Numeracy for adults: building skills with online learning links

4. Building numeracy skills with online learning links

4.1. Mapping the numeracy demands

The numeracy demands of workbook tasks were mapped against the adult learning progressions following the process described in Teaching adults to make sense of number to solve problems: supporting the learning progressions (Tertiary Education Commission, 2008b). This identified the specific numeracy demands of the concrete certificates. Three of the adult learning progressions were identified as most relevant: measurement, place value and proportional reasoning (Tertiary Education Commission, 2008a). Tasks within the workbooks required numeracy skills from steps 3 to 6 on these progressions and apprentices would need to be placed at the top step of these progressions in order to appropriately meet the numeracy demands of the qualification. For example, the qualification required apprentices to accurately measure to the nearest millimetre, which is located at step 3 in the measurement progression, and they also needed to understand and apply ratios (in particular, the water to cement ratio), which is located at step 6 on the proportional reasoning strategies progression.

Initial assessments were carried out with each of the five case study participants and their current understandings were mapped against the adult learning progressions to identify areas in which their skills were insufficient to meet the demands of the qualification. Assessment tasks were taken from resources associated with the adult learning progressions (Tertiary Education Commission, 2008b; Tertiary Education Commission, 2008c) and examples included estimating and measuring the weight of a phone book, and describing solutions to number problems. Each assessment took the form of an individual interview and lasted for approximately 40 minutes.

Areas in which the workers’ numeracy skills were found to be insufficient varied, but the most common areas were conversion between units of measure (four workers), calculating fractional amounts and percentages (four workers) and knowledge of tenths and hundredths in decimal numbers (three workers). This knowledge is required to read scales accurately.

The following section describes in detail the way the learning links approach was used to improve numeracy skills. The process is described by highlighting the experience of one worker (Jade), who can be considered representative of the group.

4.2. Highlighted case study: Jade

Jade is a 20-year-old apprentice currently studying for a National Certificate in Concrete Construction with strands in Sitework, Pre-cast Concrete, and Placing and Finishing. Learning objectives within each of the three learning progressions were identified for Jade based on results from his initial assessment. This resulted in four major focuses for his learning:

1. Knowledge of hundreds in whole numbers and tenths and hundredths in decimal numbers. This knowledge is required to read scales accurately (place value progression).
2. Conversion between units of measure, for example litres to millilitres or grams to kilograms (measurement progression).
3. Telling the time: using analogue and 24-hour digital clocks, converting from 12- to 24-hour time and vice versa (measurement progression).
4. Calculating fractional amounts, for example one-quarter of 64 (proportional reasoning progression).

A variety of online learning activities were selected to meet the numeracy needs of the five workers. Suitable sites were those which meet a set of criteria based on research evidence on the effective use of ICT to develop adults’ numeracy skills:

• The content of the learning activity is pitched at the “gap” between the worker’s current knowledge/skills and the numeracy they require to successfully complete the qualification (Mellar et al., 2007).
  
• The learning activity requires users to be active in their learning, promoting the development of reasoning skills rather than the ability to recall information (Cromley, 2000).
  
• The learning activity requires users to complete cognitively demanding tasks (Swain & Swan, 2009).
  
• Immediate feedback is provided to the user. This clearly informs them whether the answers they are providing are correct and ideally provides meaningful feedback and guidance on how to improve performance (Australian Flexible Learning Framework, 2009; Lister, 2007).
  
• The site is accessible and easy to use, with minimal text and appropriate use of audio, video, photos and diagrams (Quality Improvement Agency for Lifelong Learning, 2008).

Example learning link: the fraction bar

The diagram above illustrates one of Jade’s online learning activities: the fraction bar. This activity aims to develop the ability to calculate fractional amounts and supports the learner’s thinking by enabling the user to split the total amount into a variety of fractional parts. The learner is directed through the process and immediate feedback is provided. The site provides additional learner support through the help file, which provides both instructions on how to use the tool and information on how to proceed in finding a solution to the problem.

In total, 16 online learning activities were selected for Jade. These focused on developing the knowledge and skills identified in the four major focuses for his learning. Nine sites focused on developing Jade’s knowledge of whole numbers, tenths and hundredths. Tasks on these sites involved reading a variety of scales and modelling decimal numbers using number lines, abacus and fractions. Three sites focused on developing his ability to tell time and these required Jade to investigate an analogue and digital clock, which were synchronised, watch animations explaining how to tell the time (both analogue and digital) and practise reading clocks and converting from analogue to digital time. A game which involved converting from 12- to 24-hour time as quickly as possible was also included. The final four sites focused on developing Jade’s ability to calculate fractional amounts. These activities involved supported practice and an interactive learning object designed to teach fractional concepts.

Jade owned a computer but was provided with a broadband internet connection to enable him to participate. He was sent links to four online learning activities by email each Monday and he worked on these independently over the course of the week. His instructions were to spend at least half an hour working on the activities, three times a week, and he completed a log of the work he did. He spent a total of 11 hours and 25 minutes working on the activities over four weeks, an average of 2 hours and 50 minutes a week. This was longer than most of the other participants, who spent an average of 6 hours and 36 minutes in total, or 1 hour 40 minutes per week. Jade explained that he spent longer than he was required to because he “had time on his hands and was looking for something to do”.

