How to Get Better at Math

Thomas Frank
3 Nov 201709:40

TLDRThe video provides strategies for improving one's mathematical skills by emphasizing the importance of practice and understanding. It suggests tackling complex problems by breaking them down into simpler components, focusing on mastering fundamental concepts. The presenter recommends using tools like WolframAlpha and Symbolab for step-by-step solutions when needed. The video also advises against rushing through math problems to ensure true comprehension and mastery of the material. It concludes with a call to action to try out the learning platform Brilliant, which offers structured courses and challenges to enhance math, science, and computer science skills.

Takeaways

  • 🧠 Math is a skill that can be learned, not an innate ability.
  • 📚 To improve at math, practice solving a variety of problems, especially the tough ones.
  • 🔍 When faced with a complex problem, break it down into simpler components.
  • 📈 Understand and master fundamental principles before tackling more complex problems.
  • 📝 Practice with single concept problems to solidify understanding before combining them.
  • 🔢 Simplify problems by using smaller, easier numbers to focus on the concepts.
  • 📚 Seek out resources like books, notes, or online examples to learn from when stuck.
  • 🔎 Use tools like WolframAlpha or Symbolab for step-by-step solutions when needed.
  • 🤔 Always push yourself to solve problems before looking up answers to truly learn.
  • ⏳ Don't rush through math problems; take time to understand and master the concepts.
  • 🌟 Confidence in approaching math problems is key to improvement and success.

Q & A

  • What is the common perception of math among people?

    -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'.

  • Why is it important to challenge oneself with tough math problems?

    -Tough problems stretch one's understanding and lead to new breakthroughs, which are essential for improving mathematical skills.

  • What is the first step in solving a complex math problem according to George Polya?

    -The first step is to identify the components or operations that the problem requires and to understand the fundamental principles.

  • How can one simplify a complex math problem to make it more manageable?

    -By breaking the problem down into smaller, simpler problems that isolate individual components or operations, and focusing on one concept at a time.

  • Why is it beneficial to work through single concept problems before tackling a complex problem?

    -Working through single concept problems helps to master the underlying concepts or operations, making it easier to solve more complex problems that combine these concepts.

  • What is the significance of using smaller numbers when practicing math problems?

    -Smaller numbers help to focus on the concepts and operations without the distraction of complex calculations, making it easier to understand and practice the math.

  • What are two online tools that can provide step-by-step solutions to math problems?

    -WolframAlpha and Symbolab are two online tools that allow users to input equations and receive step-by-step solutions.

  • Why is it crucial to attempt to solve a problem before looking up the solution?

    -Attempting to solve a problem first helps to stretch one's capabilities and understanding, which is more beneficial for learning than just looking at solutions.

  • What is the main danger of relying on step-by-step solutions without fully understanding the concepts?

    -The danger is that one may only comprehend the solution process superficially without truly mastering the concepts, leading to difficulties when applying the knowledge independently.

  • Why should one not rush through math homework assignments?

    -Rushing through homework prevents deep understanding and mastery of concepts, which can lead to difficulties in applying the knowledge in tests or real-world situations.

  • What is the key to building confidence in solving math problems?

    -The key is to approach math with the confidence to tackle problems, solve them, and make mental breakthroughs, which in turn increases confidence and creates a self-sustaining cycle of learning.

  • What is the role of a learning platform like Brilliant in enhancing one's math skills?

    -Brilliant uses hands-on problem-solving to help learners master math, science, and computer science effectively, offering structured courses, weekly challenges, and a detailed wiki for explanations and examples.

Outlines

00:00

🧩 Mastering Math Through Problem-Solving

The speaker begins by addressing the common perception of math as a complex and challenging subject. They emphasize that math is a skill that can be learned and improved with practice, contrary to the belief that some people are 'not math people.' The video aims to provide practical techniques for tackling tough math problems, starting with advice from George Polya's book 'How to Solve It.' The speaker suggests that understanding and mastering fundamental principles is crucial, as complex problems are built upon simpler ones. They recommend breaking down complex problems into smaller, more manageable parts that focus on individual components or operations. An example of a summation problem with a fractional exponent is given to illustrate this concept. The speaker also advises simplifying problems by using smaller numbers to focus on the concepts rather than getting lost in complex calculations.

