Critical Numeracy

Introduction
Critical numeracy is the ability to make decisions about everyday issues that involve mathematical concepts (Watson, 2008).
The approach to prove the importance of critical numeracy was based on selected articles which were used to critically analyse percentage.
Watson (2004) suggests a three-tiered hierarchy of goals for developing the quantitative literacy skills. These tiers suggest increasing movement away from pure mathematical skills into context and then into critical thinking (Watson, 2004). By designing a set of questions for each article according to the hierarchy it led participants to think using
3- tiers of critical numeracy.

Tier 1
The first tier of Framework is the understanding of basic terminology (Watson,
2008).

Article 1: Holidays at Home Appeal

1. A third of Tasmanians are choosing to holiday in Tasmania. Can you write 1/3 in % form ?
Answer
P.1 - 33%
P.2 - 33%

2. Using a Bar model can you colour in 34%? What would fraction look like?
Answer
P.1 0% 100% 34/100 = 17/50

P.2 0% 100% 34/100 = 17/50 Both participants were clearly able to show their knowledge of basic terminology.
They were both able to show the relationship between percentage and fractions and draw a bar model correctly shading 34 %.

Article 2: Avon Advertisement

1. In week one 100% of women show improvement in skin texture What is the 100% of ?

Answer P.1 34/34 P.2 34
Both of the participants were able to understand where the value of 100% came from. They were able to show a clear understanding of the link to part-whole based on assumptions that 100% is always a whole (Watson, 2011).

Tier 2
Next set of questions focused on tier 2 of the Framework . Learning must take place in what is called the second tier of Framework for Critical Numeracy and that is the understanding of terminology in context, especially in social contexts ( Watson, 2008).

Article 1: Holidays at Home Appeal

1. If 39% of Tasmanians would like to holiday in Western Australia, 23% in Northern Territory and 15% in South Australia, what percent of Tasmania’s prefer the remaining states?

Answer P.1 23% P.2 23%
In this section both of the participants showed no problem working out the solution. They displayed their knowledge of percent being over
100.

Article 2: Avon Advertising

1. Why is the seller using percentage (%) value to represent the results?

Answer P.1 - Comes across more successful. If % high, people more likely to purchase P.2 - It is more convincing

In this section the aim was to test participants understanding of the percentage in the context of the advertisement. Both participants had similar answers to the question, they agreed that the advertiser used percentage as a way of making the product appealing to consumers and guarantee its success. However participants failed to question the exact use of % which would have fit into critical thinking. What I was focusing on was their understanding of why they use % instead of numbers. Sometimes writers tend to divert readers from the actual values by using percent so that the result looks more engaging.

Tier 3

The last set of questions focused on the 3rd tier hierarchy. Third tier of the Framework is developing the ability to think critically in context and to question claims that are made without proper justification (Watson, 2008).

Article 1: Holidays at Home Appeal

1. Considering Tasmania, Queensland and ACT, NSW and Victoria are not represented do you believe the results of this survey are correct? Why/ Why not?
Answer
P.1 No P.2 No all states need to be involved

The first participant answered ‘No’ to this question failing to elaborate why it was incorrect. The second participant was able to answer the question correctly, however it was not in depth and I was looking for more than one factor which criticises the result. He was able to view that in order to make the results more accurate, all states need to participate in the survey. Also what they forgot to mention was issues with sampling techniques, as well as the way the questions were asked to collect the results for this survey. This part of the task tends to show me that participant’s lack the ability to think critically. Where did the reporter go wrong? He should have been questioned. How can he publish a study about Tasmania and forget to mention the results. This tends to show an example of ways the media covers up insignificant numbers.

Article 2: AVON Advertisement

1. How reasonable are these figures over 4 weeks?
Answer
P.1 Fairly reasonable if 71% showed improvement P.2 Pretty good since 71% have a firm face

Over the four week period both of the participants thought the results were quite reasonable, failing to question how unrealistic the results could have been in just 4 weeks. Once again they showed no critical thinking knowledge failing to question the advertiser’s way of selling the product, and making it more appealing by showing such a success rate over just 4 weeks. If we were to look at their clinical results seventy one percent of 34 women are only 24 years old. So all of a sudden 71% does not sound that significant.

