Facts, Concepts, Generalizations, & Big Ideas
Ideas for communicating instructional goals
Questioning is the foundation of all learning.
The first step in rejecting not knowing is to ask, why?
Sweetland
Introduction
This page defines and provides examples for facts, concepts, generalizations, big ideas. It includes examples and general suggestions on how to faciliate their conceptualization and examples with supporting activities.
Explanations, examples, and instructional ideas
Concepts
Concept - An idea about a particular phenomenon people abstract from specific experiences. The idea includes the necessary and sufficient properties that distinguish examples of the concept from all the non examples of the concept.
Examples:
- Flowering plants have flowers that develop into fruits, roots, stems, and leaves.
- Heat energy is the random or disorderly motion of molecules.
The following are also concepts: area, volume, density, flowers, energy, light, magnifying glass, animals, rock, soil, erosion, magnet, force,
Concepts summarize and categorize objects. The difficulty of learning a concept depends on the number of properties or characteristics needed to define it, its abstractness or concreteness, and the reasoning that connects the properties or characteristics.
The abstractness of a concept is related to how the concept can be experienced.
- Sensory - often physical observation and manipulation of the actual object(s): playing with a puppy, bacon sizzling, burnt toast, media, sphere, cube, solids, liquids, …
- Concrete visual or physical representation with models or diagrams or mental images: solar system, cell, heart, outline, plot, mixture, solution, temperature, density ...
- Abstraction where physical observation and manipulation are not possible. Examples: fiction, nonfiction, theme, tone, style, dystopian, politics, government, democracy, volume, atom, star, fission, fusion, evolution.
Concepts are best introduced through physical observation and manipulation (hands on exploration). Followed by a grand conversation; that provides a concept name, other examples, and non examples. Some concepts can be experienced at all three levels: temperature hot - cold to touch, concrete as read on a thermometer, and the abstractness of average kinetic molecular energy.
Mathematical concepts
Martin A. Simon, 2025, defines a Mathematical concept as the knowledge of logical necessity of a particular mathematical relationship. Logical necessity means learners are able to use their knowledge to determine that a particular relationship must exist. They are certain their reasoning about a relationship is valid.
For example: area of a rectangle. They understand why area must be the product of the length and the width. For them to have conceptual understanding they must have knowledge of the logical necessity of how the length and width combine to determine the area of a rectangle. Like the number of square units in a group (column) times the number of rows determines the entire area of a rectangle.
Necessity can be thought of as two types:
- Logical necessity is based on the laws of logic and cannot be contradicted without contradiction.
- Causal necessity, on the other hand, is based on cause and effect relationships and cannot be changed without altering the outcome.
Concepts can be made more concrete by defining them operationally.
For teachers the importance of writing concepts is prepare them to be able to clearly describe the concepts necessary to achieve the desired outcomes. It is not identify how the learners will explain the concepts themselves, but to identify what supporting information is needed for learners to construct the concept and have activities selected for them to access the necessary information to successfully construct the desired concept.
See
Facts:
Fact is something that actually exists or existed, object or event, and can be verified by observation. Facts are single occurrences.
Examples:
- The American flag is red, white, and blue.
- My birthday is in January.
- A square is a plane figure with four straight equal sides and right angles.
- A triangle is a plane figure with three straight sides and three angles.
- Temperature is the measure of heat energy.
Generalizations & Big Ideas
Generalizations are statements of a relationship between two or more concepts.
Examples:
- All matter has volume and mass.
- There is a relationship between an object's volume and surface area.
- Magnets attraction is stronger the closer they are to each other.
- Solids dissolve faster if they are smaller and the solution is warmer.
- Cold water will freeze faster than hot.
- Hot water will freeze faster than cold.
- Trees have growth rings that show a direct relationship between the age of a tree and the environmental factors that affected the growth of that tree for that particular year.
- Core samples from different trees can be organized based on observations of similar properties derived from the shape of their rings to match the rings of trees to the calendar year of their growth.