05:02

🔍 Strategies for Overcoming Math Challenges

This paragraph continues the discussion on improving math skills by offering additional strategies for dealing with difficult problems. The speaker suggests avoiding complex numbers and focusing on smaller, simpler numbers to better understand the underlying concepts. They also recommend seeking out learning resources, such as books, notes, or online examples, to strengthen one's understanding of the concepts and operations involved in a problem. The speaker introduces two online tools, WolframAlpha and Symbolab, which provide step-by-step solutions to equations. However, they caution against relying too heavily on these tools, emphasizing the importance of attempting to solve problems independently to truly develop mathematical abilities. The speaker also advises against rushing through math problems, advocating for a deliberate and focused approach to mastering concepts. They conclude with a quote from Richard Feynman, highlighting the importance of confidence in approaching math and learning. The paragraph ends with a promotion for the learning platform Brilliant, which offers hands-on problem-solving courses in various subjects, including math and computer science.

Mindmap

Keywords

💡Math

Math, short for mathematics, is a subject that involves abstract concepts and complex problem-solving skills. In the video, it is presented as a skill that can be learned and improved with practice, contrary to the belief that some people are 'not math people.' The script emphasizes the importance of tackling tough math problems to stretch one's understanding and achieve breakthroughs.

💡Abstract

Abstract refers to concepts or ideas that are intangible and not easily relatable to concrete objects or situations. In the context of the video, math is described as abstract because it deals with ideas and principles that may not have a direct physical representation, which can make it challenging for some learners to grasp.

💡Fundamental Principles

Fundamental principles are the basic rules or concepts that form the foundation of a subject. The video script highlights the importance of having a strong grasp of these principles in math to solve more complex problems. George Polya's advice from 'How to Solve It' is mentioned to emphasize understanding the basics before tackling complex problems.

💡Summation

Summation, often represented by the Greek letter sigma (Σ), is a mathematical operation that involves adding a series of numbers or expressions. In the script, a summation problem is used as an example to illustrate how to break down a complex problem into simpler ones to understand and master the underlying concepts.

💡Fractional Exponents

Fractional exponents are a mathematical notation used to represent roots of a number raised to a power. The video script uses fractional exponents in an example problem to show how isolating and practicing with simpler versions of a concept can help in mastering it before combining it with other concepts.

💡Concept Mastery

Concept mastery in the video refers to the ability to understand and apply a mathematical concept accurately and confidently. The script suggests that one should not just get a concept right once but practice until they can apply it without error, emphasizing the importance of mastery for solving complex problems.

💡WolframAlpha

WolframAlpha is an online computational knowledge engine that can provide step-by-step solutions to mathematical problems. The video mentions it as a tool for learners to use when they are stuck on a problem, although it requires a subscription for step-by-step solutions.

💡Symbolab

Symbolab is another online tool mentioned in the video that offers step-by-step solutions to mathematical problems for free. It is suggested as a resource for learners to understand the process of solving problems they find challenging.

💡Rushing

Rushing, in the context of the video, refers to the act of quickly going through math problems without fully understanding the concepts. The script advises against rushing through homework assignments, as it can lead to superficial understanding and hinder the mastery of concepts.

💡Confidence

Confidence in the video is portrayed as a crucial factor in learning and improving at math. It suggests that having the confidence to approach and solve problems is the starting point for a self-sustaining cycle of learning and mental breakthroughs.

💡Brilliant

Brilliant is a learning platform mentioned in the video that uses hands-on problem-solving to help learners master subjects like math, science, and computer science. The script describes it as an effective way to challenge oneself and deepen understanding through structured courses and weekly challenges.

Highlights

Math is a skill that can be learned, not an innate ability.

To improve at math, practice solving a variety of problems, especially the tough ones.

Tough math problems stretch your understanding and lead to breakthroughs.

When stuck on a problem, break it down into simpler components.

Master fundamental principles to tackle more complex problems.

George Polya's advice from 'How to Solve It' is crucial for solving math problems.

Isolate and solve individual components of a complex problem to understand the concepts better.

Use simpler numbers to simplify tough problems and focus on concepts.

If concepts are unclear, revisit your learning materials or find step-by-step solutions online.

WolframAlpha and Symbolab are useful tools for step-by-step solutions.

Before looking up solutions, ensure you've exhausted your own problem-solving efforts.

After understanding a solution, rework the problem without reference to solidify your learning.

Avoid rushing through math problems to truly master the concepts.

Confidence in approaching math problems is key to improvement.

Brilliant is a learning platform that uses problem-solving to teach math, science, and computer science.

Engage with weekly challenges and a community on Brilliant to enhance your math skills.

Mastery of concepts comes from intentional practice and not just completing assignments.

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