2. Was the clinical study time frame and the sample size of people they used, sufficient enough to make this product successful?
Answer
P.1 No not sufficient P.2 Yes it is sufficient.

Second Participant was convinced that the product was a success. He mentions that over 12 week period 71% of women had improvement in their skin. This was incorrect because there was no mention of the success rate at 12 weeks. This shows those participants 2 requires more specific attention regarding the implications of claims and try to learn how to question studies that lack adequate justification. The first participant does show some understanding of critical analyses, questioning the sample size being too small - 34 and that the study results need to be over a long period of time to call the product successful. Participants also should have stated that things like age and skin type needs to be mentioned. The selection criteria is a big factor which can influence results, for all we know those 34 people could have been part of the Avon staff. Whether the clinical study had a place group also should be questioned.

Reflection
As part of this assessment I chose two interesting articles which clearly displayed the use of percent in the media. The Article 1 was selected from The Mercury newspaper and it looks at survey based study on Tasmanians preferring to holiday at home instead of other states. The second article is an online advertising for Avon skin care. Both articles were very different however they clearly were able to show the concept of critical numeracy in the media.
The task was challenging as it was up to me to create appropriate questions for each article using the 3-tier hierarchy. I took a few attempts with this task in order to get it correct as I noticed it was hard for participants to analyse percent in a way I needed them to. I was able to inform each subject of the overall picture I was trying to achieve from the task, which was their understanding of percentage and how it is used in the media.

Interestingly enough when I asked the participants to take the questionnaire, one of them was very hesitant, informing me he had no clear knowledge of percent.
This therefore required me to constantly guide the participant through each questions so that they had a clear understanding of what is needed in this task.
The advertisement for the Avon skin care was a fantastic piece of news to show how percentage can manipulate a buyer into purchasing the product. With its unrealistic clinical study and farfetched results, the use of percentage managed to show how successful the product is.
The article from The Mercury shows an example of ways the writers represent percent in their articles to emphasize a point. The social issues associated with the article are quite complex. The article ties up our views on the importance of using percentage in a correct way. The approach illustrated in this article emphasises the difficulty of interpreting survey data with limited information. It provided us the opportunity to recognise and explore mathematically different ways of representing the same information using
percent.
In terms of understanding basic terminology associated with ‘per cent’ from the tier one of the Framework, both participants were able to show their understanding of percent and its use in the media. They clearly were able to show the understanding of code breaking, by been able to find different uses of percent in the article. Participants showed no hesitation when they were asked to draw the bar graph to represent percent. Percent can be linked via proportional reasoning to fractions, but they are less commonly used than percent in the media ( Watson, 2011). The participants were able to demonstrate their understanding of the relationship between fractions and percent by converting fractions to percent and visa versa.
Tier 2 of the Framework focuses with respect to making meaning of the text. The questions based for this part can be used to demonstrate to people the absolute necessity to have quantitative awareness when reading product adds or newspaper articles. The understanding of intention to use percent in the advertisement to make the product more appealing to women was mentioned. While both participants were able to show the reason media uses percent to represent data, the specific reason I was looking for was not shown. Writing figures in percent form is an impressive way the writer uses to mask up absolute numbers when they seem less impressive. ( Watson, 2009).
The third tier of the Framework requires critical thinking. The questions were made to engage the participants into critical thinking in regards to the use of percent in the articles. The results to this section was not significant enough for me to be able to say that they have a clear understanding of the 3rd tier hierarchy. The process of critical numeracy seemed new to them and it required me to explain what I was looking for. The questions were focused on the clinical study results, while participant one showed some understanding of what I required from their answer the second participant completely failed to show any understanding of critical thinking. He had no concept of how Avon used percent in the study to manipulate the buyer’s decision. In the second article analysis, it was the second participant who was able to understand the concept of percentage representation while the first just wrote ‘No’ as the answer but could not explain why? In order to be able to be good at critical thinking they need to be able to question everything about the article, eg like the sample size of study, the age of people they used to get results and the time it took them to get results. The percentage is often used in the media to represent survey results, but the outcome of the results can be linked to the way the questions are asked in the survey and the use of the language in order to bias peoples responses ( Watson, 2008).
The use of percent figures tends to add legitimacy to a context that is quite meaningless (Watson, 2008). As critical thinkers we need to be more exposed to media like this so that we gain understanding of the biased voluntary surveys.

