Mathematics in the World
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# Mathematics in the World

Curated by Matt Perry
 Rescooped by Matt Perry from Math in the World

## What Americans Actually Do All Day Long, In 2 Graphics : NPR

Working, sleeping, cooking, watching TV. Here's what the average American does on a typical day, down to the second.

The artifact “What Americans Actually Do All Day Long” captured our attention because it is a simple concept that draws comparative interest. This will engage secondary students because it is very relatable. This artifact also provides an opportunity to be recreated by students. We envision students evaluating how they spend their own time and creating their own statistical representation of the breakdown. Students could also collect data and create a representation for the entire class. Incorporating percentages would also be useful in discussing the percentage of the day spent participating in a specific activity.

The mathematical and statistical literacies required for reading this artifact include visualizing the relationship among the bubbles in terms of their area. Ratio and proportion play an important role in the size of the bubbles, so students must be able to evaluate if the area and corresponding time are represented accurately. The given bubbles represent an average, so students have the opportunity to compare their own activities to how it relates to the average. A critical disposition is also valuable in asking how this data was collected and who it was collected from in terms of age, gender, occupation.

Some students may struggle with the conversion of time, which is broken into 60 seconds for 60 minutes in 24 hours, to a percentage. Finding this proportion is necessary to calculate the relative area of each bubble. Lingering questions about this artifact could include the meaning of the coloring and specific breakdown of other activities. Contextual knowledge for this artifact revolves around the definition of categories or specific activities if students are unfamiliar with them.

Via BellaSmith, Shelby Crandall, Melissa Martens
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 Rescooped by Matt Perry from Math Education ---Statistics

## Where the living is easier

This artifact caught our attention because of the visually interesting way that the data is presented and because of the globally relevant context that might spark interesting discussions. This artifact ranks cities across the globe according to their competitiveness with respect to several variables—economic strength, physical and human capital, financial institutional strength, and social, environmental and global appeal. In addition to interesting mathematics, this artifact presents information that might be relevant in a social studies or economics course; therefore, this could be very useful for teachers interested in interdisciplinary activities.

Understanding this artifact allows students to explore the idea of ratio in a visual sense. In the bar graph, each city’s competitiveness rating is shown so that the contribution of each variable can be easily seen. This gives students the opportunity to see ratios in a purely visual form, and the data on the graph can be calculated to support those visual understandings. For example, the contribution of each variable for Paris appears roughly the same. This would help support an understanding of ratios that involve more than two parts. In addition to ratios, a scatter-plot shows the relationship between each city’s cost of living and overall competitiveness. This portion of the artifact could introduce students to the idea of linear regression. Students could explore ways to find a line that best approximates each of the data points. This could also involve a discussion involving the reliability of the line found.

Students might need an overview of what exactly is meant by competitiveness and how each of the variables considered are defined and measured. It may also be necessary to pay attention to some of the cities listed because many students may not be familiar with their location.

Via Sarah Betack
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 Scooped by Matt Perry

## HIV in the United States

This is a great example of an artifact that addresses serious issues in our communities. The Department of Health and Human Service has created a website specifically for HIV/AIDS information and awareness, and this page provides interesting data regarding rates of infection among different groups of individuals. There are lots of interesting mathematical and statistical concepts embedded in the webpage that a teacher could use while studying the timely and relevant problem of HIV infection.

One of the most interesting mathematical aspects of this artifact is the rate of infection--every 9.5 minutes someone in the U.S. is infected with HIV. This raises interesting questions regarding rates of change and opens the door for exploring this rate with respect to different units. In addition to the rate of infection, this page provides the stunning statistic that 1 in 5 people are unaware of their status. This statistic is related to the rate of infection provided and could lead to interesting activities exploring how these two quantities relate. For example, students could create a new rate indicating the number of people becoming infected but are unaware. This might lead to interesting and culturally relevant discussions of how the decrease in the awareness rate could decrease the overall infection rate. In addition to rates of change, there are interesting representations of proportions. For example, the bar graph has opportunities for comparing the infection rates with respect to different groups of people according to race, gender, and ethnicity.

The only drawback to using this artifact might be that this topic may be considered controversial in certain schools. Understanding this artifact requires knowing certain acronyms such as MSM or IDU (men having sex with men and injection drug users). Therefore, in certain schools, some teachers might feel uncomfortable introducing this topic. However, in many schools, particularly urban schools, this topic is highly relevant to the students and to the communities in which they live.

