP

(2) STAFF – Enhancing CPD through the collaborative practice model.

(a) Summary of the collaborative practice model (inc. NCETM model)

PDF of Kingswood Model (from NCETM website)

(b) Case Studies – describing the process

Paul Shepherd case study redesign of curriculum materialJames Davenport case study redesign of curriculum materialJames Davenport case study lesson observation in Kingswood school

(c) Impact – old vs new course notes, personal reflections and evaluation

Paul Shepherd Original course notes.Paul Shepherd New course notes.Paul Shepherd Video clips of best practicePaul Shepherd Evaluation of resources Analysis of student responsesPaul Shepherd Evaluation of resources Paul's reflectionJames Davenport redesign of curriculum materialDiscussion notes, and evaluation of resources James' reflectionsJames Davenport lesson observation in Kingswood schoolDiscussion notes, and evaluation of resources  James' reflections

Project Highlights:

1. Identifying the very positive effect that the FMSP initiative has had on transitional issues through its lecture-style delivery system and online Moodle resources. Mathematics in Education and Industry (MEI's) government-funded initiative to support the study of Further Maths within further education

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has the added attraction of providing further study skills that are viewed as desirable by undergraduate students. This finding is backed by the endorsement of certain departments at the University of Bath to use FMSP material to support their first year undergraduates.

2. Working with HE academic staff to inform the redesign of first year degree course content to better reflect the experiences of students in schools, has proved highly successful. This work was achieved through the identification of undergraduate course content and its place within the maths and Further Maths courses. This enabled subject staff to gain an insight into the diverse nature of mathematical entrance qualifications.

3. Using the project lead’s experience of CPD models within the secondary sector to feed into the professional development review cycle of academic staff also proved a success. A collaborative approach was adopted between teacher and lecturer and informed the planning and delivery of a lecture sequence, incorporating teaching methodologies common to the secondary sector, and involving participatory mechanisms to engage students within the lecture environment. In this way, aspects of sixth form teaching that first year students would be familiar with were incorporated, aiding both transitional issues and an enhanced understanding of the material being covered.

Background and Rationale:

As a secondary teacher with 18 years’ experience of teaching sixth form students, there have been many occasions when high achieving A level students have returned to school, or have contacted me to help them with their maths related studies at university. They often bemoan the fact that "it isn't like it was at school." However, unpacking this rather bland statement is difficult as it undoubtedly contains many interrelated factors.

This issue more recently has been highlighted by a number of reports which identify concerns regarding whether current 16 to 18 qualifications are sufficiently rigorous to prepare students for HE courses1 2, especially in light of perceived year-on-year grade inflation at A level3 Partly in response to this issue, certain institutions within HE are being encouraged to have a greater say in the taught curriculum and assessment at A level4. One of the main aims of this research was the creation of sustainable links between HEIs, FE, schools and colleges which in addition to informing academic staff of current practices, would be of benefit to the HEIs through outreach, widening participation, transition and curriculum development agendas. This valuable experience would also subsequently inform the debate as academic staff become more aware of current syllabus content and teaching pedagogies within the sixth form Maths classroom.

This is pertinent and timely given the greater accountability now expected of HE staff through the introduction of tuition fees, and the parental expectation of value-for-money. Also it is hoped that the Project Lead's (PL’s) background in secondary mathematics teaching added a different perspective on the issues, which informed the debate.

Implementation:1 http://www.score-education.org/policy/qualifications-and-assessment/mathematics-in-science http://www.nuffieldfoundation.org/sites/default/files/files/Maths_in_A_level_Assessments_Nuffield_Foundation_WEB.pdf

2 http://www.nuffieldfoundation.org/sites/default/files/files/ACME_4pp_overarching_report_summary.pdf

3 http://www.telegraph.co.uk/education/educationnews/9228904/A-level-maths-content-being-dumbed-down-claim-experts.html

4http://media.education.gov.uk/assets/files/pdf/s/secretary%20of%20state%20to%20ofqual%20on %20a%20levels.pdf

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(a) STUDENTS – Researching issues of transition

Phase 1)

Using a Grounded Theory approach involved an open questioning phase; interviews with HEI staff from a range of STEM departments, and an informal group discussion with three undergraduate students taken from the Student Transcript. This enabled the PL to identify key transitional themes in the South West, outlined in the discussion stage. This phase was evaluated by an independent academic who examined the transcripts, and had an opportunity to explore the issues raised by students and those of the academic staff ensuring a balanced perspective. In his evaluation, Chris Budd commented on support mechanisms that were in place and also suggested ways to address students’ perceived concerns.

