Numeracy for adults: Latest findings from teaching and learning research Publications
Publication Details
This report identifies critical factors for successful numeracy learning in tertiary education. It is based on the latest teaching and learning research from New Zealand and overseas. It sets out the practical implications of these findings for how providers teach numeracy, particularly as part of vocational qualifications.
Author(s): Gill Thomas and Jenny Ward, Maths Technology Limited.
Date Published: July 2010
Summary
Structure of the review
The critical factors for effectively embedding numeracy are described in three sets of research-based understandings as follows:
- How adults develop their numeracy expertise.
- The features of effective embedded numeracy provision.
- Managing and sustaining change to achieve effective long-term embedding of numeracy.
Each of these three sets is developed as four understandings.
The first section of the review provides an overview of each of the three sets of understandings. The detail of these understandings is then provided in the following sections, in a format that describes the research base for each understanding, outlines the implications for practice and identifies key references in the area.
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.
- Learning programmes that are transparent allow adults to see how their learning links to their own particular purposes.
- Adults need to be involved in setting learning goals and monitoring their progress towards these. Learning is a purposeful goal-directed activity. An ongoing goal-setting process is integral to effective learning.
- Motivation is a key factor in engagement and achievement. Learners are motivated when they can see the value of learning for their own goals.
Adult learners develop expertise by building on their existing knowledge, skills and experiences.
- A constructivist approach to teaching and learning focuses on the development of learners' conceptual understandings through meaningful learning experiences.
- Teaching approaches that are based on constructivist theory build on learners' existing knowledge, experiences and understandings, and support individuals to actively construct meaning for themselves.
- As learners develop expertise in a field, they become increasingly aware of the key concepts that help to structure their knowledge and they develop meta-cognitive strategies that allow them to monitor their own learning.
- To successfully employ a constructivist approach, tutors require a sound conceptual basis of mathematics.
Adult learners develop their numeracy most effectively in contexts that have meaning to them. As learners develop their expertise, their increasing awareness of their knowledge and skills allows them to apply them in a wide range of contexts.
- Thinking and learning depend greatly on the social and cultural contexts in which they occur.
- Learning can be transferred from instructional contexts to work or other everyday situations. Transfer is enabled where learners are aware of the underlying principles behind content, where they are engaged in mathematics and where they are supported to articulate their own problem-solving approaches.
- Learning is enhanced through interaction with more knowledgeable individuals that can scaffold developing understandings.
Mathematics anxiety is experienced by many adults. This makes it difficult for them to access their working memory and think logically, and results in lower course completion rates.
- Where teaching approaches focus exclusively on correct answers and give little cognitive support, learners who experience repeated failure may develop negative perceptions of their own mathematical ability which contribute to the development of mathematics anxiety.
- Mathematics anxiety decreases the efficiency of the working memory and makes it difficult for individuals to think logically.
- Teachers who model positive attitudes towards mathematics, and instruction focused on relevant content in meaningful contexts have been found to positively influence the attitudes of anxious learners.
The features of effective embedded numeracy provision
Where tutors work as a team, learners are more likely to stay in training and complete vocational qualifications.
- Successful team approaches may involve tutors in joint planning, observation and team teaching as appropriate. Regardless of the approach used, tutors require sufficient time to be allocated to enable them to work together.
- Team approaches are supported where numeracy and vocational tutors have opportunities to learn from each other.
- Effective teaching teams in adult education are learner focused and share responsibility for learner progress.
Successful approaches to embedding numeracy clearly link literacy, language and numeracy (LLN) and vocational components of the course.
- Links between LLN learning and vocational learning are clearly and explicitly identified.
- LLN instruction is provided as it is required for the vocational task at hand.
- Teaching and learning materials reflect use of numeracy within the vocation and are differentiated for learners' varying numeracy needs.
Effective assessment in programmes where numeracy is embedded makes use of learning progressions to provide direction for teaching programmes and to monitor progress toward learning goals.
- Learning continuums clearly describe the growth of knowledge and skills that occurs as learners develop their expertise in a particular area.
- Diagnostic and formative assessment which maps student progress against learning progressions provides valuable direction for teaching programmes.
- Successful assessment procedures provide both formal and informal feedback to learners about their progress.
- There is a need to develop appropriate assessment instruments for use in adult numeracy education.
Embedded numeracy provision is facilitated by appropriate organisational policies, management structures, resourcing, and working conditions.
- Institutions that adopt a whole-organisation approach to the development and support of embedded programmes are more likely to be effective.
- It is important for administrative procedures and the allocation of practical resources to reflect the importance of both numeracy and vocational learning.
Managing and sustaining change to achieve effective long-term embedding of numeracy
Organisations are more likely to develop and maintain effective approaches to embedding numeracy when the value of LLN is understood and numeracy is viewed as an integral part of vocational training.
- Approaches are more likely to be sustained where managers understand that embedded numeracy is effective in increasing participation and raising achievement.
- Numeracy teaching is more likely to be effective where it is regarded as an integral part of vocational training.
- Tutors and employers play a key role in communicating the value of numeracy skills to learners.
Teaching materials are important tools that can substantially influence the content and enactment of instruction.
- Teaching materials are tools used by tutors as they design instructional programmes. The ways in which tutors use teaching materials are dependent upon their own understandings, the understandings and characteristics of the students they teach, and the contexts of instruction.
- Because teaching materials directly influence the process of teaching, they have been widely used as a tool in instructional reform.
- Teaching materials need to be developed in ways that clearly anticipate the role of the tutor in implementation, and include important information that enables tutors to make decisions about how and when to use the material presented.
Professional development programmes can be effective in improving tutor practice and learner performance.
- Effective professional development programmes focus directly on the link between learning and tutor practice.
- Effective professional development programmes support tutors to identify and examine their current understandings and approaches as they develop their professional knowledge base.
- Ongoing professional development programmes support tutors to take responsibility for student learning and this provides a sound basis for continual improvements to knowledge and practice.
Assessment data provides valuable information that can be used systematically to improve programmes.
- Continuous programme improvement requires organisations to clearly specify learning goals, systematically monitor the progress of all learners towards these goals and then revise teaching programmes on the basis of this information.
- Individual and aggregate measures of achievement enable organisations to focus on improving the performance of both individual learners and the organisation as a whole.
- Professional learning communities can successfully effect and sustain change by highlighting student performance.
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