How to Get Better at Math

Thomas Frank

3 Nov 201709:40

EducationalLearning

32 Likes 10 Comments

TLDRThis video explores strategies for improving math skills, emphasizing that math is a learnable skill rather than an innate talent. It highlights techniques for solving complex math problems, such as breaking them into simpler components, focusing on mastering fundamental concepts, and using tools like WolframAlpha and Symbolab for step-by-step solutions. The video also advises against rushing through homework and stresses the importance of building confidence through practice. Additionally, it promotes Brilliant, a learning platform that uses hands-on problem solving to teach math, science, and computer science.

Takeaways

🧠 The belief that one is 'not a math person' is a misconception; math is a skill that can be learned and improved with practice.
📚 To get better at math, one must engage in extensive practice, especially with challenging problems that push the boundaries of understanding.
🔍 When faced with a complex math problem, break it down into simpler components or operations to isolate and master each concept individually.
📉 Simplifying the numbers in a problem by using smaller, whole numbers can help focus on the underlying concepts without getting overwhelmed by complex calculations.
📝 Hungarian mathematician George Polya's advice from 'How to Solve It' emphasizes the importance of understanding fundamental principles before tackling more complex problems.
🤓 Mastery of a concept means being able to apply it correctly every time, not just getting it right once.
🔧 If stuck on a problem, use resources like WolframAlpha or Symbolab for step-by-step solutions, but only after genuinely attempting to solve the problem yourself.
🚫 Avoid the temptation to rush through math problems; taking the time to understand and master concepts is crucial for long-term learning.
🔄 After understanding a step-by-step solution, it's important to rework the problem independently to reinforce learning and ensure true comprehension.
📈 Confidence in one's ability to approach and solve math problems is essential; as confidence grows, so does one's skill set.
🌟 Richard Feynman's quote highlights the importance of confidence in learning and the self-sustaining cycle of solving problems and gaining mental breakthroughs.

Q & A

What is the common perception of math among people according to the script?
-The script suggests that math is often perceived as one of the most difficult subjects due to its abstract and complex nature, leading many to believe they are 'not math people'.
What is the fundamental belief the script aims to challenge?
-The script challenges the belief that people are inherently 'not math people', asserting instead that math is a skill that can be learned like any other.
What is the primary advice given for improving at math in the script?
-The primary advice given is to practice lots of math problems, especially the tough ones, as they stretch understanding and lead to breakthroughs.
According to the script, why is it important to solve tough problems in math?
-Solving tough problems is important because they stretch one's understanding and build the skill set, which is crucial for mastering math.
What technique does the script attribute to George Polya for tackling math problems?
-The script attributes the technique of breaking down a complex problem into simpler components or operations to George Polya, as mentioned in his book 'How to Solve It'.
How does the script suggest simplifying a complex math problem?
-The script suggests simplifying a complex problem by isolating individual components or operations and working on simpler problems that focus on just one concept at a time.
What is the significance of using smaller numbers when practicing math problems as per the script?
-Using smaller numbers helps to focus on the actual concepts and operations without getting distracted by complex calculations, making it easier to understand and practice the underlying principles.
What are the two online tools mentioned in the script for solving math problems?
-The two online tools mentioned are WolframAlpha and Symbolab, both of which provide solutions and step-by-step explanations for math problems.
What is the main caution given when using step-by-step solutions from online tools?
-The main caution is to ensure that one has first tried to solve the problem to the best of their ability before looking up solutions, and to rework the problem without reference after understanding the solution.
What is the script's final advice on approaching math homework?
-The script advises not to rush through math homework, emphasizing the importance of mastering concepts rather than just completing assignments.
How does the script relate confidence to the ability to get good at math?
-The script suggests that confidence is crucial for approaching math and that as one solves problems and makes mental breakthroughs, their confidence naturally increases, leading to a self-sustaining cycle of improvement.

Outlines

00:00

🤔 Understanding Tough Math Problems

The introduction addresses the perception of math as a challenging subject. Many people believe they're not 'math people,' but this video aims to change that mindset. The key to improving in math is practice, especially with tough problems that stretch your understanding. The focus of the video is on techniques to solve these difficult problems, starting with a concept from Hungarian mathematician George Polya's book 'How to Solve It.' Polya's advice emphasizes breaking down complex problems into simpler components to master fundamental principles.

05:02

🔍 Breaking Down Complex Problems

The second paragraph illustrates the concept of breaking down a complex math problem into simpler parts. The example used is a summation problem with a fractional exponent. By isolating and solving the simpler components—first a basic summation, then the fractional exponent—students can master the underlying concepts. This method ensures a deeper understanding of each part, which can then be applied to the more complex problem.

📊 Simplifying Numbers in Problems

This section highlights the importance of using simple numbers when practicing math concepts. Complex numbers can distract from the core operations and concepts. By substituting large, complex numbers with smaller, easier ones, students can focus on understanding the principles. If the fundamental concepts are not well understood, it's crucial to review study materials or find examples to follow step-by-step.

🧩 Utilizing Tools for Step-by-Step Solutions

The paragraph discusses the use of online tools like WolframAlpha and Symbolab to get step-by-step solutions for tough problems. While WolframAlpha offers more powerful capabilities with a paid plan, Symbolab provides free step-by-step solutions. The importance of attempting to solve problems independently before seeking these solutions is emphasized to ensure genuine learning and concept mastery.

