Measuring Income Inequality in Elementary and High School

Charles Collingwood, Cassidy Larkin, Victor Piercey,and Jordan Schettler, G-TEAMS, University of Arizona

Who are We?Who are We?• Charles CollingwoodCharles Collingwood: Stats, Precalculus, : Stats, Precalculus,

and AP Calculus Teacher at Rincon High and AP Calculus Teacher at Rincon High School.School.

• Jordan SchettlerJordan Schettler: Math Ph.D. Student at : Math Ph.D. Student at University of Arizona.University of Arizona.

Who are We?Who are We?• Cassidy LarkinCassidy Larkin: Fifth Grade Teacher at : Fifth Grade Teacher at

McCartney Ranch Elementary SchoolMcCartney Ranch Elementary School

• Victor PierceyVictor Piercey: Math Ph.D. Student at : Math Ph.D. Student at University of Arizona.University of Arizona.

GK-12 program housed in the UA Math GK-12 program housed in the UA Math Department.Department.

G-TEAMS stands for Graduate Students and G-TEAMS stands for Graduate Students and Teachers Engaging in Mathematical Teachers Engaging in Mathematical Sciences.Sciences.

McCartney Ranch McCartney Ranch ElementaryElementary

Located in Casa Grande, AZ.Located in Casa Grande, AZ. 1 of 9 elementary schools in the District.1 of 9 elementary schools in the District. High population of English Language High population of English Language

Learners.Learners. Increasing population of “exceeds” math Increasing population of “exceeds” math

students.students. Title I school with about 650 students, Title I school with about 650 students,

about 70% of students are receiving about 70% of students are receiving free/reduce lunch rates.free/reduce lunch rates.

Income Inequality Data Income Inequality Data AnalysisAnalysis

Each table has a piece of paper with some Each table has a piece of paper with some data and a sheet of graph paper.data and a sheet of graph paper.

Make a graph (bar, line, circle, etc.) to Make a graph (bar, line, circle, etc.) to represent this data.represent this data.

Identify any features or trends your graph Identify any features or trends your graph illustrates.illustrates.

Using ExcelUsing Excel

In the computer lab, students learned In the computer lab, students learned rudiments of Excel.rudiments of Excel.

For example, they:For example, they:

(i) entered data;(i) entered data;

(ii) used auto-sum;(ii) used auto-sum;

(iii) entered formulas; and(iii) entered formulas; and

(iv) made various types of graphs. (iv) made various types of graphs.

Is $20,000 per year a Is $20,000 per year a lot?lot?

Fifth grade students analyzed a monthly Fifth grade students analyzed a monthly budget forbudget for

local expenses.local expenses.

Income Distribution in 2009:Income Distribution in 2009:Sample OneSample One

Income Distribution in 2009:Income Distribution in 2009:Sample TwoSample Two

Income Distribution 1969-2009:Income Distribution 1969-2009:Sample OneSample One

Income Distribution 1969-2009:Income Distribution 1969-2009:Sample TwoSample Two

Poverty Rates: 1969 – 2009Poverty Rates: 1969 – 2009Sample OneSample One

Poverty Rates: 1969 – 2009Poverty Rates: 1969 – 2009Sample TwoSample Two

Sample Responses to QuestionsSample Responses to Questions

Question: Look at your graph and Question: Look at your graph and describe why some people say that describe why some people say that “the rich are getting richer and the “the rich are getting richer and the poor are getting poorer.” poor are getting poorer.”

Response: Response: Because the bottom goes Because the bottom goes down and the top goes up.down and the top goes up.

Response: Response: Because throughout the years Because throughout the years the top 5 starts and is getting a larger the top 5 starts and is getting a larger increase than the bottom 20.increase than the bottom 20.

Sample Responses to QuestionsSample Responses to Questions

Question: What do you think can be Question: What do you think can be done in order to make this line graph done in order to make this line graph (for poverty rates) decrease between (for poverty rates) decrease between 2009 and 2014? 2009 and 2014?

