How does struggle impact learning in mathematics, and why is it often viewed negatively?

Struggling with a math problem is actually a beneficial time for the brain, promoting deeper thinking and learning. However, many students in the U.S. school system believe they are either born with a 'math brain' or not. This mindset leads them to disengage when they encounter difficulty, attributing it to a lack of innate ability rather than seeing it as a necessary part of the learning process to achieve excellence.

What is the critical age when students often give up on mathematics?

Many children begin to disengage from and give up on math around fifth grade, and the middle school years (ages 11-13) are particularly pivotal. During these years, shifts to more testing and grading can make students feel inadequate, causing them to decide whether to continue with STEM subjects or abandon them. Early grades that encourage exploration help prevent this.

How can teachers effectively inspire belief in students, especially those struggling with math?

Teachers play a crucial role by communicating genuine belief in their students' capabilities. A study showed that a simple sentence, 'I'm giving you this feedback because I believe in you,' significantly improved students' performance a year later. Believing in and communicating this potential, along with encouraging hard work, can profoundly change a student's relationship with math, moving them beyond self-doubt.

What is the 'teaching to big ideas' framework in mathematics education?

The 'teaching to big ideas' framework, being implemented in California, reorganizes math education around a few core concepts and their interconnections, rather than numerous isolated standards. This approach encourages teachers to use rich, deep activities that naturally introduce multiple mathematical concepts and connections over several days, fostering a more profound and meaningful understanding for students, moving away from narrow, procedural questions.

Beyond grades, what alternative assessment methods can teachers use to measure student progress in math?

Instead of constant grading, teachers can provide students with rubrics that outline learning goals for a unit, allowing children to visualize their learning journey. This method enables self-assessment and provides teachers with opportunities to offer qualitative feedback, such as 'in the next few weeks you might like to learn to do this.' This approach shifts focus from a letter grade to a deeper understanding of mathematical progress.

What is 'groupitizing' and how does it relate to mathematical ability?

'Groupitizing' is the ability to quickly perceive the number of items in a small set without counting them individually, by grouping them visually. It's a skill that can be developed, and research suggests it predicts how well someone will do in math, potentially being a more significant indicator of mathematical aptitude than traditional speed tests on facts.

How important is collaboration in learning mathematics, and how can it be fostered in students?

Collaboration is super important for developing a connected brain and enhancing mathematical achievement, as it allows individuals to build on each other's ideas and appreciate diverse thinking. In a Stanford calculus class, students initially resistant to collaboration significantly improved their problem-solving skills and learned to value collective intelligence after being taught collaborative strategies, letting go of social comparison.

What is the impact of textbooks on math education, and what are their limitations?

While some textbooks can be good learning tools, many traditional math textbooks are criticized for presenting math as uninspiring, rigid, and procedural, often divorcing concepts into narrow, sequential exercises. This approach teaches students to follow predefined methods without understanding the 'why' or the connections between ideas, unmotivating them and stifling creativity. Modern approaches favor rich, deep activities over rote textbook problems.

What are the most effective study strategies for deeply understanding mathematics outside the classroom?

Effective studying involves actively questioning oneself rather than passively rereading material. Many people mistakenly believe they understand a concept after reading an explanation, only to realize their lack of true grasp when attempting to solve problems. Constantly testing oneself and reflecting on the 'big ideas' from lessons, identifying difficulties, and connecting concepts to real-life applications facilitates deeper comprehension.

How can students develop the skill of 'deep work' when studying challenging subjects like math?

Developing 'deep work' involves maintaining prolonged focus, which is a muscle that needs to be built. Teachers can encourage this by assigning inspiring, rich, and deep problems that require extended engagement, moving away from time-pressured, numerous short questions. Students must realize that sustained effort, even starting with just a few minutes of concentrated focus, is crucial for unlocking the rewarding experience of solving complex mathematical problems.

What is the vision for the future of education (10-100 years from now)?

The future of education is envisioned to be vastly different, moving away from the current 'factory model' that stifles creativity. Optimistic predictions include the deep integration of programming and creative tools, the dissolution of traditional subject boundaries (as exemplified by the rise of data science), and a focus on students actively learning, creating, and exploring, rather than just memorizing and reproducing information.

Key Moments

Jo Boaler: How to Learn Math | Lex Fridman Podcast #226

Lex Fridman

Science & Technology4 min read91 min video

Sep 27, 2021|208,961 views|5,591|376

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Key Moments

TL;DR

Jo Boaler on making math beautiful, visual, creative, and accessible for all learners.

Key Insights

Math is beautiful when approached with creativity, visualization, and multiple solution paths, not just rigid methods.

