Numeracy for adults - latest findings from teaching and learning research

4. Sustaining change to achieve 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.

Research findings

Senior managers play a key role in the development and maintenance of embedded numeracy programmes. When managers understand that embedded numeracy is effective in increasing participation and raising achievement, approaches are more likely to be sustained. In addition to understanding the benefits of embedded numeracy, it is important for managers to “fully understand the implications of embedding, both in terms of the practical support it requires but also in terms of pedagogy and teachers’ expertise” (Casey et al., 2006, p. 45). Where managerial support is provided, the effective embedded approaches developed by committed and enthusiastic tutors are more likely to be used by other tutors.

Numeracy teaching is more likely to be effective when it is regarded as an integral part of vocational training. This is in contrast to approaches that view numeracy as optional, required only by those learners that need additional learning support.

“Learners improve their literacy, numeracy and other key skills when the whole organisation believes key skills are an essential underpinning for learning vocational skills and technical knowledge.” (Cranmer et al., 2004, p. 4)

Positioning numeracy as an essential part of vocational training reduces the stigma associated with needing assistance, so learners are more likely to succeed.

Learners who appreciate the value of LLN skills for their future career opportunities are more likely to be motivated and achieve success. Tutors and employers play a key role in communicating the value of numeracy skills to learners. Vocational tutors are more likely to be able to effectively communicate the value of LLN skills to learners with regard to their career aspirations because they “…have a natural legitimacy… in the eyes of the learners [as] they represent the role to which the learner aspires” (Roberts et al., 2005, p. 9). Employers also play a key role in communicating the value of numeracy to learners. The active involvement and support of employers increase learner motivation and engagement.

Implications for practice

Effective embedded approaches to numeracy are more likely to be developed and maintained when:

• managers understand that embedded numeracy is effective in increasing participation and raising achievement
• numeracy is regarded as an integral part of vocational training, rather than additional support for those with particular learning needs
• tutors effectively communicate the value of numeracy to learners with regard to their future career opportunities
• employers are actively involved in learning and support attendance.
  

References: Bates (2005); Casey et al. (2006); Cranmer, Kersh et al. (2004); NRDC (2006); Roberts et al. (2005); Sagan et al. (2005); Swain et al. (2005).

Research findings

Teaching can be understood as a process of design.

“Teachers perceive and interpret existing resources, evaluate the constraints of the classroom setting, balance tradeoffs and devise strategies – all in the pursuit of their instructional goals.” (Brown & Edelson, 2003, p. 1)

Within this view, curriculum materials are a tool used by tutors as they design instructional programmes. The ways in which teachers use learning materials are dependent upon their own understandings, the understandings and characteristics of the students they teach, and the contexts of instruction. Where teachers have a sound understanding of content, they tend to improvise instruction, devising learning activities independently from teaching resources. Contrastingly, where teachers lack understanding, they offload responsibility for student learning onto teaching materials, following set instructional activities and sequences. Between these two extremes, teachers adapt learning programmes by modifying teaching materials to better address student needs, fit with their teaching style, or align with classroom circumstances.

Researchers in this area use the term ‘enacted curriculum’ to acknowledge the difference between the teaching and learning that take place in the classroom and the teaching and learning intended by content frameworks and the developers of teaching materials. This term acknowledges the active role of teachers in designing instruction; “…the enacted curriculum is actually jointly constructed by teachers, students, and materials in particular contexts” (Ball & Cohen, 1996, p. 7).

Because teaching materials directly influence the process of teaching, they have been widely used as a tool in instructional reform.

“A primary lure of curriculum materials is that, of all the different instruments for conveying educational policies, they exert perhaps the most direct influence on the tasks that teachers actually do with their students each day in the classroom.” (Brown & Edelson, 2003, p. 1)

Researchers evaluating the effectiveness of such reforms stress that “…the materials themselves matter in teacher interactions with curriculum materials…” (Remillard, 2005, p. 240). They outline that curriculum materials need to be developed in ways that clearly anticipate the role of the teacher in curriculum design. In particular, teaching materials need to include important information that enables teachers to make decisions about how and when to use the material presented. This information may include descriptions of content, effective ways to represent key concepts and the benefits and limitations of these, and information about probable student responses and the reasoning behind these.

Implications for practice

Effective teaching materials will anticipate the role of the teacher in curriculum design and therefore:

• include descriptions of important content knowledge
• include important representations that can be used to communicate key content to students  and provide information about how these can be used in teaching
• include information about probable student responses and the reasoning behind these 
• include information about the ways in which aspects of learning are related, both in terms of conceptual ideas and across time 
• are relevant  to tutors’ current understandings
• are written and presented in ways that communicate effectively with tutors. 
  

References: Ball (1990); Ball & Cohen (1996); Ben-Peretz (1990); Brown & Edelson (2003); Cohen & Ball (1999); Pea (1993); Remillard (2005); Schmitt (2000); Sherin & Drake (2004); Spillane (2006).

Research findings

Effective professional development programmes focus clearly on the link between learning and tutor practice. As an outcome of such programmes, tutors understand the ways in which their own practice affects the learning that occurs in their classrooms.  “The core question is, what do we as teachers need to do to promote the learning of our students?” (Timperley, 2008, p. 11).

Efforts to improve instruction are most likely to produce genuine changes to practice when programmes are focused on developing the professional knowledge base of tutors. Tutors require a comprehensive knowledge of the subject, an understanding of how to teach key concepts effectively, and an awareness of how to assess learners’ progress in the area.

