How to teach anything, improve learning, and help people do stuff better

Teach anything

I want to write a book. Not sure what the title will be, but I’d like this – or something similar to be the byline or subtitle. I’d like it to mainly be a picture book. Something you could give to anyone. Like the kind of book you’d pick up in an airport.

Now I just need some content… and that pesky title…

Mandatory Review of Teacher Education Qualifications – Adult Literacy & Numeracy Education Working Group

NZQA_0I’m very pleased to have been part of the working group looking at the Adult Literacy and Numeracy Education (ALNE) qualifications this week. These qualifications are part of the Mandatory Review of Teacher Education Qualifications that is underway at the moment.

It feels a little weird doing this after being asked to put my name forward for the governance group and then being turned down… and then not putting my name forward for the working group and being asked to join…

However, I’m happy to be involved now. Actually, I’ve been trying to get involved on the NZQA development side of things for these qualifications since 2007 when I started this work.

One of my reflections this week is that I think there has been a shift in the sector in terms of who the established experts are. I think the group we had working on the ALNE qualifications were highly qualified in terms of their experience working with the existing qualifications and that we’ve done a good job in terms of shaping this content moving forward.

I’ll post more about where I think we’re heading with the three qualifications at some stage soon, but for now the three qualifications are starting to look distinct in the following way:

  1. NCALNE (Voc): This will probably become the New Zealand Certificate in Adult Literacy & Numeracy Education (Vocational/workplace) or NZCALNE (Voc) for short. This is what I have a vested interest in at the moment as it represents the next evolution of what I’ve been working with since 2007. We’re not looking at too many radical changes here. The knowledge base behind this is well established now and we’re simply going to tighten things up, reduce some clutter, and give some more weight to the practical hands on teaching component. The focus here is on trades tutors and others who are embedding literacy and numeracy into specific content.
  2. NCALNE (Ed): This will probably become the New Zealand Certificate in Adult Literacy & Numeracy Education (Educator) and abbreviated to NZCALNE (Ed). There are were some questions around whether we actually need this qualification. However, it looks like it’s going to stay around. The focus here remains on developing literacy and numeracy specialists. One of the major changes to this qualification is that it will have an equal focus on both numeracy and literacy. There isn’t really much numeracy in the qual as it stands. I don’t deliver this one so I’m less interested in it.
  3. NDipALNE: This is likely to become the New Zealand Diploma in Adult Literacy & Numeracy Education and abbreviated to something like NZDALNE. I am interested in this one. I’ve spent awhile recently with my head stuck in the existing unit standards which I find a bloated and academic. This qualification is looking at the biggest amount of change – which is probably fine given that it’s not being delivered anywhere yet. We’re looking at a much simplified structure and something that lines up much better with the other two qualifications. Where the focus in the Voc will be on trades and content specialists, and the Ed on specialists, the focus here will be on developing and recognising literacy and numeracy leadership with a very approach including a couple of large action research projects.

Who is the audience for the Level 6 120 credit Diploma?

This is one of my big questions. For now it seems that we can have a wide audience for the Diploma as we’ve framed it up over the last couple of days. This is likely to include our graduates from the NCALNE (Voc) who are trades tutors developing some serious expertise in literacy and numeracy and graduates from the NCALNE (Educator) who are more traditional LN experts and specialists

But it is also likely to now include others such as programme managers and leaders or champions inside organisations of different kinds with an strong interest in driving literacy and numeracy related organisational change.

Let me know in the comments how this is sounding… Are we on the right track?

New ALEC YouTube Trailer for our professional development NCALNE (Voc) Channel

What are adult numeracy theories?

