Statistical Literacies for teaching
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# Statistical Literacies for teaching

Real-World Statistical Representations to aid teaching Math!
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## A Chicago Divided by Killings

A New York Times analysis of homicides and census data in Chicago divided the city into two groups: areas that are near homicides and those that are not.
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## How the Tax Burden Has Changed

Compare how much Americans paid in federal, state and local taxes over the past three decades.

There should be a large amount of student buy-in toward this artifact. Taxation and inequality are hot button political issues, but there is a colloquial misunderstanding of taxation. For a high school statistics course, students contact with elite material and gleaning understand from that material gets students excited about this artifact. Plus, students recognize that taxes are something that everyone is affected by. Taxes also add extra complexity to life, i.e. sales tax adding on cost to a product and income tax deduction on earnings on a paycheck. This complexity and lack of understanding opens up discussions about statistics that are authentic and interesting. Also, the type of tasks and discussions that is artifact creates fulfills the purpose of mathematics courses as Gutstein sees it. The artifact feeds community action and makes students question the social norms and understands around them. They have to confront a reality of a growing inequality and political movement toward less progressive taxation and less redistribution of wealth. They are directly affected by this through their experience at public school. Taxation is what funds their schools, and they should be made aware of who mainly funds their school, how that funding is changing, and what that means for their school.

The artifact itself requires a high degree of understanding of graphical representations of statistics. This artifact also presents a statistical argument in an unfamiliar way. Each prompt yields nine different graphs into one continuous representation with discrete parts. The artifact really features sixty-three different graphs. Each graph though has the similar y axes and the same x axis. This shows that a multitude of different statistical data can be shown similarly to make different types of arguments. The orientation of the graphs in relation to each other contributes to the statistical and political arguments by showing how different statistics orient upward or downward as income increases. There are three clear arguments that these graphs are making. First and most apparent is that the wealthier someone is he pays a higher percentage of his income to taxes. Second, there is a comparison of income taxes which have fallen vs. local taxes that have risen. Here in lies the main argument about in equality. These graphs show that local taxes burden the less wealth, so the burden of taxes has increased for the poorest relative to the wealthiest. Finally, the first graph shows that overall taxes have fallen across all groups. This is important to see because the statistical consumer needs to ask why the data are presented in a certain and why certain data are presented.

These graphs are really good to use because they open up the opportunity to talk deeply both about graphical literacy and politico-social issues. This can make statistics more appealing to students and give them access into understanding statistics. Even having the social discussion could lead to delving deeper into the meaning of the graphs and statistical arguments which I think makes this very robust. A good way to scaffold this is to get student input into their knowledge of taxation and inequality before presenting the graphs. It would be interesting to see which of their conceptions they believe about taxes are confirmed by the graphs and which are debunked by the graphs. This would help lead toward the goal of having students be able to make arguments for themselves using statistics. Again, these graphs lead to very rich discussions about statistics as long as student can make meaning out of the graphs which might be difficult considering the complexity of the representations.

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## Votes and prayers

How the presidential vote split along religious linesIN THE aftermath of Barack Obama's victory, much analysis has focused on how the president's appeal to...
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## Graphic detail

About Graphic detail -- On this blog we publish a new chart or map every working day, highlight our interactive-data features and provide links to interesting...
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## 512 Paths to the White House

Explore the routes through the electoral battleground and plot victory for either side.
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## Assessing Damage From Hurricane Sandy

More than six million customers lost power Monday as Hurricane Sandy felled trees, downed power lines and flooded substations.
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## New York City Hurricane Evacuation Zones

There are three evacuation zones in New York City that are based on the strength of the hurricane making landfall. Mayor Bloomberg has issued a mandatory evacuation of Zone A.
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## The Electoral Map - Presidential Race Ratings and Swing States - Election 2012 - NYTimes.com

A look at the battleground states in the 2012 presidential race.
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## Over the Decades, How States Have Shifted

A look at how the states stack up in the current FiveThirtyEight forecast and how they have shifted over past elections.
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## Explore Government Subsidies

Search and browse a database of business incentives awarded by hundreds of cities, counties and states compiled during a 10-month investigation by The New York TImes.

What is good about this artifact is that it is good to step back and appreciate that tabular representations are often the best way to display some statistical information. It is important to remember that the statistics is mostly presented in a raw tabular way like this artifact. For students to be statistically literate they need to be able to glean meaning from statistics presented this way. It is key for a teacher though to find a way to reach to students’ interest so that they can be engaged in the work of interpreting tabular or raw data. That is another reason why this artifact is good because where the representation is a bit boring the subject matter is interesting. The table is not completely boring; it does have the nice logos to depict the different companies. The real strength is the subject of corporate subsidy. It is a topic that gets a lot people’s goat. Students in a high school statistics course who are presented with this artifact would feel indignation about the amount of “corporate welfare.” Teenagers are very good at and fond of being indignant; so, this artifact leaves the door open for them to deeply engage in the statistical work involved with this artifact. Also, this is another artifact where a discussion about social justice is appropriate in examining the statistics.

