Analyzing Community Safety Using Statistics, Representation, and Simulation

1. Analyzing Community Safety Using Statistics, Representation, and Simulation By Doug Lenseth and Eric Sposato

2. Background With new local politicians that have been elected to office combined with the recent events that have taken place in our local communities, public safety has become a very important issue. This lesson plan will give students the opportunity to: -Analyze statistics used in the media -Recognize how statistics can be used to portray different points of view -Connect relevant mathematical concepts with the statistics used in the media -Research statistical data, including the U.S. Census Bureau website -Find supporting, or contradictory, statistical evidence of public safety in an assigned community -Create unique representations based on statistical evidence found during research -Present the evidence found using a simulation of a local news broadcast to the class

3. Background (cont.) This lesson is best suited for a seventh grade mathematics class, but it can be used in other grade levels, during a unit on statistics and probability. In addition, this lesson plan can be integrated with a social studies class in a Mathematics Across the Curriculum project. Its purpose is to give students the opportunity to create their own unique representations of statistical evidence to report on the public safety of an assigned community using a simulated local news broadcast. The lesson plan is designed to work over the course of three class periods, and Day 2 and Day 3 rely heavily on Buckingham’s concepts of representation and simulation.

4. Abstract – Day 1 • During Day 1, the teacher will divide students into groups of 3, or 4, (depending on class size) in order to analyze examples of how statistics can be used in the media. These examples will be copies of articles taken from printed and online newspapers. Each group will be asked to connect its examples to recent mathematical topics that have been covered including percentages, proportions, probabilities, and sample spaces. These examples will cover multiple topics including public safety, politics, weather, and traffic violations. The students will discuss how the statistics can be used to support various points of view and why different points of view are presented. After the groups have shared their examples with the class, the teacher will review the mathematical concepts that were discovered to show how statistical data could be used as evidence. Then, the teacher will assign a local community to each group and provide directions for Day 2 and Day 3 of the lesson plan to the students.

5. Abstract – Day 2 • Day 2 will take place in a computer lab. The teacher will introduce each group to online statistical data sources, including the U.S. Census Bureau. Each group has been asked to research the community that was assigned to them in order to find statistical evidence that would support, or contradict, the level of public safety in a given community. After the raw statistical evidence is gathered, the groups are required to translate this raw data into presentable forms using percentages, proportions, probabilities, and sample spaces. Students are encouraged to create their own unique representations of public safety in their community with statistical evidence that supports those representations. After the students have gathered their information, they will have about a week to collaborate and prepare for the simulated news broadcast on Day 3.

6. Abstract – Day 3 • Day 3 will occur in the classroom, and the groups will present their information to the class using a simulated news broadcast. Since this will take place in the classroom, there will be no actual production equipment. Instead, the students will be asked to role-play as news anchors in order to present the level of public safety in their assigned communities to the “audience”. During the presentations, students who aren’t presenting will evaluate the other presentations. After the students have given their presentations, the teacher will discuss with the class how the media can shape the way that information is presented by choosing specific statistics that can support, or contradict, a certain point of view. In addition, the teacher will discuss how even though statistics can be objective when considered alone; they can become subjective when they are used out of context to support a certain perspective. Finally, the teacher will ask the students if they think that the media uses statistics to portray specific points of view, and if the students will question the statistics that they regularly hear and see in the media. Finally the students will be required to write a reflection on the production process and on one group’s presentation, which will be due the next class.

7. Abstract – Assessment • Students will be assessed in two ways. First, each group will be asked to submit a written summary of the presentation, which includes detailed calculations of the mathematics evidence used. The mathematics content will be assessed using accuracy, variation, and relativity. The mathematics accuracy will be measured by how the raw statistics were translated into presentable information, and if they truly represent what they are intended for. The variation will measure the different types of statistical evidence used, i.e. probabilities, population densities, proportions, percentages, graphs, area, etc. And, the relativity will be measured based on how well the mathematical evidence supports the representation claimed by the group. Each dimension will be graded on a 1-5 scale.

8. Abstract – Assessment (cont.) • Second, each group will be graded on its presentation. Since this grade will be more subjective, its dimensions will include: providing a clear representation about the nature of public safety in each community, using mathematical evidence to support a stated representation, allowing all group members to participate, fulfilling the time constraints of the presentation, and creating an accurate simulation of a news broadcast. This will also be the criteria that other students use to evaluate the presentations. Using a 1-3 point scale, this presentation will be scored out of 15 points. Also an individual reflection on the production process and on another groups presentation will be required worth a total of 20 points. As a result, the whole project will be worth 50 points

9. Required Tools • Copies of printed an online news articles • Computer lab with internet access • Overhead projector (for presentations, if necessary)

10. Lesson Plan Details – Day 1 • News Article Examples and Questions for Students Public Safety – Community A has reported 25 robberies during the past year, and Community B has reported 48 robberies within the past year. The population of Community B is more than twice as large as Community A. Which is the safer community? Do we need more information? If yes, then what additional information do we need? Politics – In Greene County, Newspaper A claimed that Barack Obama was supported by 48% of the vote; however, Newspaper B claimed that Barack Obama was supported by 53% of the vote. The mean percentage of the vote that supports Barack Obama in Greene country is 52% with a 5% percent error. Which newspaper is more accurate? Why wouldn’t a newspaper use the mean percentage? Why do you think there is there a difference in reporting between the newspapers? Weather – A local weatherman claimed that since there was a 50% chance of rain on Saturday and a 50% chance of rain on Sunday, then there was a 100% chance of rain for the weekend. Is this accurate? Consider the addition rule of probability P(A U B) = P(A) + P(B) – P(A ^ B). How do you think weathermen come up with the percentage chance of precipitation? Do you think they use mathematics to determine it? Traffic Violations – The New York State Police released its yearly percentages of speeding tickets on the NYS Thruway from Exit 17 to Exit 24. Drivers speeding between 66-70 mph were stopped 8% of the time; drivers speeding between 71-75 mph were stopped 17% of the time; drivers speeding between 76-80 mph were stopped 38% of the time; drivers speeding between 81-85 mph were stopped 67% of the time; and drivers speeding over 85 mph were stopped 95% of the time. How did the police officers collect this data? What does this data represent?

