The following information is from Unit 20 of the book Teaching: A Course in Psychology by Wesley C. Becker, Siegfried Engelmann, and Don R. Thomas.
Note: Science Research Associates published the book in 1971. I am unsure if the publishers reprinted the book or if it is available to buy. I found it through a university inter-library loan program. I suspect that Becker or Engelmann use the book or some form of it in their special education teaching classes at the University of Oregon.
- Review: concept learning discriminates S+ from S- and both of these from Si
- Every concept characteristic has a value or range of values
- Fixed if only one value
- Example: 4 angles is a fixed characteristic of a square
- Range of value if more than one value
- Example: Many angles are a range of value for many figures
- The range needs to be defined
- S+ and S- are a set of values that are instances of some high-order concept
- Si characteristics are another set by themselves or are independent of what is being taught
- Example: any instance of shapes can be shown to present instances of color
- The teacher shows what characteristics are irrelevant and what are the range of relevant characteristics
- Ways to structure teaching sequences
- Teach the characteristic that leads to less possibilities available
- Switch from an instance to a non-example so that only one characteristics changes a a time
- You can do this repetitively by using different sets of irrelevant characteristics one at a time
- Good for teaching physical concepts
- Example: “the ball is ON the char. The ball is now NOT ON the chair.”
- Present a series of instances or non-examples where nothing changes but the range of characteristics to teach a range of S+ or S-
- Present of series of instances where the Si change and S+ stay the same to teach the range of Si
- Misrule: teaching something inessential to a concept
- Example: only showing brown dogs when teaching the concept “dog”
- The student may think that dogs are only brown
- Misrules happen when:
- There is no range of S+
- If an irrelevant characteristic in Si is not varied
- Avoiding memory load problems
- Do not present too much information at once
- Use pairs of instances you can compare directly
- Change one thing when going from instance to non-example
- Change one thing when going from instance to instance
- Change one thing when going from non-example to non-example
- Quickly present a sequence of instances
- Language to teach concepts through prior knowledge
- Use verbal rules
- A rule has no irrelevant characteristics
- Concepts that are more complex
- Use a verbal rule to describe how people use them
- Example: “a VEHICLE takes you places”
- Example: “FOOD is something you eat”
- Teach two levels of living things or objects with language
- Example: “Here is a horse” (show a picture)
- “The horse is brown”
- Vs. showing the picture and saying “brown”
- Example: “Here is a cup” (show the cup)
- “A cup has a handle” (point to it)
- Vs. “This is a handle” (point to it)
- To say “A cup has a” eliminates confusion on what handle might be
- “A cup has a bowl” (point to it)
The following information is from Unit 19 of the book Teaching: A Course in Psychology by Wesley C. Becker, Siegfried Engelmann, and Don R. Thomas.
Note: Science Research Associates published the book in 1971. I am unsure if the publishers reprinted the book or if it is available to buy. I found it through a university inter-library loan program. I suspect that Becker or Engelmann use the book or some form of it in their special education teaching classes at the University of Oregon.
- Discriminate or differential responding: in the field of learning, it refers to evidence of responding one way to one class of stimuli and responding another way to another class of stimuli
- Stimulus generalization: when a person responds to a new stimulus in the same way he responds to a previously taught stimulus that has similar characteristics
- Example: calling red things “red” and blue things “not red” and then calling orange things “red” also
- Three factors cause generalization
- The number of identical stimulus characteristics
- The number and magnitude of the difference in concept characteristics between two concepts
- The degree of prior discrimination training with concept differences
- If you can predict when stimulus generalization may occur, you can prevent or plan for the difficulties
- Analysis of concept universes
- Basic concept domains show that concepts from one domain do not share characteristics with concepts from another domain
- Concept domains
- Objects (living things, man-made things, etc.)
- Object properties (mass, heat, state, structure, parts, shape, size, color, surface properties, etc.)
