TAELLN702A – Analyse and Apply Adult Numeracy Teaching Practices

Table of Contents
Table of Contents 2
1 Analyse & apply conceptual frameworks and theories underpinning numeracy teaching 4 1.1 Do the learning theories that underpin literacy teaching have any relevance to the teaching of numeracy? Discuss this question by identifying the similarities and the differences involved 4 1.2 In the realm of numeracy there are a number of frameworks that pertain to the teaching of numeracy to adults. Select two and discuss their relevance to numeracy teaching 7 1.3 It is clear that several adult learning principles apply equally to the teaching of numeracy and to the teaching of literacy. Review the adult learning principles and identify any that apply specifically to the teaching of numeracy. Select a skill from each of levels 1-3 of numeracy in the ACSF and explain how you would apply a relevant adult learning principle to the teaching of each numeracy skill. 7 1.4 Learning numeracy can occur in a number of contexts. Identify three or more contexts or types of provision in which numeracy learning for vocational education and training contexts, can take place and identify which levels of numeracy from the ACSF would be applicable. 10
2 Research literacy requirements of those participating in numeracy provision 12 2.1 Adult learners have a diversity of skills and backgrounds. From your experience identify examples of learner diversity and how it impacted on their ability to learn 12 2.2 A further element that can influence what numeracy skills participants will seek to achieve is the participants’ learning goals. Identify 4 possible learning goals and explain how you would support the learning of numeracy in each context. 13 2.3 Create a table of everyday tasks including home, training and or workplace environments and the corresponding numeracy skills which are required to carry out those tasks. 14 2.4 Practitioners of numeracy need to analyse tasks and texts that can be used to build learners skills. Using the table created in 2.3 select a series of tasks that would be appropriate in developing specific numeracy skills for one of the five levels associated with the core skill of numeracy. 15 2.5 Find out the mathematical skills and knowledge required to be competent in numeracy to level 3 in ACSF. Relate these skills and knowledge to the following areas: data & statistics, measurement, number and space and location. Review your own mathematical skills and knowledge and assess which areas require attention and further skilling. Explain how you would go about improving your mathematical skills. 16
3 Select from a range of teaching approaches to develop participant’s numeracy skills and knowledge. 20 3.1 There are a number of teaching approaches that focus on mathematical information and meaning in authentic and relevant contexts. Identify five such approaches and evaluate how effective they would be in specific contexts. 20 3.2 Some numeracy skills such as reasoning, problem-solving and estimation involve a different approach to learning compared with such skills as calculation and measurement. Identify two teaching approaches to each of these skills of reasoning, problem-solving and estimation and explain why you considered them to be effective teaching strategies for these skills. 22 3.3 As a practitioner you will be training adult learners with a diversity of needs, learning styles, levels of numeracy and confidence. Given this diversity, you will need to make professional decisions as to which teaching approaches are applicable to specific adult learners or classes. Provide a profile of a class of adult learners in numeracy that addresses the above range of diverse needs. Next, discuss in detail which teaching approaches you would implement and explain why you considered them to be applicable in this environment. 23 3.4 At times practitioners will encounter issues arising from the numeracy teaching role. What are some examples of such issues and who would you refer them to? 26
4 Select from a range of learning resources to develop participants’ numeracy skill and knowledge 27 4.1 There exists a range of numeracy learning resources in our daily lives that can be utilised in promoting learner engagement and achieving numeracy learning outcomes. Identify four traditional resources and four resources from new or emerging technology, and explain how you would incorporate them into appropriate learning task and activities. 27 4.2 Practitioners need to be aware of the social and cultural background of those participating in their numeracy classes. In doing so practitioners can use materials and resources that are relevant to their social or cultural needs and so make their numeracy learning more meaningful and therefore more effective. Identify four potential cultural/social needs of a group of learners and select a set of numeracy materials/resources that relate to their cultural/social needs and explain how these would be effective in engaging learners. 29
5 Apply and evaluate strategies for teaching mathematical skills and knowledge 30 5.1 Numeracy learning involves literacy skills because of mathematical terminology. Given this context practitioners need to develop activities that integrate pertinent literacy skills that support numeracy learning. Select an area of numeracy to teach a group of learners at level 3 in the core skill of numeracy and identify any mathematical terminology that needs to be learnt. Devise 3 activities that would integrate the identified vocabulary into relevant numeracy tasks. Explain why they would be successful learning activities. 30 5.2 There are various methods of teaching a class of adult learners. Choose a numeracy level from the ACSF and develop an appropriate learning activity for each of the following numeracy topics: number, measurement, space & location, and data & statistics. Implement a different teaching strategy for each activity and make sure each activity caters for the different learning styles. 32
REFERENCES 33
APPENDICES 34

1 Analyse & apply conceptual frameworks and theories underpinning numeracy teaching
Do the learning theories that underpin literacy teaching have any relevance to the teaching of numeracy? Discuss this question by identifying the similarities and the differences involved

Traditional behaviourism and constructivism approaches for numeracy teaching has long been the approach adopted for classroom learning experiences in schools. Recent investigations into poor mathematics skills in adults and the failures of numeracy teaching and learning (i.e. adults having negative experiences and even fear of maths-related tasks) via these philosophies have been identified the traditional approach as inferior. There is a transition toward connectivism particularly with training adult numeracy learners as it is more aligned with the principles of Adult Learning. Connectivism promotes the idea of learning within a context and meaning rather than the practice and repetition of behaviorism and the building block approach of constructivism.

