MON: Tacaí - Supporting the Understanding of Mathematical Concepts in Further Education in Ireland (Paul Curran)
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8 January 2017
“Tacaí” is an online, free-to-use learning support tool, aimed at being used within the Irish Further Education sector. It supports the learning of mathematical concepts commonly encountered at QQI Level 4 in the Irish system, specifically those required in Functional Mathematics 4N2138. The support itself will be offered online and open to all, at least in its initial stage as currently envisaged. The word “Tacaíocht” is of the Irish language (or Gaeilge), which roughly translates into English as “support” and can be understood in a literal physical way but also in the context of moral support and encouragement. "Tacaí" means supporter in the same sense. The approach to learning taken by the project is one of scaffolding learning which is a metaphor referring to a structure offering physical support that is removed when it is no longer needed.
Mathematical ability and numeracy has long been linked to employment prospects as evidenced by the National Adult Literacy Agency (2014), the Programme for the International Assessment of Adult Competencies (PIAAC) report (2012), the School Completion Programme and the Programme for International Student Assessment (PISA). Hughes and Schwab (2010) describe literacy as a situated social practice. By this they mean that literacy is more than just a set of discrete skills. Numeracy is rightly considered a form of literacy by Hughes and Schwab and by NALA (2014). It is in this context that this project approaches mathematical skills. An activity system in the style of Vygotsky gives recognition to a number of factors, including mediating artefacts or tools. This is the role Tacaí envisages for itself: as a tool that supports learners who are also supported in other ways including interacting with a community of learners. It forms an artefact around which interactions can occur.
As a mediating artefact Tacaí will draw upon the theory, much cited in the context of reading and writing literacy, of scaffolding. This is the idea that during the learning process the teacher or a facilitator offers a variety of supporting mechanisms to assist the learner to grasp a concept. As Tacaí is a support to mathematical learning it will take the form of hints, suggested strategies and useful metaphors towards the aim of understanding mathematical concepts and procedures. Central to the approach taken by Tacaí is the strategy of progressing from concrete materials to abstract concepts. Thompson (1994) describes how the effective use of concrete materials can help avoid misunderstandings. Lee and Tan (2012) discuss the effectiveness of a concrete-pictorial-abstract (C-P-A) progression. They develop a role for virtual manipulatives within this progression and outline a C-V & V-P-A alternative. The use of virtual manipulatives is a tool that Tacaí will employ to allow learners to explore concepts and relationships between concepts.
The work of Richardson et al. (2014) on colour and contrast in e-learning and instructional design and the work by Murch (1987) on readability have been used to design the tool with accessibility, split-attention issues and cognitive load in mind. Development is on-going.