Learning Math

Source: Dr. Trefor Bazett

5 minute review before class
- Cover big points, i.e. big concepts
- Spaced Retrieval: pulling concepts back into memory to strengthen neural connections.
Study Topics before class, preferably early in the day before class starts and right after you wake up (Dr. K)
Previewing content, solidifying foundational concepts so you can focus on the time spent in class being more effective

Being a stenographer is the worse possible thing to do
- Do more previewing so active learning is more available in class!!
Tricks:
- Generate questions, write it down or circle a spot
- Annotate notes with stars, circles, question marks to look back on these concepts

Go over notes in class, and try to make sure you 100% understood that content
Reframing notes in your own words solidify understanding serves heavily in retaining information
More Questions? Always come up with at least 3 questions

PRACTICE!
- Spend as much time as you can on this portion
Concept Mapping!
- Write out main ideas of a particular subject in a big map
- Connecting ideas helps to strengthen understanding

Growth Mindset
- A national experiment reveals where growth mindset improves achievement (Yeager, David S. et al)
- Positive and Negative mindsets inhibit developing improvments in metrics
- Fixed mindsets are bad!
Metacognition (Dr. Sandra McGuire)
- When thinking about thinking/learning
- Pausing and reflecting on whether you’re learning effectively
- self-assessment
Simplify & Explain
- Expressing this concept in a way you are able to handle, letting you take ownership of the information being passed through
- shows a deeper understanding of material
- Feinmann technique
Questions
- Ask a lot of questions!
  - Come up with a list of good questions about that video
  - Questions that allow more deeper understanding
Intrinsic Motivation
- Internal motivation
  - Applied concepts, while nice, should also have intrinsic joy in concepts within mathematics

Example: Chess

Practice math!
Be as socially interactive as possible
Do active assessment of your own learning capabilites, take record of what you understand and don’t
Growth Mindset
Work Hard, think of being a student like a profession

Be Concept Focused!
- Sense-making: think about why the concept works and what’s going on
Big Picture
- Try to see how that problem makes sense with your intuitive idea of how the concept works
Make Predictions
- tweak problems to see trajectories on how these problems work
Spaced Practice
- Do problems that recall information from before and improve long-term retention
- Do a bunch of little studying over a long period of time
Interleaving
- Mix problems from other sections and multiple sections. Diversity in problem set allows for better long-term retention!

Identify Logical Structure
- Conditional Statement, Biconditional Statement
Proof Methods
- Direct Proof: assume p, conclude q
- Contrapositive: assume ~q, conclude ~p
- Contradiction: assume p, and ~q, and get a contradiction
- Counterexample: Find p that implies ~q
Write Down Definitions!
Aim for the Conclusion!
- Wherever you start, aim to get to the conclusion!
Understand what the proof is saying
- What does this connection look like or mean? Get a large scale understanding
Geometric Picture?
- Can you draw a picture that interprets the assumptions or conclusion?
Concrete Example
- Valuable in understanding why the conclusion might be connected to the assumption
Relevant Theorems?
- What are major theorems in a course?
- Read proofs of relevant theorems
Play Around!
- Encourage proving things as an iterative process–growth mindset!
- Going down a rabbit hole and trying many things may lead to the solution