The approach to the Numeracy capability, reflected in an optimal approach taken in schools, is informed by aspects of numeracy that were highlighted in the literature, including that: * mathematics that people use in context is better understood than mathematics taught in isolation (Carraher, Carraher and Schliemann 1985; Zevenbergen and Zevenbergen 2009) * knowledge is not automatically transferable from mathematics to other contexts (Lave 1988); numeracy requires contextual and strategic knowledge as well as mathematical skills (AAMT 1998) * in numeracy there may be more than one suitable answer or method (Cohen 2001) * numeracy moments often arise in unexpected situations (Thornton and Hogan 2005).
SOURCE: http://www.australiancurriculum.edu.au/GeneralCapabilities/Pdf/Numeracy

In his 2009 presentation to the Adults Learning Mathematics (ALM) conference in London, Klinger all but dismisses the traditional teaching approaches of Behaviorism and Constructivism in favour of Connectivism. He identifies those historic negative experiences in mathematics and numeracy learning for adult learners as having links to the traditional behaviorism and constructivism approaches and argues that these ‘traditional’ approaches don’t work for math-averse students. Traditional approaches have been based around the notion that mathematics was a ‘pure science’ which could only be right or wrong and structures need to be right for success. However, the contemporary approach toward numeracy is that it is indeed more organic where individuals can develop their own concepts and methodologies – the different ways of reaching an answer, rather than the one way to reach the one answer.
In the current political climate of contemporary Australia, the new Education Minister, Christopher Pyne has identified a return to ‘back-to-basics’ approach to teaching including numeracy. Opponents of this policy seem to dismiss the traditional “chalk-and-talk” teaching methods of direct instruction pointing to learner-centered teaching as a more effective method.

Behaviourism
As Behaviourism is based on the transfer of knowledge and the associated structures of that knowledge, numeracy has long been taught under a behaviourism model. Tradition has dictated that teachers may teach in the same manner in which they learnt, and for that matter were taught however this does not reflect with recent developments in cognitive science in the education environment.
‘Skill and drill’ teaching epitomises behaviourism in mathematics education – the ‘ideal’ learning environment focuses on hierarchical procedures and outcomes so that mastery of basic skills provides a scaffold to progressively more advanced activities… while the objective is to establish strong stimulus-response bonds, as teachers well know, these are usually short-lived – having a ‘use it or lose it’ impermanence – and uses the example of the addition of fractions, the algorithm of which is taught, re-taught, and practiced throughout early schooling only to be forgotten repeatedly.” Klinger, 2009

Transfer of knowledge from teacher to student in the classroom environment may limit the chances of successful learning. Out of context and out of practice, the student may ‘lose’ the knowledge and therefore the learning experience has been unsuccessful.

Education based on behaviorist theory typically leads to breaking down complex tasks and ideas into oversimplified components, unrelated subtasks, repetitive training, and an inappropriate focus on the “right answer.” It does not help students learn to solve problems on a more systemic level. Hull, 1999

Whilst there is merit in the traditional classroom approach, recent studies indicate that behaviourism may not be the most effective approach to lifelong numeracy learning.

Constructivism

Constructivism approach does not consider the student as an empty vessel to be filled with information, rather to take an active role on what and how they learn. The teacher takes on more of a provider role, rather than fount of expertise. The teacher prompts the students by asking good questions and facilitating an environment where students can develop their knowledge. In this theory, knowledge is viewed as more organic and fluid than following rigid patterns and conventions.

Connectivism

Connectivism relates to the formation and maintenance of connections within formal and informal networks to enhance an adult learner’s knowledge and experiences. It relies on adult learner’s ability to access available resources when seeking current, relevant and important information as it is required in a personal, social or career context.

“..there is substantial merit in considering mathematics first and foremost as language and focusing on ways and means to develop students’ fluency while utilising their existing skills and knowledge-base as leverage” Klinger, 2009

Here, Klinger compares the learning of maths as a language inferring that the principles of development of literacy and numeracy skills can take similar paths. It considers numeracy to be based on solving ‘problems’ using numbers, rather than the strict basic processes of solving mathematical equations. The learner accesses parts of the network to help identify and solve the presented problems.

In the realm of numeracy there are a number of frameworks that pertain to the teaching of numeracy to adults. Select two and discuss their relevance to numeracy teaching

ACSF
The Australian Core Skills Framework (ACSF) is a tool to identify existing skills and assess gaps in an individual’s numeracy skills required for contemporary Australian life. It was created to assist in overcoming gaps in numeracy in the Australian population. This framework is based on various contexts with the focus on core skills requirements.
The ACSF is used to identify numeracy levels relevant to an individual’s employment, education and social interactions. It is a precise tool used to identify the adult learners’ individual numeracy strengths and training needs within context. As it can be used to identify existing skills, it can also be used to plan improvements in the numeracy skills of the adult learner. The adult numeracy trainer can design targeted training programs to incorporate the tasks and benchmarks of the desired level. The ACSF is also a useful tool in monitoring an adult learner’s progress numeracy skills.

Foundation Skills Training Package FSTP
The initiative identifies that not all learners are the same and there is not a ‘one-size-fits-all’ when it comes to numeracy learning. By customising the teaching to meet the needs of the learner, identifying his/her learning gaps and modifying the contexts to suit, the leaning experience has a greater chance of success. It can be used to identify the current performance level of a student and provide information as to the areas the student can improve.

It is clear that several adult learning principles apply equally to the teaching of numeracy and to the teaching of literacy. Review the adult learning principles and identify any that apply specifically to the teaching of numeracy. Select a skill from each of levels 1-3 of numeracy in the ACSF and explain how you would apply a relevant adult learning principle to the teaching of each numeracy skill.