“Successful professional development efforts are those that help teachers to acquire or develop new ways of thinking about learning, learners, and subject matter, thus constructing a professional knowledge base that will enable them to teach students in more powerful and meaningful ways.” (Borko & Putnam, 1995, p. 60)

By contrast, where tutor knowledge is not engaged and extended in professional development programmes, participating tutors are likely to adopt surface features of the new approach while maintaining the core content of their previous practice. While information about the knowledge and skills of those teaching adult numeracy is limited, it points to relatively low levels of mathematics knowledge and achievement amongst adult numeracy tutors.

Effective professional development programmes provide opportunities for tutors to connect their professional learning with their current understandings and approaches. Because “…teachers’ knowledge and beliefs affect how they perceive and act on various messages about changing their teaching” (Borko & Putnam, 1995, p. 59), effective programmes support tutors to clarify their own understandings as they build a professional knowledge base. Effective programmes also address the contexts in which participating tutors work. New approaches are introduced in a way that “is consistent with the principles of effective teaching but also systematically assists teachers to translate those principles into locally adapted applications” (Timperley, 2008, p. 9).

Research suggests that when tutors are involved in ongoing professional development programmes that are clearly linked to their current teaching situation, they are more likely to take greater responsibility for student learning and develop effective teaching practices.

“Change appears to be promoted by a cyclical process in which teachers: have their current assumptions challenged by the demonstration of effective alternative practice, develop new knowledge and skills, make small changes to practice, and observe resulting improvements in student outcomes.” (Timperley, 2008, p. 14)

Where tutors take responsibility for student learning, there is a sound basis for continual improvement to knowledge and practice.

Research into effective embedded numeracy provision highlights the importance of professional development for both vocational and numeracy tutors. In particular, vocational tutors need support to increase their understanding of learners’ varying numeracy needs and develop their knowledge of how numeracy is used in vocational tasks. Numeracy tutors need support to develop teaching approaches that are guided by vocational content and recognise the role of numeracy in the vocation. Both vocational and numeracy tutors would benefit from professional development programmes that develop collaborative approaches to teaching.

Implications for practice

Professional development programmes are most likely to lead to improvements in tutor practice and learner performance when:

• tutors are supported to understand the ways in which their own practice affects the learning that occurs in their classrooms
• tutors are supported to identify and examine their current understandings and methods
• tutors are supported to implement new approaches in the specific contexts in which they work
• tutors have an increasing sense of responsibility for student learning
• programmes develop tutors’ knowledge of content
• programmes develop tutors’ understandings of effective pedagogy
• programmes develop tutors’ knowledge of how to assess learners’ progress
• programmes engage tutors in a range of learning activities: formal and informal, group and individual, planned and unstructured
• programmes involve tutors in an ongoing cycle of professional development
• programmes support tutors to make changes to practice and then observe the effects of these.
  

In effective embedded LLN approaches, professional development programmes:

• support vocational tutors to increase their understanding of learners’ varying numeracy needs and develop their knowledge of how numeracy is used in vocational tasks
• support numeracy tutors to develop teaching approaches that are guided by vocational content and recognise the role of numeracy in the vocation
• support the development of collaborative approaches to teaching.
  

References: Askew, et al. (1997); Borko & Putnam (1995); Butler et al. (2004); Casey et al. (2006); Coben (2003); Franke et al. (1998); Guskey (2000); Morton et al. (2006); Roberts et al. (2005); Smylie (1995); Swain et al. (2005); Swain & Swan (2007); Timperley (2008); Wilson & Berne (1999).

Research findings

Research into programme improvement highlights the value of achievement data in the process of improving instruction. Within this approach, the “achievement of student outcomes is the criterion for judging the effectiveness of all other programme practices and components” (Bingman & Stein, 2001, p. 23). Achievement data provides a measure of whether learners are successfully meeting learning goals, and this in turn provides information on the effectiveness of teaching programmes and other organisational practices.  An effective model of 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.

This approach is consistent with a learning paradigm perspective which views learning as the key responsibility of educational institutions, while the contrasting instructional paradigm emphasises the delivery of instruction as the primary duty of organisation.

“…in the Learning Paradigm, the power of an environment or approach is judged in terms of its impact on learning. If learning occurs, then the environment has power... To know this in the learning paradigm we would assess student learning routinely and constantly.” (Barr & Tagg, 1995, p. 17)

A learning paradigm perspective emphasises the importance of using both individual and aggregate measures of achievement in order to continuously improve the performance of both individual students and the organisation as a whole.

Professional learning communities can successfully effect and sustain change by highlighting learner performance. When tutors work collaboratively to reflect on achievement data and modify teaching approaches “…the entire team gains new insights into what is working and what is not, and members discuss new strategies that they can implement in their classrooms to raise student achievement” (DuFour, 2004, p. 10).

Implications for practice

Organisations are more likely to engage in ongoing cycles of improvement when systems are established to review achievement information regularly.

The use of assessment data to systematically improve programmes is facilitated when:

• learner performance goals are clearly defined
• effective assessment methods are in place to measure progress towards learning goals
• achievement information is regularly aggregated and analysed
• tutors work collaboratively to reflect on achievement data and modify teaching approaches appropriately
• instructional programmes and organisational practices are adapted on the basis of insights gained from assessment information.
  

References: Barr & Tagg (1995); Bingman & Stein (2001); DuFour (2004); Levesque et al. (1996); Timperley (2008); US Department of Education (2003).