What's math got to do with it? Numeracy & Social Studies Education

1. What's math got to do with it?Numeracy & Social Studies Education • OCSS 2009 • Alicia R. Crowe • Kent State University • March 26, 2009 • acrowe@kent.edu

2. Perhaps H. G. Wells was right when he said statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write! • S. S. Wilks (1951)

3. “The time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of the new great complex world-wide states that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write” H. G. Wells (1904)

4. Just as understanding what words mean and how they are being used in a specific context, the understanding of numeric information and how it is being used is vitally important when making decisions on issues that impact the quality of life of ourselves and others in our society

5. Examples • understand economic data and make decisions about what to do (i.e. buy a house, sell your house, take out a loan) and what to ask (i.e. Is this interest rate appropriate or is this predatory lending? Does the interest rate hike impact my daily life?); • understand scientific or medical information and make decisions about whether there is a risk to taking a drug;

6. Examples • understand polling data and ask critical questions about the way the poll was administered, who was sampled, and how the sampling occurred • understand data presented by politicians, government offices, or corporations as they make a case for a specific policy • understanding the risks of markets

7. Basically, certain aspects of mathematics and mathematical ways of thinking are fundamental to understanding social studies concepts and becoming active members of society.

8. Four Instances • 1) the ability to understand raw numeric data or numeric information in context; • 2) the ability to understand percentages in context; • 3) an understanding of the meaning of average; and • 4) the ability to interpret and question graphs and charts.

9. Numeric Data

10. A million, a billion, a trillion - so what? • 1,000,000 = 1 Million • 1,000,000,000 = 1 Billion • 1,000,000,000,000 = 1 Trillion • How many million in a billion? • What happens to our ability to compare when we simplify 1,000,000,000,000 into 1 Trillion and 475,000,000 into 475 Million? • What

11. A million, a billion, a trillion - so what? • As part of your decision-making process as a citizen it is important to know the magnitude of what you are supporting.

12. Where misunderstanding can happen • In 2004, a newspaper article from the China Daily shared that 136,340 deaths occurred in industrial accidents in the previous year (Xing, 2004). In the United States, , the Bureau of Labor Statistics reported 5,559 “fatal occupational injuries” in 2003 (BLS, 2004). • How many deaths are there in each country for the number of workers there are (a ratio of number of deaths to the whole population)? • How does each country count deaths? • What is the difference between deaths from “industrial accidents” and “fatal occupational injuries?” Does it have to be at the work-site to count in the United States? How does each country count deaths from disease caused by the workplace?

13. Population • World Population 6,760,000,000 • Ohio Population 11,459,011 • U.S. Population (#3) 306,000,000 • China (#1) 1,329,740,000 • India (#2) 1,160,139,960 • How many U.S. populations would it take to equal that of China?

14. Why does this matter? and What to do • As a citizen and a decision maker, a student should be developing an understanding of the magnitude of numbers, the value of the context of raw numbers, and the importance of the relationships among numbers being discussed as they learn to make decisions about what to support. • Highlight the differences among numbers in things that are read or numbers you present • Asking questions that help students to see the raw number in a larger context, and • Point out relationships between raw numbers and percentages when you use them or they are in the readings.

15. Percentages

16. Jeff and Jessie come home from school. Both read an article discussing population growth that day. At supper they are discussing it. Jessie claims that population growth isn't really a problem because population growth has steadily decreased over the last 40 years going from about 2% per year in 1960 to 1.5% in 1990 to an estimated 1% in 2015. Jeff argues no, that just because the percentage decreases does not mean that there isn't still a significant increase in population, and thus an area for concern – the population is still growing too fast.

17. How do two people both look at the same information and have two different readings? • Percentages can be deceiving out of context just like raw numbers can be deceiving out of context. What does this mean for understanding social studies concepts?