- The size, shape, and structure of an annual tree growth ring is a result of certain environmental conditions that positively and negatively affected the growth of the tree during the growing season.
- The rate heat energy is transferred is related to the number of collisions, size of particles, mass of particles, (or density of particles) and the force of the collisions (temperature).
- Evaporation will increase as the surface area, air movement, and temperature of the liquid increases.
- Plants grow from seeds. Generalization because it has three concepts plants, growth, and seeds. It can also predict future occurrences of the relationship - plants growing from seeds... It is also a summary statement not a one time occurrence.
Considerations to facilitate construction of generalizations
- Notice generalizations require understanding of each concept and a relationship to have meaning.
- They are also summary statements of relationships between concepts, summary statements of cause and effect, summary statements of predictions of future relationships, and a generalized condition of fact, all dogs have canines.
- Therefore, An implication for teaching is that in order for learners to generalize, they must have multiple examples from which to construct a generalization.
- Generalizations are powerful as they provide a way to consolidate information to make it more usable and easier to remember. Laws, principals, and theories are all kinds of generalizations. These generalizations require the connection of concepts by a relationship.
- Relationships can only be built with direct observational evidence and reasoning. Good teaching practices will mediate both.
- Remember - Most of the time people's conceptualizations are usually more similar than the ways they use to communicate them. This is expressed by the way that a listener's eyes light up when another person finds a word to describe to them what they have conceptualized, but has not been sufficiently able to communicate. Which is followed by simultanefous smiles of agreement and a simultaneous YES.
- Conceptualization before communication, with communication following a hard and difficult second, but learners that take the time to develop deeper ways to communicate and represent their understanding are more likely to have stronger and greater connects for their understanding to other ideas - resulting in richer more useable information that will increase their opportunities to make connections to real life and to solve problems.
Sample strategie to facilitated, learn, assessed ... generalizations?
For example consider generalizations for tree rings.
- Trees have growth rings that show a direct relationship between the age of a tree and the environmental factors that affected the growth of that tree for that particular year.
- Core samples from different trees can be organized based on observations of similar properties derived from the shape of their rings to match the rings of trees to the calendar year of their growth.
- The size, shape, and structure of an annual tree growth ring is a result of certain environmental conditions that positively and negatively affected the growth of the tree during the growing season.
A suggested opportunity to conceptualize them could be to provide a picture or better yet, samples of a tree sections with annual growth rings.
For example: One tree section might have part of it blackened and misshaped, others narrower than the others, with a third having ring parts missing.
A focus question might be, explain possible causes for what you observe about the growth rings.
Possible answers might include:
- It is possible that it was misshapen and darkened by fire.
- Might be openings where bark was missing and wood carved out and scared by insects and woodpeckers digging out other insects.
- The narrowness of the ring could have been caused by limited supply of water or light or extremely low temperatures during the growing seasons.
Another example for a generalization about rock.
- Rocks are formed from pieces of earth that are eroded and joined together with pressure and heat. Low pressure and heat sedimentary, more pressure and heat metamorphic, and enough heat to reach molten, then igneous.
Provide samples of all three kinds of rocks to explore, discuss their properties and possible ways they were created. Maybe start with something like - rocks are formed from pieces of earth that are eroded and joined together with pressure and heat. Low pressure and heat sedimentary, more pressure and heat metamorphic, and enough heat to reach molten, then igneous. Then help bridge the information with a diagram and rock cycle web and ecentually conclude with.
- Rocks are formed from pieces of earth that are eroded and joined together with pressure and heat. Low pressure and heat sedimentary, more pressure and heat metamorphic, and enough heat to reach molten, then igneous.
Goals
A goal is a broad or general statement reflecting the ultimate ends toward which the total educational program is directed. Some people sometimes refer to these as aims.
Goal can be an immediate objective or outcome that a person desires and executes a behavior or sequence of behaviors to attain.
Motivation - hunger; Goal - food; Strategy - raid the refrigerator!
More examples see planning and concept mapping.