Beyond the Formula Part I and II
Beyond the Formula — Two-Volume Collection
Physics is more than remembering equations.
Part I explores the science of understanding physics. Part II shows how active learning and conceptual assessment can help develop that understanding.
Understand the thinking. Improve the learning. Move beyond the formula.
Beyond the Formula — Part I: The Science of Understanding Physics
How Intuition, Mental Models, and Cognitive Science Shape the Way We Learn Physics
What You Will Learn
Beyond the Formula — Part I: The Science of Understanding Physics
Discover why memorizing formulas is not the same as understanding physics. Learn how intuition, mental models, misconceptions, working memory, and cognitive science influence the way we interpret the physical world. Develop a more thoughtful approach to scientific reasoning by learning to recognize physical principles, question assumptions, connect mathematical ideas with reality, and reflect on your understanding.
Beyond the Formula — Part II: The Science of Learning and Teaching Physics
Discover how physics understanding can be strengthened through active learning, meaningful discussion, physical modeling, conceptual assessment, and reflection. Learn why correct calculations alone may not demonstrate understanding, how to recognize the limitations of equations, and how evidence-informed learning strategies can encourage deeper scientific reasoning.
Together, these two volumes help readers move beyond memorizing equations toward understanding, questioning, and explaining the physics behind them.
Copyright © 2026 Albert Tan Lie Sing. All rights reserved.
First Edition — Version 1.0
Published independently by Dr. Albert Tan Lie Sing.
This publication is intended for educational and informational purposes. It synthesizes published research and presents interpretive frameworks and illustrative examples.
Purchase grants the individual buyer a nonexclusive, nontransferable license for personal reading, study, and reference. Redistribution, resale, republication, or commercial reproduction of the publication is not authorized without written permission, except as permitted by applicable law.
Short quotations and other uses permitted under applicable copyright exceptions remain unaffected.
Website: https://www.alberttls.us
Why can someone memorize equations, solve mathematical problems, and still struggle to understand physics?
Beyond the Formula — Part I explores the cognitive foundations of physics understanding. Drawing on established physics education research and cognitive science, this illustrated guide examines why formula memorization does not always translate into conceptual mastery.
Discover how intuitive reasoning, misconceptions, mental models, working memory, and metacognition influence the ways we interpret physical phenomena.
Through research-informed explanations, conceptual diagrams, and examples involving Newtonian mechanics, the publication introduces a more thoughtful approach to understanding physics beyond mathematical substitution.
Inside this 16-page illustrated guide:
- The limitations of formula-centered problem solving
- Differences between novice and expert physics reasoning
- Conceptual change and knowledge-in-pieces theory
- Intuition, context, and physical interpretation
- Working memory, multiple representations, and metacognition
- Five practical habits for understanding physics
For: Curious general readers, physics learners, parents, educators, and anyone interested in how scientific understanding develops.
Format: Downloadable, illustrated landscape PDF
Author: Dr. Albert Tan Lie Sing
Edition: Version 1.0 (2026)
Part I of the Beyond the Formula two-volume series.
Beyond the Formula — Part II: The Science of Learning and Teaching Physics
From Active Engagement to Conceptual Assessment and Evidence-Informed Educational Practice
What does it take to move from memorizing physics formulas to developing meaningful scientific understanding?
Beyond the Formula — Part II builds on the cognitive foundations introduced in Part I and examines how physics learning can be supported through active engagement, conceptual reasoning, and improved assessment.
Drawing on physics education research, this illustrated guide introduces Peer Instruction, cognitive pauses, modeling instruction, concept-focused tasks, and strategies for evaluating the physical reasoning behind mathematical answers.
The publication also addresses practical implementation challenges, including classroom design, cognitive workload, educational equity, and sustainable instructional change.
Inside this 19-page illustrated guide:
- Research supporting interactive engagement
- Peer Instruction and structured discussion cycles
- Modeling instruction and collaborative learning environments
- Conceptual assessment and changed-condition questions
- Separate evaluation of mathematical accuracy and physical reasoning
- Educational equity and a proposed implementation roadmap
For: Physics learners, educators, parents, science communicators, and readers interested in evidence-informed science learning.
Format: Downloadable, illustrated landscape PDF
Author: Dr. Albert Tan Lie Sing
Edition: Version 1.0 (2026)
Part II of the Beyond the Formula two-volume series. Can be read independently, but is designed to complement Part I.