Selected Blog Posts About the State of Math Education

Specific areas of friction that cause students to struggle with math. What needs to be done to remove friction from the learning process. Why friction remains so prevalent.

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Specific areas of friction that cause students to struggle with math:

• The Math Death Spiral: How Knowledge Gaps Lead to Student Failure -- Accumulating mathematical knowledge gaps can lead students to reach a tipping point where further learning becomes overwhelming, ultimately causing them to abandon math entirely.
• If You Want to Learn Algebra, You Need to Have Automaticity on Basic Arithmetic -- Solving equations feels smooth when basic arithmetic is automatic -- it's like moving puzzle pieces around, and you just need to identify how they fit together. But without automaticity on basic arithmetic, each puzzle piece is a heavy weight. You struggle to move them at all, much less figure out where they're supposed to go.

What needs to be done to remove friction from the learning process:

• Which Cognitive Psychology Findings are Solid, That Can Be Used to Help Students Learn Better? -- There are numerous cognitive learning strategies that 1) can be used to massively improve learning, 2) have been reproduced so many times they might as well be laws of physics, and 3) connect all the way down to the mechanics of what's going on in the brain.
• The Pedagogically Optimal Way to Learn Math -- The underlying principle that it all boils down to is deliberate practice.

Why friction remains so prevalent:

• Lots of People in Education Disagree with the Premise of Maximizing Learning -- But in talent development, the optimization problem is clear: an individual's performance is to be maximized, so the methods used during practice are those that most efficiently convert effort into performance improvements.
• Accountability and Incentives are Necessary but Absent in Education -- Students and teachers are often not aligned with the goal of maximizing learning, which means that in the absence of accountability and incentives, classrooms are pulled towards a state of mediocrity. Accountability and incentives are typically absent in education, which leads to a "tragedy of the commons" situation where students pass courses (often with high grades) despite severely lacking knowledge of the content.
• Leveraging Cognitive Learning Strategies Requires Technology -- While there is plenty of room for teachers to make better use of cognitive learning strategies in the classroom, teachers are victims of circumstance in a profession lacking effective accountability and incentive structures, and the end result is that students continue to receive mediocre educational experiences. Given a sufficient degree of accountability and incentives, there is no law of physics preventing a teacher from putting forth the work needed to deliver an optimal learning experience to a single student. However, in the absence of technology, it is impossible for a single human teacher to deliver an optimal learning experience to a classroom of many students with heterogeneous knowledge profiles, each of whom needs to work on different types of problems and receive immediate feedback on each of their attempts. This is why technology is necessary.

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