A Student Learning Perspective on Learning in Computing and Mathematics

1. A Student Learning Perspective on Learning in Computing and Mathematics Michael ProsserHigher Education Academy 1

2. Academy Mission The Academy’s mission is to help institutions, discipline groups and all staff to provide the best possible learning experience for their students.

3. Academy Strategic aims 1. To be an authoritative and independent voice on policies that influence student learning experiences 2. To support institutions in their strategies for improving the student learning experience 3. To lead, support and inform the professional development and recognition of staff in higher education 4. To promote good practice in all aspects of support for the student learning experience • To lead the development of research and evaluation to improve the quality of the student learning experience • To be a responsive, efficient and accountable organisation

4. Academy Research and Evaluation Aims at understanding and improving student learning experiences • Research • enhances our knowledge and understanding of teaching and learning • is firmly situated in its relevant literature and makes a substantial contribution to that literature. • Investigations • enhances our understanding of a local problem or issue, providing recommendations for policy and / or action • is firmly situated in its relevant literature • Scholarship of teaching • Enhances our practice through critical and evidence based reflection on practice • Draws upon the relevant literature in that reflection

5. Proposed Activities: • Research Grant Scheme • PhD Scholarship / Fellowship program • Support institutions in developing evidence based approaches to institutional change and development • Commission a series of reviews of research in strategic areas for development and improvement • Conduct an annual survey of staff and / or students on aspects of their experiences of teaching and learning • Investigations and evaluations grant scheme • Provide in-house support for research and evaluation activities, including Subject Centres, CETLs, elearning • Develop web-based support materials to enhance the quality of research, investigations and evaluations

6. Growing Interest in Pedagogic Research • Carnegie Academy for the Scholarship of Teaching and Learning (CASTL) Program in Higher Education - USA • Carrick Institute for Learning and Teaching in Higher Education – Australia • Higher Education Academy – UK • Research Assessment Exercise – RAE – UK • International Society for the Scholarship of Teaching and Learning Conferences, Research and Development Journals, Graduate Certificates in Higher Education, PhD programs

7. Focus of this Presentation What is the student learning perspective on research in higher education? How might it apply to research in student learning in mathematics and information science? What conclusions can be drawn from this research perspective?

8. Overview of the student learning perspective Figure 1: Model of Student Learning

9. STUDENT APPROACHES TO LEARNING •  Surface Approach • Intention to reproduce • - rote memorise information needed for assessment • - failure to distinguish principles from examples • - treat tasks as external impositions • - focus on discrete elements without integration •  Deep Approach • Intention to understand • meaningfully memorise information for later use • - relate new ideas to previous knowledge • - relate concepts to everyday experiences • relate evidence to conclusions  • An approach to learning represents the relationship between a student and a task • Approaches vary between tasks

10. STUDENTS’ PERCEPTIONS OF THE LEARNING CONTEXT • Early research by Entwistle and Ramsden (1983) using both interviews and questionnaires identified a number of student perceptions relating to the way they approached their studies • Student perceptions of: • Quality of teaching – including quality of feedback • Clearness of goals of course and standards of assessment • Workload so high that it was not possible to understand everything • Assessment measuring reproduction and not understanding • were found to relate to how they approach their studies and to learning outcomes (exam results and other indicators)

11. RELATIONSHIP BETWEEN PERCEPTIONS AND APPROACHES Study of over 8000 students in first year subjects around Australia Amongst the data collected were students responses to: contextualised Ramsden's Course Experience Questionnaire and a contextualised Biggs Study Process Questionnaire 1994-1996: Australian Research Council ; Academic Departments and the Quality of Teaching and Learning; Paul Ramsden, Griffith University, Elaine Martin, RMIT, Michael Prosser, La Trobe University, Keith Trigwell, UTS

12. Approaches to Study Surface Approach 32. Although I generally remember facts and details, I find it difficult to fit them together into an overall picture 35. The best way for me to understand what technical terms mean is to remember the textbook definitions Deep Approach 28. I try to relate ideas in this subject to those in other subjects, wherever possible 34. In trying to understand new ideas, I often try to relate them to real life situations to which they might apply. Biggs Study Process Questionnaire

