Jo Boaler: How to Learn Math | Lex Fridman Podcast #226 | Summary and Q&A

TL;DR

Mathematics educator discusses the beauty of mathematics lies in the creativity and multiple ways of seeing and solving problems, contrary to the traditional belief of one method and answer.

Key Insights

• 🔍 Mathematics: The beauty of mathematics lies in its multiple ways of solving problems and different methods of visualization. The misconception that math is only about one method and one answer needs to be overcome.
• 🧠 Learning Styles: While some students may naturally lean towards visual learning, research shows that all students benefit from understanding math visually. Engaging the visual pathways in the brain enhances mathematical thinking.
• 🧩 Problem-Solving: Mathematics requires creative problem-solving, intuition, and visualization. Encouraging students to think creatively, tell stories, and explore different solutions is essential for deep understanding.
• 🔁 Brain Pathways: Working on math problems activates different brain pathways. The more connections between these pathways, the more successful and high-achieving individuals become in mathematics. A multi-dimensional experience of math, involving visual, numerical, and physical approaches, helps develop these connections.
• 🌐 Intuition and Visualization: Intuition and visualization play essential roles in understanding complex mathematics. Mathematicians often rely on intuition and visualization to perceive patterns, explore solutions, and uncover fundamental truths.
• 🌱 Struggle and Hard Work: Struggling with math is beneficial for learning. Embracing the challenge and valuing the difficulty rather than fearing it fosters robust neural connections and deeper understanding.
• 💯 Excellence and Achievement: Encouraging students to strive for excellence in math is crucial. However, the belief that only certain individuals have the "math brain" limits students' potential. Allowing students to believe in their own abilities and providing effective teaching are keys to success.
• 🔄 Flexibility and Collaboration: Developing a flexible and creative mindset is vital for success in the 21st century. Collaborative learning, where students value and build upon each other's ideas, fosters the development of elastic, adaptable minds.
• 📚 Textbooks: While textbooks can be valuable resources, they must be engaging, inspiring, and flexible. Many traditional math textbooks focus on memorization and procedural methods, neglecting creativity and deep understanding. A shift towards more exploratory and problem-based approaches is needed.
• 📝 Assessment: Overemphasis on grades and tests can hinder students' motivation and learning in math. Providing a balance of summative assessments at the end of a course and more informative assessments, such as rubrics and self-assessment, can promote continuous learning and growth.
• 🧑 Collaboration and Social Learning: Collaborative and group learning, in which students collectively brainstorm and build upon each other's ideas, are vital for developing creative and flexible thinking. Celebrating others' achievements enhances the learning experience and fosters a growth mindset.

Transcript

the following is a conversation with joe buller a mathematics educator at stanford and co-founder of youcubed.org that seeks to inspire young minds with the beauty of mathematics to support this podcast please check out our sponsors in the description this is the lex friedman podcast and here is my conversation with joe bowler what to you is beauti... Read More

Questions & Answers

Q: How can mathematics be seen as a creative and visual subject?

Mathematics can be seen as a creative and visual subject when approached with different perspectives, such as visualizing problems and exploring multiple solutions. By encouraging visual thinking and creativity, students can develop a deeper understanding of mathematical concepts.

Q: How can teachers promote visual and creative learning in mathematics?

Teachers can promote visual and creative learning in mathematics by incorporating activities that encourage students to visualize problems, explore different approaches, and collaborate with their peers. Providing open-ended problems and valuing multiple solutions can also foster creativity in mathematics.

Q: What is the role of collaboration in learning mathematics?

Collaboration plays a significant role in learning mathematics as it allows students to share their ideas, learn from each other's perspectives, and build on one another's thinking. Collaborative learning can enhance critical thinking skills, problem-solving abilities, and deepen students' understanding of mathematical concepts.

Q: How do middle school years impact students' attitudes towards mathematics?

Middle school years are crucial for students' attitudes towards mathematics, as this is when many students start to form negative beliefs or disengage from the subject. It is essential to provide engaging, multi-dimensional math experiences during these years to promote a positive mindset and encourage continued interest in mathematics.

Q: How can parents support their children's learning in mathematics, even if they struggle or have math anxiety?

Parents can support their children's learning in mathematics by fostering a positive attitude and providing encouragement. Even if parents struggle with math themselves, they can demonstrate a growth mindset and celebrate their child's efforts. Avoiding negative self-talk or reinforcing math anxieties can create a supportive learning environment.