All adult learning principles can be applied to the teaching of numeracy. These principles can be applied to any adult learning situation, be it numeracy, wood-working, cake decorating or other fields. Adult Learning Principle | Application | Adults are internally motivated and self-directed | Many of my learners complain that “I’m no good at maths” when posed with a problem on a piece of paper in front of them. Numeracy is more than just mathematics problems. It is ability to use and understand numbers in our everyday lives. Rather than serving up mathematic problems and solutions on a whiteboard or worksheet, numeracy trainers need to appeal to the learner’s motivations within the group. | Adults bring life experiences and knowledge to learning experiences | By engaging students in everyday problems outside the traditional classroom such as increasing or decreasing the ingredients of a muffin mix by a fraction to cater for a party, or to measure and calculate the coverage of seed required for a new lawn, the numeracy teacher can tap into the different learning styles of their student. There is a hands-on aspect that can give a broader opportunity for the learner to develop skills in the mathematical concepts discussed. | Adults are goal oriented | The adult learner is likely to tackle a problem to find a solution. The solution is the end goal and the learner, once engaged due to their confidence through their existing knowledge and identifying the relevance of the problem posed can devote their energies into reaching their goal – a solution to the problem. | Adults are relevancy oriented | By providing context for a problem which is relevant to the student, the student is more likely to become invested in the identification and solving of the problem. The identification with a problem that could happen within the lives of the student - be it career, education or social – is more likely to attract the adult learner’s attention. | Adults are practical | By identifying the why, when and how to use the possible solutions to a problem, an adult learner is able to use this within a familiar context. If they can recognize the practicalities of the subject matter and the use within their own lives, there is a greater chance of the learning opportunity being a successful one. | Adult learners like to be respected | The one-on-one sessions I conduct are a great conduit for feedback between my students and me. Through the initial and ongoing creation and maintenance of a respectful relationship, we are comfortable in providing regular and relevant feedback. This allows me to customise activities by altering my level of support and intensity of instruction dependent on the performance capabilities of my students. |

SKILL 1
1.09 - Locates and recognises key mathematical information in simple activities or texts
Activity:
Using a copy of the train timetable, calculate how long in minutes it takes for the train to go from Ballarat to Melbourne on Tuesday mornings. Which service is scheduled for shortest time?

SKILL 2
2.09 - Identifies and comprehends relevant mathematical information in familiar activities or texts
Activity:
The weekend’s local AFL league results are printed showing the progressive goals and behinds in each quarter and the total points at the end. Reviewing each senior game from the weekend’s round, re-write this as total points scored in each quarter with a total. TIGERS | 0.3 | 5.3 | 6.7 | 7.10.52 | SAINTS | 7.6 | 10.8 | 15.10 | 19.12.126 |

SKILL 3
3.09 - Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts
Activity:
7.5m
6.3m
23.5m
9.5m
7.5m
6.3m
23.5m
9.5m
Calculate the area of this odd-shaped yard and identify how much fertilizer to add at an application rate of 100g/m2. The fertilizer comes in 5kg bag $13.50, 10kg bag $22.00 and a 25kg bag at $47.50 – what number of which size bags is going to be the least cost and least waste?

Learning numeracy can occur in a number of contexts. Identify three or more contexts or types of provision in which numeracy learning for vocational education and training contexts, can take place and identify which levels of numeracy from the ACSF would be applicable.

People try to manage or respond to a numeracy situation because they want to satisfy a purpose or reach a goal. This can be in a range of real-life contexts with different activities, hobbies and obligations requiring similar or different numeracy skills.
CONTEXT: Gaining Employment
Depending on the type of role the student is seeking, numeracy plays a part in all work situations. From the regular payslip details to counting inventory to developing complex financial budgets, workers are exposed to numbers and context within that particular workplace.
The level of performance from the ACSF would depend on the role, but more likely from level 2 and above.

CONTEXT: improving ability to make informed financial decisions and interact with financial institutions
Financial decisions can be complicated by the creation of additional wealth or debt through interest. Understanding these sometimes complex ideas can help in the student being informed and making an educated decision when posed with the options and possibilities.
Types of loans and other credit options require a performance level of 4 or above.

CONTEXT: interacting with family and community
Information is presented a number of ways and much of this includes numeracy-related portions. At the very simplest level of performance, level 1, to meet this level you need to be able to interpret basic numeric information and contribute to discussion – how much change will you get if you pay for two coffees with $10? What is the impact of a trend shown in a graph in the newspaper? What does the increase in price have on me? Etc.

CONTEXT: maintaining current job or managing promotion to next level
In a general sense, promotion within an organisation requires the person to take on more responsibility for planning and organising. This can include planning labour, organising the supply of materials and the creation and adherence to budgets. Thus, there is a likelihood that numeracy skills will need to be improved as the person is promoted to higher levels of responsibility. Due to the volume of information required and used by modern workplaces, each employee is responsible for maintaining his or her numeracy skills to meet the reporting and recording requirements of their work roles.
ACSF levels required would be related to the position and the additional requirements of that (i.e. for promotion from level 3 to level 4).

2 Research literacy requirements of those participating in numeracy provision
Adult learners have a diversity of skills and backgrounds. From your experience identify examples of learner diversity and how it impacted on their ability to learn

In my experiences, each of my students has a unique background and particularly so when It comes to their numeracy skills. As most are from low socio-economic backgrounds, they often surprise me with the knowledge of their expenditure as they are limited in earnings to their welfare payments. They appear to maintain up to the minute balances of their bank accounts, however other elements of their numeracy skills are quite low. I frequently encounter early school leavers who disliked school overall and identify numeracy and maths as part of that painful past. Overcoming that perceived lack of ability and identifying areas of confidence is quite a challenge. Here, context plays a huge part in the student initially identifying the problem and then developing a solution to that problem. A familiar or recognizable context helps the student acquaint themselves with the problem, rather than a foreign concept.
Everyone has the cognitive capacity to learn and it is the information and structures present in the environment that create the conditions for learning. Teachers acknowledge and respond to their learners' cultural, socio-economic, ethnic, linguistic and learning profiles. They build on learners' prior knowledge, skills and understandings and respond to these individual learning needs with specific and targeted learning. High expectations, sufficient time, adequate support and focused learning provide the conditions for effective literacy and numeracy learning, in particular for learners of English as an additional language or dialect. NT Government 2010

I have also found that my students are unsure of the assumed knowledge when developing solutions to problems. They ask me ‘how many weeks in a year?’ ‘How many days in a month?’ etc. where this information is usually memorized as ‘common knowledge’ for use in various contexts. Hence, revision on these points and guiding the student where to locate this information is important in them being able to revisit this context at a later time.