13. Student Perceptions Of Learning Environment Good Teaching 15. The staff made a real effort to understand difficulties students might be having with their work. Clear Goals and Standards 1. It was always easy to know the standard of work expected 6. I usually had a clear idea of where I was going and what was expected of me in this subject. Appropriate Workload 25. The sheer volume of work in this subject meant that it couldn't all be thoroughly comprehended (-). Appropriate Assessment 8. To do well in this subject, all you really need is a good memory (-). Ramsden’s Course Experience Questionnaire

14. Factor Analysis of Perceptions of T & L Context and Approach to Study ___________________________________________________________________ Scale Factors _________________________________________ 12 ___________________________________________________________________ Perceptions of Context Good teaching .80 Clear Goals and Standards.67 Appropriate Workload -.69 Appropriate Assessment -.65 Approach to Study Surface Approach .81 Deep Approach .73 __________________________________________________________________ Principal Components, Varimax Rotation, n=8837

15. In each subject: • 1.   A deep approach is associated with perceptions that the teaching is good and the goals and standards are clear • 2.   A surface approach is associated with perceptions that the workload is too high and assessment tests reproduction • That is, variation in students’ perceptions of the learning environment within subjects is associated with the approaches to study within subjects – within subject variation in perception is not measurement error. • 1994-1996: Australian Research Council ; Academic Departments and the Quality of Teaching and Learning; Paul Ramsden, Griffith University, Elaine Martin, RMIT, Michael Prosser, La Trobe University, Keith Trigwell, UTS

16. Overview of the student learning perspective Figure 1: Model of Student Learning

17. Example for student learning in first year mathematics • In a study of first year university mathematics students in a large research intensive university, analyses of short open ended written statements by 236 students identified: • Conceptions of Mathematics: • Fragmented Conceptions • Maths as numbers, rules and formulae • Maths is the study of numbers, and the application of various methods to changing numbers • Maths as numbers etc with applications to problems • Maths is the study of numbers and their applications in other subjects and the physical world

18. Cohesive Conceptions • Maths as a way of thinking • Maths is the study of logic. Numbers and symbols are used to study life in a systematic perspective and requires the mind to think in a logical and often precise manner • Maths as a way of thinking for complex problem solving • Maths is an abstract reasoning process which can be utilized to explore and solve problems • Maths provides insights for understanding the world • Techniques for thinking about observable, physical phenomena in a quantitative way and also for thinking more abstractly with little or no relation to the directly observable universe.

19. Approaches to Studying Mathematics: • Surface approach – focus on reproducing • Learning by rote memorisation – to reproduce knowledge and procedures • I liked calculus because I could remember formulas which is how I used to study. I would rote learn all the formulas and summarize all my theoretical notes • Learning by doing lots of examples – to reproduce knowledge and procedures • The way I go about studying for mathematics is by doing lots of examples and questions. Firstly I would study the notes and learn the formulas, then I put all of that to use by doing heaps of examples

20. Deep approach – focus on understanding • Learning by doing lots of examples – to understand theory and concepts • To understand a topic well it was important to gain an understanding of the basic concepts involved, backed up by doing some problem solving on the topic. However, concepts which were not fully comprehended could become well understood through extra work on related questions: i.e. it is essential to do a wide range of questions on a topic to fully understand it. • Learning by doing difficult problems – to understand and to relate to other knowledge • After listening to explanation of how a particular maths works the most essential features a repetition to develop speed (this usually consists of boring menial tasks) and an equal component of very difficult problems which require a great deal of thought to explore that area and its various properties and their consequences • Learning by doing difficult problems and studying theory to look for situations that theory may apply. • Read the relevant theory and try to get on the same “wavelength” as the person who actually discovered it. Before I attempt any problems I try to think where you can use the concept: i.e. what the concept was invented for. Then I attempt problems (on my own).

21. Structure of approaches to study

22. Relationship between Prior Conception of Mathematics and Approach to Studying Mathematics  _____________________________________________________________ Conception Approach Total _________________________ Surface Deep ______________________________________________________________ Fragmented (A & B) 179 17 196 Cohesive (C, D, E) 4 36 40 Total 183 53 236 ______________________________________________________________ Chi-square=126, p<.001 Phi=.57 ES=2.1 Crawford, K., Gordon, S., Nicholas, J. and Prosser, M. (1998) Qualitatively different experiences of learning mathematics at university. Learning and Instruction, 8, 455-468.