18. The reference point matters • When the government announces a rise in the unemployment rate citizens should ask themselves - “What exactly does this mean?” (January the rate was 7.6% and in February it was 8.1%) • What does the rise signify? • How many people is this really? • What does this look like historically? • Check out the Bureau of Labor Statistics for this info! http://www.bls.gov/

19. What can we do? • To start - embed questions about the ways in which percentages and raw numbers can be deceiving into everyday classroom conversations about readings from the text, newspaper articles, government documents, or other readings you have included for your class.

20. What can we do? • In a U.S. Government class have the students bring in newspaper articles that reflect a connection to the current topic of study. In addition to the questions normally asked, add questions like: Where are places in your newspaper article that numbers are used? What does this data tell you? Is there more data that would make this easier to understand? • In US History or US Government course that includes a focus on the creation of the Constitution and the bicameral legislative branch you could use the issue of representation (large state population vs. small state population) as an example of percentages and a way to bring mathematics in as you study the American Revolution.

21. When numbers and percentages come together • The population in City A was 40,000 in 1990 and 50,000 in 2000. The population in its county rival, City B was 60,000 in 1990 and 70,000 in 2000. • City A claims in their literature to have grown more than any other area in the county. • When are they right? • City B argues that this is untrue, that they have grown equally. • They are both right! How?

22. A Quick Activity • Explore current news to find the need for mathematical understanding. • Describe where the misunderstanding could occur and possible results of the misunderstanding.

23. Meaning of Average

24. The Meaning of Average • There are at least three ways to describe the “center” of a set of data • the mean (arithmetic average) • the median (the center of the data if lined up in order) • the mode (the most common figure)

25. What does it matter? • Historical data like census record • mean income vs median income • Current Topics • Campaign finances • How much did the “average” contributor give? If I am running for a small local office and 99 people give $100 and 1 person gives $10,000 - the mean will be $199. How might this mislead perceptions if the mean is used? The median or the mode better represents the “average” contributor.

26. An Example • Reports from local, state and federal government agencies in the United States often use both median and mean as they discuss average and some reports use only the term average and do not clarify. • This can be confusing if as a citizen we automatically think of all of these terms meaning our everyday definition of average. • For example, if a community or county included mostly households with incomes from $35,000 to $65,000 but happened to have two or three households with incomes in the millions, the mean would be so high that it could mislead someone while the median would best represent the income of the middle of the area.

27. Helping Students • The U.S. Census Bureau collects and reports data on both mean and median household income • For example, you could use their table http://www.census.gov/hhes/www/income/histinc/h06ar.html as a “bell-work” item to begin a lesson that related to understanding changes in the United States in the last 30 years. • With the chart projected on the screen in the room, where both the median and mean are next to one another, students could be asked to examine the chart and write some questions they have about the data, then, the class could discuss their questions and begin to hypothesize why there would be a nearly $20,000 difference between the median and mean income for 2006. and learning.

28. Helping Students • When the term “average” comes up, ask students about what is meant in the context and how they know. • When data is presented, have students figure out mean and median to see which might might represent a set of data

29. Interpret and Question Graphs

30. Graphs do double duty • They reaches all learners in a different way • They helps students see change over time, number, and proportion (for example) • They help students develop skills to be used in everyday life as a citizen and • They help develop a richer understanding of concepts, events, issues, etc.

31. Basic Types of Graphs • Bar Graph • Comparison among categories • Pie Chart • Comparison using percentages • Line Graph • To show change over time

32. Basic Elements to Consider • Labels • Purpose • Scale and proportion

33. An example • It is often hard for an adolescent who lives in the United States to visualize the impact of wars on the European or Asian continents without the help of graphs and charts. • In a unit on World War II, pie charts could be show the devastating loss of life both military and civilian. • Teacher or students could create pie charts showing the percentage of population (military and civilian) who were not physically harmed, who were killed, and who were wounded from Poland, Russia, and China (as three examples) during the war to illustrate the impact of the war on these nations. • Or, this could be an opportunity to help build connections across time by illustrating how smaller nations that are sometimes overlooked by our textbooks were also impacted significantly by the war, Yugoslavia for example, areas that come back in to the conversation in later years under study. With a pie chart students would be able to compare these countries with very different total populations while also seeing the magnitude of the devastation in each country based on that country’s size.