A further element that can influence what numeracy skills participants will seek to achieve is the participants’ learning goals. Identify 4 possible learning goals and explain how you would support the learning of numeracy in each context.

GOAL 1 “I want to get a job”
(gaining employment) Identify the performance capability from the ACSF for the position they are going for and conduct activities in line with the next level (i.e. from level 2 to 3) until the student reaches that level.

GOAL 2 “I wish I finished High School”
(completing equivalent to compulsory schooling in Australia)
Encourage the participation in a structured course based on the student’s areas of interest. Often social and other issues have led to the withdrawal from High school. Investigate this and there may be a role to play in overcoming the student’s anxiety of the ‘school environment’ and to create a safe learning environment for the student.

GOAL 3 “I need to do my VET before I can be trade qualified”
(completing VET course)
Review with the student the area in which they are seeking a career. Identify the key numeracy areas together and match this against the student’s existing level of performance (e.g. against the criteria in the ACSF). Emphasise the importance of numeracy skills on the success of the chosen career.

GOAL 4 “I’d love to be able to build things out of wood”
(pursuing own interests)
Develop and deliver activities and instruction on the key areas including measuring, estimation and calculation activities within the context of wood working. Complex engineering calculations and trigonometry may be required at latter stages so I would introduce this to a student as to the importance of numeracy in wood work, not just as simple calculation activities for future development.

Create a table of everyday tasks including home, training and or workplace environments and the corresponding numeracy skills which are required to carry out those tasks.

ACTIVITY | Estimating and calculating with whole numbers | Recognising and using patterns and relationships | Using fractions, decimals, percentages, ratios and rates | Using spatial reasoning | Interpreting statistical information | Using measurement | Heating & cooling | | | | | | | Buy groceries | | | | | | | Plan & cook meals | | | | | | | Drive and maintain a car | | | | | | | Take public transport | | | | | | | Household budget | | | | | | | Rent application | | | | | | | Government formsE.g. Centerlink, ATO | | | | | | | Sports | | | | | | | Arts & Crafts hobbies | | | | | | | Gambling | | | | | | | Medication & Health | | | | | | |

Practitioners of numeracy need to analyse tasks and texts that can be used to build learners skills. Using the table created in 2.3 select a series of tasks that would be appropriate in developing specific numeracy skills for one of the five levels associated with the core skill of numeracy.

ARTS & CRAFTS – WOOD WORK
In the context where the student is a keen wood worker for leisure, the following activities may apply in context for each of the levels of the ACSF. LEVEL | SAMPLE ACTIVITY | CONTEXT | 1 | Estimates lengths of familiar objects using metric units, e.g. a person’s height, lengths of fabric or lengths of rooms | Identifies lengths of timber from a stack which are long enough to assist with the building of a table. | 2 | Writes a purchase list and calculates the cost to undertake a simple task, e.g. lunch for a group of friends or planting a vegetable garden | Creates a ‘Shopping list’ for the hardware and ancillary items required from the hardware store for building the table. | 3 | Uses the rate of application to work out the amount of a product required for a particular area, such as a rectangle or square, e.g. the amount of paint needed to cover a room or the amount of lawn seed needed for a rectangular lawn | Identify the type of lacquer and determine the quantity required based on the rate of application for a large table. | 4 | Draws up a scale plan and uses simple formulae and rates to calculate and interpret dimensions, quantities and costs required for making a personally relevant item, e.g. constructing a child’s playhouse, making furniture or a garden shed, painting the exterior of a house or designing a patio | Draw up plans for a table based on an existing design intended to seat 6 people and modify the plans so it seats 8 people. Create a modified BOM (Bill of Materials) to reflect the changes in this and determine the additional cost. | 5 | Provides a materials list for a building project that requires trigonometric calculations to determine outcomes, e.g. roof structure with bull nose veranda and 30° pitch | Design and plan a pergola with a pitched roof and of octagonal shape to suit a large country garden. |

Find out the mathematical skills and knowledge required to be competent in numeracy to level 3 in ACSF. Relate these skills and knowledge to the following areas: data & statistics, measurement, number and space and location. Review your own mathematical skills and knowledge and assess which areas require attention and further skilling. Explain how you would go about improving your mathematical skills.

