Category Archives: Literacy & Numeracy project

Travels Through Asia-Guangzhou

Well there happens to be a laptop available in this hostel in Singapore and as I am waiting for Adrienne I thought I’d login. Three years have past since I last posted. This will be a travel log – though I don’t know how often I’ll get to a computer.

WE flew to Guangzhou, really didn’t know what to expect, however google maps certainly helped to prepare me. I was able to navigate my way from the metro station I had managed to remember (Cultural Park, line 6) and walk to our cheap hotel in Shamian Island. This was definitely the place to stay!  We had to walk through the small recreation area of the military academy to get to our room. There were lovely young Chinese boys playing badminton.


The Steady State Economy

I recently heard John Key speak to a gathering of Chamber of Commerce people plus other Dunedin employers (education sector). He was giving us a very positive message about the health of the economy and how it was  beginning to grow again. Economic growth was going to be our future and our saviour. More jobs would flow from drilling oil and gas just off our coast. No mention of the greenhouse gas emissions this would ultimately lead to of course.

Here is an article about an alternative to “Growth” which is worth reading: The Benefits of Steady State Economy



Instruction videos on embedding Literacy & Numeracy

The embedded literacy and numeracy process 

The embedded literacy and numeracy process is designed to facilitate successful learning environments for learners who may otherwise have difficulty with the literacy or numeracy demands of their programme or target vocation. This workshop explored how the embedded literacy process is informed by learners’ results with the Assessment Tool. Through the careful mapping of demands, the Assessment Tool informs educators and learners as to specific areas that require development. This allows educators to scaffold demanding tasks to ensure positive learning experiences for learners and to priorities key areas of literacy or numeracy to develop. Link to video

Developing a teaching and learning sequence

Using Assessment Tool results to guide the development of a teaching and learning sequence Lynette Winter.

Link to video

Analysing  numeracy questions

Analysing the numeracy questions from the Assessment Tool provides rich information for knowing the learner -Lynette Winter. Link to Video

Monitoring progress for reading comprehension

Progress in decoding skills is relatively quick and is easily checked. Reading comprehension skills take longer but progress can be seen through increased engagement with the reading texts and also by learners transferring their reading skills to new texts -Dr Sue Dymock. Link to video

What information is immediately and easily accessible from Assessment Tool reports

The webinar includes a case study using a Youth Guarantees group of learners of what information is immediately and easily accessible from Assessment Tool reports, and what information can be gleaned from ‘digging deeper’. It looks at how the Assessment Tool results compare with a more contextualised formative numeracy assessment given to the same group of learners, and what it might mean for educators. Link to video


Musings on Learning Theories and their Applications

I am being inspired by reading Katherine Safford-Ramus’s book, “Unlatching the gate. Helping adult students learn mathematics (2008).

She asks ” Do these ideas sound familiar?

  • Practice makes perfect
  • Students should be rewarded for correct responses
  • Specific goals should be stated for every grade level
  • Testing will inform us as to the success of our educational programme.

If so then you are already familiar with some of the ideas of the theorists called behaviorists” (p.37). This is also known as stimulus response psychology (S-R psychology), whereby a certain stimulus causes a conditioned response in the subject (or a change in behaviour). In the area of mathematics education there is a common condition in our students called “maths anxiety”. As  Safford-Ramus states , “Math anxiety, as it is experienced by many of our adult students, is a clear example of classical conditioning. Past failure in maths (probably at school) causes mind numbing anxiety attacks when faced with having to do maths in their tertiary setting. This response to the stimulus of a  mathematical problem takes a lot of work to eradicate on the part of the teacher and student alike. Ideas for eradication could include:

  • acknowledgement of the fear
  • safe, welcoming, non-judgemental environments
  • early success
  • small incremental progressions in difficulty
  • positive reinforcement (praise, food etc)

Safford-Ramus  goes on to explain that operant conditioning techniques are useful in the treatment of anxiety. For example “assessment tasks that assure student success can be made incrementally more difficult so that students cease associating math assessment with failure and begin to look forward to tests as a way to demonstrate what they have mastered rather than a qualified indicator of deficiency” (p.41).

