Initial Prototype – Revision 1

Background

In South Africa there are a number of factors that contribute to mathematics being regarded as a killer course at first year level. In response to these factors students tend to favour surface learning approaches and survival strategies. As a result of this learning approach students struggle to apply the mathematical concepts in other disciplines. 

Students in science and engineering all state that mathematics is important in their fields of study but cannot elaborate or provide examples of this connection. This has a negative impact on student motivation and anxiety levels and results in first year mathematics being seen as a rite of passage.

Learning Problem

Students employ a recipe like approach when solving mathematics tutorial problems.  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 understanding of the conceptual nature of assigned problems
• Develop an appreciation for the applicability of mathematical content
• Initialise a reflective practitioner approach to problem solving

Task.

Collaborative learning is a powerful knowledge building tool in mathematics (Johnson and Johnson 1996).  It is frequently used in a variety of science and engineering contexts and can be use a zero technology environment (Marshall, Schroeder, Lesai 2007) or be employed in a technology rich environment (SCALE-UP). In a web environment it can be deployed in an online, asynchronous manner (Curtis and Lawson 2001). This type of learning can increase the depth of knowledge developed by the student (Cohen et al 1989).

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 add, edit and comment on content that is posted online.  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 contain a component of work that must still be formally covered. 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 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 progress (at weekly meeting), 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 “view of mathematics” and “depth of mathematics” instruments available, course evaluation questionnaires and interviews of selected students.

Affordance Matching

The affordances of the task was 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.

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
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	√	√	√	√	√
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, Ruth, Zhou (conf proc), Ben-Zvi (2007)).  Elements of a chat room might be required as part of the collaborative process but this still requires further investigation.  The choice of wiki type is also crucial as not all wikis are math 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

      References