Phase 2)

Informed by the themes emerging from phase 1, an online survey for sixth form students was created to explore transition themes further. This was sent to 3,000 students across a diverse range of HE STEM subjects in the south west and more widely across the UK.  The project team ensured relevant data was captured and analysed. This enabled the PL to begin to quantify the extent of each transitional theme. Also, this phase had unintentional benefits, such as anecdotal evidence to suggest that FMSP’s pedagogy and support resources were an excellent preparation for university study.  This phase enabled the PL to create a series of outlined themes and strategies to tackle issues as suggested by students or indeed from relevant literature.

(b) STAFF - Enhancing CPD through the collaborative practice model

Phase 3)

As an integral part of his Chartered Maths Teacher designation, the PL is committed to the CPD of other mathematics professionals, including those within HE. This final phase built on the PL's experience in CPD within secondary school; to explore the impact of CPD to support academic staff; inform their practice; and to help address some transitional issues highlighted in earlier phases. This phase encouraged academic staff from the Computer Science and Engineering departments at the University of Bath to engage with local schools, and comprised three distinct parts, providing HE staff with an opportunity to:

1) Visit sixth form lessons:

The PL encouraged a member of the Computer Science Department to visit his school to observe a series of sixth form Maths and Further Maths lessons. The visits were designed to coincide with the teaching of both Matrices and Vectors in school as these were components of the first year undergraduate course material.

2) Engage with current teachers of mathematics to inform the structure of course materials, and also;

3) Work with sixth form maths teachers to help plan, deliver and self-critique a lecture sequence, using a collaborative practice model of CPD. This aspect of the study was initially conceived to support the Professional Development of a lecturer within HE, and involved discussing the well-established Collaborative practice model of CPD as outlined in the Kingswood School CPD model. During the initial discussion we agreed on a manageable way to practically implement such an approach within HE. This approach consisted of Paul (the lecturer) outlining a negotiated theme for his observation; in this case “student engagement during lectures”. Then during the lesson planning phase the PL visited the University and during a 3 hour session, together with Paul discussed the structure of the lecture both in terms of the A level syllabus, and also delivery mechanisms which from a secondary perspective students may find familiar or indeed engaging. Paul then wrote up the lesson planning sheet which outlined the material to be covered. The lecture was subsequently videoed, and evaluated by both Paul and also the PL,

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Each of these three initiatives was a valuable learning experience as the personal reflections of the academic staff testify in the “Discussion Learning and Impact” section.

Evaluation:

Each aspect of the project was designed to enable a quantifiable and meaningful evaluation and to allow the impact of the research to emerge.

Approach to evaluation:

Across the project, the research attempted to use recognized methods to evaluate the effectiveness of the work that had been completed. In this, it drew heavily from A Guide to Practice: Evaluating your Teaching Innovation, an excellent reference text.

The project was evaluated using a fusion of the three conceptual frameworks attributed to Chelimsky (1997); accountability, development, and knowledge. The project lead considered each of these when appropriate, with certain aspects of the project requiring a mixed approach.

Evaluative methods including analysis of data collected:

Phase 1)

This involved:

an open questioning phase; interviews with individual HEI staff from a range of STEM departments; an informal group discussion with four undergraduate students.

The core evaluative methodology adopted was the creation of a focus group of students and staff (a sample size of 4 in both instances), to provide illuminative data to inform a subsequent student research survey. This enabled the Project Lead to identify key transitional themes in the South West , which were then supported by a relevant literature review.

To ensure this focus group would prove representative of the cohort, this phase was evaluated by an independent academic who examined the transcripts, and had an opportunity to explore the issues raised by students and those of the academic staff thereby ensuring a balanced perspective. The academic discussed possible support mechanisms that were in place or suggested ways to help address students’ concerns.

Phase 2)

This involved generating transitional data by an online survey of sixth form Maths students. The project team ensured relevant information was captured and analysed. The survey captured the following samples:

Further Maths Support Programme (FMSP) Sample size 147; capture rate 147 out of 3,000. Non-FMSP Sample size 80; capture rate 80 out of approx. 1,000 students

Total sample 227 out of 4,000; capture rate of 5.7%

This enabled the Project Lead to begin to quantify the extent of each transitional theme (both convergent - aligned to particular goals identified in the planning stage of the research and divergent – unintended outcomes that have added value to the research and informed current thinking on the issues). Divergent evaluative outcomes in this case suggested that FMSP’s pedagogy and support

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resources were an excellent preparation for university study.  The phase enabled the Project Lead to create a series of outlined themes and strategies to tackle issues as suggested by students or indeed, from relevant literature.

Analysis of FMSP summary of responses .

Evaluation of efficacy of FMSP also contained anecdotal evidence from Maths and Computer Science, in addition to sound bite from Tom Button; Student Support Manager; from FMSP.