Developing interconnected brain pathways through multi-dimensional math experiences (visual, physical, verbal) enhances learning.

Struggle in math is crucial for brain development and learning, but requires a belief in one's capability.

A multidimensional approach to math education is vital to accommodate diverse learning styles and neural wiring.

Teachers' belief in students, conveyed through encouraging words and genuine optimism, significantly impacts their achievement.

Shifting from rote memorization to teaching 'big ideas' and rich, deep activities can transform math education.

Collaboration and valuing diverse thinking are essential skills that boost learning and problem-solving.

Effective math learning involves active engagement, asking 'why,' and developing deep work habits over quick answers.

Parents' math anxiety can negatively impact children's achievement; faking optimism about math is beneficial.

Online resources and accessible platforms like YouCubed are crucial for sharing effective math teaching strategies globally.

THE BEAUTY AND MULTIDIMENSIONALITY OF MATHEMATICS

Jo Boaler defines mathematics as beautiful when it embraces multiple solution paths, visualization, and creative approaches, rather than adhering to single methods. This multidimensional perspective is key. She emphasizes that engaging with math visually, physically, and verbally builds connections between different brain pathways, leading to deeper understanding and higher achievement. This contrasts with the traditional view that often focuses solely on numbers and rigid procedures, a disservice to many learners.

THE NEUROSCIENCE OF LEARNING AND THE ROLE OF STRUGGLE

Neuroscience reveals that high-achieving individuals connect multiple brain pathways when solving math problems. Boaler advocates for a 'multi-dimensional experience of math,' encouraging students to see problems through numbers, visuals, words, and physical manipulatives. Importantly, she highlights that struggle is not a sign of inability but a crucial catalyst for brain development and learning. The belief that one can overcome these challenges, even when they are difficult, is paramount for sustained engagement and success in mathematics.

FOSTERING INTUITION AND CREATIVITY IN MATHEMATICS

Mathematical intuition, often absent in traditional classrooms, plays a vital role in problem-solving, as noted by mathematicians themselves. Boaler suggests that intuition is developed by seeking patterns and visualizing problems, much like physicists or mathematicians like Einstein. She argues that creativity is not separate from math but is inherent in exploring diverse ways to see and solve problems. This creative, flexible thinking is essential for the 21st century, contrasting with tasks easily replicated by computers, like memorization.

RETHINKING EDUCATION: MOVING BEYOND TRADITIONAL METHODS

Boaler criticizes the traditional 'factory model' of education and textbooks that chop complex mathematical ideas into isolated, uninspiring standards. She champions a new framework, 'teaching to big ideas,' which focuses on overarching concepts and rich, deep activities that allow students to explore mathematics engagingly. This approach aims to accommodate diverse learning styles and neural differences, making math accessible to more students, including those with unique learning needs or who have historically struggled.

THE CRUCIAL ROLE OF TEACHERS AND MENTORS

Teachers and mentors are pivotal in shaping a student's relationship with mathematics. Boaler stresses the profound impact of a teacher's belief in a student, conveying that 'I believe in you' can significantly improve long-term achievement. She advocates for a shift away from a performance culture driven by constant grading towards more informative assessments like rubrics. Similarly, mentors who believe in individuals can inspire them to pursue their potential, even when facing societal or familial doubts.

EMBRACING COLLABORATION AND DEEP WORK

Collaboration is presented as a powerful tool for learning, allowing students to build on each other's ideas and diverse perspectives. Boaler shares her experience teaching calculus to Stanford undergraduates, where initial resistance to collaboration transformed into valuing mutual thinking. She also emphasizes the importance of 'deep work'—the ability to focus intensely on challenging problems for extended periods. This contrasts with the common trait of giving up on problems within minutes, highlighting the need to cultivate sustained focus and perseverance in mathematical pursuits.

THE POWER OF VISUALIZATION AND PATTERN-SEEKING

Visualization is a cornerstone of Boaler's approach, evident in the work of figures like Grant Sanderson. She highlights how visual representations and programmatic animations can illuminate complex mathematical concepts, making them more accessible and engaging. Humans are naturally drawn to patterns, symmetry, and unexpected variations, which are fundamental to mathematics. Encouraging students to be 'pattern seekers' in all aspects of math helps them develop a deeper, more intuitive understanding of the subject.

REFORMING ASSESSMENT AND THE FUTURE OF EDUCATION

Boaler suggests that while grades can serve a summative purpose, the constant use of grades in classrooms fosters a performance-driven culture detrimental to deep learning. More informative assessments, like rubrics and self-reflection, are preferable for tracking progress. Looking ahead, she envisions a radically different education system, moving away from rigid subject boundaries and embracing tools like programming and data science. This evolution aims to foster creativity, personalized learning, and lifelong intellectual curiosity, preparing students for a dynamic future.

