Rethinking what it means to learn math (with Eugenia Cheng)
1. Cultivate Growth Mindset
Adopt the belief that you can always learn and improve, regardless of age or past experiences, as this positive mindset is crucial for overcoming perceived limitations and engaging in lifelong learning.
2. Focus on Logical Thinking
Approach math as a tool to develop clear, logical thinking skills, rather than just solving specific problems, to make the learning transferable to any domain.
3. Use Math for Empathy
When encountering strong disagreements, use a mathematical mindset to trace another person’s logic back to their fundamental premises, acknowledging their starting point without necessarily validating it, to foster empathy and understanding.
4. Normalize Confusion in Math
When learning math, recognize that feeling confused or not understanding immediately is a normal and expected part of the process, rather than a sign of personal failing.
5. Prioritize Curiosity Over Speed
Focus on developing endless curiosity and a desire for deep understanding in mathematics, rather than prioritizing speed or quick answers, as true mathematical skill is about exploration.
6. Clarify Argument Definitions
Before engaging in divisive arguments, ensure all parties agree on the definitions of terms and the starting premises to avoid talking past each other.
7. Assess Information Logically
Apply logical frameworks, as taught in math, to critically evaluate information, distinguish good from bad, and effectively communicate findings to others.
8. Ask Insightful Math Questions
Cultivate the ability to ask ‘good questions’ in math, which means probing the limits of when something is true or why something doesn’t work, rather than just seeking correct answers.
9. Deconstruct Complex Learning
When faced with a complex skill or concept, break it down into its smallest, most understandable components, and learn each piece incrementally, building a ‘bridge’ of knowledge.
10. Engage in Playful Math
Approach math learning through playful exploration, ‘messing around’ with concepts and data (e.g., interactive visualizations) to understand how they behave, rather than focusing solely on solving specific problems or getting right answers.
11. Understand Concepts in Context
When learning or applying mathematical concepts, always consider the broader context and relationships, as characteristics can change depending on the surrounding elements (e.g., a number’s properties in different number systems).
12. Grasp Full Data Distributions
When encountering statistics like the ‘mean,’ remember that it’s an abstract central point and consider the entire data distribution to avoid misinterpreting it as universally applicable.
13. Foster Math Literacy
Encourage a general appreciation and basic understanding of mathematical concepts (like exponentials or probability) in society, even if not for personal calculation, to enable effective communication of scientific information.
14. Separate Math Reading/Writing
In math education, distinguish between ‘reading’ (understanding concepts and interpretations) and ‘writing’ (producing calculations or proofs), allowing individuals to excel in comprehension even if they struggle with production.
15. Internalize Math via Patterns
Instead of rote memorization, internalize mathematical facts (like multiplication tables) by recognizing patterns in everyday contexts to reduce cognitive load without fostering math hatred.
16. View Math as Pattern Language
When encountering real-world phenomena, identify underlying patterns and translate them into mathematical representations to rigorously analyze and understand them.
17. Avoid Rote Math Memorization
Educators and parents should prioritize understanding over memorization of facts like times tables, especially when calculators are readily available, as memorizing things people won’t use makes math seem useless and can lead to math hatred.