Phase 3)

Part 1 case study –

A Computer Science lecturer from the University of Bath observed a series of sixth form Maths and Further Maths lessons covering Matrices and Vectors and then produced a reflective log detailing how the observation helped them to develop their first year undergraduate teaching practice

Part 2 case study –

A Civil Engineering lecturer from the University of Bath engaged with current teachers of secondary school mathematics to inform the structure of first year, undergraduate course materials.

To assess the experience and the new course materials produced from it, various evaluation methodologies were used: a student questionnaire (sample size 43 responses; out of 90; capture rate of 48%); goal-oriented evaluation [student engagement feedback sheets], completed at the end of the lecture sequence and a reflective log from the lecturer detailing his experiences of the process.

Part 3 case study –

A Civil Engineering lecturer from the University of Bath worked with the project lead using a collaborative practice model of CPD to help plan, deliver and critique a lecture sequence. The lecture sequence was observed with the theme of ‘student engagement’.

As part of the observation, the lecture sequence was recorded. This had various convergent outcomes but also had divergent evaluative outcomes. This was the creation of a series of short video clips of good practice demonstrating “student engagement techniques within the “HE classroom”. The video recording also helped inform the second part of the evaluative process, a reflective summary of the lecturer’s experiences.

Please note that the research project adhered to the following set of ethical considerations, which comply with the host institution, The University of Bath.

Discussion, Learning and Impact:

(a) STUDENTS – Researching issues of transition

Phase (1)

Staff and Student transcripts

This was an immensely useful opportunity to explore the issues as perceived by staff members and by students. This enabled particular themes to emerge, which included:

The motivation for studying maths, at both A level and (STEM subjects) at undergraduate level.

Transition; the effect that a diverse range of prior mathematical experiences will have on undergraduate student progress and transition (e.g. A level Maths), and including other

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qualifications such as the International Baccalaureate and Further Maths The availability of good careers advice in schools The lack of understanding of course content; what one might actually study within a numerate

discipline at university Student experiences of the teaching at A level vs undergraduate level. Work /(social) life balance at university Adopting successful study skills, or a supportive network to aid progress Identifying good practice of content delivery within HE STEM disciplines The availability of institutional support mechanisms before the course started The availability of institutional support mechanisms during the course

This diverse number of elements contained in this list illustrates that there is no simple solution to the issue of transition, indeed Clarke (2008) articulates this well below; citing other relevant literature stating that;

There is no doubt that the secondary-tertiary transition in mathematics is a complex issue, involving a whole spectrum of problems and difficult situations. (Barnard 2003; Crawford, Gordon, Nicholas, & Posser, 1994, 1998; Gruenwald, Klymchuk, & Jovanoski, 2003; Guzman, Hodgson, Robert, & Villani, 1998; McInnes, James, & Hartley, 2000; Schoenfeld, 1994; Tall, 1992,1997; Wood, 2001)

It is important to note however that not all of these themes will be fully explored in the later phases of the research.

One common theme acknowledged by all students and staff members, was the importance of a support structure to help the students, whether through formal structures such as Maths Cafes or through more informal routes such as chats about problem sheets with other students; as one student stated;

I think that trying to do the first year on your own would have been awful, but because we had each other we realised that most of us were finding it difficult…

That same student tried to put into words what he felt were the main differences between teaching & learning at A level and undergraduate study; he said;

…the massive fundamental difference for me was at school the teachers were generally coaching you for the exam which is such a big thing. They are coaching you and they do not really care whether or not you understand the theory but here [at university] some of them [lecturers] are not trained to teach, and some of them have English as an additional language and they are not trying to coach you to get it.

This student hints at a number of perceived problems;

The students’ prior perception of A level teaching pedagogies vs. current perception of undergraduate teaching pedagogies. Students enter university having been part of relatively small classes with high levels of student-teacher interactions. Teachers invest time and energy in the students to help them achieve their required grades which doesn’t necessarily fit with students’ perceptions of HEI staff; teachers in schools have a very structured approach to delivery with high levels of feedback both in class and through homework tasks.

There is a natural friction between students’ prior perception of learning A level content, and the very different requirements of undergraduate study. This comment illustrates that students perceive the sixth form course requirements for exam success as focusing on “teaching to the test”. They recognize that although this approach enables them to answer exam style questions, success only requires a superficial understanding of the material being covered; they therefore lack the problem solving skills which they require at university, a sentiment which was echoed by a recent IoP publication Mind the Gap. Equally staff raised concerns that students were being taught to question spot and to answer regulation questions in a mechanistic way at A level, leaving their problem solving skills and ability to model a situation poorly developed for HE study; something highlighted by the

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National HE STEM Programme’s Director, Michael Grove;

…current mathematics and physics provision at A-level leads to students learning by rote rather than through their own independent techniques.