Summary

This interview with Joe Bowler, a mathematics educator at Stanford and co-founder of youcubed.org, explores the beauty of mathematics and the importance of teaching it in a creative and flexible way. Bowler emphasizes the significance of visual thinking in mathematics and advocates for a multi-dimensional approach to learning math. She also discusses the role of teachers, parents, and collaborative learning in fostering a love for math and developing flexible and creative minds.

Questions & Answers

Q: What do you find beautiful about mathematics?

Bowler expresses her love for mathematics that goes beyond traditional methods and solutions, appreciating the beauty of creative and visual mathematics. She believes that math can be seen and solved in multiple different ways, offering various methods and solutions for any given problem.

Q: Are most people better visual learners or is visual learning complementary?

While there are individuals who are naturally inclined towards visual thinking, Bowler explains that neuroscience research suggests that everyone should approach math visually, as thinking about math in different ways activates different visual pathways in the brain. Thus, visual approaches to learning math can benefit all individuals, even those who don't consider themselves visual learners.

Q: How does visual thinking connect with non-visual thinking in math?

Bowler highlights the findings from neuroscience studies that reveal five different brain pathways involved in solving math problems. The most successful mathematicians have more connections between these pathways, and visual thinking can create connections between these pathways. This shows that visual thinking and non-visual thinking are interconnected and can enhance mathematical problem-solving abilities.

Q: How can intuition play a role in solving math problems?

Intuition is an essential aspect often neglected in math education. Bowler mentions that mathematicians commonly rely on intuition when solving problems. Intuition involves thinking deeply, making connections, and having a deep understanding of the problem. It is crucial to foster intuition in math classrooms and acknowledge its significance in problem-solving.

Q: Can storytelling and visualization help in understanding math problems?

Bowler acknowledges the importance of storytelling and visualization in math education. She refers to physicists like Einstein, who relied on visualization to understand complex concepts. By imagining physical scenarios and engaging in storytelling, students can better grasp mathematical concepts and develop intuition about problem-solving.

Q: How can teachers encourage creativity and flexible thinking in math?

Bowler believes that teaching math should focus on developing an open and creative mindset in students. She emphasizes the role of teachers in valuing creativity and providing visual, interesting, and multi-dimensional mathematics. By giving students the opportunity to approach math problems using different methods, teachers can foster flexible and creative thinking.

Q: What role do parents play in supporting math learning?

Parents' attitudes towards math impact their children's achievement. Bowler shares that parents' math anxiety affects their child's performance, especially if they help with homework. She suggests that parents who struggle with math can fake positivity and optimism to create a more supportive learning environment. Additionally, providing opportunities for collaborative math activities at home can be beneficial.

Q: Should math be challenging or easy?

Bowler believes that challenging math is excellent, but it is essential for students to have faith in their ability to handle the challenge. Many students give up on math because they believe they are either born with a "math brain" or not. It is crucial to change this mindset and encourage students to embrace struggle and believe in their capacity to overcome challenges.

Q: At what age do people quit or give up on math?

Bowler states that students often start giving up on math in fifth grade and during middle school years. The transition to middle school, with its increased focus on grades and tests, can negatively impact students' self-perception in math. Fifth grade is considered a pivotal year, as students' mindset and confidence about math can significantly determine their future engagement and success in the subject.

Q: What can teachers do to support students who struggle or have different learning styles?

Bowler emphasizes the importance of a multi-dimensional approach to math education. By providing different ways of experiencing and understanding math, teachers can accommodate different learning styles. This approach benefits students with varying aptitudes and enables more inclusive learning environments.

Q: How can teachers support students who show exceptional talent or interest in math?

Bowler encourages teachers to recognize and nurture students' exceptional talent or interest in math. By providing additional challenges, extension tasks, and opportunities for exploration and creativity, teachers can help students further develop their skills and love for math.

Takeaways

Mathematics can be seen and solved in multiple ways, and teaching math should balance traditional methods with creative, visual, and flexible approaches. Visual thinking and intuition play essential roles in mathematics and should be cultivated in classrooms. Teachers, parents, and collaborative learning environments are crucial in supporting students' math learning and developing a love for the subject. Math education should focus on developing flexible and creative minds, valuing different learning styles, and promoting a growth mindset.

Summary & Key Takeaways

• Mathematics is beautiful when approached creatively, with visualization and different solutions to problems.

• Current education systems often emphasize memorization and one method, neglecting the beauty and creativity of mathematics.

• Visual thinking and collaboration play crucial roles in developing a deep understanding of mathematics.