This artifact allows students to look at data about corporate subsidies in tables. They can look at the data of different companies and state-by-state data about it. It allows users to adjust the order the data is presented in by different variables. There are tidbits of different data that pop-up. Tasks from this would have to involve how students are able to make sense of all this data. They could explain in their own words what a table about a company truly represents. For example, they could look at the table for General Motors and explain that they receive large subsidies from Michigan and other states and that these subsidies tend to be property tax breaks and free labor training by the states. In this same vein, a task for student s could be for them to create their own representations for a few companies or a few states. For example, they could create bar graphs that compare and contrast the percent of state budget going to subsidies between a northeastern state vs. a state in the southern plains. Since there is a lot of data, the point of any task would be for students to create their own statistical stories complete with their own representations to build their statistical arguments. This all can be leveraged toward discussions about how to make statistical arguments and about social justice.

The difficulty with this artifact is that it would require explanations of terms and meaning of what subsidies are and what they do. This is a clear difficulty, but the statistical analysis itself might lead to students finding meaning. For example, the question of why would states give subsidies could be parsed out through comparing the type of companies states subsidize. An industrial state like Michigan subsidizes car manufacturers whereas an agricultural state like South Dakota subsidizes meatpacking and fertilizer companies. Seeing what representations and arguments students come up with in a whole class discussion could bring out many of these issues and help explain a lot of what this all means.

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## StatsLab - Stats on NFL.com

NFL Stats Lab is a visual exploration of stats for players and games. Find passing leaders, rushing leaders, receiving leaders, sack leaders, tackling leaders and interception leaders.

This artifact would be fun for students who are football fans. It is a really cool program that allows comparison between players across multiple variables. It is relevant to the time at hand because, when someone clicks on it, it shows a comparison relevant to a game that day or week. For example, tonight it compared the running back in the Monday Night Football game, Arian Foster and Stevan Ridley. Kids who are sports fans love to argue about who is the best player. This creates buy-in for those students because they have a statistical representation that gives them fodder for their arguments. Monday morning quarterbacking can become an opportunity to conceptualize statistical ideas with this artifact.

The statistical literacy that this artifact potential engrains is creating a critical eye for how representations are presented and how statistics is presented. This artifact has a circle with different variables surrounding it. The circle represents the number of who has the most of that statistic. For example, Adrian Peterson has the most rushing yards, 1600; so, the area for another player is set in relation to 1600. So, presumably the larger the shaded area for a player the better they are. Clearly, this is very confusing and potential unreliable. Students should develop suspicion about the representations. Discussions of comparing two players lead to asking what should each statistic be weighted evenly on these, does it show the true relation between these players, and what do the numbers mean on this representation. The artifact gets students interested, but the problems with it forces students to really question how robust are these representations in actually showing the real numbers.

There is a cultural bias with this representation. It could not be used in a class where the majority of students do not care about football because then the buy-in is lost. The context would have to be set up so that all students can approach these representations.

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## As Nation and Parties Change, Republicans Are at an Electoral College Disadvantage

Even if Mitt Romney had won the popular vote by two percentage points, President Obama would still have won the Electoral College.
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## Money, votes and imponderables

A map of swing-state campaigningIT IS difficult to gauge the effectiveness of advertising and campaign visits during a presidential campaign. Vast sums have been...
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## A Close Look at Power Failures in New York City

Hurricane Sandy knocked out power to hundreds of thousands of people in the New York City area. Data updated every 15 minutes.
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## Climate change on political 'back burner'

President Barack Obama and former Massachusetts Gov. Mitt Romney haven't been saying much about climate change during the presidential campaign, but experts say the problem is only getting worse.
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## Map of Hurricane Sandy’s Path

Follow the path of the storm and the five-day forecast.
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## Election Forecasts - FiveThirtyEight Blog - NYTimes.com

FiveThirtyEight is devoted to rigorous analysis of politics, polling, public affairs, sports, science and culture, largely through statistical means.
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## One Report, Diverging Perspectives

Friday’s jobs report is the second-to-last of the presidential campaign.

This article and these representations got my attention because they do some interpretational footwork for the keen statistical eye.  These graphs point out that data and graphs can be manipulated to make diametrically opposing political arguments.  A democratic viewpoint sees the graphs tell a story of job growth, whereas a republican viewpoint sees the graphs tell a story of consistently high unemployment.

For a statistics course, I think this article and graph can first be used to teach graphical literacy.  Students must be able to interpret the graphs, like understanding what the x and y axes stand for, interpreting bar graphs and line graphs data, and contrasting bar graphs and line graphs.  It would be interesting to have students then to interpret the data for themselves.  The students could tell their own story about the data and graph.  After that, the republican and democrat viewpoints could be revealed and students could examine how compelling the political arguments are and how they measure up against their own argument.  This all leads to a larger statistical lesson about how statistics are presented.  The same data and graphs can be used to make completely different and even opposing arguments.  This gives students motivation and builds skill to become mindful statistical consumers.

What might be difficult with this article is to present the contextual framework for these students, especially since this is more for the realm of civics or political science class.  Nevertheless, it would be important to explain that these data are coming out in an election year where each party wants to win the election.  The democratic party is in power and wants it to look like their policies have led to economic and job growth.  Conversely, the republicans want to cede power from the democrats by winning the election so they want it to seem like democratic policies have led to economic stagnation and slow job growth.

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