Lecturers are perceived as not understanding the students’ prior experience, making assumptions of their mathematical competency. There can be issues with [foreign] lecturers, who [students] perceive to have little idea of the content and structure of the mathematics A level. I think this is a very important point and one which I explored later in phase 3 of the project.

Are lecturers trained to “teach”? This is an interesting point raised, as the student who made the comment was implying that teaching a la A level was the desired medium of delivery.

There are also “English as an Additional Language” EAL issues raised here – do overseas lecturers have the linguistic and communicative skills necessary to fulfill their teaching obligations effectively?

When contemplating transitional issues from a student perspective, the most telling response came from one of the female students, regarding her complete lack of appreciation of what studying a mathematics degree course would entail;, she said;

“I thought it was going to be like A level but harder”,

This highlights a major issue students experience with their “expectation of the course”, as there is commonly a lack of understanding of exactly what an undergraduate course entails. This was by no means a surprise to the project lead, and indeed anecdotally was one well recognized from conversations with his former students at school. As a Head of Mathematics at a secondary school, the Project Lead is often looking for resources to introduce bright, motivated Maths and STEM students to abstract topics and concepts found in undergraduate courses. However these aren’t often available, as most universities simply list topics such as “linear algebra”, within course contents; but of course school algebra is worlds apart from algebra courses at degree level. There will always be a natural step up from school maths to undergraduate study, but to address the misconception highlighted above there is a need for better careers and UCAS guidance for schools.This point was picked up by Thomlinson et al (2010);

[It is] …evident that in general on arrival [students] have a very hazy picture of what university maths might be like…it also possibly illustrates a need for a better explanation of university mathematics in layman’s terms for those considering embarking on it. (pg.67)

Also with the added emphasis on Public Engagement, Widening Participation and Outreach work within HE, this presents an ideal opportunity for HEIs to seriously engage with schools to at least raise awareness of this issue in a more coordinated way. There needs to be development of a readily accessible bank of web-based resources; designed collaboratively by school teachers and lecturers, and produced by HEIs.

In summary:

The thematic concerns regarding transition and retention that were raised by staff equally reflected the concerns of the students. Academic staff are acutely aware of these complex issues, and much research has been conducted in this area within STEM disciplines here in the UK. The mathematics education research team at the University of Manchester has undertaken ESRC funded projects investigating students' trajectories in and across mathematics programmes from compulsory school, through college to Higher Education. These draw attention to important issues in relation to programme design, institutional implementation practices, teachers' pedagogies and students' developing attitudes, dispositions and identities and hence their decisions and choices regarding their study (or otherwise) of mathematics. This research has enabled Williams et al to develop quantitative tools to gain a deeper understanding of many of these themes, and to develop the excellent strands of the Transmaths initiative. The output of this body of research will undoubtedly inform the debate

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regarding the issues highlighted by the students and staff.

Evaluation of Phase 1

I asked local Maths Professor Chris Budd to comment on the student transcripts, and he then answered a number of questions and offered his insight into the transitional issues raised by both staff and students. In the transcript of Chris’ interview he agreed with the sentiments of both students and staff and illustrated initiatives that seek to address many of their concerns. He was also able to draw on his considerable experience to help focus the issues, and illuminated some of the themes with anecdotal evidence:

School Maths doesn’t really introduce students to abstract maths and proof; a known known. A levels are very modular and very structured, whereas courses are linear and are very unstructured. I really blame the A level system for the concept of retakes that is available, and students enter their course expecting to be able to retake courses and this is not the case…

…also students and parents are expecting more because of the increase in tuition fees, but there is nothing wrong with that. Drop in centres and Lecturer training [which are now key features in our support] were unheard of ten years ago. Also, the use of the virtual learning environment by students mean that there is greater interaction between staff and students…

…however some students are becoming much better prepared, and receive much better support to prepare them for university study. For example considering the effect of [Further Maths Support Programme] FMSP - we have specifically asked students that question [does FMSP help you to prepare for undergraduate study at university] regarding the study skills and support FMSP provides in their A level studies, and such students were very positive in their feedback.

Overall I think the interviews and Chris’ comments outline that “transition” from school mathematics into STEM subjects can be complex mix of interrelated factors.

From a research perspective I was very happy with this phase as I felt that the grounded theory approach did indeed enable a number of themes to emerge from the data; I wanted to pick up on some of the themes explored in phase 1. I also wanted to pick up on the last comment by Chris regarding Further Maths Support Programme (FMSP) and to explore exactly what students found useful regarding this particular support mechanism to help identify strategies for course structure, course content, and course delivery.