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 Rescooped by Matt Perry from Math in the World

## Tracking American Poverty & Policy

With this interactive data visualization users can parse 40 plus years of Census data and see the effect of policy on poverty in America.

This artifact is initially attention grabbing because the topic of tracking American poverty and policy is socially relevant, important, and controversial. Looking deeper, the visualization demo is even more engaging because it is interactive. This artifact allows the user to delve into each statistical argument by focusing in on specific aspects of race, gender, education, age, and family type. We believe the interactive quality and social significance of this topic will engage secondary students.

The statistical representations in this artifact focus on pie charts and bar graphs while the mathematical content is focused on percentage. As students explore this artifact they can zoom in to look at the percentage of people in poverty, in deep poverty, and near or in poverty for a specific demographic. The ways these percentages are overlaid in the pie chart and separated in the bar graph provide an opportunity for students to compare different statistical representations. It is important for students to know how to interpret these percentages in relation to one another.

Students may require some contextual knowledge about poverty and desire to do further research about what it means for someone to be in poverty, especially how it has been defined quantitatively from year to year. This is a real world issue so students may relate to poverty and the demographic break downs differently. However, it is a worthwhile and useful context in which to see the presence of mathematics and statistics.

Via Melissa Martens
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 Rescooped by Matt Perry from Math in the World

## Sizing Up The American Dream : NPR

In a nation as diverse as the United States, the idea of "the American dream" means different things to different people. Many associate the dream with intangible ideals like freedom of expression, freedom of religion, optimism and family ties.

The “Sizing up the American Dream” artifact caught our attention because it encompasses a variety of mathematical and statistical concepts with a socially relevant context. We believe this would engage secondary students by tapping into student’s opinions and personal goals or hopes for the future. By applying quantitative analysis to a very ambiguous and qualitative topic, students can apply mathematical reasoning to any situation.

Many mathematical and statistical literacies are used when reading or remixing this artifact including critically interpreting visual representations of data and reading various charts and graphs (100% stacked area chart, donut charts, line charts, pictograph charts). The mathematical/statistical concepts in this artifact encompass average, median, percentages, change over time, rate of change, and statistical trends. The variety of representations used in this artifact provide an opportunity for classroom use where students could work in pairs or small groups to investigate one of the five areas described in the artifact. Students could spend time investigating their topic and deciding if the representations are correct. Using the listed sources of data, such as the U.S. Census Bureau, students could compare the statistics listed for to their own state or investigate the statistics for a different year. Students would then present the original representations to the class along with a representation they have created on their own, describing the pros and cons of each one.

In order to engage with this artifact productively, students must have some contextual knowledge about the concept of the “American Dream.” Teachers may want to briefly discuss the history of “American Dream” and elicit student input about their definitions. This artifact contains a variety of terms that may need to be defined for students to have an accurate understanding of the context such as educational attainment, average student loan balance, total tuition and room and board, household median income, living below the poverty level, personal saving rate. This topic could be used in conjunction with a social studies course as well. One concern would be causing classroom division for students whose families identify with achieving or not achieving “American Dream” as it is described here. However, we think this would be a great opportunity to have discussions about personal values compared to the values of society. Students would have to reason and justify their arguments, which would serve to support communication of mathematical ideas in the classroom and aid in the development of a positive mathematical disposition.

Via Melissa Martens
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 Rescooped by Matt Perry from Math in the World

## Statistical Review of World Energy 2012 | BP

The BP "Energy in Numbers" video captured our attention because it is visually appealing. The continuous flow of information accompanied by music hold the attention of the viewer. The dynamic images complemented the text description of trends and made the data easier to understand. The information is timely and relevant to current global events related to energy. We believe this would engage secondary students by drawing on students’ imaginations though the representations and connecting to relevant societal discussion about energy, current events, and climate issues.

This video would be a wonderful introduction to a unit about statistical literacy. After stimulating student interest with this introductory video, students could work in groups to investigate a specific topic or trend in energy of their choice presented in the video summary. The printed edition of the 2012 Statistical Review could be utilized as a resource to support student research and develop statistical literacies.

Many mathematical and statistical literacies can be applied to this artifact. Some of these literacies include reading charts and graphs and critically interpreting visual representations of data. The mathematical concepts of percentages, percent change, and rate of change are key factors in this statistical review. In order to engage with this artifact productively, students may need to do further research on different types of energy and the impact of world events on production or consumption. Familiarity with basic energy terms and measurements is also necessary. As students investigate the data, questions of causation can spur further analysis.

Via Melissa Martens
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