NUMERACY LEVEL 3 - SAMPLE ACTIVITIES | DATA & STATISTICS | MEASUREMENT | NUMBER | SPACE & LOCATION | Personal and community – Compares the costs of purchasing everyday items in different sized containers to work out the best way to purchase (e.g. compares the cost of buying drinks in three different sized containers – 500 ml, 1.25 litre and 2 litre), taking into account the rate of usage and wastage | | | | | Personal and community – Gives instructions, including a sketch map and an estimate of distance and travel time, for an everyday route, e.g. for a friend to drive home from work | | | | | Personal and community – Accurately measures a range of quantities to follow a recipe or operating instructions incorporating making a product of a smaller or larger size than specified, e.g. follows a recipe for six people and can adjust it to cater for 24 people | | | | | Personal and community – Compares and contrasts costs of alternate types of travel, e.g. travel options for three people using a plane, a bus, a train, a taxi or a hired car for a journey between two large cities | | | | | Personal and community – Reads and explains costs, data and graphical information on a bill or invoice from a utility organisation, e.g. a phone, gas, electricity or water bill | | | | | Personal and community – Collects data and information about a community or social issue from newspapers or the internet and writes a report presenting the information using everyday tables and graphs, e.g. showing the impact of a drought on a community, road accident statistics for a dangerous local intersection or sporting team results | | | | | Personal and community – Uses a calculator to compare the cost of a particular item from different retail outlets, e.g. from listings in a sales catalogue, from a local shop or from the internet, decides on the best buy and explains the reasons for that choice | | | | | Personal and community – Uses the rate of application to work out the amount of a product required for a particular area, such as a rectangle or square, e.g. the amount of paint needed to cover a room or the amount of lawn seed needed for a rectangular lawn | | | | | Personal and community – Creates a personal weekly budget in a spreadsheet | | | | | Workplace and employment – Works in a group to undertake a simple survey and record the results, including at least one everyday or routine graph, e.g. a workplace survey of workers’ OHS knowledge or accident rates | | | | | Workplace and employment – Works in a team to organise and cater for a meal or event (e.g. afternoon tea for a meeting) and decide on the cost per person | | | | | Workplace and employment – Identifies and explains uses and application of shapes in different work-related contexts, e.g. use of 2D and 3D shapes in building plans or in industrial packaging | | | | | Workplace and employment – Selects, totals and orders items from a catalogue within budgetary constraints, e.g. a workplace stationery order or food for a special event | | | | | Workplace and employment – Prepares a bill of materials or parts list for a particular job, e.g. to build a fence of a set length | | | | | Workplace and employment – Uses rate of application to work out the quantities required for a routine task, e.g. to paint a room or calculate the amount of pesticide required | | | | | Workplace and employment – Correctly enters data onto an electronic cash register and undertakes end-of-day summaries and the balancing of a till or accounts ledger | | | | | Workplace and employment – Uses appropriate technological devices to measure and record data and interpret the results, e.g. uses a blood pressure machine or reads micrometers and temperature gauges | | | | | Workplace and employment – Correctly adjusts quantities and follows operating instructions, including measuring quantities in order to make a product of a smaller or larger size than specified, e.g. adjusts and follows instructions specified for five litres of spray for volume of 20 litres | | | | | Education and training – Uses a calculator and/or a spreadsheet to undertake the numerical calculations required as part of a course of study and discusses the results, e.g. the impact of percentage increases and decreases on values, profit and loss statements, and analysis of the state or national economy | | | | | Education and training – Uses familiar timetables and fare information to estimate the total daily time taken and total weekly travel costs to get to and from home to a course/training venue | | | | | Education and training – Collects, collates and discusses data from a survey undertaken and prepares a report, e.g. makes a PowerPoint presentation on data that includes a routine chart or graph | | | | | Education and training – Measures a number of different quantities to make a product according to given specifications, e.g. to follow a recipe (hospitality course) or to build a wooden box (building and construction course) | | | | |

My profile based on the ACSF would be levels indicated in the below table. With strong skills and experience in Personal and Community and Workplace and Employment domains, the slightly lower level of performance in Education and Training is due to the longer term absence from formal education and training. | Numeracy Performance Level | Personal and Community | 5 | Workplace and Employment | 5 | Education and training | 4 |

To improve this, I would need to have more experiences with the data collection and analysis in my current role. Whilst I have created and delivered similar projects in other workplaces, I am confident in being able to deliver this to meet level 5 performance level. The areas of numeracy where I feel there is a gap is dealing with financial concepts and ideas and therefore would need to upskill if I were required to deliver these types of training. Further skilling would take place in an informal environment using information available on websites such as YouTube and Khan Academy. 3 Select from a range of teaching approaches to develop participant’s numeracy skills and knowledge.

There are a number of teaching approaches that focus on mathematical information and meaning in authentic and relevant contexts. Identify five such approaches and evaluate how effective they would be in specific contexts.

I one on one coaching
As I work on a one-on-one basis with my students rather than a classroom scenario. In this environment, I am able to accurately gauge the student’s numeracy strengths and weaknesses and work with the student to develop new or hone existing skills to perform tasks. This is an effective method as it gives the student an opportunity in a comfortable environment to seek assistance with numeracy whereas the student may remain silent in a confronting classroom situation.

II encouraging use of own life experiences to illustrate and clarify learning Context is extremely important for my learners. For them to identify with mathematical problems we have designed activities which are relevant to them and to which they can readily identify. Household budgeting, earnings, supermarket shopping, cooking and a major project to plan a trip all have relevance to the individual because it is about them and they have control over the subject matter. III projects and investigations
A great project we undertake is the process of planning to build a shed. The shed needs to serve a purpose at the student’s home –e.g. to store lawn mowers, motorbikes, cars, or horses etc. We look at: Estimating From the location in the yard, how long and wide will the shed be? How high will it need to be? Will you be able to open the doors fully (i.e. not encumbered by trees or other structures in the yard)? Will it be suitable in 5 years? Numbers Complete a Bill of Materials – What quantity and lengths of materials are available? How will you join/cut them? How much is this going to cost if you design and build your own, compared to a kit shed? Measurement What lengths are the uprights, beams, battens, roof sheets, wall sheets etc? How much concrete is needed for a 100mm floor? Space & location Draw your house block to reasonable scale and show the shed sitting in its planned location –i.e. ‘mud map’ vs. scale drawings IV verbal-based approaches, such as discussions and 'questions and answers' to explore, plan, generalise, hypothesise, test ideas and form conclusions Within the scope of our program, we cover numeracy disguised as ‘real-world problems’ such as home budgeting and grocery shopping. For those students who identify themselves as ‘bad at maths’ some consider themselves good with money as they are well-practiced in the handling and management of small payments (e.g. Youth Allowance) on a regular basis. In our supermarket shopping exercise, we look at similar products and compare size, quality, wastage etc. to help identify the most appropriate purchase. I ask the student to guess how much the items are before we enter the store and estimate the cost of buying ingredients for their project. Some items are familiar, some not so but the idea of estimating the money required to purchase the goods brings the problem back to a familiar context.

V using strategies to overcome the effects of numeracy and number anxiety
As my students are identified as disengaged youth, there is a requirement to build the confidence of each student for them to perform tasks under my tutelage. Therefore, it is essential for the success of my students that we build a close relationship – one where they are comfortable and confident in seeking support from me. I tell them “this is not school, I am not a teacher” as we sit in a café, sipping away at coffee as we discuss the week’s activities. Some are scared to make mistakes and therefore don’t try. I hand them a note pad and ask them to work it out, write it out and make mistakes because it shows that you are trying. Trying to remember the ‘how’ from school seems difficult, so I offer the scaffold of support as is required. I find that the nerves increase as the student rushes through the work. A misplaced decimal point here, pressing a multiply button instead of addition button on their smart phone there can heighten their anxiety. We work to slow it all down and make our way through the task in a more relaxed and focused manner.