Phase (2)

Introduction

The themes outlined in phase 1, subsequently formed the basis for a questionnaire to be sent to students in the South West, and more widely across the UKThe project lead entered into a dialogue with members of the Further Maths Support Programme Team to develop a suitable questionnaire and associated text that could be sent to all 3,000 former FMSP students nationwide, in addition to local STEM undergraduates here in the SW. Further details of this dialogue with FMSP manager Janice Richards can be found here

Data Analysis:

An overall analysis of responses was conducted,

The quantitative data was relative straightforward to analyse and can be seen in the summary of responses document.

The project lead then sought to categorise the data to enable themes to emerge. So - for example - to help inform the government’s current debate on HE input into A levels; when asking the question which aspects of sixth form teaching would you change given your experiences of undergraduate

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study, the comments were categorised into three main areas; course content; course organization; and course delivery. See image below for an example of how this took place. (NB. “A level maths was too easy for me” (2) means two students cited similar answers).

When exploring the effect of FMSP on the transition of students into undergraduate courses, students were asked: “How was FMSP material different from other A level materials?” The comment below is typical of the responses received;

Having now completed university (Engineering) FMSP material was much more typical of that found at university, rather than that which was usual at A-Level. This was much more useful, and gave me a head start compared to my peers at university.

As the following image illustrates, student responses were overwhelmingly positive, illustrating just how much students rated FMSP’s effect on their experiences at university.

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Subject staff at some universities already recognize this effect and have invested in using FMSP “integral style” online resources to help support their students in the first year of study:

We [The University of Bath, Maths Department] have collaborated with the FMSP to create a series of materials that have been specially developed for us, and that goes on the web. So the students can either access that before they come to us, or they can also access it during their course. This is to help the transition…… having monitored the students, over 1/3 of them are still accessing the material throughout the course in their second and third years. (Professor Chris Budd, University of Bath)

In addition to using the FMSP as a support mechanism within HE, I also wanted to explore the types of skills students felt the FMSP gave them to aid their transition to undergraduate studies. In relation to this, student comments included: Nothing in the A-Level course challenged me, but the Further Maths Network (FMN) made me get used to seeing problems where I had literally no idea how to start.

The way in which Further Maths was taught was much more intuitive than in sixth form. I understood the reason behind certain methods, which was something I appreciated when studying Maths at university.

We only had further maths lessons for one afternoon a week. This meant that I had to do a lot of independent study to fully understand the topics covered. As the mathematics taught at university is taught in a much more condensed way with a much quicker pace of teaching and with only the basics shown, then it (Further Maths) has proved very useful that I am able to study independently and to understand the concepts thoroughly.

The teaching style helped me to learn different ways of learning which helped with the different style of lecturing to teaching in college

Having on-line lessons, gave me experience of learning in a new way, which was helpful in

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becoming more organised.

The ability to use detailed written explanations to complete problems without teacher aid was a fantastic skill learnt through FMN.

The e-learning lectures proved a good introduction to university lecturing styles (I suppose since they were given by a university lecturer).

By learning to cope with such a large workload and harder subjects. In my uni course, exposure to harder material reduced the intimidation factor when trying to pick up new methods, especially under the greater time pressure and lack of resources.

Being introduced to the lecture environment was helpful, useful and taught me the note taking skills that are valuable in uni.

Evaluation of Phase 2:

This phase was very positive, and added much evidence, both quantitative and qualitative, to inform the debate regarding transition. The evaluation of the data by Tom Button; Student Support Manager; FMSP was also very constructive;

[I was very pleased with the data collected by the study and am very happy that the student findings reflect our own aspirations for the FMSP…. studying through the FMSP helps students to be better prepared for the transition to university. This is something we have always believed in and it's great the know that your findings support it. The FMSP's message to teachers and students has been that in addition to the benefits of studying FM [further maths], the experience of learning though the FMSP helps students to become self-motivated independent learners and can also help develop skills in working together, time-management and using IT. It is good to see additional benefits highlighted by students too.

(b) STAFF - Enhancing CPD through the collaborative practice model

Phase (3)

A) Visit sixth form lessons:

This phase of the project enabled the Computer Science (CS) department at the University of Bath to gain a true insight into the practices of sixth form students, and to develop an understanding of the subject matter they can expect students to have experienced during A level courses.

This phase was highly effective in changing current practice, and in initiating curriculum innovation, with the development of online templates to help students understand aspects of the programming course. Professor James Davenport visited Kingswood School and saw a lesson which covered “Proof by Induction”. James was struck by the formulaic treatment of the delivery of this method of rigorous proof and as a result of his experience has sought University funding to develop the teaching and fitting of induction templates via computerised assessment, since experience shows that students still write down lines that don’t fit the [proof by] induction method;

XX10190 has certainly been a success, one of the other professors, not involved in this course but teaching a second-year course, remarked that the students were [subsequently] much better prepared for MatLab programming.