As with our discussion about adult numeracy theories, adult numeracy theories are simply ideas about how adults learn maths and numerical concepts. To some extent, these mirror some of the content we’ve already covered regarding adult education in general and adult literacy in particular. Three key theories of adult numeracy include:

  1. Behaviourist: For behaviourists, if you can observe a change in your learner’s behaviour due to some stimulus that you have provided as educator. The behaviourist approach promotes the idea that the teacher should provide mathematical knowledge perhaps in the form of a problem (the stimulus), which the learner absorbs and then produces a solution for (the response). Following the rules correctly results in the correct answer which educators can measure easily with tests.
  2. Constructivist: As with ideas about literacy, numeracy has shifted towards a constructivist approach in recent years. In the constructivist point of view, learners actively construct mathematical knowledge as they bring what they already know together with new information and experiences. Constructivist theories of adult numeracy usually follow either Piaget, who emphasised ways in which individual learners make sense of mathematics, particularly through the importance of developmental stages, or Vygotsky who or saw learning as a social activity where teachers provided “scaffolding” to help learners move to higher levels of development.
  3. Sociocultural: Sociocultural theories of adult numeracy build on Vygotsky’s approach. As with the sociocultural approach to literacy, the basic idea is that numeracy learning and teaching is influenced by different social and cultural factors. A good illustration of this is the kind of “hands on” numeracy knowledge that a trades person would use to estimate or measure area in a real life work situation as compared to a textbook area calculation that you would find in a school setting. Textbook mathematics problems do not usually prepare apprentice farmers, gardeners, or horticulturalists for the kinds of issues associated with area, ratios, and measurement that they experience in the reality of their daily work.

Professional Reading

Review the questions below then read the article

  1. What theories underpin the approach to numeracy taken by the adult numeracy progressions that we use in Aotearoa New Zealand?

What is numeracy?

The term numeracy is relatively new. It was first used in 1959 in the UK Crowther Report, where it was characterised as the mirror image of literacy. Since then, numeracy has been interpreted in different ways internationally, mostly because of the very different needs of the users of the term. The view of numeracy that underpins the numeracy learning progressions is about knowing and understanding: it is therefore both broad and contextualised. The following definitions most closely represent the view taken here.

To be numerate is to have the ability and inclination to use mathematics effectively in our lives – at home, at work and in the community.
Ministry of Education, 2001, page 1

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.
Coben, 2000, cited in Coben, 2003, page 10

We believe that numeracy is about making meaning in mathematics and being critical about maths. This view of numeracy is very different from numeracy just being about numbers and it is a big step from numeracy or everyday maths that meant doing some functional maths. It is about using mathematics in all its guises – space and shape, measurement, data and statistics, algebra and of course, number – to make sense of the real world and using maths critically and being critical of maths itself. It acknowledges that numeracy is a social activity.
Tout, 1997, cited in Coben, 2003, page 11

The view of numeracy that underpins the numeracy learning progressions places an emphasis on the need for learners to gain:

  • a conceptual understanding of mathematical knowledge, and
  • the ability to use mathematical knowledge to meet the varied demands of their personal, study and work lives.

The numeracy learning progressions are based on the belief that in order to meet the demands of being a worker, a learner and a family and community member, adults need to use mathematics to solve problems.

key concepts

Several key concepts can be identified as central to the understandings about numeracy and about adult learners that have informed the development of the numeracy learning progressions. These concepts are covered below, under the following headings:

  • Meaningful contexts and representations
  • Understanding and reasoning
  • Degree of precision
  • Algorithms.

Meaningful contexts and representations

In 1992, the International Adult Literacy Survey (IALS) was redesigned to include a numeracy survey that assessed the distribution of basic numeracy skills in adult populations. The concepts underlying the assessment included the recognition that mathematical ideas are embedded within meaningful contexts and may be represented in a range of ways, for example, by objects and pictures, numbers and symbols, formulas, diagrams and maps, graphs and tables, and texts. The importance of teaching mathematics in meaningful contexts was also emphasised in the SCANS report (1991) and is an integral part of national adult education standards in Australia and the United Kingdom.

When adult learners need to know and use mathematics, the need always arises within a particular context. Numeracy is the bridge between mathematics and the diverse contexts that exist in the real world.

In this sense … [there] is no particular ‘level’ of Mathematics associated with it: it is as important for an engineer to be numerate as it is for a primary school child, a parent, a car driver or a gardener. The different contexts will require different Mathematics to be activated and engaged in.
Johnston, 1995, page 54

Many adults are unaware of the ways in which they use mathematics in the course of their everyday lives. For example, measurement is used in a great many routine activities.

