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Concepts, Generalizations, Big Ideas, Facts, & Objectives

Ideas for communicating instructional goals

Questioning is the foundation of all learning.
The first step in rejecting not knowing is to ask, why?
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Overview

Introduction

This page defines and provides examples for goals, big ideas, facts, concepts, generalizations, and objectives.

It includes examples and general suggestions on how to faciliate the conceptualization of concepts to attain goals, outcomes, and objectives. Also includes examples.

Goals

Goal is a broad or general statement reflecting the ultimate ends toward which the total educational program is directed. (Sometimes refered to these as aims.)

Goal an immediate objective or outcome that a person desires and executes a behavior or sequence of behaviors to attain.

Motivation - hunger; Goal - food; Objective - raid the refrigerator; Outcome - eat and be satiated.

Concepts with explanations, examples, and instructional ideas

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:

  1. Logical necessity is based on the laws of logic and cannot be contradicted without contradiction.
  2. 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 strategies to facilitated, learn & assess 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 section 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.

More examples see planning and concept mapping.

Outcomes

Outcome is a statement specifying desired knowledge, skills, processes, and attitudes to be developed as a result of educational experiences.

Outcome is a description of what learners do to demonstrate understanding, skill, or competence.

Outcome levels describe different levels of what learners may do to demonstrate a level of skill, competency, or conceptualization of a concept they have achieved from beginning to advanced.

See - Determining outcomes in assessment article

Objectives

Objective is a statement specifying the purpose of a particular activity or action. There can be several different ways to communicate this information. Ranging from general to specific and for different domains of understanding. Six different types (General, Specific, Instructional, Behavioral, Performance, Expressive, and Domain Referenced Objectives) selection and types are reviewed below with examples.

Selection of objectives

Objectives can be selected from:

  1. An organizational topic, subtopic, theme, subject, subject dimension or category, disposition, process, ...
  2. Previous skills or objectives.
  3. A teaching-learning experience, both the learner's and teacher's experiences.
  4. Curriculum documents, standards, school, district, state, national.
  5. New ideas related to the scope and sequence of a topic, standard, or big idea from a problem that arises or identifiction of content that wasn't previously identified or foreseen.

Types of Objectives

General objectives

A statement reflecting the purposes of a particular unit or level of the school program, such as elementary, middle level, or high school.

  • (The learner will) Be critical consumers of literature.
  • (The learner will) Be mathematically literate.
  • (The learner will) Understand and use science content, processes, and inquiry to make sound personal and social decisions.

Specific objectives

A statement reflecting a short-range or more immediate purpose involved in a specific teaching-learning activity, such as unit or daily plan.

  • (The learner will) Complete pages 121-122 with 85% or better.
  • (The learner will) Count on when rolling two dice (die 1 = 4, die 2 = 3. Student will think or say 4 and count 5, 6, 7. Then move game piece) while playing Race to the Finish.

Instructional objectives

Clarify for the teacher what the learner will do (instructional purpose). This clarification can guide the design and selection of meaningful content, activities, and resources as well as guide the learners' progress. This is based on the belief that students need to be told how they are to be active in order for them to learn.

  • Today we will learn how to play the game - Race to the Finish.
  • To count onyou start with one of the numbers (the bigger is better) and count on the value of the other number. For example - to add two dice. Roll the two dice, select the larger number, say or think it, and count on (die 1 = 4, die 2 = 3. Think or say 4 and count 5, 6, 7).

As the task becomes more complicated an instructional object can be thought of as becoming a scoring guide or rubric. One example is the use of scoring guides or rubrics with Six or more Traits Writing as instructional objectives.

Behavioral objectives

Were origninally used for changing or developing behavior when the philosophy was that only obsewrvable behavior could be measured, therefore what happened inside the brain was irrelevant. To list ... To write .... To state... Today these may be also be called performance objectives.

Performance Objectives

Performance objectices have five components:

  1. What is done,
  2. Who is to do it,
  3. When is it to be done,
  4. What level of proficiency, and
  5. With what.
  • Given paper and pencil the learner will write solutions for 30 basic facts of addition in less than one minute, with 100% accuracy, by Friday the 13th.
  • After reading the story the learner will write answers to five literal comprehension questions by recall or rereading the story within the class period on Friday 13, 2013, with 80% accuracy.

Expressive objectives

Are used to personalize instruction to meet a wide range of possible outcomes.

  • (The learner will) Go on a nature walk and record observations of three organisms they choose.

Domain Referenced Objectives

Domain referenced objectives are objectives that relate to one or more of the three general domains of learning.

  1. Cognitive;
  2. Affective and;
  3. Psychomotor.

All activities involve all three domains, however, not all are usually identified, depending on the instructional focus. Which is usually cognitive. Hence, the popularity of Bloom's taxonomy when cognitive domains are referenced. For examples see taxonomies information.

Examples in curriculum areas planning, activities, & curriculum documents:

 

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