Response: Response: I think we could help the I think we could help the homeless and hungry get money.homeless and hungry get money.

Response: Response: More people should leave the More people should leave the United States.United States.

StandardsStandards

Collect, record, organize and display data.Collect, record, organize and display data.

Formulate and answer questions by Formulate and answer questions by

interpreting displays of data.interpreting displays of data.

Describe patterns of change.Describe patterns of change.

Summarize mathematical information.Summarize mathematical information.

ReflectionsReflections

The real-world application along with the The real-world application along with the use of real world data was a great use of real world data was a great motivator for students!motivator for students!

Some students who had been previously Some students who had been previously unengaged became enthusiastic. The unengaged became enthusiastic. The context led to student “buy-in”.context led to student “buy-in”.

When brought back to first principles and When brought back to first principles and properly motivated, young students can properly motivated, young students can understand fairly complicated concepts.understand fairly complicated concepts.

This type of activity is very difficult to fit This type of activity is very difficult to fit within every-day teaching constraints.within every-day teaching constraints.

Reflections Reflections (continued)(continued)

Students tended to not think about meaning Students tended to not think about meaning after they finished making the graph.after they finished making the graph.

Some students didn’t understand that they Some students didn’t understand that they had to read their instructions in order to had to read their instructions in order to know what to do next.know what to do next.

Some students had trouble understanding Some students had trouble understanding when to use their instructions and when to when to use their instructions and when to use their data sheet.use their data sheet.

Rincon High SchoolRincon High School

Located in Tucson, AZLocated in Tucson, AZ 1 of 22 high schools in TUSD1 of 22 high schools in TUSD Rincon qualifies as Title I, but is not Rincon qualifies as Title I, but is not

receiving fundingreceiving funding DemographicDemographics: s: 48.5% Hispanic, 48.5% Hispanic, 34.1% 34.1%

White, 9.0% African American, 6.7% Asian White, 9.0% African American, 6.7% Asian American, 1.3% Native American, 0.4% American, 1.3% Native American, 0.4% MultiMulti

Significant % of free/reduced lunchSignificant % of free/reduced lunch

Mathematical Practices in the Mathematical Practices in the New Common Core StandardsNew Common Core Standards

1.1. Make sense of problems and persevere in solving them. Make sense of problems and persevere in solving them.

2.2. Reason abstractly and quantitatively.Reason abstractly and quantitatively.

3.3. Construct viable arguments and critique the reasoning of others.Construct viable arguments and critique the reasoning of others.

4.4. Model with mathematics.Model with mathematics.

5.5. Use appropriate tools strategically.Use appropriate tools strategically.

6.6. Attend to precision.Attend to precision.

7.7. Look for and make use of structure.Look for and make use of structure.

8.8. Look for and express regularity in repeated reasoning.Look for and express regularity in repeated reasoning.

Interpolating Lorentz CurvesInterpolating Lorentz Curves

The Gini Coefficient The Gini Coefficient GG

Computing Gini CoefficientsComputing Gini Coefficients

Point of Maximal Inequality Point of Maximal Inequality (POMI)(POMI)

Point of Maximal Inequality Point of Maximal Inequality (POMI)(POMI)

The POMI is a min of The POMI is a min of LL((xx) - ) - xx

Tracking the POMITracking the POMI

DiscussionDiscussion In most schools today, teachers have In most schools today, teachers have

constraints. Curriculum calendars and constraints. Curriculum calendars and scripted curricula do not leave students scripted curricula do not leave students with the opportunity to have in depth with the opportunity to have in depth exploration time. Are we producing exploration time. Are we producing tomorrow’s problem solvers?tomorrow’s problem solvers?

What kinds of ideas do you have that could What kinds of ideas do you have that could turn into a possible project that relates to turn into a possible project that relates to real world problems, yet that have fidelity real world problems, yet that have fidelity to school districts?to school districts?

ELEMENTARY: LEFT SIDE OF ROOM.MIDDLE AND HIGH: RIGHT SIDE.