34. Another example • If it is early in the year and your students are still not as comfortable with questioning data then you might have them create and alter some graphs to begin to see the differences. The National Council for Teachers of Mathematics (http://illuminations.nctm.org/ActivityDetail.aspx?id=63) provides a useful tool that helps to quickly show how manipulating the scale of a graph can alter our initial perceptions of the data set. If you want to highlight how much the United States has changed since the days of the creation of the Constitution then you might ask your students to create a line graph of the United States population in ten-year increments from 1790 to 2000. • To also teach about critically looking at data, you could ask some to use a scale where 100,000 people were represented by one increment and have other groups create the graph where 500,000 people were represented by the same increment. Then discuss see how the use of scale can alter perceptions.

35. Starting simple • Problematize the textbook -- Start by modeling through questions such as: • What does this chart really tell us? • Does this scale distort the data? • Is more information needed to make a decision? • Then, as the year progresses, help them to develop questions of their own as they encounter data on a daily basis. • Problematize the news! • How might altering the scale on this chart change the way that readers of this newspaper react to the issue?

36. How can we help students develop mathematical literacy through social studies? • Help them develop a certain level of statistical understanding in the context of what they study with us. • Help them learn to ask the right questions • Help them develop the habit of mind that pushes them to consistently look beyond the surface • Use mathematics in real world contexts that support the learning of social studies content

37. For example • As a beginning activity early in the year, you could provide your students with a set of questions to help them think about and discuss a current or historical news piece as part of a larger conversation about the content for the day. • What do the numbers in this piece mean? How could they be represented differently? Where are the places that misunderstanding can take place as a result of the author’s use of numbers, percentages, or this chart or graph? • These can be expanded upon in discussions. • As the year progresses, add other questions, then begin to take away the questions you ask and help them to develop their own critical questions.

38. For example • Provide a policy document from a current or past administration • Ask the students to develop a set of questions that they wonder about based on the document. • Then, add key questions you want about the numeric data if they do not develop them themselves.

39. Developing habits of mind • Using the current news pieces you found as a starting point, develop a set of basic questions that you can pose in class that would help your students develop their abilities to understand numeric data. • What is the context in which the data is presented? • Who is reporting the data? • What is the scale?

40. Connect to your classroom • Come up with at least two ways to explore the mathematical aspects of social studies understanding in your classroom.

41. Helpful Resources • Dewdney, A.K. (1993). 200% of nothing: An eye opening tour through the twists and turns of math abuse and innumeracy. Hoboken, NJ: John Wiley & Sons, Inc. • Gutstein, E., & Peterson, B. (eds.) (2005). Rethinking mathematics: Teaching social justice by the numbers. Milwaukee, IL: Rethinking Schools. • Huff, D. (1954). How to lie with statistics. New York: W.W. Norton & Company, Inc. • Paulos, J.A. (1988). Innumeracy: Mathematical illiteracy and its consequences. New York : Hill and Wang. • Paulos, J. A. (1991). Beyond Numeracy: Ruminations of numbers man. New York: Knopf. • Paulos, J.A. (1996). A mathematician reads the newspaper. New York: First Anchor Books.

42. Helpful Resources • Data and Statistics - General Reference Resources: USA.gov: http://www.usa.gov/Topics/Reference_Shelf/Data.shtml • Statistics Canada: Canada’s National Statistical Agency: http://www.statcan.ca/english/edu/power/ch9/using/using.htm • Create-a-Graph: http://nces.ed.gov/nceskids/createagraph/default.aspx • A review of bar graphs: http://cstl.syr.edu/FIPSE/TabBar/RevBar/REVBAR.HTM & http://cstl.syr.edu/FIPSE/TabBar/BuildBar/BUILDBAR.HTM • A review of of Pie Charts: http://cstl.syr.edu/FIPSE/TabBar/ReadCirc/REVCIRCL.HTM & http://cstl.syr.edu/FIPSE/TabBar/BldCirc/BUILDCIR.HTM