#226 – Jo Boaler: How to Learn Math

Podcast Summary

• The Multidimensional Beauty of Mathematics: Mathematics has multiple ways to visualize and solve problems beyond one method and answer. Intuition is essential to understand patterns and simplifying explanations. All students can benefit from this multidimensional experience.

  Mathematics can be beautiful and creative, with multiple ways to see and solve problems beyond just one method and one answer. Visualizing math problems can help build connections in the brain and develop intuition for solving problems. All students can benefit from a multidimensional experience of math, regardless of whether they consider themselves to be visual learners or not. The role of intuition in solving math problems is frequently overlooked in education, but can be crucial for understanding patterns and getting to the simple explanation of why things are the way they are.

• Embrace the Struggle: A Multidimensional Approach to Learning Math: Everyone can learn math with a growth mindset. Educators should focus on different learning styles and use visualization and color-coding to help struggling students understand difficult concepts, leading to a deeper appreciation of math.

  Math can be challenging, but it's important to value the struggle and know that you can do it. The problem is that many people believe they're either born with or without the "math brain", leading them to give up when they struggle. As educators, it's important to make room for different learning styles, since everyone's brain is wired differently. A multidimensional approach to math, including visualization and color-coding, can help students understand difficult concepts and appreciate the subject more. By valuing the "hard" parts of math, students can develop a growth mindset and overcome obstacles.

• Approaching Math Differently to Promote Learning and Excellence: Math education should value hard work and excellence while providing good teaching and resources that allow for creativity and engagement. There are many ways to excel in math and it should be made accessible to all students.

  In order to make math more accessible to students, it's important to open up different ways of learning and approaching the subject. It's not just about excelling in math, but also about valuing excellence and the hard work that's required to achieve it. While it's important to work hard, it's equally important to have good teaching and access to resources. In countries such as the Soviet Union, there was a strong emphasis on math education and excellence, but it's also important to remember that not everyone is wired the same way and there are many different ways to excel in math. Ultimately, the goal is to make math interesting and creative in order to engage students and help them learn.

• The Importance of Math Education in Fifth Grade: Fifth grade can be a critical turning point for students' attitudes toward math. Teachers can have a significant impact by believing in their students, and the education system should provide support for non-standard learning styles.

  Research suggests that fifth grade can be pivotal for students when it comes to their relationship with math. Many kids start to give up on themselves and the subject at this age, as they enter their middle school years and experience more pressure with grades and tests. These middle school years are critical for many students as they are deciding whether to pursue STEM subjects or not. Teachers play a significant role in this process by communicating belief in their students and their potential. Additionally, the education system needs to move away from an uninspiring, one-size-fits-all approach to math education, and instead, support students who have a non-standard way of learning.

• Approaching Mathematics Positively: A positive relationship with math, valued through visual approaches and enthusiastic teaching, can combat math anxiety and transform achievement in the subject.

  Mathematics can be approached and valued in different, visual ways. The first woman to win the Fields Medal in mathematics, Maryam Mirzakhani, was known for her entirely visual work. However, many students and parents have a bad relationship with math, which can lead to math anxiety and a negative impact on achievement. Teachers and parents have the power to change this by valuing and approaching math in a positive way, even if it requires faking enthusiasm. Teachers can also connect previously unconnected areas of math by opening up the subject to different approaches. Overall, a positive relationship with math can change lives and achievement in the subject.

• Teaching Two Big Ideas: A New Framework for Math Education: Math education expert Jo Boaler suggests that instead of focusing on many narrow procedural statements, teachers should teach a few big ideas and connections between them. This new approach values connections and encourages deep, rich activities, while moving away from grades and tests.

  Jo Boaler, a math education expert, believes that traditional ways of teaching math are uninspiring and do not promote deep learning. She suggests a new framework called "teaching two big ideas," which focuses on teaching a few big ideas and connections between them rather than many narrow procedural statements. This new approach values the ways these big ideas are connected and encourages teachers to use rich, deep activities to teach these concepts. Boaler is not a fan of grades and tests and believes that they create a performance culture that is not conducive to deep learning. Instead, teachers can assess students using rubrics that outline their learning journey over the course of a unit or a few weeks.

• Importance of informative feedback and personalized attention in mathematics education: Providing informative feedback and personalized attention to students in math can help them understand their skills, identify areas of improvement, and extend their learning. Teachers should use interactive methods to encourage diverse ways of thinking and problem solving.

  Teachers should focus on providing informative feedback to students rather than relying on grades alone. Self-assessment and rubrics are effective tools to help students understand their mathematical abilities and identify areas of improvement. Teachers should also challenge students to extend their learning beyond the basic curriculum and offer personalized attention to those who show exceptional talent or interest. However, teachers must be careful not to push students beyond their abilities and understand that teaching requires sensitivity and individualization. To captivate students' interest in mathematics, teachers should use interactive methods that encourage diverse ways of thinking and problem solving.

• How Dots can Predict Math Ability and the Importance of Teaching Flexible Thinking in Math: Grouping items is a learnable skill that predicts math ability. Teaching flexible and creative thinking, emphasizing collaboration and group work is important in developing a mathematically creative mind.

  In this conversation, Jo Boaler explains that the way children group items like dots can predict how well they will do in math. This ability to group is not a raw talent, but something that can be learned and developed in all children. Boaler believes that schools should focus more on teaching flexible and creative thinking in math rather than just memorization and procedures. Collaboration and group work are also important in developing flexible and creative minds. Boaler shares her experience of teaching calculus to undergrads at Stanford and how they were able to learn to collaborate and work together to solve math problems.