Evaluation of phase 3A)

James Davenport wrote up a reflective log outlining the lesson observations at Kingswood, and subsequently exploring the impact of his experience on both curriculum development and course delivery. James’ commentary was very positive; he was so struck by what he saw, he stated during a

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London Mathematical Society (LMS) meeting that:

“Any lecturer who is about to embark on first-year teaching should know the [nature of the A level course content, and its delivery], and this one-day intensive exposure is the best way to do it”

B) Engage with current lecturers of mathematics to inform the structure of undergraduate course materials:

Through working with two difference academic departments (Computer Science and Architecture & Civil Engineering), I was able investigate how enhancing academics’ understanding of A level syllabi might influence their design of first year undergraduate Maths course materials.

Professor James Davenport (Computer Science)

See below for James’ reflective comments on the outcomes of a discussion with the project lead on A level content;

Many thanks for coming along to the department and talking through A-level content, both at A level and also within further maths; and their relationship to the Mathematics we teach in Computer Science. It was a very valuable experience and I have taken away the following major points:

*) Set theory is optional, and, when covered, is, at least in Edexcel, in the S1 option. This is also where much "logic" will actually be used.*) There is no such thing as a "typical" Maths A-level, Edexcel offering six different choices for the straight A-level alone.*) We cannot rely on the students understanding '=>'.*) We therefore need to target our use of 'Integral' resources quitefinely, e.g. "if you're Edexcel and haven't done S1, then here's theresource on S1 Chapter 3" etc.*) A survey of incoming students to know what they've actually done would also help.

As James’ Davenport’s comments illustrate, there are a number of outcomes which will inform future course content and delivery. James intends to share this with other first year lecturers - Guy McCusker and John Power - therefore engaging in the wider Professional Development of other members of the CS department.

Dr Paul Shepherd (Architecture & Civil Engineering)

The opportunity to work with Paul as a part of his professional development review cycle using a Collaborative Practice Model of CPD was invaluable. The experience was (hopefully) non-threatening, as the observation was examining features of a lecture sequence which we had both collaboratively designed, and therefore we could pick up on features of the negotiated focus for the observation; “student engagement”. I do think that my experience within the secondary sector enabled Paul to gain an insight into current teaching pedagogies in mathematics, and we were able to use this to inform the structure and delivery of Vectors and Matrices material to students. It was also a useful process as it enabled Paul to reflect on his practice and to discuss this with me.

Through talking to Garrod [project leader] I feel like I got a very clear understanding of the structure of A-level maths (topics covered and in what detail), and was able to build parts of that structure into my own lectures, without letting it dominate. I also have a clearer picture of the divide between Maths and Further Maths, and how some students will have seen some topics and not others.

Paul was also very pleased with the opportunity to get students’ feedback midway through a lecture, which in turn identified features which helped address transitive issues.

The student feedback underlined the fact that relating what I teach back to what they have done in A-level (especially by using the same terminology) can help them understand it better. Whilst there is also the danger that they will then think that they have done it already and switch off, by careful structuring of the lectures I think they can be dragged forwards to develop what they already know and will find it easier to grasp the new concepts.

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The opportunity to help inform curriculum design was invaluable; the student feedback to the layout of Paul’s revamped Vectors and Matrices course was extremely positive and illustrated that students who attended the lecture found the material “easier” to understand when compared to material from other lecture sequences.

I was surprised by how positive the student responses were. Whilst I get good feedback from them during the lectures on what they know or how well they have understood things, I never really have a handle on what they think of me and my teaching style, and it’s not the sort of thing I can ask then directly myself, so I have to wait until the formal end-of-year anonymous feedback.

Evaluation of Phase 2 B):

These outcomes suggest that these CPD experiences have been very positive ones, and the project lead hopes to continue to work with the Computer Science department at the University of Bath to develop resources to aid other Computer Science departments within UK HEIs. The work with James Davenport was highly effective in changing current practice.

I feel that working with Paul Shepherd through a Collaborative Practice Model of CPD has also proven successful. Implementing the process has been very informative and has helped shape both curriculum delivery and also Paul’s reflective practice. To evaluate this part of the study Paul wrote a short summary of his experiences; reflections of the collaborative CPD process, which highlight a number of tangible outcomes. For example; the student feedback brought home the fact that transitive issues are real:

…some of the feedback drew attention to the fact that they had covered some of the material before. Whilst not always done in a negative way (“Reminded me of topics…”, “An excellent revision…”) it shows that the difficulty in teaching to such a broad range of abilities is a real one and full engagement will always be difficult.

Indeed, acknowledging this when devising and delivering course material is a key strategy in diminishing any negative transitive effect.

