Sustainability Math A Quantitative Literacy and Mathematics Resource for Instructors

Propublica’s article, Miseducation – Is There Racial Inequality at Your School? by  Lena V. Groeger, Annie Waldman and David Eads, (10/16/18), provides data by state on the percent of nonwhite students, the percent of students who get free/reduced-price lunch, high school graduation rate, the number of times White students are likely to be in an AP class as compared to Black students, and the number of times Black students are likely to be suspended as compared to White students. The comparison is also available for Hispanic students.

The graph here was created with their data and compares the percent of students on free and reduced lunch with the number of times Black students are likely to be suspended  compared to White students (state data isn’t available for HI, ID, MT, NH, NM, OR, UT, or WY).  The red lines uses all the data where as the blue line removes the outliers of DC and ND. The blue regression line has a p-value of 0.012 and R-squared of 0.15.  This suggests that wealthier states, as measured by free and reduced lunch programs, have a greater disparity is suspensions between black and white students. The impact of outliers is instructive here and there are other scatter plots worth graphing from the article. There are also statistics projects waiting to be created with this data.

The article also has an interactive map or racial disparities by districts, but the map can be misleading based on missing data from districts. Can you see how?  This makes the map itself useful for QL courses.  R Script that created this graph. Companion csv file.

The EPI article,  Student absenteeism – Who misses school and how missing school matters for performance by Emma García and Elaine Weiss (9/25/18) provides a detailed account of absenteeism based on race and gender.  For example, their chart here is the percent of students that missed three or more days in the month prior to the 2015 NAEP mathematics assessment. There are noticeable differences. For instance, the percentage of Black, White, and Asian (non ELL) that missed three or more days in the month is 23%, 18.3%, and 8.8% respectively.

Why does this matter?

In general, the more frequently children missed school, the worse their performance. Relative to students who didn’t miss any school, those who missed some school (1–2 school days) accrued, on average, an educationally small, though statistically significant, disadvantage of about 0.10 standard deviations (SD) in math scores (Figure D and Appendix Table 1, first row). Students who missed more school experienced much larger declines in performance. Those who missed 3–4 days or 5–10 days scored, respectively, 0.29 and 0.39 standard deviations below students who missed no school. As expected, the harm to performance was much greater for students who were absent half or more of the month. Students who missed more than 10 days of school scored nearly two-thirds (0.64) of a standard deviation below students who did not miss any school. All of the gaps are statistically significant, and together they identify a structural source of academic disadvantage.

These results “… identify the distinct association between absenteeism and performance, net of other factors that are known to influence performance?”  The article has 12 graphs or charts, with data available for each, including one that reports p-values.

The is too much in the new IPCC report (released this week) to cover here, but we can highlight a couple of points. The first is their graph copied here.  The main graph provides projections for change in global temperature based on what happens to CO2 and non-CO2 radiative forcing gasses.  For example, if net CO2 emissions reach zero by 2055 (CO2 emitted minus CO2 absorbed graph b) and non-CO2 gases are reduces (graph d), then we are likely to stay below the 1.5 °C threshold.  What the graph does not say is what happens if society does nothing.

We recently posted about see level and here is an excerpt from the report about that:

Model-based projections of global mean sea level rise (relative to 1986-2005) suggest an indicative range of 0.26 to 0.77 m by 2100 for 1.5°C global warming, 0.1 m (0.04-0.16 m) less than for a global warming of 2°C (medium confidence). A reduction of 0.1 m in global sea level rise implies that up to 10 million fewer people would be exposed to related risks, based on population in the year 2010 and assuming no adaptation (medium confidence). {3.4.4, 3.4.5, 4.3.2}

The executive summary and/or the graphs could be used in QL rich courses.

The Pew Research Center’s article Partisans are divided over the fairness of the U.S. economy – and why people are rich or poor by Amina Dunn (10/4/18) provides interesting results about perceptions of our economic system.

The article lends itself to interesting questions. Why is there such a divide? Can both sides be correct or is the economic system either fair or not?  A student project could focus on trying to answer the question of whether or not our economic system is fair. There are three other graphs in the article regarding the partisan divide on why people are rich or poor.

NASA’s Vital Signs of the Planet feature,  Keeping score on Earth’s rising seas by Pat Brennan (9/1918) summarizes a recent paper that  “ ‘closes’ the sea-level budget to within 0.3 millimeters of sea-level rise per year since 1993.”

A just-published paper assembles virtually all the puzzle pieces – melting ice, warming and expanding waters, sinking coastlines and a stew of other factors – to arrive at a picture of remarkable precision. Since 1993, global sea level has been rising by an average 3.1 millimeters per year, with the rise accelerating by 0.1 millimeter per year, according to the study published Aug. 28 in the journal, “Earth System Science Data.”

“Global mean sea level is not rising linearly, as has been thought before,” said lead author Anny Cazenave of France’s Laboratory for Studies in Geophysics and Oceanography (LEGOS). “We now know it is clearly accelerating.”

The above paragraphs can be used as calculus in the news and sea level data is available from NASA’s Sea Level page.

The World Bank report, New child and adolescent mortality estimates show remarkable progress, but 17,000 children under 15 still died every day in 2017, by Emi Suzuki and co-author Haruna Kashiwase ( 9/18/18) provides a summary, as well as a number of charts. The good news:

There has been remarkable progress in reducing mortality among children and young adolescents in the past several decades. Between 1990 and 2017, the global under-five mortality rate dropped by 58 percent from 93 deaths per 1,000 live births to 39 deaths per 1,000 live births. During the last 17 years, the reduction in under-five mortality rates accelerated to an average 4% annual reduction, compared to an average 1.9% annual reduction between 1990 and 2000. For children aged 5-14, mortality dropped by 53 percent, from 15 deaths to 7 deaths per 1,000 children.

