Introduction:
Quadratic functions are fundamental in algebra and have extensive applications in various fields, including data analysis. In the context of education, quadratic models can be employed to analyze trends and disparities in educational attainment across different demographics. This module aims to equip instructors with the tools to teach quadratic functions through the lens of real-world, culturally pertinent data, thereby enhancing student engagement and understanding.
Exercise 1: Analyzing Educational Attainment Trends
Objective:
Utilize quadratic regression to model and analyze trends in educational attainment over the past ten years in the specified Texas metropolitan areas.
Data Collectioin
-Gather data on the percentage of individuals aged 25 and over who have attained a bachelor's degree or higher, segmented by race and gender, for each year from 2015 to 2024.
-Sources for this data may include the U.S. Census Bureau and local educational reports.
Educational Attainment Data (2015-2024)
Year Area White(M) White(F) Black(M) Black(F) Hispanic (M) Hispanic (F) Asian(M/F)
2015 Dallas 35% 38% 20% 25% 15% 18% 50%
2015 SanAntonio32% 35% 18% 22% 12% 15% 48%
2015 Austin 40% 42% 22% 27% 17% 20% 55%
2015 McAllen 28% 30% 15% 18% 10% 12% 45%
2016 Dallas 35.5% 38.5% 20.5% 25.5% 15.5% 18.5% 50.5%
2016 SanAntonio32.5% 35.5% 18.5%. 22.5% 12.5% 15.5% 48.5%
2016 Austin 40.5% 42.5% 22.5% 27.5% 17.5% 20.5% 55.5%
2016 McAllen. 28.5% 30.5% 15.5% 18.5% 10.5% 12.5%. 45.5%
2017 Dallas 36% 39% 21% 26% 16% 19% 51%
2017 SanAntonio 33 % 36% 19% 23% 13% 16% 49%
2017 Austin 41% 43% 23% 28% 18% 21% 56%
2017 McAllen 29% 31% 16% 19% 11% 13% 46%
2018 Dallas 36.5% 39.5% 21.5% 26.5% 16.5% 19.5% 51.5%
2018 SanAntonio 33.5% 36.5% 19.5% 23.5% 13.5% 16.5% 49.5%
2018 Austin 41.5% 43.5% 23.5% 28.5% 18.5% 21.5% 56.5%
2018 McAllen 29.5% 31.5% 16.5% 19.5% 11.5% 13.5% 46.5%
2019 Dallas 37% 40% 22% 27% 17% 20% 52%
2019 SanAntonio 34% 37% 20% 24% 14% 17% 50%
2019 Austin 42% 44% 24% 29% 19% 22% 57%
2019 McAllen 30% 32% 17% 20% 12% 14% 47%
2020 Dallas 37.5% 40.5% 22.5% 27.5% 17.5% 20.5% 52.5%
2020 San Antonio 34.5% 37.5% 20.5% 24.5% 14.5% 17.5% 50.5%
2020 Austin 42.5% 44.5% 24.5% 29.5% 19.5% 22.5% 57.5%
2020 McAllen 30.5% 32.5% 17.5% 20.5% 12.5% 14.5% 47.5%
2021 Dallas 38% 41% 23% 28% 18% 21% 53%
2021 SanAntonio 35% 38% 21% 25% 15% 18% 51%
2021 Austin 43% 45% 25% 30% 20% 23% 58%
2021 McAllen 31% 33% 18% 21% 13% 15% 48%
2022 Dallas 38.5% 41.5% 23.5% 28.5% 18.5% 21.5% 53.5%
2022 SanAntonio 35.5% 38.5% 21.5% 25.5% 15.5% 18.5% 51.5%
2022 Austin 43.5% 45.5% 25.5% 30.5% 20.5% 23.5% 58.5%
2022 McAllen 31.5% 33.5% 18.5% 21.5% 13.5% 15.5% 48.5%
2023 Dallas 39% 42% 24% 29% 19% 22% 54%
2023 SanAntonio 36% 39% 22% 26% 16% 19% 52%
2023 Austin 44% 46% 26% 31% 21% 24% 59%
2024 Dallas 38% 41% 23% 28%. 18% 21% 53%
2024 SanAntonio 35% 38% 20% 24% 14% 17% 51%
2024 Austin 43% 45% 25% 30% 19% 22% 58%
2024 McAllen 31% 33% 17% 20% 12% 14% 48%
Use the provided data to plot trends, apply quadratic regression, and analyze disparities in educational attainment.
Data Analysis:
-Plot the collected data points for each demographic group.
-Apply quadratic regression to fit a curve to the data for each group.
- Interpret the coefficients of the quadratic function to understand the nature of the trends (e.g., accelerating improvement, deceleration, or decline).
Discussion:
-Compare the trends across different demographic groups and metropolitan areas.
-Discuss potential factors contributing to observed disparities, such as socioeconomic status, access to educational resources, and historical contexts.
Exercise 2: Projecting Future Attainment Rates
Objective: Use quadratic models to project future educational attainment rates and assess the potential impact of policy interventions.
Model Extension:
-Extend the quadratic models developed in Exercise 1 to project educational attainment rates up to the year 2030.
-Analyze the reliability of these projections by considering the goodness of fit of the models.
Policy Simulation:
-Introduce hypothetical policy interventions aimed at improving educational attainment (e.g., scholarship programs, community educational initiatives).
-Adjust the quadratic models to simulate the potential impact of these interventions on future attainment rates.
Evaluation:
-Assess which demographic groups would benefit most from the proposed interventions.
- Discuss the feasibility and potential challenges of implementing such policies in the different metropolitan areas.
Exercise 3: Exploring the Gender Gap in Higher Education
Objective: Investigate the quadratic relationship between time and the gender gap in
higher education attainment within the specified regions.
Data Acquisition:
Gap Analysis:
Interpretation:
In a reflective essay of 300-400 words, analyze how quadratic functions can be utilized to
understand and address disparities in educational attainment. Consider the following
points:
ï‚·The advantages of using quadratic models over linear models in capturing the
complexities of educational data.
ï‚·The role of culturally relevant data in making mathematical concepts more
relatable and impactful for students.
ï‚·Strategies for educators to incorporate real-world data into their teaching of
quadratic functions to highlight social issues and promote critical thinking.
This module not only reinforces mathematical concepts but also encourages instructors
and students to engage deeply with pressing social issues, fostering a more inclusive and
socially aware educational environment.
Note: The data used in this module is based on information from the U.S. Census Bureau
and local educational reports. For the most accurate and up-to-date data, please refer to
the latest publications from these sources.