Certainly the opportunity to help collaboratively plan a lecture was a fruitful one, and students engaged far more with the revamped material, where content had been structured to better reflect the student experience at A level, This seemingly relieved many of the transitional issues identified by phase 1, with 40 out of 43 students making positive comments about the course content, including;

“Reminded me of the topics I did last year”; “helpful as we went over a topic that I wasn’t confident on”; “Breaking the topic into parts which help understanding topic more”; “The visual aids and examples helped enormously”; “really good notes”; “Nice example and exercises to do, and well explained lecture”; “logical walk through that helped refresh my memory”; “Paced in a way that information came back in an appropriate order”; “Given time constraints lecturer communicated the maths ideas very well”; “step by step explanation”; “everything is explained pretty clearly and is similar to A level, so helps recall what I learned at school”; “I was able to keep up today with a new topic (matrices) that I had not previously studied”.

Given the strength of student comments regarding this process, it is hoped that the project lead can engage with the professional development departments of HEIs in the South West to see if this model can be developed further within HE. Equally, the value of such professional development opportunities within mathematical sciences was recognized by Chris Budd;

A teacher fellow in Mathematics would be fantastic to give tutorials to staff on what students know when they come here because a huge majority of university teaching staff in mathematics in this country were not educated in the UK, and therefore many of them are completely unaware of what our undergraduates have learned when they arrive

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Further Development and Sustainability

Will the activity continue in the future?

Yes (in a modified form)

How will the continuing activity differ, for example, in its structure or delivery?

Sadly, I will not have the excellent support I have received from the National HE STEM Programme team at the University of Bath spoke. However, through the project I have developed links with a range of HEI professionals that I hope to sustain into the future. Any future work will need to have partners who are willing to actively participate, and one of the real obstacles to the project to date is the lack of engagement from some HEIs within the region. However, it is hoped that the evidence base generated by the research from this project will encourage engagement from HEIs who have previously been reticent.

How will the activity be sustainable and continue as a result of this modification?

The planned work will continue with Bath University, and potentially when the project has been written up and disseminated via the National HE STEM Programme conference and via the SW Spoke website, it is hoped that interested staff may contact the project lead to engage with similar projects at their institutions. The SW Spoke team will also facilitate an approach to the University of Bath’s Staff Development team to ascertain their interest in the work and to identify whether any promotional or training opportunities might arise.

For example in Paul Shepherd’s final conclusion;

I am pleased that I took the opportunity to engage with Garrod on this project. However, by identifying the relevance of scaffolding learning on top of what has come before, it has left me with the question of how to achieve this with the other 30% of my students who did not study A-levels (IB, etc) before coming to University.

This observation does highlight a real problem for some course leaders, as there is a real need for a differentiated approach which enables Further Maths students to remain challenged throughout a first year course whilst also support non-Further Maths A level, or indeed identify particular support that is necessary for non-Alevel students to bring everyone up to the same level of experience.

This is something that I hope to explore in the future.

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In relation to the approaches to sustainability outlined below, we are very interested in activities and commitments which have occurred within the timescale of the project. However, we recognise that some approaches may still be in the development phase at the official project end date and it would also be valuable to include these examples in the template.

Approaches to Sustainability

Examples In relation to your project

Continuance (finding alternative sources of funding)

Commitment from institutions to provide continuation funding

Network/ communities likely to be sustained through inclusion in future funding bids

As a local Methodist foundation boarding school, the senior management of Kingswood School [add hyperlink] have expressed an ongoing commitment to their work engaging with the community in the broadest sense of the word. Therefore, there will be opportunities for the Project Lead to continue to work within HE to develop the themes identified and explored within this research project. Please note this commitment is one in kind, with the project lead enabled to give up his time free of charge to engage with HEI’s in the South West and, if feasible, further afield.

Embedding (within institutional activity)

Identification of institutional strategies that the project has informed

Uptake which has taken place, or is likely to take place, within

Supporting undergraduate students through online A level style resources; this project has outlined the positive effect that FMSP has had on the preparation of students for undergraduate study, and it is very encouraging to see University departments that have now embraced such resources to help support their students through their first year.

The take up of the FMSP

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own/other HEIs

Influencing of organisations external to HE Sector which has occurred through partnership working

resources by Computer Science based on the experiences of the Maths Department at Bath, and the adaptation of Civil Engineering first year modules.

Mainstreaming (changes in working practices)

Staff development which is planned or has taken place as a result of your project

Curriculum enhancement that has occurred or is likely to take place as a result of your project

Influence of senior managers that has arisen as a result of the project

Staff members have had specific targeted professional development support which has involved lesson observations in schools, helping to inform the structure of undergraduate courses and also, assistance in collaboratively planning and delivering a lecture sequence containing material new to a Civil Engineering course, but designed to fit the structure of maths and further maths courses.

