Section 1 Introduction 1 1 Introduction What is numeracy? What makes a person numerate? In broadest terms, numeracy (or numeric literacy or quantitative liter- acy) can be viewed as a combination of specific knowledge and skills, which are needed (but do not suffice) to function in the modern world. What other skills, apart from numeracy, do we need to posses? For instance, social intelligence, cross-cultural competency, and new-media literacy. Numeracy involves reasoning from, and about, numeric information (data), which can be presented in a variety of ways (such as numeric, graphic, narrative, visual, and dynamic forms). Inspired in part by questions we routinely ask in mathematics (What is this? Why is this true? How do we know?), we expand numeracy to include critical, evidence-supported thinking, common sense, and logical reasoning in situations and/or contexts that do not explicitly nor implicitly involve numbers or quantitative information. (Examples follow.) In our conceptualization of numeracy, and for the purpose of this course, a numerate person is assumed to be a university student, rather than a general member of our society. (One reason lies in the fact that we must make certain assumptions about the background, mathematical and otherwise.) To make this concept of numeracy more transparent, we now illustrate its aspects in several examples (which are in no way an exhaustive). In the article After 7,500% rally, cryptocurrency founder sells his coins pub- lished in the Globe and Mail, on 20 December 2017, we read “Litecoin dropped about 4 per cent to $ 319 at 1:02 p.m. in New York, according to prices on Bloomberg. The coin is still up about 75-fold since the end of 2016, according to http://coinmarketcap.com prices. The market value was $ 17.5-billion.” A numerate person is able to understand and work with the percent infor- mation (for instance, they know that the value of the Litecoin, before it dropped 4% to $ 319, could not have been $ 500); they understand that 75-fold increase means 75 times, i.e., that the Litecoin value at the end of 2016 is multiplied by 75; they can visualize $ 17.5 billion, by comparing, or relating to other quantities, such as saying that “$ 17.5 billion is the salary of 175 thousand top paid high school teachers in Ontario.” A numerate person can compute their body mass index (from a formula they recovered from Wikipedia, for instance), lookupitsvalueinthecharttodetermine whether they are deemed overweight or not. They can interpret results of their blood test by relating numbers: if their cholesterol reading is 5.78, and the desired level is less than 5.20, they realize that their cholesterol level is outside normal limits. A numerate person can reason logically: they understand that while nausea, headache, fever, and vomiting are symptoms of bacterial meningitis, they do not cause meningitis; as well, someone showing these symptoms does not necessarily have meningitis. (Thus, one has to be careful how to interpret answers from online symptom checkers.) A numerate person understands the difference between causation and correlation. A numerate person has basic understanding of probability and risk. For in- stance, if something is known to occur twice a week, then 4 occurrences in a certain week might not constitute an epidemic, but rather reflect a probabilistic fact that unlikely events nevertheless do occur. As well, a numerate person will recognize that statistics derived from a small sample is very likely worthless, and often not in any way representative of the population from which the sample has been drawn. 2 NUMERACY A numerate person is aware of their digital footprint in social media and elec- tronic marketplaces, and is concerned about privacy and confidentiality. Mathe- matical algorithms can spy on the interactions within social media, in order manip- ulate the users’ behaviour. For instance, read about the case of Cambridge Analyt- ica at http://www.cbc.ca/news/opinion/cambridge-analytica-opinion-1.4588857). A numerate person is familiar with basics and biases of search algorithms and targeted marketing. A numerate person is able to use graphs to understand, illustrate and illumi- nate concepts, presented in both static and dynamic forms. In the article This chart shows how bread prices soared during the price-fixing scheme published in MacLeans, 22 December 2017, https://goo.gl/U5CV7A we find the following figure (Source: Statistics Canada, CANSIM Table 326-0021): We read: “A glance at Statistics Canadas data on food prices and the consumer price index, which compares the cost of a fixed set of goods and services over time, seems to show the price fixing in action.” A numerate person is able to look up the meaning of consumer price index (CPI), and by learning that CPI was