All in all, measurement is revealed as a complex and somewhat contradictory area for teaching and learning: at once at the heart of mathematics and surprisingly absent, for some people, from activities which are commonly assumed to involve a lot of measurement, such as cooking, shopping and merchant banking.
Baxter et al., 2006, page 52

By grounding learning within authentic contexts, the numeracy learning progressions can raise learners’ awareness of the mathematics all around them – and of the mathematical knowledge, skills and strategies they already possess.

Understanding and reasoning

The demands for adult numeracy arise from three main sources: community and family, the workplace and further learning. While each of these sources is likely to require different mathematical skills at varying achievement levels, all mathematics needs to be learnt with understanding so that it can be generalised and adapted by the learner for a variety of situations.

Knowing certain mathematical facts or routines is not enough to enable learners to use that knowledge flexibly in a wide range of contexts. Being able to do mathematics does not necessarily mean being able to use mathematics in effective ways. Knowledge of procedural operations and facts is essential to reasoned mathematical activity, but is of little value in itself. A learner who counts decimal places to determine the number of decimal places in an answer without understanding the number operation involved may get 0.7 x 0.5 correct, but 0.7 + 0.5 incorrect. The learner’s lack of understanding of the mathematical process means that they have no way of knowing why some of their answers are correct and others incorrect, because they are unable to use reasoning.

… the notion of understanding mathematics is meaningless without a serious emphasis on reasoning.
Ball and Bass, 2003, page 28

Degree of precision

In real-life problems that require adults to use mathematics for a solution, there is generally a certain amount of flexibility around the degree of precision necessary. When students in schools solve mathematics problems, the problems are often purely theoretical, but adult learners need to make decisions about how to manage problems in real-life situations. In order to choose the best approach to solving a problem, an adult needs to begin by making a decision about the degree of precision required. For example, a practical problem may involve working out how much carpet is needed to cover the floor of a room. As a classroom exercise in school, the purpose of setting the problem may be to have the students learn and practise measuring skills. The task would probably involve scaled drawings with precise measurements. The students might be expected to use calculators or to apply what they have learnt about formulas and multiplying numbers to arrive at a solution. As a real problem for an adult, solving this problem may involve first asking and answering practical questions, for example:

  • “How accurate do I need to be?”
  • “What tools (such as a calculator, a measuring tape, or pen and paper) should I use?”

Depending on their specific purpose in this situation, the adult judges the degree of precision that would be reasonable. This could vary from very precise (for ordering and cutting the carpet) to a rough estimate (for thinking about whether or not to re-carpet). The degree of precision required dictates the measurement units and tools to be used, for example:

  • “Will I use hand spans, strides, or a tape?”
  • “Should I measure in metres, centimetres, or millimetres?”

Journal Task

Write at least 250 words on how adult numeracy theories underpin your approach to teaching and training.

If you need to, use the prompt to get yourself started:

  • How much of your approach to teaching adult numeracy is underpinned by behaviourism?
  • How much of your approach to teaching adult numeracy is supported by a constructivism?
  • What about sociocultural theory? Do you think your approach is underpinned by any aspects of this approach to teaching adult numeracy?


What are adult literacy theories?

Adult literacy theories are ideas about how adults learn literacy skills, like reading. There are a range of theories and different educators tend to subscribe to different theories – although sometimes without really knowing. Here’s a selection of some of the main adult literacy theories:

  1. Functional. This refers to the ability to read and write in order to do things, such as carry out a task at home or in a workplace. Literacy skills in this approach are a kind of technical skills that learners need because they are the foundation for other higher level functions.
  2. Sociocultural. Literacy is shaped by social practices and it’s also culturally specific. In this viewpoint, literacy is often about multiple literacies. The sociocultural approach holds that the main purpose of literacy is is to encourage greater understand, challenge the status quo, and perhaps contribute to social justice movements.
  3. Freirean. This approach is based on the work of Brazilian educator and philosopher Paulo Freire who say literacy as a means for oppressed or marginalised groups to rise to critical consciousness, collective social action, and eventual overthrow of oppressive structures and political or other discourses. Freire’s social justice approach grew into the critical literacy approach that encourages learners to analyse texts from a critical point of view in order to uncover the underlying messages.

Professional Reading

The background to the listening, speaking, reading and writing progressions outlines a mostly sociocultural framework.

Review the questions below then read the article

  1. What are some of the groups mentioned here that illustrate how they can both influence and be influenced by the communications of its members.
  2. What are some of the reasons critical thinking (and critical reading) is important?