I believe naturally a majority of people fail to approach the media with a critical eye. They tend to fall for their exaggerated studies and surveys and forget to notice that sometimes they have no adequate justification. This task allowed me to see how the media uses numerical terms such as percent to strengthen their own point of view without actually giving us numbers. We need to learn how to interpret mathematical information and use our abilities to draw sound conclusions based on mathematical reasoning. People need to be aware of this issue and build their critical thinking skills by questioning everything they read.

Critical numeracy is important to me because we all need adequate numeracy skills for a variety of reasons. To be numerate is to use mathematics effectively to meet general demands of life (Watson, 2004). We need to be able to calculate, estimate and use measuring instruments, and maths aims to contribute to the development of the broad range of our numeracy skills. In my professional life as a Laboratory Assistant I was constantly required to work with numbers while doing mathematical calculations, measurements and precise mixing of 20 %, 50%, 100% of solutions.
For many years teachers have been focusing on the importance of teaching literacy across the curriculum failing to notice the importance of numeracy and how much we use it in the real world. As a teacher the following task reassured me of the importance of teaching critical numeracy in the classroom. My students will need to gain ability to reason and work with numbers and be able to use and understand other mathematical concepts before moving to more critical thinking. Some children struggle with numeracy at some stage of their lives and struggle to develop deep contextual understanding of mathematical concepts. For better teaching of numeracy as a teacher I must pay attention to those students and understand their numeracy issues, give time to numeracy across the curriculum in the classroom and reflect on the way I will teach mathematics. I must support and encourage students with numeracy so that they can build their confidence in that area.

REFERENCES

Watson, J. 2011, ‘Lecture 1 Notes: Personal and Professional Numeracy’, 25 February

Watson, M. J., Beswick. K. (2009), Which is Bigger? 250 Tonnes or 17%: A Tale Of Salt, University of Tasmania, Journal Article, p. 1-14

Watson, M.J. ( 2004), Quantitative Literacy in The Media An Arena for Problem Solving, University of Tasmania, AAMT, p.15

Numeracy in The News. Available on the World Wide Web at http://www.simerr.educ.utas.edu.au/numeracy/critical_numeracy.htm

Watson, M.J. (2008). National Literacy and Numeracy Week : Critical Numeracy In Context. University of Tasmania. Retrieved from www.nlnw.nsw.edu.au/videos08/crtical_numeracy/pdf/jane_watson.pdf

Holiday At Home Appeal. (2001, March 20) . The Mercury, p.11

Avon Australia,(2010). Anew Ultimate Age Repair Day Cream SPF 15, Retrieved from www.avon.com.au/PRSuite/productdetails.page

Appendix

Article 1

Holidays at home appeal A THIRD of Tasmanians are choosing to holiday in their own back yard a national tourism survey has found. The See Australia - study found 34 per cent of
Tasmanians had taken their last holiday in Tasmania. The study, which surveyed more than 2000 people across the nation, also found that most of the other Tasmanians liked to travel to the eastern states of
Australia with one in four choosing Queensland as their holiday destination. Asked where they would most like to holiday, 39 per cent opted for Western
Australia 23 per cent choosing Perth. The Northern Territory was chosen by 23 per cent and 15 per cent chose South
Australia.

Article 2

Article 1 Questions

Question 1
A third of Tasmanians are choosing to holiday in Tasmania how much is that in % ?

Question 2
Using a bar graph can you colour in 34% ? What would the fraction look like?

Question 3
If 39% of Tasmanians would like to holiday in Western Australia, 23% in Northern Territory and 15% in South Australia, what percent of Tasmanians prefer the remaining states?

Question 4
Considering Tasmania, Queensland and ACT, NSW and Victoria are not represented do you believe the results of this survey are correct? Why/ Why not?

Article 2 Questions

Avon Advertisement online

Question 1
In week one 100% of women show improvement in skin texture What is the 100% of?

Question 2
Why is the seller using percentage (%) to represent the results?

Question 3
How reasonable are these figures over 4 weeks?

Question 4
Was the clinical study time frame and the sample size of people they used, sufficient enough to make this product successful?