• Nathan Belcher

Learning and Models

Updated: May 6, 2019

Humans are model-making machines—one author suggests that instead of Homo sapiens, we should be called “Homo modelus” [1]. In order to make sense of the world, we use our mind to construct systems, structures, and representations; these form the foundation of a model. We share our models with others so that we can collectively create, modify, analyze, and apply our models. After doing this process over many generations, we have established our current world—for better or worse, our models manage the way we interact with nature, each other, and ourselves.

If models are the central method for making sense of the world, then I believe that models should be at the center of any learning experience—especially during our time in mandatory education.


A definition of “Learning:” The act of creating, modifying, analyzing, and applying models.


A definition of “Model:” A mental representation for a concept.


A model contains the following:

  • System: Set of related objects in the model;

  • Structure: Set of relations among objects in the model; and,

  • Representations: Methods for describing and communicating the model.

The goals of mandatory education are the following:

  • Provide information and experiences for students to create accurate models of the world.*

  • Help students understand and use the modeling process—the practice of creating, modifying, analyzing, and applying models.

*World in this instance means the broadest form of the word, including nature, emotions, relationships, communication, science, mathematics, and many others.


The representations of a model are the following:

  • Written/Verbal Language;

  • Non-Verbal Language/Physical Movement;

  • Mathematics;

  • Diagrams/Pictures;

  • Graphs; and,

  • Computational.

Each model also contains the following:

  • Applications of the model; and,

  • Limits of the model.

Thoughts about models:


A model is not required to have all representations.


Using the idea of “models” as the basis for learning creates a bridge between educators who prefer direct instruction and those who prefer free-form inquiry. Students must create a model for themselves in a given educational experience, so they need some aspects of free-form inquiry; however, students must also create accurate models, which requires some direct instruction to allow comparison with established models. Combining aspects of both pedagogies—while retaining a focus on models—provides a robust learning experience for students.


The “modeling process” is defined as the practice of creating, modifying, analyzing, and applying models. Students modify models by comparing new information with their current model; when interpreting information, students must choose to modify their model to accept the new information or create a new model that represents the information. Though an activity could focus on only one part of the modeling process, the modeling process is typically performed in a cycle.


With this framework of models, assessments for students could focus on the following:

  • A student’s holistic understanding of a model;

  • One specific representation within a model;

  • The interplay between representations within a model; or,

  • Application(s) of a model.

Although students should create an accurate model of an “established model,” students should also examine and challenge the fundamental tenets of the established model. I recognize that many personally- and collectively-established models are detrimental to the person individually or society collectively, so students need practice analyzing models. The process of analyzing models may be transferred to their own models, allowing a metacognitive approach to creating and modifying models.


The modeling process of creating, modifying, analyzing, and applying models is a crucial skill throughout life in all domains; however, schools have typically neglected discussing or explicitly teaching students the modeling process. In Peak [2], Ericsson and Pool state that “everyone has and uses mental representations [models]. What sets expert performers apart from everyone else is the quality and quantity of their mental representations [models].” By providing opportunities for students to engage in the modeling process in many domains, students can be the best versions of themselves and become “expert performers.” As students repeat the modeling process throughout school, they will be well-equipped to continue the modeling process in their professional and personal lives.

For more information, please see this article on the Modeling Theory of Cognition.


This post was inspired by my dissertation research, upcoming presentation on Modeling Instruction at the NSTA conference, and chapter 3 (Mental Representations) in Peak [2].

[1] Hestenes, D. (2006). Notes for a modeling theory of science, cognition and instruction. Proceedings of the 2006 GIREP conference.


[2] Ericsson, A. & Pool, R. (2016). Peak: secrets from the new science of expertise.

Boston, MA: Houghton Mifflin Harcourt.

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© 2020 by NATHAN BELCHER

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