Graduate courses can feel repetitive

What we covered:

– In elementary school, there's often an intense focus on conceptual understanding, but not enough time spent building real fluency with core skills. And this has left many kids without automaticity on basic things like multiplication facts. Math is extremely hierarchical, and when students don't have the basic facts at their fingertips, they quickly run into bottlenecks as the material gets more complex.

– Sure, drills can be made more fun, but the bottom line is that they have to get done. In high school and college, most of the class time is spent copying notes from the board -- and these notes are often copied by the instructor from a textbook or from other source material. This game of telephone through transcribing is just a performative activity. It's theater. It's passive and it does next to nothing for learning and retention.

– In upper level college math courses especially, students may only receive short weekly problem sets, which really aren't enough to build mastery, even if the problems are really hard, because students just spend most of their time flailing around.

– The bottom line is that students need reps: lots of them, building up scaffolding to the highest, hardest levels that they're expected to reach. High school assignments tend to be better in that regard, but students frequently don't receive timely feedback, and often their work isn't even graded for accuracy. That feedback loop is so critical: without it, students won't know what they're doing wrong or how to improve.

– So rather than just pattern matching to how math has traditionally been taught, what actually makes training effective? There's a few core principles:

1) Maximize the amount of time spent actively learning, interleaving minimum effective doses of explicit guided instruction active practice.

2) Make sure students are consistently working at the edge of their abilities: not bored, but not overwhelmed.

3) Provide frequent, timely feedback so students can adjust and improve.

These principles should be applied to math education and training environments everywhere.

Outline:

0:00 - Introduction

3:13 - Professors often wing pedagogy

5:37 - Too much class time is spent transcribing notes

7:41 - College problem sets are too short

12:53 - A lot of homework isn’t even graded for accuracy

18:22 - Copying notes in class is performative productivity

22:29 - Alex taught math courses at University College London

25:35 - Teaching is often an annoying obligation for research professors

30:03 - The bar for teaching is on the floor

32:34 - Even football practices often waste players’ time

34:20 - Most training is inefficient because people pattern match to the status quo

34:57 - First principles for effective training

37:13 - Too many models can paralyze and become a crutch for kids

39:24 - Kids can get stuck using training wheels in math forever

42:05 - Non-standard methods are often distracting and inefficient

46:18 - Designing 6th-8th grade courses to align with school curricula

52:30 - Conceptual understanding without ability is useless

55:17 - Skills practice can and should be gamified

Follow on X:

Math Academy - https://x.com/_MathAcademy_

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Jason Roberts - https://x.com/exojason

Alex Smith - https://x.com/ninja_maths