Friday, December 18, 2020

Book Club: High School Mathematics Lessons to Explore, Understand and Respond to Social Injustice

Hi team,

We* are currently reading High School Mathematics Lessons to Explore, Understand and Respond to Social Injustice (Berry, Conway, Lawler and Staley 2020).

We divided ourselves into two breakout groups by content area: (1) Algebra & Functions, (2) Statistics & Probability. Each group is choosing a lesson to analyze in more detail.

The book emphasizes, Content Matters, Context Matters, When Matters, and How Matters.

I appreciate that Critical Mathematics Education has been included alongside Standards-Based Mathematics Instruction (SBMI), Complex Instruction (CI) and Culturally Responsive Pedagogy (CRP).

Any teachers planning to do this kind of work must attend to power dynamics and status differences in their class. Expect contributions from each and every student. Leverage students' cultural funds of knowledge. Pursue generative themes that come from dialogues with students. These skills are difficult to obtain. The authors have provided a great primer for folks seeking educational equity and social justice.

The stats+prob group chose to analyze, "Do Postal Codes Predict Test Scores?" (pp. 182-187)

I did the lesson for myself below.

1) Access

What do you notice?

- I notice that CA no longer releases SAT averages - scores are from 2016
- Average scores range from roughly 800 to 1300 (low: 746, high:1374)
- Lower income seems to score lower in L.A., Houston and Boston.

What do you wonder?

- I wonder how the size relates to the number of students for the school.
- What these data tell us?
- What can we do about it?
- How do we measure what we value rather than value what we measure?

2) Explore

What data do I want to analyze?

I am interested in which correlation is stronger: scores ~ income or scores ~ adult education. I am interested in building a model with all of the available features and seeing which describes the majority of the variability in test scores.

Create a table of data points (by hand?!)

Collecting values by hand seems ridiculous given modern tech. I'd prefer to access to the database entries that are being visualized - I'll accept that data challenge soon. 

But for the sake of this task - by hand - I'm game. I zoomed into Northeast Los Angeles, where I taught. 
I collected data from the schools in and around this region to make the following table,

School Avg SAT CensusTract % Unemploy % College % 2-parents % Private Sch Median Income
Benjamin Franklin 991 1835.10 .07 .26 .68 .04 64000
Academia Avance 889 1838.10 .08 .25 .49 .03 33000
Eagle Rock 1046 1816 .14 .43 .66 .06 69000
Los Angeles International 923 2013.02 .1 .58 .91 .34 66000
Los Angeles Leadership 888 1993 .11 .38 .72 .07 53000
Renaissane Arts 1083 1871.02 .08 .34 .8 .03 51000
Alliance Tennenbaum 920 1871.02 .08 .34 .8 .03 51000
PUC ECALS 930 1871.02 .08 .34 .8 .03 51000
Sotomayor 851 1871.02 .08 .34 .8 .03 51000
Alliance Leichtman-Levine 985 1864.01 .1 .13 .51 .05 32000
Lincoln 998 1992.02 .11 .24 .59 .09 47000
Wilson 911 2014.02 .08 .19 .7 .11 55000
Alliance Stern 973 2017 .14 .28 .59 .13 58000
Alliance Smidt 873 1997 .08 .3 .53 .04 32000
South Pasadena 1253 4807.04 .09 .61 .7 .04 77000
Blair 1037 4640 .06 .79 .88 .68 107000
John Muir 945 4609 .08 .25 .44 .05 69000
Aveson Global 1060 4603.02 .07 .33 .74 .21 83000
La Canada 1307 4607 .05 .74 .91 .25 184000
Glendale 1099 3021.04 .12 .4 .79 0 54000
Hoover 1149 3012.05 .08 .55 .94 .17 86000

Appropriate Units

A nice conversation can be had around independent and dependent variables. The question I decided to ask is, "Can we predict average SAT scores with census tract data?" Given that question, the Range of possible outputs will be 400 to 1600 for SAT scores, and the Domain will be from 0 to 1 for percentages and 0 to +inf for income. 

Graph the Data

I did some plots using SAT scores as the independent and dependent variable. I restricted SAT scores and income to 600 -1400 and 20k - 200k respectively to better display the data.

- Is there a correlation?
It seems like schools in lower income areas have lower scores. By looking at the deviation from the mean in both data sets, we can see how correlated the variability is.

- Correlation coefficient r
I measured the correlation coefficient between Avg SAT and each of five census tract variables (% unemployed, % college, % 2-parent, median income, % private) using =CORREL(Y, X) in sheets. 

Correlation coefficients between Avg SAT, % unemployed, % college, % 2-parent, median income, % private
% Unemploy % College % 2-parents % Private Sch Median Income
Avg SAT -0.15960 0.60929 0.39436 0.19450 0.72320
% Unemploy -0.28184 -0.29719 -0.31252 -0.43266
% College 0.71028 0.68975 0.76143
% 2-parents 0.46960 0.53873
% Private Sch 0.54839

From these data (n=21) income and college education are most correlated with SAT scores, so those are the plots I am including here.

3) Summarize

With a class, this is where we have a gallery walk of everyone's graphs and discuss similarities and differences. We should come to some conclusions about correlation coefficients. The fact that they lie between -1 and 1 and the closer to either of those extremes the more linearly correlated the points are.

From the graphs, it looks like SAT vs Education is more linear than SAT vs Income. So that is interesting, and worth investigating. Why is the r 15-20% higher for the income data compared to the college data? (.72 versus .61). What happens when we remove that one outlier (La Canada)?

Another interesting point is Blair, with the highest adult education but an average SAT score. Looking into it further, they also have 6 times the average % private school for schools in the area! 

Our stats group brought up how important a conversation around correlation is not causation is to have here. Using real-world data that highlight social injustices will raise a lot of important issues in the class and it is critical that we as teachers are prepared to field student questions and honor their perspectives.

A student could takeaway from this lesson that "poorer kids are dumber than richer kids" - even though that isn't our intention at all. They might go spreading rumors to their parents and other teachers that they learned this fact in math class.

The fact is that quality education is not a constitutional right in this country and we don't know how to measure what we value. Rich kids may be "better prepared for college as measured by the SAT on average" but what about collaboration, communication, and creative problem solving skills? How about respect, responsibility and integrity?

Don't let the system fool you. You are not a test score.

Enjoy work.

* Algebra Project Los Angeles (APLA) is a regional branch of the We the People Alliance: Math Literacy for All. A network of educators, researchers, organizers, parents, students and policy-makers committed to quality education as a constitutional right - particularly relating to math literacy for all.

National Laboratory for Education Transformation (NLET) is largely a volunteer based nonprofit where extraordinary individuals and organizations work together to try to understand and unite the pieces of the education, training and personal learning puzzle that are necessary to truly change student success, college completion and access to well-paying jobs.

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