At the same time there is work to be done:

However, while a substantial reduction from the 14.3 million in 1990, an estimated 6.3 million children under age 15 still died in 2017, mostly from preventable causes.

The charts on the page are interactive but can’t be downloaded. On the other hand, the data is easily available and charts can be made for download. The chart here was made at the World Bank’s DataBank.  Note that the European Union has a lower under 5 mortality rate than the U.S. There are numerous variables to choose. Data can be downloaded and charts for download can be highly customized.

According to the Climate Central post, Fall Warming Trends Across the U.S. (9/5/18), the average fall temperature for the U.S. has risen nearly 3°F since 1970 (see their graph copied here).  Why does this matter:

Insects linger longer into the fall when the first freeze of the season comes later in the year. A new study from the Universities of Washington and Colorado indicates that for every degree (Celsius) of warming, global yields of corn, rice, and wheat would decline 10 to 25 percent from the increase in insects. Those losses are expected to be worst in North America and Europe.

The article has a drop down menu to select cities across the U.S. to see a graph similar to the one copied here for the selected city.  They don’t post the data that was used to create the graphs but they do explain their data sources under methodology.

A statistics project could have students create this graph for their hometown.  One way to obtain the data was noted in our post, What do we know about nighttime minimum temperatures?: Go to  NOAA’s Local Climatological Data Map. Click on the wrench under Layers. Use the rectangle tool to select your local weather station. Check off the station and Add to Cart. Follow the direction from their being sure to select csv file. You will get an email link for the data within a day.  Note: You are limited in the size of the data to ten year periods. You will need to do this more than once to get the full data set available for your station.

NASA’s Vital Signs of the planet post, Scientists ID three causes of Earth’s spin axis drift (9/19/18) explains changes in the spin axis.

Earth is not a perfect sphere. When it rotates on its spin axis — an imaginary line that passes through the North and South Poles — it drifts and wobbles. These spin-axis movements are scientifically referred to as “polar motion.” Measurements for the 20^th century show that the spin axis drifted about 4 inches (10 centimeters) per year. Over the course of a century, that becomes more than 11 yards (10 meters).

In general, the redistribution of mass on and within Earth — like changes to land, ice sheets, oceans and mantle flow — affects the planet’s rotation. As temperatures increased throughout the 20^th century, Greenland’s ice mass decreased. In fact, a total of about 7,500 gigatons — the weight of more than 20 million Empire State Buildings — of Greenland’s ice melted into the ocean during this time period. This makes Greenland one of the top contributors of mass being transferred to the oceans, causing sea level to rise and, consequently, a drift in Earth’s spin axis.

The article explains why the Greenland Ice sheet has such an impact. NASA has also produced an interactive simulation on how different processes contribute to the wobble. There could be a nice vector calculus, linear algebra, or geometry exercises here.

Wage growth has varied depending on numerous factors such as gender, race, income level, and education. The EPI article,  America’s slow-motion wage crisis-Four decades of slow and unequal growth by John Schmitt, Elise Gould, and Josh Bivens (9/13/18) summarizes the findings with 30 graphs or tables (data included). For example, the cumulative percent change in inflation-adjusted hourly wages for workers in the 10th, 50th, and 90th percentile is given in the graph here (downloaded from the article).

The first key trend since 1979 is the historically slow growth in real wages. In 2017, middle-wage workers earned just 16.8 percent more than their counterparts almost four decades earlier. This corresponds to an annualized inflation-adjusted growth rate over the 38-year period of just 0.4 percent per year. The real wage increase for low-wage workers (those at the 10th percentile) was even slower: 8.9 percent over 38 years, or a 0.2 percent annualized growth rate.

This slow growth is particularly disappointing for two reasons. First, as we will see in the next section, U.S. workers today are generally older (and hence potentially more experienced) and substantially better educated than workers were at the end of the 1970s.10 Second, for workers at the bottom and the middle, most of the increase in real wages over the entire period took place in the short window between 1996 and the early 2000s. For the large majority of workers over the last four decades, wages were essentially flat or falling apart from a few short bursts of growth.

Quiz Questions: What was the cumulative change in hourly wages from 1979 to 2017 for

1. What was the cumulative change in hourly wages from 1979 to 2017 for workers with an advanced degree?
2. What was the cumulative change in hourly wages from 1979 to 2017 for workers with less than a high school diploma?
3. Which ethnic group had the greatest change?
4. What was the cumulative change in hourly wages from 1979 to 2017 for Women in the 50th percentile?
5. What was the cumulative change in hourly wages from 1979 to 2017 for Men in the 50th percentile?

The article and/or corresponding data is ready for use in a stats or QL course in the 90th percentile.

Answers: (1) 30.0% (2) -9.6% (3) Asian American/Pacific Islander non-Hispanic 23.3% (4) 33.8% (5) 8.1%.

The answer to the question depends on how it is measured.  The post  in statista, The Countries Spending the Most on Education by Martin Armstrong (9/12/2018) reports spending as a share of gross domestic product for primary, second and post-secondary non-tertiary education as well as tertiary education.  By this measure Norway spends the most. But, if the measure used is expenditure per student as a share of GDP per capita, the high spender is (south) Korea (Norway is fifth). Our graph here is a scatter plot of the two measures by country.

The data is from OECD.Stat. Go to Education and Training, Education at a Glance, Financial resources invested in education, Education finance indicators, and finally Expenditure per student as share of GDP per capita.  Under indicator at the top of the spreadsheet the measure can be changed.  Definitions of measures can be found in the OECD Handbook for Internationally Comparative Education Statistics (page 99).

Download the csv file and R-script used here.