reset to 100 in 2002, note that the graphs are accurate, as they all cross the CPI of 100 line in 2002. As well, they would realize that indeed the CPI for bread, rolls and buns has been increasing at a fast pace since 2002, and grew substantially larger than other quantities represented in the graph. For instance, they could determine that it is about 50 units larger than the CPI for all items in 2015. A numerate person is a critical person, and asks what “ecotourism,” or the label “green” on a laundry detergent actually mean. They do not pay for an “all inclusive” vacation before insisting to know what is not included. A numerate per- son reads the small print and, for instance, understands how the annual percentage rate (APR) is used to compute the monthly interest on their credit card. As well, a numerate person holds certain beliefs and values. They understand and appreciate the importance of mathematical and logical reasoning for living Section 1 Introduction 3 and making decisions; they accept the fact that numeracy takes time and practice to achieve and is an important part of life-long learning; they are willing to adopt attitudes, beliefs and work habits in order to overcome potential learning and other (personal) barriers that might exist; they are inquisitive, motivated to learn on their own, and are willing to engage with challenging topics and ideas. Why numeracy? A survey conducted by the Conference Board of Canada in 2012-2014 [1] claims that about 55% of Canadian adults have inadequate numeracy skills, and that it is a “significant increase from a decade ago.” Based on the first results of the Programme for the International Assessment of Adult Competencies, Statistics Canada reports that “Canada ranks below the OECD average in numeracy, and the proportion of Canadians at the lower level is greater than the OECD average.” [2] (References appear at the end of this chapter.) First steps ... Numeracy is about looking critically at information (often involving numbers), and making sense of it. But above all, is it about asking questions, actually, asking good questions, so that we can understand, and based on our under- standing, make good decisions. To illustrate this, we look at several examples. (1)Whatdoesnatural in Natural spring water mean? In 100% natural spring water?Whatdoespure in Pure Life premium drinking water mean? In pure drinking water? (All of these were taken from labels of bottled water.) When we look at food labels on bottled water, we find ingredients such as magnesium sulfate, potassium chloride, salt, calcium chloride, magnesium chloride, and potassium bicarbonate, together with - of course - purified water (i.e, filtered tap water). Routinely, bottled water companies purify water, and then add some of the ingredients listed above (or some others) back into it. Why? Usually, they claim, to give taste to water. So natural is not really natural, and neither is pure pure, 100 percent water. (2) The table below shows a sodium content for four beverages, together with the percent daily value of sodium. Drink Sodium content % daily value Monster Rehab Energy Iced Tea 110 mg/240 mL 5 Coca Cola 30 mg/250 mL 1 Starbucks Doubleshot Fortified Coffee Drink 160 mg/444 mL 7 Gatorade Perform Orange Thirst Quencher 250 mg/591 mL 11 So what is the daily value of sodium? Based on Coca Cola, if 30 mg is 1 percent, then the daily value is 3000 mg. If 110 mg represents 5% (Monster), then the daily value is (110/5)*100 = 2200 mg. If 160 mg represents 7% (Starbucks), then the daily value is (160/7)*100 = 2285 mg. If 250 mg represents 11% (Gatorade), then the daily value is (250/11)*100 = 2272 mg. According to Health Canada (https://goo.gl/Q4qqjm), adequate intake of sodium for teens and adults is 1500 mg/day, with upper limit of 2200-2300mg/day. Comments? (3) Shinerama is Canada’s largest post-secondary fundraiser in support of Cystic Fibrosis Canada (McMaster students routinely participate). What is there to ask about, isn’t this a good cause? 4 NUMERACY Yes it definitely is, but – it costs to raise money! Let’s check how Cystic Fibrosis Canada does it. The web page 2017 Charity 100: Grades at https://goo.gl/ED1pA4 gives a ranking of charitable institutions, by evaluating them on important parameters. The screenshot from the web page shows that, in terms of charity efficiency, Cystic Fibrosis Canada is given the grade of D. What does it mean? Comparing with other organizations, we see that that’s a fairly low ranking (actually among the worst two in its category Fundraising Organizations). Probing further, we look at two important parameters: charity efficiency (de- fined as the percentage of total funds collected that actually go toward the cause), and fundraising efficiency (the amount of money needed to raise $ 100).