🚶‍♂️ The Importance of Not Rushing

Rushing through math homework is discouraged. Properly mastering concepts is essential, and brute-forcing answers or using shortcuts can lead to gaps in knowledge. Taking the time to understand and solve problems thoroughly is crucial for long-term success in math, especially during tests or practical applications.

📚 Recap and Final Tips

The final section recaps the key points for improving math skills: isolate and master individual concepts, simplify numbers, seek help for concepts as needed, and avoid rushing through problems. Emphasis is placed on the importance of mastering concepts rather than just completing assignments. A quote from Richard Feynman is included to inspire confidence in approaching math challenges.

🌟 Introducing Brilliant for Learning

The video promotes Brilliant, a learning platform that uses hands-on problem-solving to teach math, science, and computer science. The narrator shares a personal experience of learning new math concepts through Brilliant's computer science fundamentals course. Brilliant offers structured courses, weekly challenges, a community for learners, and a detailed wiki. A link is provided for viewers to sign up and get a discount on the annual premium subscription.

👍 Thanks and Encouragement

The conclusion thanks viewers for watching and encourages them to like the video, subscribe, and share it with others. Additional content is suggested, including a free book on earning better grades, a podcast on job interviews, and more videos from the channel. The narrator expresses gratitude for Brilliant's sponsorship and the support from viewers.

Mindmap

Keywords

💡Math

Mathematics, often referred to simply as 'math,' is the abstract science of number, quantity, and space, which includes various operations and relations in the manipulation of abstract concepts. In the video, math is portrayed as a challenging but learnable skill, with the script emphasizing the importance of practice and understanding fundamental concepts to tackle complex problems.

💡Abstract

Abstract, in the context of the video, refers to the intangible and theoretical nature of mathematical concepts, which can make them seem distant from concrete, everyday experiences. The script mentions that math's abstractness contributes to its perceived difficulty, but also suggests that breaking down complex problems into simpler, more tangible components can aid understanding.

💡Fundamental Principles

Fundamental principles are the basic rules or concepts that form the foundation of a subject. The video script stresses the importance of having a strong grasp of these principles in math to solve more complex problems effectively. For instance, understanding basic operations is essential before attempting complex equations.

💡Summation

Summation, represented by the Greek symbol sigma (Σ), is a mathematical operation that involves adding a series of numbers or expressions. The script uses a summation problem as an example to illustrate how breaking down a complex problem into simpler parts can help in mastering the underlying concepts.

💡Fractional Exponents

Fractional exponents are a mathematical notation used to express roots of a number in a simplified form. In the video, the script simplifies a problem involving fractional exponents to demonstrate how isolating and practicing specific concepts can lead to a better understanding of complex problems.

💡Mastery

Mastery, in the context of the video, means achieving a level of proficiency where one can correctly apply a concept or operation without error. The script emphasizes that true mastery is not just getting a concept right once, but being able to apply it consistently and correctly, which is crucial for solving complex math problems.

💡WolframAlpha

WolframAlpha is an online computational knowledge engine that provides step-by-step solutions to mathematical problems. The script mentions it as a resource for students who are stuck on a problem, highlighting its power and the need for a subscription for detailed solutions.

💡Symbolab

Symbolab is another online tool for solving mathematical problems, which the video script contrasts with WolframAlpha. While Symbolab may be less intuitive, it offers free step-by-step solutions, making it a valuable resource for learning and understanding math problems.

💡Conceptual Understanding

Conceptual understanding refers to the ability to comprehend the underlying ideas and principles of a subject, rather than just memorizing facts or procedures. The video script advocates for a deep conceptual understanding in math, suggesting that it is more beneficial than merely finding answers through memorization or looking up solutions.

💡Confidence

Confidence, as discussed in the video, is the belief in one's ability to succeed in a task or learn a new skill. The script connects confidence with the ability to approach and solve math problems, suggesting that as one's problem-solving skills improve, so too does their confidence, creating a positive cycle.

💡Brilliant

Brilliant is a learning platform mentioned in the video that uses hands-on problem-solving to teach subjects like math, science, and computer science. The script describes it as an effective way to learn and master concepts through challenges and quizzes, which can lead to a deeper understanding of complex subjects.

Highlights

Math is a skill that can be learned just like any other subject.

To get better at math, you need to practice lots and lots of math.

Tough problems will stretch your understanding and lead to new breakthroughs.

If you're stuck on a problem, identify the components or operations it involves.

Break complex problems into simpler ones that focus on individual concepts.

Use smaller, easier numbers to simplify tough problems.

If you're struggling with concepts, refer to books, notes, or online resources.

Tools like WolframAlpha and Symbolab can provide step-by-step solutions.

Always push your brain to the limit before looking up solutions.

Mastery means not being able to get it wrong, not just getting it right once.

Don't rush through math homework; focus on mastering the concepts.

Seeing step-by-step solutions can be helpful, but rework the problem yourself afterward.

Use hands-on problem-solving techniques to learn math effectively.

Confidence in solving problems increases with practice and mental breakthroughs.

Brilliant.org offers courses and challenges that promote intense and effective learning experiences.

Transcripts

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