• The Power of Collaboration in Math Education: Collaborating with diverse perspectives can enhance problem-solving skills and build a culture of celebrating each other's ideas. Providing the right materials and support is crucial for effective math education.

  Collaboration is a key skill that boosts achievement in problem-solving among students. Through collaboration, students learn to value other people's thinking on a problem and can build on each other's way of thinking, as well as put aside social comparison and ego. Celebrating others and collaborating with diverse perspectives is a skill, and it pays off in the long term. Although textbooks can have pretty pictures and be useful, not all math textbooks are good experiences for students. It is essential to provide students with the right materials and support to learn math effectively through collaboration and diverse perspectives.

• Teaching Mathematics in a Multidimensional Way with You Cubed: Math education should focus on progress and small achievements. Textbooks and online courses can help, but engaging pedagogy and multidimensional approaches, like those offered by You Cubed, are key.

  Mathematics should be taught in a multidimensional way, with a focus on progress and celebration of small achievements. Textbooks can be a helpful tool, but it's important to consider the content and the pedagogy. Online education, particularly MOOCs, can be effective for extending the reach of great teachers, but it's important to ensure that the pedagogy is effective and engages learners in active ways. You Cubed is a website that offers resources and tools for teaching math in a more engaging and multidimensional way. They have had over 52 million visitors and offer resources for both teachers and learners.

• YouCubed: A Resource for Inspiring Math Education: YouCubed provides resources for teachers, parents, and students to improve their math education, including "Week of Inspirational Math" and K-8 math books. They also encourage self-testing for deeper understanding.

  YouCubed is a website that focuses on sharing good ideas for teaching math with teachers, students, and parents. They aim to raise math anxiety while highlighting the beauty and creativity of the subject. The website provides lessons, videos, and tips for parents, and they encourage teachers to try their "Week of Inspirational Math" to ignite students' interest in the subject. Furthermore, YouCubed produces K-8 math books with big ideas, rich activities, and visuals to supplement traditional textbooks. For students studying math at home, YouCubed recommends giving yourself questions and tests to understand concepts deeply and effectively.

• The Power of Reflective Questions in Math Class: Encouraging students to ask reflective questions about math can deepen their understanding and encourage them to think about real-life applications. Valuing and encouraging students' questions helps them develop important skills that are crucial for success.

  The key takeaway from this section is that asking reflective questions about what students have learned in math class can potentially lead to deeper understanding of the subject. This approach goes beyond just doing lots of questions for homework and encourages students to think about the big ideas and real-life applications of the material they are learning. It is important to value and encourage students' questions, as asking "why" is crucial in every aspect of life, including choosing a career, a romantic partner, and solving problems. Unfortunately, research shows that the questions kids ask in school tend to decrease over time as they learn not to ask questions.

• How Teachers Can Foster a Positive Relationship With Math in Their Students.: Teachers can positively impact their students' interest and engagement with math through small actions like promoting collaboration and encouraging deep problem-solving. Building focus is important in achieving success in mathematics and can be developed with practice.

  Teachers can have a profound impact on their students' relationship with math, even with small actions like encouraging collaboration and deeper problem-solving. It's important for teachers to be aware of their tone and approach, as even one statement can have a significant impact on a student's interest and engagement in math. Deep work and prolonged focus are crucial for success in mathematics, and teachers can encourage this by giving students inspiring deep problems and allowing them the time and space to work on them. Building focus is a skill that can be developed with practice, and can be crucial in developing a strong relationship with math.

• Conquering Math Problems with Visualization and Persistence: Don't give up too quickly when solving math problems. Visualize concepts and patterns to better understand them. Tools like Mathematician Grant Sanderson's animations and Python library Manam can help create a transformative learning experience.

  In a conversation with Lex Fridman, Jo Boaler highlights the importance of not giving up too quickly when solving math problems. According to a survey, on average kids give up after only two minutes of work on a math problem. Boaler emphasizes the role visualization can play in conquering this hurdle. Mathematician Grant Sanderson has inspired millions of people by converting mathematical concepts into visual representations through animation. Python library Manam allows users to animate equations and shapes, creating transformative learning experiences. Boaler encourages students to be pattern seekers as math is a subject of patterns, both visual and not.

• The Power and Challenges of Online Learning: Reaching All Learners: Online learning can provide education globally, but access must be ensured. Quality online pedagogy can improve learning outcomes. Believing in oneself and having supportive mentors aids personal growth. Ignore negative messages, seek positive encouragement.

  Online learning has the potential to provide access to education worldwide, but there is still work to be done to ensure it reaches all learners, including those from underprivileged backgrounds. However, quality online pedagogy can be effective in improving student engagement and learning outcomes. For example, Jo Boaler's free online class, "How to Learn Maths," has shown to improve student engagement in math classes by 68%. Another key takeaway is the importance of believing in oneself and surrounding oneself with mentors who believe in one's potential. It's essential to ignore negative messages and seek out those who will support and encourage personal growth.

• The Evolution of Education and the Integration of Data Science: The education system is changing slowly but surely, and data science is a prime example. Integration of programming and creativity is crucial for preparing students for future job markets, and change happens gradually but can go viral.

  Education is evolving, and change is slow, but possible. Data science is a great example of how subject boundaries are changing in high school curriculums. With education technology advancing, it's hard to imagine what the education system will look like in the next 100 years. However, education needs to inspire creativity and integrate programming in everything, preparing students for future job markets. The current education system has been compared to a factory model, but the integration of data science illustrates how subject boundaries don't make much sense. Change in education happens in small spaces, but once it expands, it goes viral.