- Events in time and space (conservation of mass, movement, change in energy, change in group composition)
- Relationships among events in time and space (cause and effect)
- Casual relations
- Teach lower-domain concepts before higher-domain concepts
- Example: teach what a car is before you teach the color red or the student may think that when you show a red car and say it is red, the student will think that “red” means car
- Example: the student should know the names and characteristics of things being taught for relative size
- The idea is to teach the lower concepts with concept instances and non-examples
- Then teach more complex concepts in comparison to the simple concepts
- Concept hierarchies: lower order concepts are joined together to form higher order concepts
- A higher concept has more instances (examples) than a lower concept
- To teach a hierarchy you teach concepts from two levels at the same time
- Example: to teach about mammals, teach mammals and not-mammals
- Then teach sub-groups of mammals
- Teaching two levels teaches:
- How concepts are related and teaches
- How one concept can be an instance of another concept
- Related concepts and instances need to be carefully discriminated
- Concept analysis examples
- Two concept pairs (S+) and (S-) and two other groups of concepts
- Concepts whose characteristics are irrelevant to the central concept instances (Si)
- Higher-order concepts whose characteristics are common to the two concepts being analyzed (Sc)
- Horses vs. dogs example
- Differences
- Horses (S+): hooves, large, mane, whinny
- Dogs (S-): paws, small, no mane, bark
- Irrelevant stimuli (Si)
- Higher order characteristics common to S+ and S- (Sc)
- Both: Mammary glands, four legs, move, grow, living
- Police dog vs. wolf
- Differences
- Dog (S+): bark, small, dull teeth
- Wolf (S-): no bark, big, sharp teeth
- Irrelevant stimuli (Si)
- Higher order characteristics common to S+ and S- (Sc)
- Both: canines, colors, move, grow, living
- Dog vs. tree example
- Differences
- Dog (S+): dog shape, move, noise, legs
- Tree (S-): tree shape, no moving, no noises, branches
- Irrelevant stimuli (Si)
- Higher order characteristics common to S+ and S- (Sc)
- Square vs. triangle example
- Differences
- Square (S+): 4 angles, 90 degree angles
- Triangle (S-): 3 angles, variable angles
- Irrelevant stimuli (Si)
- Both: size, position, color, surface pattern
- Higher order characteristics common to S+ and S- (Sc)
- Both: closed figures, straight sides
- To teach concepts
- If there are many differences between S+ and S-
- Teach some differences
- Example: dog and tree
- If there are few differences between S+ and S-
- Teach all differences
- Example: dog and wolf
- Common characteristics (Sc)
- Likewise teach more discriminations from S+ to S- if the concepts have few differences
- Irrelevant characteristics (Si)
- Make sure to teach most concepts in different angles or positions just in case a student may think that location is relevant
- Higher order concepts have more irrelevant characteristics
- The ratio of essential characteristics to irrelevant characteristics shows how abstract a concept is
- Example: the more Si and the less S+, the more abstract
- After you analyze the concepts you want to teach, you can group concepts
- You can determine what is higher-order
- You can determine teaching sequences
The following information is from Unit 18 of the book Teaching: A Course in Psychology by Wesley C. Becker, Siegfried Engelmann, and Don R. Thomas.
Note: Science Research Associates published the book in 1971. I am unsure if the publishers reprinted the book or if it is available to buy. I found it through a university inter-library loan program. I suspect that Becker or Engelmann use the book or some form of it in their special education teaching classes at the University of Oregon.
- Concept teaching
- Terms
- Concept: idea you want to teach
- Example: you want a student to say that some red things are red
- Teaching set: the examples you use to teach
- Example: the red things that you present
- Concept instances set: all things related to the concept
- Example: all possible red things
- Non-examples: things unrelated to the concept to discriminate
- Example: other colored things
- A concept is taught when any or all members of the concept set are correctly identified
- Even if some members were not in the teaching set
- Non-examples are responded to differently (not identified)
- Behavioral view of teaching
- Stimulus control of behavior: how stimulus events control a response
- In the presence of examples of the concepts, reinforce one response
- Example: reinforce a student pointing to a red thing when you ask, “Is it red?”
