Numeracy for adults - latest findings from teaching and learning research

2. How adults develop their numeracy expertise

Adults engage in learning for their own larger purposes. These purposes are associated with their roles in society as workers, family members and community members.

Research findings

Children attend school because of legal mandates and strong social and cultural forces that view school as the “work of childhood” (Comings et al. 2000, p. 1). In contrast, adults generally make an active choice to participate in educational programmes and they do so in order to achieve broader purposes in their lives.  

We undertake cognitive tasks not merely as an end in themselves but as a means of achieving larger objectives and goals that have meaning in the community (Scribner, 1988).

Adults seek to develop their LLN skills in order to gain access to information, give voice to their opinions and ideas, take action to solve problems and create future opportunities in the form of further qualifications. Achieving the purposes they set for themselves enables adults to more effectively fulfil their roles in society as workers, family members and community members.

Adults are more likely to engage in learning programmes for sustained periods and achieve success when it is clear to them how their learning is linked to their own particular purposes. Transparent learning programmes acknowledge and support learners’ purposes by helping them to establish specific learning goals in line with these. In addition, where learners are involved in monitoring their progress towards learning goals, they are more likely to persist and achieve success in learning programmes.

Motivation is a key factor in engagement and achievement.  Learners are motivated when they can see the value of learning for their own goals.  Adults are more likely to be motivated to engage with LLN learning when it is embedded within a vocational or leisure course which is their primary motivation.  

Implications for practice

Adult learners are more likely to be engaged and achieve success when:

• learning programmes clearly articulate course content and outcomes to enable adults to be clear about how the learning links with their own particular purposes
• course information is clear, unambiguous and accessible. Specific examples of content can be useful in communicating with potential learners 
• adult learners are involved in setting learning goals and monitoring their progress towards these
• learning activities incorporate clearly specified outcomes.
  

Embedding LLN learning within vocational courses will increase adults’ motivation for developing their knowledge and skills in LLN.

References: Bingman & Stein (2001); Coben (2003); Comings, et al. (2000); Gillespie (2002b); Roberts et al. (2005); Scribner (1988); Swain et al. (2005).

Research findings

A constructivist approach to teaching and learning focuses on supporting learners to develop conceptual understandings through meaningful learning experiences. This is in contrast to a behaviourist approach, where skills and knowledge are developed through reinforcement.

Teaching approaches that are based on constructivist theory build on learners’ existing knowledge. Learners actively construct knowledge as they make sense of new information and experiences by extending or changing their current ideas and understandings. Within this approach, the role of the tutor is to support individuals to actively construct meaning for themselves.

“...taking a constructivist approach to building knowledge and skills focuses on helping students develop their understanding and make sense of the world.” (Bingman & Stein, 2001, p. 19)

Instruction is aimed at developing a “richly structured knowledge base” (Gillespie, 2002c, p. 2) rather than acquiring a selection of isolated facts or mastering a number of operational procedures.  The connections between areas of learning are valued and emphasis is given to the ways in which different areas of content are related. Teaching is structured around key concepts and big picture ideas.

As learners develop expertise in a field, they become increasingly aware of the key concepts that help to structure their knowledge. As with experts in the field, these key ideas give structure to their developing knowledge and enable them to discern and remember significant new information. In addition, learners can be supported to develop meta-cognitive strategies similar to those used by experts to monitor and control their own thinking processes. Assisting learners to develop and measure their success by reflecting on what they have learnt helps them to take responsibility for their learning and develop independent learning and study skills.

To successfully employ a constructivist approach, tutors require a sound conceptual understanding of their subject area and an appreciation of the ways in which different aspects of learning within their area are related. Effective teachers of mathematics possess deep conceptual knowledge which is based on the ability to reason rather than simply apply rules for operating.

Implications for practice

A constructivist approach to teaching and learning has been shown to support learners to develop conceptual understandings.  Constructivist approaches:

• acknowledge and value learners’ existing knowledge by supporting learners to identify their current understandings and investigate these in the process of developing new ideas
• are focused on the development of conceptual understandings rather than the memorisation of facts and procedures for operating
• develop reflective thinking and reasoning
• utilise teaching and learning activities that are relevant and meaningful to learners
• articulate the key ideas within a field and organise learning around these
• make explicit links between areas of learning within a field
• support students to reflect on their own learning in order to gain increased control over their own thinking processes and  develop independent study skills
• promote the development of conceptual knowledge among tutors.
  

References: Askew et al. (1997); Bingman & Stein (2001); Cobb (1994); Coben (2003); Fosnot (1996); Gillespie (2002c); Ma (1999); Piaget (1978); Swain et al. (2005); von Glasersfeld (1995).

Research findings

A large body of literature has demonstrated that adults’ thinking is influenced by the social and cultural contexts in which it occurs. Research examining the mathematics processes of adults working in a wide variety of fields has found that adults have significant control over the problem-solving processes in their everyday lives, calculating mentally with the original context in mind. This is in contrast to students working in traditional school mathematics programmes, where problems are usually defined by the teacher, there is often one preferred method, and numbers are extracted from problems, operated on and then interpreted back into context.

