Why Math Education Fails (And How to Fix It)

Course Overview and Target Audience

Making Math Click is a Coursera course co-created by Barbara Oakley and John Mighton that teaches how to learn math effectively, combining neuroscience insights with practical teaching strategies. It targets university students avoiding math courses, parents coaching children, teachers seeking evidence-based methods, and anyone with math anxiety or insecurity.

Primary audiences for Making Math Click course

Personal Journeys: From Math Aversion to Expertise

Both creators overcame deep math anxiety. Barbara learned languages first, then discovered at age 26 that language-learning techniques transfer to math. John struggled with calculus but discovered through tutoring that mysterious concepts become obvious with practice and proper explanation. Both now use their hard-won understanding to teach others.

Course Content: Neuroscience Plus Practical Math

The course blends how-to-learn principles with actual mathematics concepts. It covers the two learning systems (pattern recognition through repetition and learning through explanations), why both matter, and specific topics like division visualization and problem-solving strategies—all grounded in brain science.

Two Learning Systems Teachers Ignore

The brain learns through two distinct systems: one thrives on rote repetition and pattern recognition, the other on hearing and seeing explanations. Modern education has discarded the first system based on outdated pedagogical theories that predate neuroscience, crippling students' ability to learn deeply.

Two complementary learning systems; modern education often uses only one

Retrieval Practice and Automaticity

Practicing problems until answers come automatically—like memorizing multiplication tables—does far more than create rote knowledge. It builds intuitive feel for mathematical patterns, similar to how musicians internalize rhythms or language learners develop fluency. Without automaticity, students cannot see deeper patterns or solve complex problems.

The Worked Example Effect

Students learn best by studying solved problems, then practicing similar ones themselves—not by struggling with novel problems from scratch. This mirrors how Sylvia Plath learned to write by memorizing and imitating poems, building deep mental models before finding original voice. Teachers rarely teach this method despite strong research support.

Building Schemas: Mental Representations

A schema is a rich, interconnected mental model of how concepts relate. Chess masters recognize board positions instantly because decades of play built deep schemas; they are not geniuses, just experienced. Math students who practice key problems develop schemas that let them see relationships, transfer knowledge, and solve novel problems—appearing like naturals.

The 85% Challenge Zone and Dopamine

Learners are happiest and most efficient when about 85% proficient—the Goldilocks zone where they must stretch slightly but not overwhelm. In this zone, the brain releases dopamine, rewarding effort. Students in groups in this zone naturally choose to practice and find it fun. Pushing beyond this zone causes anxiety and misbehavior; staying below it causes boredom.

85%

Optimal proficiency for learning and dopamine reward

The Goldilocks zone: not too easy, not too hard

Narrowing the Solution Space Through Questions

Expert teachers like John Mighton ask strategic questions that narrow the vast space of possible answers (100 trillion potential brain connections) to a tractable zone where students can find solutions. This creates the illusion that students discovered the answer themselves while actually receiving guided practice—combining creativity with the dopamine reward of success.

The Misconception About Manipulatives

Common belief: children must start with concrete objects. Research shows this is oversimplified. For older students and even preschoolers, starting with abstract or generic representations (gray circles, not colorful flowers) often works better because engaging visuals distract from the underlying structure. Manipulatives are often oversold because companies profit from them.

Jennifer Kaminsky's Research on Transfer

Psychologist Jennifer Kaminsky found that students taught fractions with colorful flower petals transferred knowledge worse than those taught with gray-and-white circles. The engaging concrete representation became bound to students' neurons, making it hard to apply the concept elsewhere. This challenges the assumption that authentic, engaging materials always help.

Kaminsky's grade 2 fraction study: generic representations outperformed engaging ones

Fade Quickly to Abstract Representation

If concrete objects are used, fade to abstract representations within 15-20 minutes. For example, use algebra tiles briefly, then draw squares for bags and circles for blocks on a whiteboard, then move to pure symbols. This prevents students from becoming dependent on manipulatives and allows more problems and complexity.

Rapid fading from concrete to abstract within a single lesson

Math as a Mental Sport

Mathematics is fundamentally a mental activity. The goal is for students to roam the universe with pencil and paper, sitting at a desk—like Einstein discovering laws of physics. Manipulatives should facilitate this transition, not become a permanent crutch. An abacus works well because it explicitly teaches students to put it away and use mental calculation.

Emphasizing Explanation Over Correctness

Many classrooms reward explanations even when answers are wrong, devaluing accuracy. This creates real-world dangers: nurses who cannot catch calculation errors may administer wrong medication dosages. It also prevents students from developing number sense—the internal alarm that 12 × 12 = 299 is obviously false.

