Tuesday, 5 June 2012

Initial Prototype – Revision 2

Background
In South Africa there are a number of factors that contribute to mathematics being regarded as a killer course at first year level. Students view mathematics as collection of recipes to be rote learnt (Mji,2003).  Disadvantaged students in South Africa are generally unprepared (Davidowitz & Rollnick, 2010) and face severe financial constraints (Mdepa & Tshiwula, 2012).  The majority of students have no intention of becoming mathematicians and struggle to relate to mathematics (Leitze, 1996). These factors combined with a traditional teaching approach results in first year mathematics being a rite of passage for many.

Learning Problem
Students employ a recipe like approach when solving mathematics tutorial problems indicating that they have not integrated this new information into their knowledge structures.  Engagement with the content is limited to ensuring the correct steps are followed and students see these problems as being disconnected from their desired fields of study.

Educational Goals
  • Facilitate a deeper exploration of the mathematical concepts via asynchronous collaborative learning
  • Develop an appreciation for the applicability of mathematical content by exploring real world examples
  • Initialise a reflective practitioner approach to problem solving by having to constantly review their group’s work over a period of time

Task.
We will use a collaborative learning (Smith & MacGregor, 1992) approach where students work together in groups to understand and solve a real world problem.  Collaborative learning is based on a social constructivist approached and is used in variety of forms in classrooms and lectures.  This type of learning environment enables students to explore topics more deeply than in traditional situations (Smith & MacGregor, 1992).  In these environments students challenge and adapt their existing knowledge frameworks and integrate the new knowledge.  This approach is frequently used in a variety of science and engineering contexts and can be used in a basic classroom environment with no computing devices (Marshall, 2007) or be employed in a technology rich environment such as a SCALE-UP classroom (Beichner, 2008).

The lecture is not the primary knowledge building location for students.  Students require time to process the information and integrate it into their knowledge structures and this generally happens in the library, where they live etc.  Collaborative learning can thus be deployed in an online, asynchronous manner (Ben-Zivi, 2007. Minocha & Thomas, 2007. Lipponen, 2002) and can then facilitate active engagement in their major or primary learning spaces.  This environment allows the student to review, explore and process before engaging again with the content and group members.   

The students will function in assigned groups.  As an initial task students will be asked to work on a single qualitative aspect of modern or historical mathematics.  They will be required to repeatedly review content that is posted online by group members and add, edit and comment as they see necessary.  Part of this work will be in a supervised computer laboratory and support will be provided to ensure that all students have developed the necessary digital skills.  The lecturer will initially facilitate the collaborative process and will provide clear details regarding the assessment strategy, group member expectations and conflict resolution procedures.

Following on this the students will be given a min-project/long-assignment that requires the application of mathematics (Martin and Premadasa 2010).  This will also be required to cover a component of the work that has not been formally covered in lectures yet. Each group will be given a single problem.  There will be a variety of problems and each problem will have different aspects ensuring that no groups will have an identical problem. The students will work on this collaboratively (review, edit, modify, comment) over 4-5 weeks and produce an edited document as the final outcome.  This will include an analysis of the problem, a detailed solution and an attempted computational approach.  Group members will meet formally once a week. A tutor or lecturer will be in attendance for part of this time.  Marks will be assigned for milestones achieved, the final product and for a final presentation by a random group member.

These tasks will contribute to the assignment/tutorial component. The impact of this task will be measured using the “Conceptions of Mathematics Questionnaire”(Crawford et al 1998) and “Approaches to Studying Questionnaire” (Richardson 1990), “Experiences of Teaching and Learning Questionnaire”(Ramsden 1991), course evaluations and interviews of selected students.

Affordance Matching
The affordances of the task were assessed using Bowden (2008) as a guide.  The following affordances were added:

Math-ability - the ability to use mathematical symbols directly in the wiki.
Edit-ability - the ability to view the current version of the document only.
Revision-ability - the ability to review changes in the content.
Message-ability – the ability to leave note for group members that does not form part of the document

Table 1: Affordances required by the task
Affordances
Required
Read-ability
View-ability
Listen-ability

Watch-ability
Write-ability
Edit-ability
Math-ability
Revision-Ability
Draw-ability
Speak-ability

Video-produce-ability

Resize-ability
Move-ability
Playback-ability

Accessibility
Record ability

Synchronous-ability

Message ability
Browse-ability
Search-ability
Data-manipulation-ability

Link-ability
Highlight-ability

Focus ability

Permission-ability
Share-ability



The affordances of the task was then compared to the various tools available.

