Welcome to Hattennoki's blog/article series! I am Jaspreet Sethi, the author and founder of Hattennoki, and I’m excited to share my thoughts on brain science, learning, and development with all of you.

In any professional kitchen, an apprentice spends hours mastering the onion – the dice, the mince, the julienne – until the movement becomes second nature. It's an essential foundation, and there's genuine craft in it. But the journey toward becoming a chef also involves understanding why: how those onions transform in a hot pan, how they sweeten a stock, why they anchor a mirepoix. Technique and understanding, together, are what make the whole kitchen come alive.

Mathematics education sometimes finds itself at a similar crossroads. We invest years – rightfully so – in building procedural fluency: the long division, the FOIL method, the reliable mechanics of calculation. These are real skills, and they matter. But imagine if we also invited learners, more often, to taste the soup – to see where the mathematics lives in the world, why it works, and what it can create. The goal isn't to replace the chopping which is essential. It's to make sure the chopping leads to the art of cooking.

The Myth of the “Basics First”

There is a common misconception that one must master every procedure before "applying" math to the real world. Research suggests the opposite. According to the National Research Council’s seminal report, Adding It Up, mathematical proficiency is not a ladder of skills but an interwoven cord of five strands:

1. Conceptual Understanding: Comprehending mathematical concepts, operations, and relations.

2. Procedural Fluency: Carrying out procedures flexibly, accurately, and efficiently.

3. Strategic Competence: The ability to formulate, represent, and solve mathematical problems.

4. Adaptive Reasoning: Logical thought, reflection, explanation, and justification.

5. Productive Disposition: Seeing math as sensible, useful, and worthwhile.

Stopping at procedural fluency is like training a cook who can dice anything – but has never been let near the stove. A student might solve for x perfectly in isolation, yet have no idea how to carry it into a real problem: designing a structure, planning finances, or tracing the arc of an outbreak. The x was never the destination. It was always the ingredient.

The Relational Chef versus The Instrumental Technician

In 1976, cognitive researcher Richard Skemp introduced a framework that changed how we view learning: Relational Understanding versus Instrumental Understanding.

• Instrumental Understanding is “rules without reasons.” It is memorizing that to divide fractions, you “flip and multiply.” It works for the test, but it is easily forgotten because it has no “hook” in the brain.

• Relational Understanding is knowing both what to do and why. It is understanding that dividing by a half is the same as doubling.

When we teach math holistically - integrating the scientific (patterns and logic), the artistic (symmetry and design), and the historic (how humans solved problems 4,000 versus 400 versus 40 years ago) - we move from memorization to mastery.

A Recipe for the Classroom

To build a mathematical mind, we must stop teaching math in silos. Every lesson should be a “new dish” that requires a little bit of everything:

• The Scientific Lens: Using math to model the natural world, from the Fibonacci sequence in sunflowers to the physics of a basketball shot.

• The Artistic Lens: Finding the elegance in a proof or the geometric perfection in tiling.

• The Historic Lens: Understanding that algebra was a tool for trade and inheritance, giving the symbols a human heartbeat.

When we show children only the chopping, we risk losing them to boredom before they ever discover what the kitchen can become. But when we invite them into the full experience – the science behind the sear, the story carried in a spice, the intention behind a thoughtfully composed plate – they pick up the knife with something far more powerful than compliance. They pick it up with purpose.

Mathematics is not a rulebook. It is a landscape – vast, surprising, and worth exploring. The goal was never to produce apprentices who can follow a recipe. It was and will be to help them find and perfect their own.

The Curriculum Blueprint: Integrating all the Lens

To move from “chopping onions” to “creating a feast,” we need a vertically aligned curriculum that prioritizes depth over speed. As a curriculum designer, I don’t see creating the curriculum as the primary challenge – securing school-wide buy-in is. My blueprint illustrates how a single mathematical concept, the Pythagorean Theorem, can be taught as a holistic experience rather than reduced to a memorized formula.

Phase 1: The Scientific Lens (The “Why” of the Universe)

Instead of starting with a^2 + b^2 = c^2, we start with the geometry of space.