When we use programmed instruction (PI) or computer-aided instruction (CAI) in our courses we are  applying operant conditioning. Skinner (1968) saw many advantages of this over traditional classroom instruction. Computers can provide immediate responses to questions put forward so individuals can progress at their own pace and provides opportunities for exercise or drill.

Here are some examples where I have made use of PI in my teaching;
Skills practice for drug calculations for  nursing and midwifery students:

These sorts of websites cannot be used in the absence of other teaching methods for the majority of students. They are a useful addition to the classroom but they are not the whole story.

I have to admit that my own experience of mathematical education was very much grounded in the behaviourist methods and I progressed through algebra and calculus at school into basic mathematical and statistical methods at university by applying rules and methods to find the correct answer without ever really having a clue what the application of this maths was about. Passing the course became a means to an end rather than an expansion of my mind and leading to a deeper understanding of mathematics. I had an instructional understanding of mathematics, rather than a relational understanding (Skemp 1976). It has not been until more recently that I have had to develop a relational understanding of maths so I can help my students with their foundational understanding of the concepts. It is a more concrete understanding and way of teaching and involves a cognitive approach rather than a behavioural one.

Behaviourism may work very well for students mastering a particular skill (learning by rote e.g. the times tables) but what happens when they are faced with a completely new type of problem? The student needs to develop insight, “which is a Gestalt description of the form learning takes when there is a sudden reorganisation of the field of experience to create a new idea” (Gagne, 1985 as cited in Safford-Ramus 2008). The psychologists who began to move away from the behaviourists are known as the cognitive theorists. They believe that learning involves the reorganisation of experiences in order to make sense of stimuli from the environment.

The cognitive theories include Social Learning Theory. This is applicable to mathematics teaching particularly when applied to the concept of modelling behaviour. According to Safford-Ramus a form of modelling that is especially pertinant for mathematics instruction is that of abstract modelling. This generates behaviour that goes beyond what they have actually seen or heard (Banbura, 1977 as cited in Safford-Ramus 2008). Examples would be problem solving behaviour and mathematical communication skills in students. A teacher employing this theory would hope that by modelling good problem solving strategies, students may begin to imitate these over time.

Another Cognitive Theory is Information-Processing Theory. This theory supports the practice of consciously connecting new material to old. “Asking students to see similarities to, as well as differences from, a series of problems invites students to call on previous knowledge and expand on it” ( Safford-Ramus 2008). Where this method of learning can be obstructive is when a student has an incorrect understanding of something previously learned and continues to call on this faulty knowledge confounding the understanding of the new knowledge. I see this time and time again and it is really important to identify these gaps in understanding as soon as possible. This is where a really good diagnostic assessment tool comes in handy.  If you drill down into the student’s answers in this assessment tool it will highlight incorrect thinking which can then be fixed.

Finally I am going to discuss the Theory of Constructivism.  This is another cognitive theory and has great influence on contemporary mathematics education. Safford-Ramus (2008, p48) briefly describes constructivism as ‘the notion that all knowledge is constructed by individuals acting in response to external stimuli and assimilating new experiences by building a knowledge base or altering existing schemas”.  One constructivist theorist, Jean Piaget described a staged development theory of learning, where each stage depends upon the completion of the preceding one. One such stage named the concrete-operational stage is when children begin to use deductive reasoning but they often require tangible objects to  manipulate to draw conclusions. We as maths teachers in tertiary education settings are encouraged to use manipulatives with adults who are struggling with mathematics, suggesting they are still functioning at this stage. My experience concurs and concrete materials have been very useful to explain abstract concepts. Opponents to Piagetian theory hold that students may construct erroneous rules that it will be difficult to deconstruct.

Vygotsky is another constructivist who’s theories I personally model much of my teaching on. His idea of the ‘Zone of Proximal Development” (Wilson et al., 1993 as cited in Safford-Ramus 2008) makes a lot of sense to me and the method of “scaffolding” is one I use all the time. There are four basic steps to the process:

  • The student observes the teacher modelling an activity
  • The student tries the activity under the guidance of the teacher.
  • The teachers prompt with cues only when needed.
  • The student is free to practice the skill independently (Wilson et al., 1993 as cited in Safford-Ramus 2008, p.51)

Student Activities

Here are a list of ideas I have for activities students could undertake as part of their courses in order to learn about aspects of living sustain-ably.