Some numeracy skills such as reasoning, problem-solving and estimation involve a different approach to learning compared with such skills as calculation and measurement. Identify two teaching approaches to each of these skills of reasoning, problem-solving and estimation and explain why you considered them to be effective teaching strategies for these skills.

REASONING
Mathematical reasoning involves drawing logical conclusions based on assumptions and definitions.
One-on-one: discuss with the student how they would approach the problem and why they chose that path. Assist in identifying the known information, assumptions and unknown information to find a result to the problem.
Small group: provide some of the information to the group and for the group to discuss the elements of the problem. Facilitate the discussion by providing additional information during the group discussion to enhance or steer the conversation to the right course.

PROBLEM-SOLVING
Modelling numeracy operations: by using scribble pads, pens and having the ability to attempt different ways of approaching and solving the problem by providing instant feedback and allowing the student to attempt the problem as far as they can on their own.
Sequencing activities to reflect increasing level of skill development: where a student has been comfortable in coming to a conclusion or solution to a problem, I will often further challenge them to perform the same task with slightly different conditions in the problem. For example, in a supermarket shopping activity where the students are to plan a meal within the budget restraints, if they have been able to add the cost of ingredients without too much difficulty, I ask them to calculate the cost of ingredients in the actual dish e.g. how much does the 200g of cheese cost from the $5.59 for 500g block, 150ml of cream from the 300ml bottle @ $1.89 etc.

ESTIMATION
One-on-one: As I work closely with my students, I encourage my students to guess if they think they know about all answers they are to complete. This not only gives me an understanding of the student’s life experiences and general knowledge, but can assist in building their confidence if they do make a ‘ball park’ estimate which is close to the correct answer.
Using own life experiences to illustrate and clarify learning: In the estimation activity we deliver, we ask students to select a list of 10 small things (e.g. items that can be carried with one hand) and 10 large things (e.g. cannot be carried by one person) and we ask them to estimate the weight, length or height or the item. We discuss the estimates then check these with a measuring tape or scales, make a calculated estimation, or conduct research to find out.

As a practitioner you will be training adult learners with a diversity of needs, learning styles, levels of numeracy and confidence. Given this diversity, you will need to make professional decisions as to which teaching approaches are applicable to specific adult learners or classes. Provide a profile of a class of adult learners in numeracy that addresses the above range of diverse needs. Next, discuss in detail which teaching approaches you would implement and explain why you considered them to be applicable in this environment.

Class Profile – General information, Career & Education Aspirations, ACSF Performance profiling General | Career/Education Aspirations | ACSF Level | Confidence /10 | Gender | ATSI Status | LOTE / ESL | Education Level Completed | Employment / Study Status | Pre-existingMedical Conditions & Special Needs | Career Area | Highest education level | Learning | Reading | Writing | Oral Communication | Numeracy | | M | Y | - | 8 | S | | Navy Officer | Ba. Degree | 2 | 2 | 2 | 2 | 1 | 3 | M | | - | 8 | E | | Building Trades | Cert III / Apprenticeship | 2 | 2 | 2 | 2 | 1 | 5 | F | | - | 10 | S | | Hospitality | Cert III / Apprenticeship | 2 | 3 | 2 | 2 | 2 | 3 | M | | - | 9 | S | Anxiety, Depression | Retail | Cert II/ Traineeship | 2 | 2 | 2 | 2 | 1 | 2 | F | | - | 8 | S | | Nursing | Ba. Degree | 2 | 2 | 2 | 2 | 1 | 3 | F | | - | 9 | S | Psychological | Hospitality | Cert II/ Traineeship | 2 | 2 | 2 | 2 | 1 | 2 | F | | - | 8 | S | | Childcare | Cert III/IV | 2 | 2 | 2 | 2 | 1 | 2 | M | | - | 8 | S | | Mechanic | Cert III / Apprenticeship | 1 | 1 | 1 | 1 | 1 | 2 | M | | - | 9 | S | | Mechanic | Cert III / Apprenticeship | 3 | 2 | 1 | 2 | 1 | 2 | M | Y | - | 8 | S | | Archeology | Ba. Degree | 2 | 2 | 1 | 2 | 1 | 4 | F | Y | - | 9 | S | | Hairdressing | Cert III / Apprenticeship | 2 | 2 | 2 | 2 | 1 | 3 | M | | - | 9 | S | | Manufacturing | Cert II/ Traineeship | 2 | 1 | 1 | 1 | 1 | 1 | F | Y | - | 10 | E | Anxiety, Depression | Aged Care | Cert III/IV | 3 | 2 | 2 | 2 | 1 | 2 | F | | - | 9 | E | | Army/Mechanic | Cert III / Apprenticeship | 2 | 2 | 2 | 2 | 1 | 3 | M | | - | 9 | S | Depression | Building Trades | Cert III / Apprenticeship | 2 | 2 | 1 | 2 | 1 | 3 | M | | - | 8 | S | ADHD | Mechanic | Cert III / Apprenticeship | 2 | 2 | 1 | 2 | 1 | 5 | M | | - | 9 | S | | Engineering | Ba. Degree | 3 | 3 | 2 | 2 | 2 | 7 | M | Y | - | 10 | S | | Social Welfare | Ba. Degree | 2 | 3 | 2 | 2 | 1 | 4 | M | Y | - | 11 | S | | Musician | Ba. Degree | 2 | 3 | 2 | 2 | 1 | 4 | *
Increasing numbers of individuals need to be able to think for themselves in a constantly changing environment, particularly as technology is making larger quantities of information easier to access and to manipulate. They also need to be able to adapt to unfamiliar or unpredictable situations more easily than people needed to in the past. Teaching mathematics encompasses skills and functions which are a part of everyday life. (Taplin)
Given that my learners are of low overall performance level when matched against the ACSF, it is important that my delivery is: * one-on-one matching the capability of the student with the content of the learning opportunity * contextualized relative and relevant to the learner and the life experiences he/she brings * varied so as not to bore the student – engage them through exciting and challenging activities to improve their skills and confidence when dealing in numeracy
At times practitioners will encounter issues arising from the numeracy teaching role. What are some examples of such issues and who would you refer them to?