- In the presence of non-examples of the concepts, reinforce another response
- This can also be NO response
- Example: reinforce a student for NOT pointing or for shaking his head “no” when you show a blue thing
- Teach the student more and more critical concept characteristics to insure a concept is taught
- Example of when critical concepts characteristics are not taught
- A student can identify a square by saying its name
- The teacher has shown him a small black square and a big white circle
- The teacher shows him a small black circle (he says “square”)
- The teacher shows him a small white box (he says “not square”)
- The teacher shows him a big black circle (he says “square”)
- The teacher shows him a bigger black circle (he says “square”)
- The student discriminates the shapes on the colors (all black things are squares)
- What to do:
- Pay attention to teach the concept based on the shape and present a variety of colors and sizes
- OR teach both the circle and square at the same time with the exact same size and color
- Further example of misunderstanding of concept characteristics
- The teacher presents the circle and square at the same time with the exact same size and color (white and medium size)
- The student correctly says “square” and “not square”
- The teacher shows him a medium white rectangle (he says “square”)
- The teacher shows him a medium white triangle (he says “square”)
- The teacher shows him a medium white circle (he says “not square”)
- The student knows to look for corners or straight sides, but not for FOUR EQUAL ANGLES and FOUR EQUAL SIDES
- Present more non-examples as the student internalizes the the concept
- Example: present a rectangle, triangle, and circle while teaching the square
- Teach only the essential characteristics of a concept
- Rules
- It is not possible to teach a concept through one example and one non-example
- You must show a concept instances set and non-examples
- The concept instances set must have all essential concept characteristics
- The non-examples must lack all or some of the essential concept characteristics
- Vary stimulus characteristics that are not essential to the concept set and non-examples
- Concept learning happens through two discriminations
- Discriminate relevant characteristics of the concept set from relevant characteristics of the non-examples
- Discriminate irrelevant characteristics in the concept set and non-examples
- Example of teaching color
- Red cannot be taught without also showing non-examples of red such as blue, orange, green
- You are not teaching to discriminate blue from orange at this time
- Red needs to be taught by teaching that texture, pattern, shape, brightness, position, or size of things are all irrelevant
- Engelmann’s definition of concept from his book Conceptual Learning
- Uses all three concepts of a functional definition of behavior (stimulus event, procedure, and behavioral response)
- A concept: set of characteristics shared by a group of instances and not shared by other instances in a universe of concepts
- Terms
- Shared characteristics: physically definable characteristics
- Instances: basic units to give examples of a concept
- Universe of concepts: the set of concepts that the concept comes from and will be discriminated from
- Procedural and functional steps
- Identify a stimulus event that shares specified physical characteristics
- Reinforce one response for this stimulus event
- Reinforce another response for anything other than the stimulus event
- To test a concept
- Present new members of the concept class
- Check for correct responses (behaviors)
- Look at sets of concepts and common characteristics to design teaching strategies
- Essential characteristics of a concept change as other concepts included in the universe of concepts change
- Example: essential characteristics of a dog are paws, small size, light weight, and bark
- If you introduce a horse (non-example of dog) its essential characteristics are hooves, big size, heavy weight, and whinny
- If you introduce a mouse (non-example of dog) its essential characteristics are claws, small size, light weight, and squeaks
- Now you have to refine the characteristics for small size and light weight for dogs
- You specify the essential discriminations that you teach to avoid confusing the concept instances with non-examples
- Concept analysis
- Determine the essential characteristics of the concept set you want to teach
- Known as S+ (S for stimulus)
- Determine the essential characteristics that make non-examples of the concept set different
- Determine irrelevant characteristics of the concept set and/or the non-examples
- Example: “squareness”
- Teach squareness in a universe of concepts with closed geometric figures (like circles, triangles, polygons, etc.)