Teacher Math Anxiety Perpetuates Failure

Many teachers lack deep math understanding and no resources to learn it. When asked what fraction of kids are girls in a town with 4 girls per 5 boys (out of 36 kids), some teachers guess 80% or 4/5, missing that the answer is 4/9. Teachers without number sense pass guessing instincts to students, threatening both economic productivity and human development.

The Loss of Human Potential

Failing to teach math well causes enormous loss of human potential, similar to failing to teach reading. Students graduate without understanding the invisible beauty of mathematics and science, losing cognitive development, executive function, ability to focus, and resilience. Math rewires the brain; denying it to students stunts their growth as human beings.

Economic and Societal Consequences

In Texas, students without college certification within 6 years of high school have less than 20% chance of earning a living wage. The number one barrier to college certification is math courses. Even trades like carpentry and culinary arts require passing math. Additionally, a population without math literacy is easily misled on budgets, climate, and financial disasters.

Less than 20%

Chance of living wage without college certification (Texas)

Math course failure is the primary barrier to economic mobility

The Taiwan vs. New Zealand Divergence

Taiwan adopted constructivist approaches in the 1990s; within 6 years, results were disastrous. They switched back to traditional approaches and now have a well-educated population with thriving tech sectors. New Zealand continued constructivism for 30 years and now cannot find elementary teachers because so many fear math. The two countries' trajectories diverged dramatically.

Taiwan's course correction vs. New Zealand's 30-year constructivist experiment

Success Drives Engagement, Not Vice Versa

Educators often try to make math fun first, hoping engagement leads to learning. Research shows the arrow points the other way: if students succeed at math, they naturally like it and engage. Teaching math that doesn't involve real math (skateboarding projects with minimal math content) leaves students unsuccessful and disengaged from actual mathematics.

The Air Guitar Analogy

Teaching math without rigor is like teaching air guitar: students have fun, clown around, applaud each other, and love the experience—but they are not learning guitar. Teachers may report kids love the class while students are not actually learning math. Enjoyment of the teaching method does not equal learning.

Practice Is Not Grueling in Math When Done Right

Andrew Ericsson noted deliberate practice is grueling and lonely, discouraging many. But math is unique: when kids succeed together in the 85% zone, they actually beg for more work. Practice becomes fun, not lonely, and there is no age cutoff like in basketball or music. Math is accessible to every brain at any age.

Gradual Development vs. Overwhelming Novices

The biggest mistake in education is confusing the end goal (resilient problem-solvers tackling rich problems) with the method to get there. Novice learners need narrow, highly scaffolded zones with only one or two varying concepts. The zone expands as confidence and schemas build. Overwhelming novices with complex problems from the start causes failure.

Replication Crisis in Education Research

Only 0.13% of education studies are replicated, meaning most published findings are never verified. Many famous educators promote approaches with published studies that, under scrutiny, have serious flaws or did not actually measure learning. Districts must demand rigorous evidence and be skeptical of well-known names without replication.

0.13%

Education studies that are replicated

Massive replication crisis in educational research

What Education Ministers Should Do

Adopt programs aligned with science of learning (like Jump Math). Run multiple programs simultaneously and compare results, not adopt-and-dump single programs. Ask hard questions: Do you have the right consultants? Are leaders compromised by past approaches? If almost all kids are not thriving, it is a leadership problem, not a student problem—kids can learn math.

The Research-Ed Grassroots Movement

Teachers and consultants are running pilots aligned with science of learning and seeing real improvement. This grassroots, teacher-driven movement is more promising than top-down mandates. It represents a turning point in education, similar to how medicine moved from quackery toward evidence-based practice.

Overcoming Cognitive Dissonance in Teachers

Change is slow because teachers must admit they may have harmed students by using ineffective methods. Historians found doctors resisted germ theory because it meant admitting they killed patients. Similarly, teachers must overcome the psychological barrier of accepting that all kids can learn math and they need to change. Heroic teachers do this; it is the path forward.

Bonus Questions: Stretching Without Overwhelming

Present problems that look harder but are not. If students can add a quarter plus a quarter, they can add three quarters. To kids, three quarters looks like a harder problem, but it is a trivial generalization. This keeps them in the 85% zone, excited, and stretching. Gradually make problems genuinely harder, creating a ramp all students want to climb.

Teaching Strategies, Not Just Problems

Instead of asking grade 4 students to find all ways to make 17 cents with pennies and nickels (where they get one answer and cannot verify completeness), teach a simple strategy: start with zero of the bigger unit, then one, then two, etc. This strategy transfers to finding rectangles of a certain perimeter, then to complex probability problems. Students become problem-solvers, not problem-guessers.

One-on-One Tutoring Principles for Whole Classes

Teachers surveyed said they would tutor by finding the starting point, breaking into chunks, scaffolding, giving lots of practice, expecting mastery, and incrementally raising the bar. These are supported by learning science but often contradicted by district mandates. Teachers can justify these methods using neuroscience and apply them to whole classes.