Low level of math skills/knowledge is quite often the result of maths being delivered in a classroom environment where the child student has not found this an environment conducive to learning. Revisiting these uncomfortable times, the student may see maths as an intrinsic part of the unpleasantness of school memories. As a practitioner, we are required to overcome this disaffection amongst our students to encourage and promote the benefits of strong numeracy skills – building the student from a “I can’t do maths” to someone who identifies as someone who can indeed do maths.

There is a very clear link between endemic adult innumeracy in modern Western societies and the spectrum of mathematics anxiety, negative mathematics attitudes and aversion to the learning of mathematics that practitioners so often encounter among adult learners… The challenge for teachers and practitioners in adult mathematics education at any level is to find effective ways to break through the barriers of anxiety and disaffection and to allow students to experience success, often for the first time, at a level that is at least sufficient for their immediate needs. Ultimately, the greatest achievement will arise when students can overcome their anxiety and aversion to become independent learners with the capacity to extend willingly their engagement with mathematics. Klinger 2009

As a trainer, not having industry experience to develop context can hamper the success of the learning experience. How does a trainer with a career in the health or child care sector identify with a student with significant interests in automotive or construction? It is through consultation with subject matter experts, e.g. the automotive trainer; the numeracy trainer can develop training activities and contexts with which the student identifies.

4 Select from a range of learning resources to develop participants’ numeracy skill and knowledge

There exists a range of numeracy learning resources in our daily lives that can be utilised in promoting learner engagement and achieving numeracy learning outcomes. Identify four traditional resources and four resources from new or emerging technology, and explain how you would incorporate them into appropriate learning task and activities.

TRADITIONAL 1 Activity sheets
Activity sheets work well because they can contain the description of the type of numeracy activity within. We create these to progressively increase the intensity and/or complexity of the task to add to the learner’s challenge and reward from the task.
2 Measuring devices
The proper use of measuring devices such as a scale or measuring tape can greatly assist the learning experience for both the student and the tutor. The kinesthetic learner is able to take a hands-on approach to the tasks where their skills are tested and they are the ones responsible for identifying data for the maths problems.

3 Newspapers Newspapers usually hold much information presented in tables and charts. Weather, stock market details, sports results, boat arrivals and even prayer times are printed in daily newspapers making it a great resource for numeracy activities. By asking students to find the world weather and identifying the cities with the hottest and coldest recorded temperatures this as an example activity, this also taps in to their literacy skills.

4 Blackboard/Whiteboard
As some bad experiences in learning maths in the past have been due to the emphasis on ensuring every part is correct, the student can use a board to brainstorm, draw diagrams, write calculations and importantly erase incorrect work. This can involve other students in the classroom, offering advice or opinions on how to undertake numeracy tasks.

NEW/EMERGING 1 SmartPhone
I encourage my students to develop a list of important number in their mobile phones for reference in an emergency. Poisons information centre, local police station, hospital, emergency services and other emergency contacts are entered in their phone with phone numbers and addresses as appropriate. Students have the phones on them most of the time and this gives them an opportunity to 2 Online games and puzzles
With the availability of games and puzzles online, there is scope for these to be utilised within our program. Space and location can be tested with games such as Tetris whilst there are other more obvious maths based games such as www.sheppardsoftware.com/ caters for various ages and abilities. 3 Khan Academy
This free website offers a variety of tips and techniques on many subject matters including mathematics. Using the visual aids they have on YouTube to show how to perform operations. This is like an ‘on call’ classroom lecture and there may be some issues with the American phrases and notations but it is a great resource in supplying another explanation of mathematics.
4 Supercoach
One of the most effective and engaging tasks we put our learners through is the AFL Supercoach competition. Particularly for young males, the engagement and excitement of competing against his teacher and other learners helps ‘conceal’ the fact that all activities require and improve the learner’s numeracy skills. Basically, SuperCoach is a fantasy AFL football competition where participants ‘buy’ teams of players from different clubs within the constraints of a salary cap and the player’s performances are rated are awarded points. A player’s value or sale price may increase or decrease during the season, depending on form, injury and performance. The teams compete against each other on a weekly basis and points awarded for wins and percentages gained or lost to determine placing on the league ladder.
Practitioners need to be aware of the social and cultural background of those participating in their numeracy classes. In doing so practitioners can use materials and resources that are relevant to their social or cultural needs and so make their numeracy learning more meaningful and therefore more effective. Identify four potential cultural/social needs of a group of learners and select a set of numeracy materials/resources that relate to their cultural/social needs and explain how these would be effective in engaging learners.

* low levels of formal schooling

From the table in part 3.3, I have included the school level my students completed. The average is around years 8 or 9 of formal schooling. Usually, this is the year in which they left a formal school setting perhaps after a period of absenteeism and truancy. My role is to identify what numeracy skills these students have and at what performance level they match against the ACSF. Assessment tools are available online to formally assess both the literacy and numeracy skills of my students such as the COMPASS Literacy and Numeracy Assessment developed by the Australian Council for Educational Research (ACER) * physical, intellectual, learning or socio-emotional disabilities that impact on learning

Through close personal contact in my one-on-one sessions with students, I am able to explore and identify the reasons and circumstances as to why the student has finished school at a relatively early age. Emotional factors such as bullying, poor relationships with teachers and other students, aggressive behaviour, depression and anxiety have affected my students in one way or another (Anderson, 2013). These stressors have contributed to unhappiness in the student’s school life and in many cases have led to resentment and disdain for school and education in general. Combined with other impediments such as learning disabilities these students, lack of family support and even intellectual disabilities, this creates a ‘perfect storm’ for the students. Trying to learn in an environment where adolescent hormones and social pressures are raging, an early exodus from the traditional school system is a common conclusion.