Mentioned in This Episode

●Software & Apps

●Companies

●Organizations

●Books

●Concepts

●People Referenced

Common Questions

Neuroscience indicates that when we engage with math problems, two visual pathways in the brain are activated. Thinking visually, alongside numerical and other approaches (like writing or building), creates more connections between the five different brain pathways, leading to a more profound and connected understanding, especially for high-achieving individuals. This multi-dimensional approach makes math more accessible and meaningful.

Topics

Mental Health & Psychology Learning & Education Science & Mathematics Collaborative Learning Curriculum Development Mathematics Education Teacher Training Visual Learning Math Intuition Student Mindset Educational Psychology Data Science In Education

Mentioned in this video

People

Sebastian Thrun

Mathematician and AI expert who intuitively solved a problem related to robots picking up white noise, but it took him weeks to prove it mathematically.

Eric Weinstein

Mathematician who received his PhD from Harvard and felt like an outcast of the education system due to his non-standard way of learning.

Lex Fridman

Host of the Lex Fridman Podcast, engaged in a conversation with Jo Boaler about mathematics education.

Maryam Mirzakhani

Iranian mathematician, the first woman to win the Fields Medal, whose work was entirely visual. She was told at age 13 that she couldn't do math but went on to achieve global recognition for connecting unconnected areas of mathematics.

Daniel Kahneman

Renowned psychologist and economist, known for his famous collaboration with Amos Tversky and his genuine curiosity and listening skills in collaborative efforts.

Grant Sanderson

Creator of 3Blue1Brown, inspires millions by converting mathematical concepts into visual, animated representations using programmatic visualization, helping to illuminate complex ideas and make people fall in love with concepts.

Cal Newport

Mathematician and theoretical computer scientist, author of 'Deep Work,' who emphasizes the necessity of focus for complex tasks like those in mathematics.

Jo Boaler

Mathematics educator at Stanford University and co-founder of YouCubed.org, advocating for creative, visual, and multi-dimensional approaches to math education.

Richard Feynman

Physicist known for his emphasis on intuition and starting with experiments, often seen as a form of visualization.

Amos Tversky

Daniel Kahneman's famous collaborator, exemplary of successful intellectual partnership.

Albert Einstein

Famous physicist known for thinking visually and using intuition in his problem-solving approach. A quote from him about pure mathematics being the poetry of logical ideas is shared at the end of the podcast.

Software & Apps

How to Learn Maths

A free online class for kids by Jo Boaler/YouCubed that teaches math as a visual, creative subject, incorporates brain science, and has been shown to increase engagement and achievement in middle school math classes.

Manim

An open-source Python library created by Grant Sanderson (3Blue1Brown) for programmatic animation, allowing users to create animated explanations of mathematical concepts.

JavaScript

A programming language recommended for creating mathematical visualizations.

3Blue1Brown

A popular YouTube channel by Grant Sanderson that uses animated visualizations to explain mathematical concepts.

Python

A programming language recommended for creating mathematical visualizations.

Legislation & Policy

California Mathematics Framework

A new statewide math framework for California, co-written by Jo Boaler, recommending teaching to 'big ideas' and connections instead of isolated standards.

Books

Deep Work

A book by Cal Newport that discusses the focus required for complex tasks, relevant to studying mathematics effectively.

Limitless Mind

Authored by Jo Boaler, this book explores how people can overcome negative beliefs and realize their potential in subjects like mathematics, including interviews with individuals who had been discouraged but later excelled.

Concepts

Fields Medal

A prestigious award in mathematics, mentioned in relation to Maryam Mirzakhani being the first woman to win it.

Companies

Udacity

An online learning platform that emphasizes active learning pedagogy, such as breaking down content into short segments followed by interactive activities or quizzes.

Organizations

Stanford University

The institution where Jo Boaler is a mathematics educator and where YouCubed runs summer camps and conducts research.

YouCubed

An organization co-founded by Jo Boaler that aims to inspire young minds with the beauty of mathematics, share good teaching ideas, and combat math anxiety. Its website offers lessons, videos, and parent tips based on research.

MIT OpenCourseWare

An initiative by MIT that provides free online access to course materials from its undergraduate and graduate level courses, contributing to online education.

Studies & Research

Harvard University

University where Eric Weinstein earned his PhD, indicating a high level of academic achievement despite his non-standard learning approach.