11. Lesson Plan Details – Day 1 (cont.) • General Questions -What kind of mathematics do you see in these examples? -How do you think that this information is gathered? -Are there different ways to present information using mathematics? -What other examples have you seen where the media uses mathematical evidence? -Can math in the media be presented objectively? Why or why not?

12. Lesson Plan Details – Day 2 • Group Directions (Given on Day 1, but applicable to Day 2) “You are a member of the Action 7 news team, and you have been asked to report on the public safety of Community X. Using mathematical evidence gathered in your research, you have been asked to report on the nature of public safety in your community on the Action 7 10 o’clock News next Thursday.   We will be spending a class in the computer lab to research the statistics that you will need for your mock news report which will occur next Thursday. This project will include a written summary of your news report, which will show all of the calculations of your gathered data, a “newscast” where you will present your information to the class, and an individual reflection to be handed in after the presentations. The summary should be no longer than 2 double-spaced pages, the presentation should between 8-10 minutes, and the individual reflection should be about 1-2 double–spaced pages. You are encouraged to present the information using any point of view that you’d like as long as your statistical evidence supports your argument. Be sure to think about: -Using percentages, proportions, areas, population densities, probability, and comparative statistics in your presentation (graphs are always helpful) -The message that you wish to convey based on your research -How you want to design your newscast • Your group will be graded on the following criteria for the written summary: mathematical accuracy, types of statistics used, and relevance. The summary should be clear and well written. The written summary will be worth 15 points and the presentation will be worth 15 points , while the reflection will be worth 20 points for a total of 50 points. Be creative, and good luck!”

13. Lesson Plan Details – Day 2 (cont.) • Statistical Sources U.S. Census Bureau http://factfinder.census.gov/home/saff/main.html?_lang=en U.S. Department of Justice http://www.ojp.usdoj.gov/bjs/ NYS Division of Criminal Justice Services http://criminaljustice.state.ny.us/crimnet/ojsa/stats.htm FedStats http://www.fedstats.gov/ • General Questions -What concepts do you need to keep in mind when collecting data? -What are the easiest pieces of information to look for? -What is the difference between good data and bad data?

14. Lesson Plan Details – Day 3 • Presentations Students who aren’t presenting will have the responsibility of evaluating those who are presenting based on the rubric we will be using to assess them, minus the participation criteria. Students will also be required to write a reflection about the presentation process and also on one of the other presentations and what message they thought that group was trying to convey. • General Discussion Questions After the Presentations -Were you surprised by the evidence that you found? -What do you think about how the media can use statistics to shape their own points of view? -Is the media always objective? -Will you interpret the statistics used in the media any differently after this project? -How can two different media organizations report on the same event, but send completely different messages? Why do you think they would do this? -What is the most important thing you learned about the media over the last three class periods?

15. Lesson Plan Details – Assessment • Written Summary Mathematical Accuracy 1 2 3 4 5 Variation of Statistics Used 1 2 3 4 5  Relativity to Presentation 1 2 3 4 5

16. Lesson Plan Details – Assessment (cont.) • Presentation Clear Representation 1 2 3 Use of Mathematical Evidence 1 2 3 Participation 1 2 3 Time 1 2 3 News Broadcast 1 2 3

17. Lesson Plan Details – Assessment (cont.) Written Reflection -Reflection on the production process will be worth 10 points. -Reflection on viewing another group’s presentation and writing about the meaning they got out of their presentation based on the statistics they presented will also be worth 10 points. Note: Both these parts will be written as one reflection, so the total amount of points for the reflection will be 20 points

18. Lesson Plan Relevance to Media Literacy This lesson plan gives students an opportunity to use mathematical evidence in order to create their own unique representations not unlike how the media creates representations for viewing audiences. Using representations is one of Buckingham’s key concepts, and this lesson plan can show students how statistical data can be used in a variety of ways to portray different points of view. In addition, Buckingham also mentions how simulations can be beneficial to students by giving them an opportunity to experience what an actual production would be like. Yes, there is no actual production equipment for this lesson plan. However, students are responsible for presenting a simulated local news broadcast based on the representations that they created. Since there is a tremendous amount of responsibility associated with representations that are distributed through mass media channels, students will need to carefully think about how they want to shape their presentation for their “audience”, another one of Buckingham’s ‘key concepts’. Integrating representations and simulation into this lesson plan is beneficial for students because they can appreciate the power and influence that the media has. Since students can use statistical evidence in any way that they choose, as long as it supports their representations, then they can see how the media can shape the message that they want to deliver by selecting specific information. By asking the follow-up questions at the end of Day 3, we feel that our students might question statistics in the media a bit more after this project based on their own research and experience.

19. NCTM Standards • The following are some of the NCTM Standards that will be followed in this lesson: • formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population • select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots. • find, use, and interpret measures of center and spread, including mean and interquartile range; • discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots. • use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken; • make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit; • use conjectures to formulate new questions and plan new studies to answer them. • understand and use appropriate terminology to describe complementary and mutually exclusive events; • use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations; • compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models. Source: http://standardstrial.nctm.org/document/chapter6/data.htm