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Session 10 Linking Theory to Practice and Evaluation An Adult Literacy and Numeracy Curriculum Framework for Scotland Definition ‘To be numerate means to be competent, confident, and comfortable with one’s judgements on whether to use mathematics in a particular situation and if so, what mathematics to use, how to do it, what degree of accuracy is appropriate, and what the answer means in relation to the context.’ from Shifting the Focus Affect: Beliefs, attitudes and emotions The role of affect in adult learning and adults’ ‘numerate practices’ has been explored by Evans (2000). He argues that thinking and emotion are inseparable, so that human mathematical (or numerate) activity is always emotional as well as cognitive. He notes the way in which an operation or situation involving mathematics may trigger unexpected feelings of pleasure or loathing in the learner, encouraging or impeding the transfer of mathematical skill, knowledge and understanding. Critical Numeracy This group of approaches starts from the position that adults are active agents in the world, rather than seeing them as inadequate individuals with a numeracy deficit. Adult education in this approach is seen as a tool for social justice, aiming to equip people with knowledge and tools to examine, criticise and seek to change the economic, political, and social realities of their lives. Effective, connectionist teaching and deep progress Making connections between different aspects of mathematics. This includes, addition and subtraction or fractions, decimals and percentages. Making connections between different representations of mathematics. This includes: moving between symbols, words, diagrams and objects. Making connections with children’s methods. This included valuing these methods, being interested in children’s thinking and sharing the children’s methods. Profound Understanding of Fundamental Mathematics Profound understanding of fundamental mathematics (PUFM) is more than a sound conceptual understanding of elementary mathematics – it is the awareness of the conceptual structure and basic attitudes of mathematics inherent in elementary mathematics and the ability to provide a foundation for that conceptual understanding and instill those basic attitudes in students. Students are able to build on strong foundations and make connections in mathematics throughout their lives. Many numeracy tutors do not have sophisticated academic mathematics experience but they may become better mathematics tutors while teaching. Adult Numeracy: shifting the focus connectionist teaching PUFM positive attitudes deep progress critical numeracy realistic maths A Research Report and Recommendations for Adult Numeracy in Scotland Diana Coben, Scottish Executive, 2005 Scottish Energiser for Tutors of Adult Numeracy Be creative – numeracy isn’t just sums