• The Experiment: Learners use physical squares (manipulatives) to build off the sides of a right triangle. They discover that the physical area of the two smaller squares literally “pours” into the larger one.

• The Observation: This isn't just a rule for a worksheet; it is a physical law of Euclidean space.

• Modern Application: How GPS satellites use trilateration (a 3D version of the theorem) to find my location in New Orleans.

Phase 2: The Historic Lens (The Human Story)

Math didn't appear in a textbook; it was observed in nature.

• The "Harpenodaptai" (Rope Stretchers): In Ancient Egypt, surveyors used knotted ropes to reset property lines after the Nile flooded and to lay foundations for temples and pyramids. Tradition holds that they employed a rope knotted in a 3-4-5 ratio to create perfect right angles – a story that, whether precisely historical or not, captures something true: that this mathematics was born from the urgent, practical need to impose order on a landscape that flood waters erased every year.

• Global Convergence: Discuss how this same relationship was discovered independently by the Babylonians (Plimpton 322 tablet), the Indians (Sulba Sutras), and the Chinese (Zhou Bi Suan Jing).

• The Narrative: Math is a universal human language developed to solve the problem of “fairness” and “stability.”

Phase 3: The Artistic Lens (The Beauty of Patterns and Design)

Math is the architecture of aesthetics.

• Symmetry and Design: Explore how proportional relationships and geometric structure shape what the human eye perceives as beautiful – from the recurring ratios that Renaissance artists wove into their compositions to the clean angles that govern modern architectural facades.

• The Spiral of Theodorus: Learners construct a “Square Root Spiral” by applying the theorem repeatedly, each new triangle growing from the hypotenuse of the last. The result is a beautiful, shell-like curve – not the exact logarithmic spiral of a nautilus, but a compelling echo of it, the kind of resemblance that makes learners look twice at both the mathematics and the natural world.

• The Activity: Learners create a “Concept Map” or a mathematical mandala that visually represents these square relationships through color and geometry.

Phase 4: The Strategic Application (The Holistic Dish)

Finally, we apply the “chopped” skills to a complex, multi-step problem.

• The Challenge: “Design a flood-resistant ramp for a local community center.”

• The Requirements: Learners must calculate the slope (using algebra), the length of the stringer (using the Pythagorean theorem), the cost of materials (applying arithmetic), and the ADA compliance (civic application).

• The Consequence: The learner isn’t merely solving for x; they’re thinking like an engineer, creating like an artist, and interpreting like a historian – just as mathematicians once did, when they were also thinkers, philosophers, and poets.

A visual example illustrating what “the onion” versus “the dish” looks like within a Geometry curriculum is shown below.

By “thinking in dimensions,” we ensure that a child in elementary school exploring area is actually laying the groundwork for geometry in middle school and trigonometry in high school. Mathematics taught holistically is not merely a collection of procedures to memorize – it is a connected language of reasoning that builds upon itself.

The question of whether these concepts are truly necessary will always arise, and the answer is always yes. A civil engineer calculating load distributions and a chef scaling recipes both draw from the same well of mathematical intuition, whether they recognize it or not.

If we reduce math instruction to isolated steps and formulas, we rob learners of the deeper understanding that makes those real-world connections possible.

Teaching mathematics holistically means teaching learners not just how to solve a problem, but why the solution works – and that understanding, cultivated mindfully and early through play and exploration, is what follows them into every school or life classroom long after the procedures are forgotten.

About the Author

Jaspreet’s journey reflects a deep and evolving commitment to learning and child development. She has grown from scholar to educator and, ultimately, to mother - each role shaping and enriching the next. Along the way, she has consulted with schools, partnered with educators, supported homeschooling families, developed curriculum, and worked directly with children as a teacher, with educators as a trainer, and with parents as a mentor. These experiences have shaped a well-rounded perspective, allowing her to understand learning and development through the lenses of study, teaching, and parenting. She strives to thoughtfully bridge theory with real-life practice.