Sociocultural practices

Written and oral language practices exist within specific social and cultural contexts.13 This means that individuals are members of a society (which consists of groups or organisations that are not all organised on a formal basis) and the language practices of individuals can be seen as part of the activities of those groups or organisations. The group both influences and is influenced by the communications of its members. For example, consider the graffiti and rap music associated with hip-hop culture, in which the graphic and oral forms of communication are important parts of the identity of the group. The legal jargon used by lawyers is another example of the way in which a group influences the form of communication used by its members and is in turn influenced by it.

This has implications for adult education, where social and cultural factors are particularly significant for adults who are developing their expertise with written and oral language. Adult learners bring a wealth of diverse social and cultural experiences to most learning situations and belong to a wide variety of social and cultural structures, all of which influence and inform their learning.

Purpose and audience

All oral and written texts have a meaning and a purpose. The ability to distinguish between the different purposes of texts may be developed through examining the purposes that adults themselves have as they prepare to listen, speak, read or write. These purposes can be very diverse, for example, to entertain, to build a friendship, to get something done, to comfort, to influence, to subvert, to deceive, to persuade, to build community or to shock. The purposes can be direct, indirect, or a combination within one text. The purpose may be to express the writer’s or speaker’s point of view, perspective or attitude and these may be expressed in direct or indirect ways. Listeners and readers who think critically are able to consider different perspectives along with the different intentions of texts.

Given that all texts (oral and written) have a purpose, it follows that all texts have one or more intended audiences. Even personal diaries have the writer of the diary as an audience. The audience may be obvious (a children’s picture book is usually assumed to be written for children), less obvious, or even obscured (sometimes adults may speak to children in a way that carries a different meaning for an adult audience)


The concept of vocabulary, as used in the progressions, encompasses understanding as well as recognising words in written and spoken language. More than this, knowledge of vocabulary includes knowledge of how words work in relation to each other and within specific contexts.

Learning vocabulary is a complex and sometimes difficult task for adults. For many adults, understanding the differences between oral and written language can pose problems. The fact that about 70 percent of English words have more than one meaning14 adds to the complexity of the task and the different ways in which words are learnt can make it even more complicated. Learning new words takes time. A word is unlikely to become part of a learner’s vocabulary after a single exposure to the word or one definition of it.

Adult learners have several different and overlapping kinds of vocabulary. Stein (2000) identifies the following four:

  • Receptive vocabulary. The words an individual understands, either orally (heard) or in print (read).
  • Productive vocabulary. The words an individual is able to use orally (by speaking) or in print (by writing).
  • Oral vocabulary. The words an individual can use or recognise in speaking or listening.
  • Reading vocabulary. The words an individual recognises in a printed form.

Because of this complexity, word learning is incremental and occurs over many exposures. For example, the word bright has numerous shades of meaning and it takes multiple exposures to the word in different contexts to understand the full complexity of its meanings and applications (The light is bright; The future looks bright; John is bright; Sarah has a bright personality).

Critical thinking

Texts are never neutral. The values and beliefs of the writer or speaker affect the messages that are communicated. For this reason, it is important for adult learners to develop the skills for thinking critically about the texts they read, view or hear. Thinking critically involves analysing and interpreting meanings, responding critically to texts when reading and listening, and being critically aware when writing and speaking. Adult learners need to develop their awareness of speakers’ and writers’ different perspectives and purposes in order to gain deeper levels of meaning, to avoid being manipulated by writers and speakers, and to gain insights and enjoyment from the texts they engage with.

Journal Task

Write at least 250 words on how some aspects of literacy theories underpin your teaching.

If you need a prompt to get started, answer one or more of these questions:

  • What aspects of your teaching or training embraces aspects of a functional approach to literacy? Why? Can you give examples?
  • What aspects of your teaching or training embraces aspects of a more sociocultural approach to literacy? How? Can you give examples?
  • Does any part of your teaching lean more towards a Freirean approach? Explain in more detail.


What is embedded literacy and numeracy?

Embedded literacy and numeracy combines the development of literacy and numeracy skills with vocational and other skills.