Table 2: Affordances of Tools vs Task
Affordances
Blog
Chat
Forum
Wiki
Task
Read-ability
View-ability

Watch-ability

Write-ability
Edit-ability



Math-ability



Revision-Ability
Draw-ability

Resize-ability


Move-ability


Accessibility
Message-ability




Browse-ability
Search-ability
Link-ability

Permission-ability
Share-ability



From table 2 the wiki is the obvious choice and has a history of use in education (Augar, 2004. Ben-Zvi, 2007).  A message-ability will be required for students to communicate ideas and briefly behind their modifications.  This will be similar to a chat or forum tool. The choice of wiki type is also crucial as not all wikis are math or chat enabled.

Deployment Context
This task will be used in one of the two first year mathematics classes for academic development students in the science faculty.  The class size is approximately 150.  Based on the trend observed over the past few years only a fraction of these students would consider becoming mathematicians.  The majority of these students are not English first language speakers.

The asynchronous collaborative environment provides an ideal platform for these students to engage with their peers in a ‘safe’ environment.   The nature of this activity also allows students with the space needed to think about aspects of the problem before re-engaging with the content and their group members.

Challenges
During semester 2 of 2012 details of this task will be explored and if possible a pilot project will run during November/December.  The challenges include:

  • Developing and refining the assessment details
  • Developing the facilitation skills required for this environment amongst the teaching staff
  • Development of the problem details for this task.
  • Assessing the need for a glossary component

Future projects
  • Broadening collaboration to include national and international student projects
  • Collaborative textbooks
  • Adobe connect interviews to address motivational issues
  • Concept mapping from both lecturer and student perspective for deeper understanding
  • Reflective learning journals via blogs
  • Flipping the classroom using vodcasting
  • Integrating the use of 3D visualisation software

References
Augar, N. Raitman, R. Zhou, W. (2004, December) ‘Teaching and learning online with wikis’, Proceedings of the 21st ASCILITE Conference, Perth, Australia: 95-104

Beichner, R. (2008) ‘The SCALE-UP Project: A Student-Centered Active Learning Environment for Undergraduate Programs’, BOSE Conference on Promising Practices-Innovation in Undergraduate STEM Education, Washington, DC.

Ben-Zivi, D. (2007) ‘Using Wiki to promote Collaborative Learning in Statistics Education’, Technology Innovations in Statistics Education, Center for the teaching of Statistics, UCLA, UC Los Angeles

Bower, M (2008). ‘Affordance Analysis – matching learning tasks with learning technologies’, Educational Media International, 45(1): 3-15

Crawford, K. Gordon, S. Nicholas, J. Prosser, M. (1998) ‘University mathematics students' conceptions of mathematics’, Studies in Higher Education, volume 23 (1): 87-94

Davidowitz, B. Rollnick, M. (2010) ‘Adjustment of underprepared students to tertiary education’, in Rollnick, M. (eds) Identifying Potential for Equitable Access to Tertiary Level Science. Springer: 89-108

Leitze, A.R. (1996) ‘To major or not major in mathematics? Affective factors in the choice-of-major decision’, in Kaput, J. Schoenfeld, A. Dubinsky, E. (eds) CMBS Issues in Mathematics Education 6:83–100

Lipponen, L. (2002) ‘Exploring Foundations for Computer-Supported Collaborative Learning’, Proceedings of CSCL 2002: 72-81

Martin,P. Premadasa,K. (2010), ‘effective use of Wikis in College Mathematics Classes’, Journal on Systemics, Cybernetics and Informatics, Volume 8(6): 76-78

Marshall, D. Lesai, M. Schroeder, I.  (2007, December) ‘Making the Tacit Explicit: Accessing the Discourse of Physics’, For Engineering and Science Educators, Volume 11, 4-6.

Minocha, S. Thomas, P. (2007, December) ‘Collaborative Learning in a Wiki Environment: Experiences from a software engineering course’, New Review of Hypermedia and Multimedia, volume 13 (2): 187-209.

Mji, A. (2003) ‘A three-year perspective on conceptions of and orientations to learning mathematics of prospective teachers and first year university students’, International Journal of Mathematical Education in Science and Technology, volume 34 (5): 687-698

Ramsden, P.(1991) ‘A performance indicator of teaching quality in higher education: The Course Experience Questionnaire’, Studies in Higher Education, volume 16 (2): 129-150

Richardson, J. (1990) ‘Reliability and replicability of the Approaches to Studying Questionnaire’, Studies in Higher Education, volume 15 (2): 155-168

Smith, B. MacGregor, J. (1992) ‘What is Collaborative learning’, Goodsell, A. (eds) Collaborative learning: A Sourcebook for Higher Education, National Center on Postsecondary Teaching, Learning and Assessment, University Park, PA: 10-29

Wandisile, M. Tshiwula, L. (2012, January) ‘Student diversity in South African higher education’, Widening Participation and Lifelong Learning, Volume 13, Special Issue: 19-33

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