* 'spiky profiles', where numeracy skill levels are different from literacy or oral communication skill levels

Spiky profiles when referencing the ACSF can indicate areas of experience and confidence as well as identify training gaps. Some of my students have developed ‘avoidance’ skills when it comes to dealing with numeracy as they have low confidence and/or low performance level. The student’s ‘street smarts’ of avoiding or changing the subject when encountering numeracy-related tasks and activities can conceal the student’s actual abilities. Therefore, it important to identify with the student’s numeracy ability at an early stage of our program to help build on any downward spikes within the ACSF and to promote the learner’s performance level across all core skills.

* where skills in numeracy limit ability to achieve goals

As a key part of our program, we identify the student’s career and leisure aspirations. Whilst the students don’t necessarily identify careers that do not require numeracy skills, they are generally surprised when we discussed what numeracy skills are required in their chosen vocation. How many scoops of formula are required in a baby’s bottle when working in child care? How many patterns appear in music based on notes, bars and songs? How do you ensure the right bolts and nuts are used when maintaining a vehicle? The students, whilst they say they are ‘not good at maths’ require a level of numeracy in both the vocational and recreational areas of their lives and we work these contexts into their studies in order to achieve a successful learning experience.

5 Apply and evaluate strategies for teaching mathematical skills and knowledge

Numeracy learning involves literacy skills because of mathematical terminology. Given this context practitioners need to develop activities that integrate pertinent literacy skills that support numeracy learning. Select an area of numeracy to teach a group of learners at level 3 in the core skill of numeracy and identify any mathematical terminology that needs to be learnt. Devise 3 activities that would integrate the identified vocabulary into relevant numeracy tasks. Explain why they would be successful learning activities.

Here is a selection of activities I have developed for students at ACSF Level 3 Numeracy (REFER TO APPENDICES) Numbers & Algebra ACTIVITY | MATHEMATICAL TERMINOLOGY | TARGET GROUP | REASON | Trucking Supervisor | Time | Level 3 Adult Learner | Engage students through real life problems with restrictions and conditions T=l+t+u (T) Time taken = (l) loading + (t) transit + (u) unloading | Clearing the Till | Money | Level 3 Adult Learner | Many people handle cash in employment and social circumstances. Understanding the principles of the end of day process could be helpful in future work and recreation activities. T=n+c+e-f (T) Take =( (n) notes + (c) coin + (e) eftpos ) – (f) float | Magic Garden Spray | Ratios Measuring Rounding | Level 3 Adult Learner | There is tangibility to this exercise where different customers are requiring custom volumes and ratios. The cost is rounded. V=c+w (V) Volume = (c) concentrate + (w) water |

There are various methods of teaching a class of adult learners. Choose a numeracy level from the ACSF and develop an appropriate learning activity for each of the following numeracy topics: number, measurement, space & location, and data & statistics. Implement a different teaching strategy for each activity and make sure each activity caters for the different learning styles.

ACSF LEVEL 2
As many of my learning cohort have low numeracy skills (i.e. a mean performance level of 1), improvement in the learners’ performance capability to level 2 or above should be taken in gradual steps i.e. level 2, then level 3 etc. (REFER TO APPENDICES) TOPIC | ACTIVITY | NUMBER | Best Before | MEASUREMENT | Netball Court | SPACE & LOCATION | Albury CBD | DATA & STATISTICS | Victorian Rainfall |

REFERENCES

Anderson, R.A. ‘5 Characteristics of Adolescent Social and Emotional Development’ By, Demand Media http://everydaylife.globalpost.com/5-characteristics-adolescent-social-emotional-development-4827.html

Compass Literacy and Numeracy Assessment Overview http://www.acer.edu.au/tests/compass

Handal, Boris PHILOSOPHIES AND PEDAGOGIES OF MATHEMATICS
The University of Sydney
SOURCE: http://people.exeter.ac.uk/PErnest/pome17/handal.htm Web 4 Oct 2013

Hull, D. 1999, ‘Teaching Mathematics Contextually - The Cornerstone of Tech Prep’
CORD Communications, Inc.

Klinger , 2009 Behaviourism, cognitivism, constructivism, or connectivism? Tackling mathematics anxiety with ‘isms’ for a digital age http://www.alm-online.net/images/ALM/proceedings/alm16/Articles/15klinger.pdf Northern Territory Government of Australia, 2010
Principles of literacy/numeracy teaching and learning
SOURCE: http://www.education.nt.gov.au/teachers-educators/literacy-numeracy/evidence-based-literacy-numeracy-practices-framework/principles

Numeracy in English Australian Curriculum, Assessment and Reporting Authority Web 4 October 2013 http://www.australiancurriculum.edu.au/GeneralCapabilities/Pdf/Numeracy Taplin, Margaret
Teaching Values Through A Problem Solving Approach to Mathematics
Institute of Sathya Sai Education, Hong Kong
SOURCE http://www.mathgoodies.com/articles/teaching_values.html

http://www.sheppardsoftware.com/

APPENDICES

NUMERACY TASK - LEVEL 3 1 TRUCKING SUPERVISOR
NUMERACY TASK - LEVEL 3 2 CLEARING THE TILL
NUMERACY TASK - LEVEL 3 2 MAGIC GARDEN SPRAY

NUMERACY TASK – NUMBER - BEST BEFORE
NUMERACY TASK – MEASUREMENT - NETBALL COURT
NUMERACY TASK - SPACE & LOCATION -ALBURY CBD
NUMERACY TASK - DATA & STATISTICS - VICTORIAN RAINFALL