An embedded approach situates relevant and meaningful literacy and numeracy skill development firmly in the context of some other content such as a trade. An example would be teaching the underpinning numeracy knowledge and skills required to estimate and then measure the m2 of farm paddock.

An embedded approach to teaching adult literacy and numeracy is explicit. Literacy and numeracy are not in “stealth mode” in an embedded approach, although sometimes educators have to be “stealthy” about how they get to the stage of making it explicit with learners. Learners and educators should be able to point to the literacy and numeracy in the curriculum and say “there it is…!”

An embedded approach is also deliberate. What we mean by that is that the focus that the educator brings to important literacy and numeracy skills is not an accident. Sometimes, these learning moments just occur in the course of everyday teaching. And at other times, the teacher sets them up in advance.

However, they arise in an explicit embedded approach the educator is self conscious about doing literacy and numeracy. The educator’s approach is informed by all the aspects in our model.

As a subject experts in their trades or vocational training areas with further developing specialised knowledge in literacy and numeracy, educators need to:

  • Understand relevant issues and contexts
  • Assess literacy and numeracy needs
  • Design embedded literacy and numeracy skills development and resources
  • Deliver embedded literacy and numeracy outcomes in the context of trades or vocational training.
  • Assess learner literacy and numeracy gains
  • Evaluate embedded literacy and numeracy training.

Professional Reading

The Tertiary Education Commission (TEC) recently summarised key research findings relating to effective practice for embedding literacy and numeracy. This was their conclusion:

  • Embedding (the practice of combining / integrating literacy and numeracy into vocational and workplace training) improves the likelihood of retention and success when:
    • vocational and literacy tutors work together;
    • literacy and numeracy content is deliberately connected to vocational or real life contexts; and
    • there is a whole of organisation approach.

[quote starts]

Casey, H., Cara, O., Eldred, J., Grief, S., Hodge, R., Ivanic, R., Jupp, T., Lopez, D., and McNeil, B. (2006) “You wouldn’t expect a maths teacher to teach plastering…”: Embedding literacy, language and numeracy in post-16 vocational programmes – the impact on learning and achievement. London: National Research and Development Centre.

The research took place with around 200 learners in 15 Further Education Colleges and one large training provider in five regions in the UK . It looked at students whose primary aim was to achieve a vocational qualification . The key factors related to embedding that contributed to students’ retention, achievement and attitudes included:

  • teamwork between literacy, ESOL, numeracy teachers, and vocational teachers (note, in this work this sometimes meant literacy/numeracy specialists working in classrooms alongside vocational tutors) – where a single teacher was asked to take dual responsibility for teaching vocational skills and LLN, learners were less likely to succeed;
  • staff understandings, values and beliefs – positive attitudes towards the learners and the subject matter makes a difference;
  • aspects of teaching and learning that connect literacy, ESOL and numeracy to vocational content; and
  • policies and organisational features at institutional level, such as support from senior management, means that resources can be directed into embedded programmes .

This was one of the few reports sourced for this bibliography that reported on outcomes for learners. Here the researchers found that:

  • where LLN skills were embedded in courses, there were more positive outcomes than in courses in which these skills were treated separately; and
  • there was a positive impact on retention, achievement and success rates, particularly at level 2, and success rates were higher in embedded than in non-embedded courses .

Higher retention rates were attributed to two factors:

  • embedding literacy, ESOL and numeracy skills in vocational programmes reduced the stigma associated with these areas; and
  • teaching LLN within programmes enabled learners to cope more effectively with the content of the course .

This can be considered one of the seminal works on embedding literacy and numeracy. The findings of this research were used to inform much of the TEC’s work to date on LLN . The findings of this research are also cited in other publications in this bibliography that attest to the impact of embedding

[Quote ends]

Journal Task

Write at least 250 words on how an embedded approach to teaching literacy and numeracy underpins your teaching.

If you need a prompt to get started, answer one or more of these questions:


  • How do you understand an embedded approach?
  • How do you work to embed literacy and numeracy into your trade or vocational training?
  • What are the key literacy and numeracy demands that your education programme requires you to embed?
  • What are the kinds of literacy and numeracy weaknesses and challenges that your learners face, and that you need to try and embed into your work?
  • Has your experience been positive or negative when trying to embed key aspects of literacy and numeracy skills development into your training?