Black Mathematicians' Impact

Overview

This 90-minute lesson celebrates Black mathematicians' contributions and inventiveness, linking historical context to mathematical concepts aligned with the International Baccalaureate (IB) Mathematics: Analysis and Approaches SL/HL syllabus (specifically focusing on development of critical thinking, application of mathematics in real-world contexts, and the appreciation of diversity in mathematics).

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Learning Objectives

By the end of this lesson, students will be able to:

• IB MAA SL/HL Objectives:
  • Identify and analyze the contributions of Black mathematicians within the history and application of mathematics.
  • Develop reasoning and justification skills by connecting historical narratives to mathematical concepts.
  • Create and solve problems inspired by real-life mathematical inventions.
• Develop cultural awareness and appreciation for diversity in STEM fields consistent with IB Learner Profile attributes: Open-minded, Reflective, Knowledgeable.

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Standards and Competencies

• IB Mathematics: Analysis and Approaches SL/HL Topic C1 (Algebra: Structure and reasoning) and Topic D (Calculus - optional HL enrichment).
• IB Learner Profile: Open-mindedness, Knowledgeable, Reflective.
• Approaches to teach: Inquiry-based learning, Interdisciplinary links (History & Social Studies), Communication skills through presentation.

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Materials Needed

• Printed worksheets (profiles and questions on mathematicians)
• Projector or large display for images/slides
• Markers and poster paper (optional)
• Printed photos of each mathematician (for tactile engagement)

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Lesson Activities

1. Warm-Up and Engagement (10 minutes)

• Begin with an open question: "Can you name any Black mathematicians or inventors related to mathematics? What impact do you think they have had?"
• Display images of the three Black mathematicians to be studied (see below) without names.
• Briefly introduce the IB Learner Profile attributes to be cultivated today.

2. Introduction to Black Mathematicians (15 minutes)

• Present three key figures:
  1. Elbert Frank Cox – First African American to receive a PhD in Mathematics.
  2. Katherine Johnson – NASA mathematician who calculated trajectories for space missions.
  3. David Blackwell – Renowned statistician and game theorist.
• For each, show:
  • Picture
  • Short story summarizing their life and work (see below)
  • Key mathematical ideas they contributed to

3. Reading and Reflection Activity (15 minutes)

• Hand out a worksheet featuring:
  • Brief bio and story of each mathematician
  • Reflective questions linking their life stories to mathematical concepts and IB attributes.
• In pairs, students read and discuss these.
• Sample questions:
  • How did societal challenges shape their mathematical careers?
  • What mathematical challenges did they solve?
  • Which IB Learner Profile attributes might they embody?

4. Mathematics in Action – Problem-Solving Workshop (30 minutes)

• Each student chooses one mathematician to focus on.
• Using the worksheet’s problem section inspired by each mathematician’s work, students solve carefully constructed mathematical problems:
  • Example: For Katherine Johnson – Calculate the parabolic trajectory of a projectile using quadratic functions (coordinate geometry application).
  • For Elbert Frank Cox – Explore a polynomial equation proof problem.
  • For David Blackwell – Simple probability or game theory problem to enhance statistical thinking.
• Groups/pairs can check answers collaboratively.
• Teacher circulates to guide reasoning and provide formative feedback.

5. Creative Synthesis and Presentation (15 minutes)

• Students create a mini-presentation (poster or slide) summarizing:
  • The mathematician’s story
  • Their key mathematical contribution
  • How their work applies to today's mathematics or real-world applications
• Volunteers present to the class, emphasizing the societal and mathematical legacy.

6. Closing and Assessment (5 minutes)

• Exit Ticket: On a note card or digitally, students respond to:
  • "Which mathematician inspired you the most and why? What new understanding do you have about the role of diverse mathematicians?"

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Short Stories on Each Mathematician

Elbert Frank Cox

Born in 1895, Elbert Frank Cox became the first African American to earn a PhD in Mathematics in 1925. He studied at Cornell University and later focused on solving polynomial equations, which are foundational in algebra. Overcoming racial barriers, Cox paved the way for future generations in mathematical academia.

Katherine Johnson

Katherine Johnson was a pioneering NASA mathematician whose precise calculations of space trajectories were critical to the success of early space missions, including Apollo 11’s moon landing. She used coordinate geometry and calculus to plot safe paths for astronauts, demonstrating the vital role of applied mathematics in space exploration.

David Blackwell

David Blackwell (1919–2010) was an influential mathematician and statistician known for his work in game theory and probability. As the first Black member of the National Academy of Sciences, his innovations in Bayesian statistics continue to influence areas from economics to computer science.

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Worksheet Highlights (Excerpt)

Section 1: Biographical Reading

• Read short bios.
• Highlight key points about challenges faced and accomplishments.

Section 2: Reflection

• How might Katherine Johnson’s work involve functions studied in our Algebra unit?
• Why is proving polynomial theorems, like Elbert Cox’s thesis, important in mathematics?
• What real-world problem could David Blackwell's probability theories solve?

Section 3: Math Problems

Katherine Johnson (Coordinate Geometry):
A spacecraft’s path can be modeled by ( y = -0.01x^2 + 0.5x + 2 ), where ( y ) is altitude and ( x ) is time in minutes.

• Find the maximum height reached.
• At what time will the spacecraft land (height = 0)?

Elbert Frank Cox (Algebra):
Solve the cubic polynomial equation ( x^3 - 6x^2 + 11x - 6 = 0 ). Verify the roots.

David Blackwell (Probability):
Two players play a game where each draws a card from a deck. What is the probability both draw an Ace? Use basic probability principles.

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Photographs of the Mathematicians

(Place printed or digital images here, formatted for classroom use. Use images that are historically appropriate and publicly available. Examples: patriotic NASA photos of Katherine Johnson, university portraits of Cox, or professional photos of Blackwell.)

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Teacher’s Notes

• Adjust difficulty of math problems according to SL or HL level.
• Encourage reflecting on the impact of diversity in STEM during discussion.
• Use IB ATL skills: Communication, Reflection, and Critical Thinking throughout.

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By following this detailed plan, teachers can engage students in meaningful historical context while deepening their mathematical understanding consistent with IB learning frameworks.