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An Investigation of Interactive Online Modules for the Teaching of Mathematics

PhD by Dr Kuva Jacobs, Director Redpoint Consulting.

 

The following modules were developed as part of my PhD for two mathematics courses at the University of South Australia. I am hosting these modules to provide students and academics with better online mathematics resources. Log onto quizzes using the ID of Guest.

Feel free to use these modules on this website for teaching purposes, however reuse on other websites or for commercial use is not permitted without explicit authorisation from the author.

 

Background

The two courses for which the modules were created provide a notable contrast in their difficulty, content, purpose and target audience. Differential Equations is a second year mathematics course offered to students enrolled in a mathematics degrees whereas Mathematics for Computing is a first year service course focussing on discrete mathematics with a student cohort consisting largely of computer science students, many of whom have little or no interest in mathematics.

 

Features

Two unique sets of online modules have been tailored specifically for the pair of different courses. They have been developed using a student-centred, interactive approach that adheres to the fundamental constructivist guidelines in order to create an effective online learning environment. The modules aim to be autonomous, guiding students through information whilst providing flexibility in navigational sequences. This information is presented both visually and verbally, with the aim of accommodating a wider range of perceptual styles of learning. A conceptual overview is presented, with an emphasis on drawing together complex relationships using well-defined tasks. The modules have been created with an interface that is both visually appealing and intuitive.

Venn Diagrams

 

Log in with the User ID of Guest.

 

Online Randomised Quizzes, with inbuilt randomised parameters and adjustable graphs test conceptual understanding. The quizzes work on the principle that practise makes perfect, by retesting incorrect answers with a new randomly selected set of numbers.

Combinations &
Permutations

 

Online Walkthroughs that introduce new concepts and definitions in a step-by-step format, governed by a clearly labelled navigational structure. Interactive graphs and animated simulations of real-world examples are included to encourage students to actively explore and interact.

For Loops

 

 

Online Worksheets, which also feature randomised parameters, allow students to work through lengthy problems and provide a more open style of assessment, such as testing the creation of a circuit diagram for a given Boolean logic expression.

Boolean Algebra
Theta Notation

Nonlinear Differential Systems

Water Tanks

Research

Analysis of feedback from the two student cohorts provided insight into the influence of these variations upon the effectiveness of the modules. This lead to a conclusion of whether the value of these innovative teaching tools is provides a basis for a deeper level of understanding.

 

To read more about my research & the outcomes, please refer to my PhD thesis or the below papers

 

Jacobs, K. (2006). Candy-Coated Mathematics, a more Digestible Approach. Paper presented at the 3rd International Conference on the Teaching of Mathematics at the Undergraduate Level, Istanbul, Turkey.

 

Jacobs, K. (2005). An Investigation of Interactive Online Visual Tools for the Learning of Mathematics. Paper presented at the Kingfisher Delta '05, The Fifth Southern Hemisphere Symposium on Undergraduate Mathematics and Statistics Teaching and Learning, Fraser Island, Queensland, Australia.

 

Jacobs, K. (2005) Differential equations online: an interactive visual approach. Paper presented at the OLT-2005 Beyond Delivery Conference, Brisbane, Queensland, Australia.