- Essential characteristics of the concept set: closed figures with 90 degree angles, equal length sides, and straight lines (S+)
- Non-examples: closed figures with any other angles, or unequal sides, or curved lines, or irregular lines (S-)
- Irrelevant characteristics for both groups: size, color, etc. (Si)
- To teach squareness you teach S+ from S- and Si
- Examples of pictures to use
- Squares with different colors and sizes and positions
- All other shapes with white color only and different positions
- How to design programs
- Use the essential characteristics to teach discriminations
- Use knowledge of some discriminations to move onto new ones
- Focus on teaching concepts relevant to what the student already knows
- Example with saying sounds for letters
- The universe of concepts is letters and sounds
- The first concept is the letter and sound “m”
- The non-example is a picture of anything (such as a fish)
- Introduce more letters and sounds
- Start with letters and sounds that are least similar (easiest to discriminate)
- Like “m” and “a”
- But “m” and “n” or “d” and “b” are NOT similar
- Avoid similar letters and sounds for later when the student knows more concepts
- Concepts and operations
- Operations or generalized response classes: behavior that functions outside of where it was taught
- Concepts: essential stimulus characteristics that are shared by a set of instances and not shared by non-examples in a universe of concepts
- Operations: essential response characteristics shared by a set of response in a given universe of operations
- Instances are the same for concepts as individual responses are for operations
- Examples
- Concept of color instances: blue bucket, red paper, green plant
- Concept of placing instances: place the box on a table, place the clothes in the dresser, place the paper on the desk
- A program teaches concepts through a set of instances
- The program teaches the range of instances, the range of non-examples, and the range of irrelevant stimulus characteristics
- A program teaches operations through a set of tasks
- The program teaches the essential characteristics of the operation, the essential characteristics of non-examples, and irrelevant response characteristics
- Reinforce correctly performed tasks
- Teaching both concepts and operations at the same time is possible
- Example: move something in relation to something else
- You can make unlimited operations such as place the box on a table, throw the clothes in the dresser, lift the paper on the desk
- An operation can become a concept
- Your observation of a student performing a learned operation is your concept of that operation
- Example of teaching imitation
- A student was in a class for low-functioning students and did not know how to talk or imitate others
- The signal the teacher chose to teach imitation was the words “do this” and then follow the words with the action to imitate
- The first task was for the student to raise her arm
- The teacher said “do this” and raised her arm
- The student did nothing
- So the teacher raised her arm for her (passive shaping)
- After several responses the student raised her arm on her own
- The second task was for the student to tap the table
- The teacher said “do this” and tapped the table
- The student raised her hand
- To discriminate between the two operations, the teacher took her hand and tapped the table for her
- After several responses the student tapped the table on her own
- Then the teacher went back and forth between the operations
- To teach that “do this” (imitating) involves looking at what the teacher does and then perform it
- New tasks were introduced as the student imitated the previously learned tasks accurately
- She learned the new tasks faster and faster
- After 50 tasks, the student imitated over half the new tasks the first time they were shown to her
- She learned the operation of imitation
- The student also learned how to imitate chains of responses
- Such as “do this,” then stand up, walk across the room, and clap your hands
- The teacher also started teaching the student to imitate sounds of words by inserting the sounds in the middle of a chain the physical actions
- Such as “do this,” then stand up, turn around, say “ah”, and sit down
- Operations needed for school success
- Imitation
- Follow instructions
- Pay attention
- Respond on signal
- Work for periods of time
- These operations must be taught if the student does not demonstrate them
- Habits and operations
- Concept teaching and operation teaching can be taught in a classroom but applied anywhere else
- Example: Verbal instructions to “turn left” can be taught in school but later used to learn how to drive a car
- Habits are done efficiently when they are done the same way each time
- The problem with habits is when the conditions change for the habits and they must be unlearned for new ones to be taught
- Example of using teaching concepts and operations to teach single-digit addition without regrouping
- Steps
- The student is taught to count up to a number (rote chain, like 1, 2, 3, 4 to 10)
- The student is taught to count objects up to that number
- Counting objects is an operation to determine how many there are
- The student is taught to identify symbols (numbers) that represent the counting
- The student is taught to make pictures of the symbols
- The student is taught that plus (+) means more
- The student is taught that equals (=) means what is on the left side of the sign must be on the right side of the sign
- 4+5= ? can be solved by drawing 5 pictures under the 5 and counting, “4, 5, 6, 7, 8, 9”
- The student is taught to use his fingers to solve the problems instead of drawing pictures
- The student is taught to count from one number to another to solve problems like 4+?=9 or 9=4+?
- What is good about this system is that after just a little teaching of the operations, the student can do solve many sets based on the operations
- Also the student learns algebraic equations concepts
- Example of using teaching concepts and operations to teach reading by learning ten sounds
- Steps
- Teach the ten sounds
- Teach blending skills at the same time as the sounds
- Now the student can potentially read 720 three sound words, 4320 four sound words, and 21,6000 five sound words!
- This is permutation of words (some are nonsense words but would give practice of the sounds)
- Teach all forty sounds of English
- Now the student can read much of the words in our language
- Teach irregular words at the same time as decodable words
- Operations for reading
- Blending (example: “maaaaaaaaaan”)
- Saying the word as a whole unit (example: “man”)
- Changing a sound in the word (example: “map” or “pan” or “men”)