23. Defining Items from the Conceptions of Mathematics Questionnaire

24. Cluster Analysis of Prior Experiences and Understandings, Perceptions and Approaches and Post Experiences and Understandings Subscales _____________________________________________________________________ Variables Mean Surface cluster Mean Deep cluster (n=147) (n=127) _____________________________________________________________________ Prior Experiences and Understandings Prior Fragmented Conception of Mathematics 0.31 -0.46 Prior Cohesive Conception of Mathematics -0.39 0.45 Prior Surface Orientation 0.34 -0.44 Prior Deep Orientation -0.56 0.59 Prior Academic Ranking (TER) -0.29 0.35 Perceptions and Approaches Good Teaching -0.37 0.37 Clear Goals and Standards -0.23 0.24 Appropriate Workload -0.30 0.32 Appropriate Assessment -0.12 0.12 Surface Approach 0.44 -0.45 Deep Approach -0.54 0.57 Post Experiences and Understanding Post Fragmented Conception 0.34 -0.41 Post Cohesive Conception -0.27 0.27 Achievement (Final Mark in Mathematics) -0.34 0.40 _____________________________________________________________________

25. Conclusions • The Table shows clear relations between student prior experiences of studying mathematics, their perceptions of teaching and approaches to study in their university course and their post experience and understanding. • The analysis identified 2 groups of students • In particular, those students: • with more fragmented and less cohesive conceptions of mathematics on entry, describe having adopted more of a surface approach to studying mathematics at high school and less of a deep approach, • perceive the teaching to be poorer, to adopt more of a surface and less of a deep approach to studying mathematics at university, and • have more fragmented and less cohesive conceptions after studying and poorer achievement • The opposite was found for the other group

26. Overview of the student learning perspective Figure 1: Model of Student Learning

27. Example for student learning in first year information systems • In a study of first year university information systems students in a relatively large research intensive university, analyses of interviews with23 students identified: • Conceptions of an Information System • A personal search of a static information system • A simple information retrieval system • A data manipulation system supporting an individual within a single organisational structure • A computerised data manipulation system supporting many people within a single organisational function • A computerised data manipulation system and all the people and the data related procedures they perform to support a single organisational function • A number of communicating information systems within a single organisation Cope, C. (2000). Educationally critical aspects of eh experience of learning about the concept of an information system. Unpublished PhD Thesis, La Trobe University: Melbourne

28. Approach to Learning about an Information System • Surface: Seeking the meaning of the content with the intent of developing or deepening understanding • I mainly take down notes that the lecturer puts down on the overhead and that’s where I mostly get my information from. In can be very hard to write down what the lecturer is saying – so I mainly get the information from the overheads and I write that down and mainly skip over what the lecturer is saying because I’ m concentrating on the overheads • Deep: Acquiring knowledge associated with isolated aspects of the content with an intention of being able to recall or apply that knowledge in assessment situations • Rather than just visualize what is on the paper and just have it memorised in my mind what we’ve actually been given, rather I sort of use it to come up with my own version sort of thing, in my own words kind of thing, in a way that I understand

30. Conclusions Again, a clear qualitative variation in what was being studies was identified and a clear qualitative variation in approach to learning was identified. Even though this was a small scale, intensive interview, the relationship between conception and approach was again identified – and strongly supported by more detailed analyses of the interview transcripts.

31. Overall Conclusions • students vary their approach to study within and between subjects • students approaches to study relate to their individual perceptions and experiences of the teaching and learning context • students within the same subject perceive and experience the teaching and learning context in different ways • students within the same subjects vary in their understanding of what they think the subjects are about • students approaches to study relate to what they think the subject is about • student approaches, perceptions and conceptions relate to their learning outcomes

32. A more student focussed approach to teaching would have an awareness of these variations in student experiences, and would adjust teaching and learning experiences to address these experiences. • The identification and addressing of issues such as these lie at the heart of more scholarly approaches to teaching and learning, and to the scholarship of teaching and learning. • While scholarship and research in the last 20 years has focused on addressing such issues in a generic sense, by scholars and researchers outside the disciplines and fields of study, scholarship and research in the next 20 years will: • need to focus more on the disciplines and fields of study themselves, by scholars and researchers within those disciplines and fields if study • situate these learning experiences in the broader context of students overall life experiences