The issue of the extent to which numeracy skills are transferable from one context to another is central to adult numeracy education. Some researchers emphasise the situated nature of cognition and learning and consider all knowledge to be inextricably linked to the context in which it occurs. Within this approach, the transfer of learning into contexts that differ from the instructional context is highly problematic. An alternative body of work asserts that learning can be applied to new contexts, in a process called translation.  Within this view, the role of the tutor is to teach in such a way that learners are able to apply what they have learnt to a variety of new situations.

“The question of the ways in which knowledge, skills and understanding are situated and embedded in contexts and whether or not they are transferable (or translatable) is a key one for all mathematics educators. It is particularly acute for adult numeracy educators because of the expectation that ‘numeracy’ should be usable…in adult life.” (Coben, 2003, p. 53)

Several factors have been found to influence the transfer of learning from instructional contexts to work or other everyday situations. Learning is more easily transferred where learners are aware of the “underlying principles, patterns and relationships” (Gillespie, 2002a, p. 1) within content; where instruction is linked to larger ideas that can be translated across contexts learners are more likely to make this translation. Learners are also more likely to gain transferrable knowledge when the instruction is meaningful. Instruction is meaningful for learners when it is engaging, not necessarily when it is realistic in the sense that it mirrors an authentic everyday situation. In addition, approaches that acknowledge students’ own problem-solving methods and encourage them to articulate these have also been found to enable transfer.

Learning is enhanced by social interaction. Vygotsky, and other researchers working in the socio-cultural tradition, highlight the importance of social interaction in teaching and learning programmes. These researchers outline how learning is enhanced through interaction with more knowledgeable individuals that can scaffold developing understandings. Where adults work collaboratively to develop knowledge and skills in a social context, a learning community is developed within the classroom and new understandings are “generated from disjunctions, conflicts and contradictions that occur in the course of people being involved in activity” (Coben, 2003, p. 41).

Implications for practice

Learners will develop numeracy skills and are most likely to transfer their learning to new contexts where teaching and learning programmes:

• clearly convey the key principles and larger ideas within the subject area
• engage learners in meaningful mathematics contexts
• support students to articulate their own problem-solving approaches.
  

Learning is enhanced where learners are part of a collaborative learning community and are given opportunities to:

• be supported by more knowledgeable individuals
• support each other’s learning by giving and receiving assistance and advice
• engage in group work.
  

References:    Bingman & Stein (2001); Bruner (1985); Carraher & Schliemann (2002); Cobb (1994); Coben (2003); Evans (2000); Gillespie (2002a); Lave (1988); Saxe (1988); Swain et al. (2005); Vygotsky (1987).

Research findings

Mathematics as a subject is perceived by many people as abstract and lacking in relevance. Where teaching approaches focus exclusively on correct answers and provide little cognitive support, learners that experience repeated failure may develop negative perceptions of their own mathematical ability which contribute to the development of mathematics anxiety. Although mathematics anxiety generally develops in childhood, its effects are still felt in adulthood and it is widespread throughout the population.

“Math anxiety is a bona fide anxiety reaction, a phobia with both immediate cognitive and long-term educational implications.” (Ashcraft, 2002, p. 184)

Mathematics anxiety decreases the efficiency of an individual’s working memory as intrusive thoughts and worries take the focus away from the mathematics task at hand. This makes it difficult for individuals to think logically and results in increased errors and longer processing times when solving problems mentally. In the longer term, mathematics anxiety leads to decreased competence and reduced course completion rates, which may restrict the career options available to adults.

Teachers that model positive attitudes towards mathematics have been found to positively influence the attitudes of anxious learners and mitigate the effects of mathematics anxiety on learning. Where learning programmes are focused on relevant content in meaningful contexts and learners are involved in open-ended activities with extended opportunities for problem solving and discussion, anxiety is also reduced.

Adult learners that aspire to a particular job or career experience a socialisation process as they train for that position. Where LLN skills are integral to vocational training, learners accept these as part of their new professional identity, leading to increased motivation and confidence for learning LLN and decreased mathematics anxiety.

Implications for practice

Adult numeracy educators need to be aware that mathematics anxiety will be affecting the learning of some course participants.

The effects of mathematics anxiety on learning can be mitigated by:

• tutors that model positive attitudes towards mathematics
• instructional programmes focused on relevant content in meaningful contexts
• teaching and learning programmes that provide learners with extended opportunities for problem solving and discussion
• vocational programmes that include LLN skills as an integral part of vocational training.  
  

References: Ashcraft (2002); Ashcraft & Kirk (2001); Coben (2003); Evans (2000); Roberts et al. (2005); Swain et al. 2005); Torgerson et al. (2004).