# NCALE (Vocational)

## Content and Learning

Determine the numeracy and literacy demands on learners in the context of the learners' course of study, workplace and /or cultural environments.

## Suggested teaching and learning activity 1

### Using interview skills

Purpose: to identify the literacy and numeracy demands of an employee, and to understand a manager's perspective of workplace literacy and numeracy.

Interview a workplace manager and identify the literacy and numeracy demands faced by an entry-level employee. Collect examples of the workplace documentation used by the employee. Identify which tasks occur most frequently and cause the most difficulties for employees. (They may not be the same tasks.)

## Suggested assessment activity 1

### Portfolio

Provide a collection of contextual realia for an identified learner and analyse them using the learning progressions. Discuss how this analysis will affect a programme of study

## Suggested teaching and learning activity 2

### Mapping activity

(see “Knowing the demands” in Teaching Adults To Make Sense of Number or any of the other resource books in this series)

Purpose: to map a text to one or more strands or progressions of the learning progressions. Choose an on-the-job activity in your work context then work in groups (using the numeracy strands of the learning progressions) to identify and map the underpinning numeracy concepts in the activity. Refer to Teaching Adults to Make Sense of Number to Solve Problems pages 6 – 8. See Appendix D.1 (below) for a simple example of this in a Raranga (weaving) class.

## Suggested assessment activity 2

### Report or visual presentation

Produce a grid that identifies the underpinning numeracy skills and knowledge required to complete a task, where the skills and knowledge sit on the numeracy progressions, and hence the requisite concepts that may need to be taught. See Appendix D.2 (below) for an example of this.

### Appendix D.1

Numeracy Scenario: Raranga

A weaving (raranga) tutor teaches students to weave a kete (basket). She explains the importance of checking the number of strands of flax (whenu) which run in opposing directions. It‟s important to have the same number in each direction for the kete to be successful: if there are different numbers, the kete will not close. It is not important whether the number is odd or even: having the same number on each side is what matters. Careful counting and checking has to be done before the final stage. If the numbers are not correct, students will find out the hard way because their kete will not succeed. This critical check involves the first step (up to 20 whenu) or second step (up to 100 whenu) of the Number Sequence learning progression.

### Appendix D.2

Jeff works in logging mill with a machine that cuts boards to 3000mm (3 m) lengths. As a quality assurance measure, three boards are measured in the morning and three in the afternoon. The boards are chosen by taking every 10th board from a randomly selected starting point. The average of the 3 boards is checked to make sure the average falls within the tolerance range of 2995 to 3005 mm.

Problem Underpinning ideas Teaching Points
Measure length of 3 randomly selected boards * Sample selection

Step 6 interpreting data

• Sense of 1mm, 10 mm and sense of length measured in mm

Measurement step 4

• Measuring accurately and why

Measurement step 5

1. What is random sample/why randomness?
2. Benchmark for mm (what does 10, 100, 1000, 2000, 3000, look like?)
3. Accurate estimating of measurement
4. Make sure measuring instrument at 0
5. Reading in mm on measuring instrument
6. Degree of accuracy
Average the three lengths * Which average is appropriate (mean, median) and why
• How to calculate mean

Step 6 analysing data

• Estimate sum of the 3 lengths and use calculator or mental strategy to find exact answer

Step 4 additive strategies

• Estimate sum divided by 3 and use calculator or mental strategy to find exact answer

Step 4 multiplicative

• Know that average is reasonable (i.e., somewhere between the original 3 measurements)

Step 6 analysing data

1. Why use mean and not median?
2. To find a mean you add the lengths and divide by the number of lengths
3. If you are using a calculator estimate the answer first and check reasonableness of calculator answer

Discuss possible mental strategies

For example for sum: 3001 + 3002 + 3003 = 9000 + 1 + 2 + 3 = 9006

2995 + 3003 + 3004 = 5mm under 3000 and 7mm over 3000 gives 2 mm over so answer is 9002 mm

For example for division: 9006 ÷ 3 = 9000 ÷ 3 and 6 ÷ 3 = 3002

4. Discuss why the average must lie between the biggest and smallest measurement.

Decide whether the average calculated is within tolerance range (eg., 2995 – 3005) * Make a judgement about numbers.

Step 4 number sequencing

• Take appropriate action.
1. Does calculation fit within tolerance range?
2. . Recalibrate machine or not?

## References

• Adult Literacy and Life Skills (ALL) Survey (2006) This survey defines and gives the impetus for efforts to improve adult literacy and numeracy.
• Looney, J. (2008). Teaching, learning and assessment for adults. Improving foundation skills. This book contains a background chapter on NZ that could also be used in US21191.
• NZCER. (2006). Assessment for foundation learning
• Tertiary Education Commission. (2008a-i). The learning progressions outline the steps towards competence; the accompanying resource books contain suggestions for determining the demands of literacy and numeracy tasks.
• FitzSimons, G. & Mlcek, S. (2004). Doing, thinking, teaching and learning numeracy on the job: an activity approach to research into chemical spraying and handling. The researchers visited twelve sites and found that though there were many comparatively straightforward calculations in this industry, there were many complexities in the actual practice.

### Performance criteria

3.1 Context-specific reading demands are identified.

3.2 Context-specific writing demands are identified.

3.3 Context-specific listening and speaking demands are identified. Range: verbal, non-verbal.

3.4 Context-specific numeracy demands are identified.

3.5 Context-specific information and communications technology (ICT) demands are identified.

Candidates will demonstrate that they are able to determine the literacy and numeracy demands on learners in the context of the learners' course of study, workplace and/or cultural environments.