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Concepts

In this course, it is important to give the term "concept" a precise definition. Borrowing from the World-Wide-Web (W3C) standard for storing knowledge (SKOS), here is the definition for the term "concept" they use:

Definition for Learning Graphs

SKOS Definition of Concept: A unit of thought, an idea, or a notion, which is considered as an atomic unit of meaning within a given context.

This is a broad definition and to make it a little more useful, we will add one additional property: let's require concepts to have a name. We also refine "given context" to a specific learning context such as a course or curriculum. Here is the full definition we can use for this course:

Course Definition of Concept: A named unit of thought, such as an idea or notion, which is considered as an atomic unit of meaning within a given learning context.

In general, think of opening a high-school or college textbook and looking at the index at the back of the book. Each item in the index is typically a concept in that course. If the authors for the book think that it is important enough, they will list it in the index.

There are certainly concepts that don't have names. Our neocortex stores around 82 billion neurons and LLMs have trillions of neuron-like structures in their neural networks. Studies have shown that some LLM models can enumerate around 20 million named concepts. But for all practical purposes, in this course all concepts have a name. Technically, the primary name given to a concept is called a Preferred Label. If a concept has other names they are called Alternate Labels

Concepts vs. Content

It is important to not confused an abstract Named Concept from specific content such as a lesson plan, a wikipedia page, an instructional simulation (MicroSim) or a video. In general, content has references to one or more concepts, but concepts are more atomic building blocks that help us arrange content.

How Many Concepts in a High School Course?

The number of concepts covered in a typical high-school course can vary significantly depending on the subject, the curriculum, and the level of depth expected. However, a general estimate can be made. In this analysis, we will use the term "core concept" as being a concept that is introduced within a course, has a clear name, and is used consistency across many educational systems.

The number of core concepts introduce in a course also varies by subject area. Here are some examples.

  1. Mathematics: A high school algebra or geometry course might cover around 100 to 150 key concepts. These include foundational ideas such as solving equations, graphing functions, and understanding geometric proofs. Advanced courses like calculus might introduce 50 to 100 additional, more specialized concepts.

  2. Science: In a typical biology, chemistry, or physics course, students might learn around 200-300 major concepts. For example, a biology course might introduce cell structure, genetics, ecosystems, and evolution, while a chemistry course could cover atomic theory, chemical reactions, and thermodynamics. Physics might introduce concepts related to motion, energy, and electricity.

  3. Literature/Language Arts: An English literature course may cover 50 to 100 major literary concepts, such as themes, symbolism, metaphor, and narrative structure. It might also include concepts related to specific literary movements, authors, and genres.

  4. Social Studies: A history or civics course may focus on 150-200 key concepts, including historical events, political theories, government structures, and cultural movements.

Each course typically emphasizes a set of core concepts while also encouraging students to connect these ideas with broader themes or related areas of study. The number of concepts can be thought of as the core building blocks students are expected to understand and apply by the end of the course.

These estimates are drawn from educational standards such as the Common Core and subject-specific curriculum guides from various educational boards.

Counting Indexed Concepts

The number of concepts typically listed in the index or glossary at the back of a high-school or college textbook varies depending on the subject and depth of the material. However, here are general estimates:

  1. High-School Textbooks:

    • Science (e.g., Biology, Chemistry): 200--400 key terms and concepts. For instance, a biology textbook may include concepts like "photosynthesis," "cell division," and "genetic inheritance."
    • Mathematics (e.g., Algebra, Geometry): Around 100--250 concepts, including "quadratic equations," "trigonometric functions," and "coordinate geometry."
    • Literature/Language Arts: 100--200 literary terms, including concepts such as "alliteration," "foreshadowing," and "narrative structure."

    • College Textbooks:

    • Introductory Courses (e.g., Psychology, Economics, Physics): 300--500 concepts, covering key definitions, theories, and models. For example, an introductory psychology textbook might list terms like "cognitive dissonance," "classical conditioning," and "neuroplasticity."

    • Advanced Courses (e.g., Organic Chemistry, Advanced Calculus): 400--600 concepts, especially in subjects with extensive technical terminology.

In most textbooks, the index or glossary is a critical tool for students to reference important concepts, which are often highlighted in bold or italic throughout the text. The number of concepts aligns with the complexity of the course and the learning outcomes set by educational standards.