There are plans to create an INSET course for all academic staff within the mathematics department at Bath university to raise an awareness among lecturers of transitional issues, and to develop a better understanding of maths topics and material to be found within A level maths and F maths syllabi

Many of the senior managers that I have spoken to already possess a very deep understanding of the issues. However, the opportunity to engage with the project has enabled the implementation of specific interventions and curriculum development to take place. There also seems to be a commitment to continue to engage with similar projects in the future.

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Legacy (passing on important elements of the project)

Networks/communities likely to be continued

Dissemination of project outputs

Evidence of impact of activities

Dissemination has occurred through the RSC event talk dated, Nov 2011. Further dissemination will take place through FMSP networks, SW Spoke regional website and staff development contacts at local HEIs.

Evidence of impact:

Very positive comments from students re FMSP, and the use of FMSP resources by HEIs in the South West to support their students. Therefore, have highlighted a potential source of support for HEIs in mathematical methods.

Civil Engineering lecture observation; Student questionnaires illustrated the positive effect of restructuring the material through collaborative planning.

The creation of a series of short clips illustrating aspects of good practice when engaging students in the classroom/lecture theatre. These clips are backed up by evidence and a literature review.

Anecdotal evidence and quotes from academic staff involved in phase 2 of the project who indicated that their involvement in the project has informed changes to current practice which, in turn, has had a positive effect on student engagement and attainment.

A commitment to continue to work with Maths dept and Comp Sci dept within the

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University of Bath.

References: Black, L. (2010) Developing a leading identity across the transition to mathematically

demanding, presented at BCME7. Clark M. Lovric M. “Suggestion for a Theoretical Model for Secondary- Tertiary Transition in

Mathematics” Mathematics Education Research Journal (2008), Vol. 20, No. 2, 25-37

Davis, P., Harris, D. & Jooganah, K. (2010) Transfer of mathematics learning to problems of electrical and electronic engin, presented at BERA

Davis, P., Harris, D. & Jooganah, K. (2010) Using mathematics to solve engineering problems and mathematical subjectivities, presented at ECER

Farnsworth, V. (2010) Learning to Learn in STEM Subjects: Lessons Learned from Problem-Based Learning, presented at BERA

Farnsworth, V. (2010) The place of maths in a different 'space': Value of mathematics in student narr, presented at AERA

Grove M. The Mathematical Transition: A Multi-Stage Problem? MSOR Connections Vol 12 No 1 Winter 2011/Spring 2012 http://mathstore.ac.uk/headocs/Connections_12_1_Grove.pdf

Harris, D., Davis, P. & Jooganah, K. (2010) Mathematics as a 'tool': what does that mean for first year engineering student, presented at ECER

IoP publication Mind the Gap http://www.iop.org/publications/iop/2011/file_51933.pdf

Jooganah, K. & Williams, J. S. (2010) The Transition to Advanced Mathematical Thinking: Socio-cultural and Cognitive   , presented at BCME7

Pampaka, M. & Williams, J. S. (2010) Measuring Mathematics Self Efficacy of students at the beginning of their Highe, presented at BCME7

Robinson M. Challis N. and Thomlinson M. “Maths at University reflections on experience, practice and provision” (2010) More Maths Grads (MMG project) http://maths.shu.ac.uk/moremathsgrads/

Wake, G. (2010) Learning university mathematics: a case for expansive learning, presented at PME34

Wake, G., Haworth, A C., S Nicholson. "Applying mathematics in the post-16 curriculum: teacher practices, student perspectives and emerging issues." Research in Mathematics Education 6(2004) : 77-98. eScholarID:1b1569

Wake, G., Haworth, A C. "Mathematics post-16: understanding and involvement." Mathematics Teaching 189(2004) : 16-19. eScholarID:1b1568

Williams, J. S. & Hernandez-Martinez, P. (2010) Teaching mathematics in school and university: the case of a boundary crosser, presented at PME34

Williams, J. S., Hernandez-Martinez, P. & Harris, D. (2010) Diagnostic testing in mathematics as a policy and in practice in the transition, presented at BERA

http://www.score-education.org/policy/qualifications-and-assessment/mathematics-in-science http://www.nuffieldfoundation.org/sites/default/files/files/Maths_in_A_level_Assessments_Nuffield_Foundation_WEB.pdf

http://www.nuffieldfoundation.org/sites/default/files/files/ ACME_4pp_overarching_report_summary.pdf

http://www.telegraph.co.uk/education/educationnews/9228904/A-level-maths-content-being- dumbed-down-claim-experts.html

http://media.education.gov.uk/assets/files/pdf/s/secretary%20of%20state%20to %20ofqual%20on%20a%20levels.pdf

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Quotes: All quotes are in blue in the body of the text of the discussion section.

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