Jade worked on the activities at home, usually when he had just returned from work. He established a daily pattern in which he first worked on the activities, and then moved on to look at other sites on the computer. This was consistent with the other case study participants, who all found different ways to slot the learning into their daily and weekly routines. For example, one worker spent time on the activities every week night while his partner cooked dinner, one worked with his brother on the activities three nights a week after Shortland Street, and one worked around his teenage daughters, who dominated the computer in the evenings. Overall, two of the workers spent time on the activities daily, two completed them three times a week as instructed and one did the work in one longer session each week. The flexibility of the approach enabled the workers to structure their learning to fit in with their existing commitments.

Jade received plenty of support from his girlfriend with the work he was doing.

We sat at the computer and did it together. She teaches me little things and I teach her little things; it’s given her some skills as well.

When questioned about the support he received from his girlfriend, Jade commented, “I could have emailed you but it’s easier when someone’s right there.” Jade’s girlfriend also extended his learning into their everyday routines, asking him at various times to read the analogue clock to practise his skills. In terms of assistance from the researcher, Jade received a minimal amount, only once asking for help, when he was having difficulty using a password to access a site. This pattern was consistent with the other case study participants. In total, three of the five workers acknowledged receiving support from family and friends in their home environment as they worked on the activities.

A final assessment showed that Jade had made progress in three of the four focus areas of his learning. More specifically, he moved from steps 2-3 to step 4 on the measurement progression and from step 3 to step 4 on the place value progression. He developed the ability to:

• read scales accurately by applying his increased knowledge of place value
  
• convert between units of measure, for example converting from 1,400g to 1.4kg
  
• tell the time using analogue clocks
  
• tell the time using 24-hour digital clocks
  
• convert between 12- and 24-hour digital time and vice versa.

Jade was able to identify accurately what he had learnt. He clearly described his increased ability to read scales:

Volume, like how to measure it…say you got like a litre, and then a litre and a half and then two litres and you got the bits in the middle…the wee lines going up, if you know what I mean. Some of them you multiply them by 5, going up…there’s different amounts between different lines.

Jade’s progress was consistent with that of the other case study participants, who each moved one or two stages in one or two of the learning progressions. The key skills gained by workers varied but included the ability to calculate fractional and percentage amounts, an increased knowledge of addition and subtraction basic facts, the ability to solve multi-digit multiplication and division problems mentally and the ability to add and subtract fractions. As with Jade, other case study participants were also able to identify and describe their own progress.

Jade described how he uses his new skills, both at work and at home. He explained that because he can now read a tape measure he has started wearing his glasses at work and has become more accurate in his measurements:

Mostly what we use here is a tape measure; we measure how big the area of the panels are. I’ve started wearing my glasses. I never used to wear them ’cause I wasn’t sure how to read the tape. I used to keep stuffing things up; usually I was about 5mm out with some of them.

At home Jade has made use of his ability to read scales by weighing the ingredients for some muffins he made, and because he can now read the analogue clock for himself he no longer has to ask his girlfriend for the time.

I used to say to my girlfriend, “What’s the time?” She’d say, “You can see it,” and I’d say, “But I can’t read it.” Now I can read it for myself.

He has also stopped having to ask his girlfriend to read the Sky Television timetable for him. As it is written in 24-hour time he previously used to ask her help to find out what time certain programmes were on. He commented, “Now I know you just take off 12.”

Although Jade had not yet found anything he had learnt useful for his BCITO workbooks, this was because he was currently focused on practical components of the qualification. He was anticipating using his new knowledge in a unit he had coming up on mixing concrete.

There’s one unit I haven’t gone through yet, mixing concrete, and you need to have a certain amount of quantities of each different chemical to make the mix. I haven’t done that one yet. I saw it and it looked too hard; I put it in the too hard pile. But what I’ve learnt probably will be useful for that.

In line with the results from Jade, all of the other workers reported using their new knowledge, with examples provided for both home and work situations. These included:

• One worker reported he now uses less raw product at work as he is able to accurately measure out additives to concrete mixes, such as water-proofing agent. His previous practice was to add more than enough to ensure the mix was satisfactory, although he admitted this would cost the company more than necessary for ingredients.
  
• One worker became more accurate at calculating the amount of dye required for each batch of coloured concrete. Each shade is prepared using a percentage weight of the total cement in the mix, for example 5 percent, 10 percent or 15 percent. He previously used to estimate the amount required but can now calculate this accurately.
  
• One worker increased his ability to add, and as a result was able to keep a running tally as he did his grocery shopping and avoid having to put items back once he got to the checkout.
  
• One worker was able to save himself a trip to the garage in the weekends by applying his new ability to measure volume accurately to mix his own two-stroke for his chainsaw.

All of the workers reported using the skills and knowledge they had learnt in very context- and task-specific ways, even though the online learning activities were not set in these particular work or home contexts. They were able to transfer the skills and knowledge they developed online and apply them to a range of situations and tasks.

In the final interview all of the case study participants were questioned about the merits of the approach and all thought it would be successful. Jade identified that “most people these days have a computer” and would be prepared to spend the time it takes to work on the online activities; “three-quarters of an hour is nothing out of your day”. He also thought the approach had the potential to provide another avenue of support for apprentices:

It would be good to have another place to go to for help. The only other person we can go to is the boss and he’s usually busy.

Jade’s employer agreed that the learning links approach had great potential as a means to support and develop the numeracy skills of concrete apprentices:

It’s a great model for the future. It would be great for employers as well, to know that the apprentices had support. I try to give them all the help I can with their workbooks but there are lots of other jobs that compete for my time.