Focus on Politics

1.Choose an issue e.g. Child Poverty (How to tackle), Transport (future strategies), Energy (future strategies), Trade (future strategies)

Make an appointment to interview local party representatives (National, Labour, Greens, Act) and find out what their party’s policies are in response to the chosen issue. Compare and contrast the party’s policies and try to make predictions or judgement on the effectiveness of these policies and which party you think would be the better party to vote for with respect to this particular issue.

2. Look up the National Party policy for an issue (social, economic or environmental) and compare it to two other political parties

What is the same, how do they differ, what are the possible effects of each policy?

3. Research Southern Basin Oil drilling. Write a persuasive argument for or against. References:,,

Focus on Food Security

Develop a group/community project to increase the local food production of Dunedin.

  • Create a permaculture garden either in their own garden, a community garden or a friend’s garden. (
  • Network with local food producers (meat and vege)  to increase  production, develop community sharing networks, labour for food exchanges etc. Try to decrease reliance on supermarkets.
  • Lobby the DCC to increase community gardens and form a working group (

Join the local Student Environmental group and get involved with a project. STUDENTS FOR ENVIRONMENTAL ACTION (SEA)

An OUSA society with a focus on sustainable environmental practices in Dunedin. They have many different projects, field days, workshops etc. on the go during the university year, including gardening initiatives such as seedling giveaways. web page: email:
Campus Greens
Young Greens
Focus on Climate Change Action
Compare the main political party’s policies on climate change.

Reorientation of Education for Sustainability

It is argued that “Education is an essential tool for achieving sustainability. People around the world recognize that current economic development trends are not sustainable and that public awareness, education and training are key to moving society toward sustainability” (Hopkins & McKeown 2000).

Reference: Hopkins, Charles and McKeown, Rosalyn. (2000). Chapter 2, Education for sustainable development: an international perspective in Tilbury, D., Fien, J., Stevenson, R.B., and Schreuder, D. (2000). Education and Sustainability: Responding to the Global Challenge

The following are the main points I have pulled from this reading and my reflections regarding our apprroach to EFS.

There are two differing approaches to sustainability in the world: “sustainable economic growth” and “sustainable human development”. The former does not support the transformation of current social or economic systems and the latter demands radical departures from the current system.

I don’t think Otago Polytechnic’s current  aims, visions and policies will lead to a reorientation of education which would equip our students with the knowledge to distinguish between these two approaches to sustainability. A more radical change is needed to develop a  “new world ethic of sustainability”. This new ethic is based upon two interdependent sets of principles
– one related to our responsibility to care for nature (or ecological sustainability) and another related to our responsibility to care for each other (social justice).

The long-term task of environmental education is to foster or reinforce attitudes and behaviours compatible with this new ethic. It should
focus  sharply on developing understanding of and links between environmental quality, human equality, human rights and peace and their underlying political threads.

Issues such as food security, poverty, sustainable tourism, urban quality, women, fair trade, green consumerism, ecological public health and waste management as well as those of climatic change, deforestation, land degradation, desertification, depletion of natural resources and loss of biodiversity are primary concerns for both environmental and development education.

This entails involving people in questions about the ownership of common property resources, issues of international and intergenerational equity, investigations into regional and national ecological footprints and, most importantly, engagement in debates about qualitative versus quantitative growth.

My conclusion is that as a country and as an institution we need to decide where we stand politically, and radically and rapidly respond to the challenge of  educating for sustainability.

Steve Keen: Economic Crisis and solution – abolish debt

from Saturday Morning on Saturday 26 May 2012

Professor of economics and finance at the University of Western Sydney, author of Debunking Economics, and one of a minority of economists to predict the current financial crisis.

Professor Steve Keen comes up with a radical solution to the gobal economic crisis. He targets neo-classical economics which is a consumer oriented economy.  He suggests we need to think collectively and socially and abolish debt. We need to bail out people rather than the finance sector (listen from about 30 mins in).