Classroom Applications of Cognitive Psychology

Classroom Applications of Cognitive Psychology

Dr. Stan Hartzler     HartzlerSJ@aol.com

www.classappcogpsych.com

 

Perspectives

Cognitive psychology is the scientific study of human learning.  As a field of study, cognitive psychology began to emerge in the early 1980’s, when the first textbooks on the subject appeared.

Aided by (1) precision eye-movement machines for discerning attention, (2)  fMRI technology for following brain activity, and (3) well-designed experiments, cognitive psychologists were able to establish principles of learning.  Most of these affirmed the common sense of experienced teachers and of careful observers of human behavior.

But teacher trainers in colleges of education were largely unaware of these principles, or maliciously chose to ignore same.  Future teachers were presented with the customary theories of learning from Piaget, Dewey, Bruner, Skinner, and a newcomer, Stalin’s Vygotsky, among others .

The stated intention was to train future teachers to think like teachers.  Ignored were principles of learning needed for productive teacher thought.

Future teachers learned to abhor the idea that valid learning principles exist.  From many education professors who themselves failed as teachers, the idea was planted that every teacher muddies through a few early years until principles of professional survival have been learned.

The profession easily accepted silly ideas: new math, whole language, hands-on, block scheduling, and more.

Why should educators and school boards study cognitive psychology?  As a physician must understand biology (principles of life), an educator must understand cognitive psychology  (principles of learning).

The tragedy is that almost none of the well-meaning educators DO understand cognition principles.  We waste money and human potential unintentionally.

A definition of learning is important.  Otherwise, focus on principles of learning is difficult.  Learning is growth in knowledge, skills, and processes, to be recalled at will, and concepts/understanding, ability to apply and create, persistence, confidence, curiosity, and desire to learn more.

Given how important learning is, it is shocking how rarely definitions of learning are offered.  Ask an educator or education professor to define learning.  The result is often silence, or recitation of types of learning, or other avoidance.

The purposes of this writing are these:

• To establish that there ARE reliable principles of learning that apply to nearly everyone at any age and for any discipline;
• To offer that most teacher training programs and administrative functions never touch on these principles; and
• To begin the process of getting these principles and examples of their use in the hands of Texas teachers.

An initial effort to clear the fog begins with emphasis on the denial by many of the existence of universal principles of learning, often with distracting emphasis on individual differences.  Common similarities, the basis for learning principles, are more prevalent and more useful for classes.

Cognitive Psychology Themes

1.  Attention  (involuntary)
2.  Development of verbal & visuospatial potential
3.  Initial Learning
4.  Recall and Synthesis
5.  Application
6.  Associative networks
7.  Generalization and discrimination
8.  Affective goals

The eight categories above can be “chunked” above, as with font variations:

• The first two are preliminary considerations.
• The next three are the main themes of cognition textbooks, and of the classroom experience.
• The next two involve recurring themes, and applications or outgrowths of the previous three.
• The last is a happy, natural consequence of success with the other categories.

 

Distinctions between categories often blur.  Authors of cognition textbooks often assert that getting started in writing those books is difficult, as everything is closely intertwined.

Cognitive psychology is defined here as the study of how people learn, recall, and apply.  The classroom applications have been identified from background cognition principles, clinical (classroom) research, and teacher testimony (converts)

Serious educators often encounter jargon in teacher training courses and at professional meetings, in breakout sessions as well as when visiting with exhibitors.  Here are examples, none of which are involved with serious learning principles:     “Brain-based”  **   “Best Practices”  **   Educational Psychology  **  Theory  (Piaget , Skinner, Vygotsky, Dewey)  **   Brain Hemispheres  **  Learning Styles  **  “We only use X % of our…”

Hopefully, this presentation will clear the air considerably of such pop psychology distractions.

The outline of eight aspects of cognitive psychology may be schematized as shown below, albeit with some oversimplification.  The emphasis here is on how the “generalization/discrimination” and “associative networks” columns pertain to the previous four categories.

The foundation idea in all learning is attention, far beyond someone saying “Now please pay attention” – – though such requests are more helpful than is commonly suspected.  Attention is most powerful when it occurs involuntarily, and is then the foundation for all aspects of learning.

Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

I.  Attention (Involuntary)

The Familiarity Principle (over novelty) states that when presented with a familiar object (or idea) and a new object (or idea), the mind automatically and rapidly engages a comparison search, looking for possible recognition.  When such is found, attention is focused.

A student’s own name is a fundamental example.  Salesmen know that the sound of his or her own name is a most beautiful sound to anyone.

The Organizing Schema Principle states that involuntary attention is given to organization and symmetry.  When shown an outline or chart, attention is given to an effort to discover the basis thereof.

The Action Principle states that action usually demands attention.  A primary-grade teacher may say to a busy class, “Clap if you hear me.”  After a few clap, the teacher says, “Clap twice if you hear me now.”   Many more now clap.  Knowing the routine, the students disengage from what they are doing in orderly fashion, their attention drawn away by the clapping action.

The “Digestion” Principle states that adequate sleep each night is needed to absorb the day’s experiences, including those involving formal learning.  Students should sleep without sleep-aid drugs, and wake without an alarm clock.

At some point late in each night of adequate sleep, the mind replays the day’s events in order, and sorts familiar events from one-day occurrences.  Familiar events add to concept development and recall potential.  Evidence also exists for development of problem-solving insight during sleep.  (Nature, ….)

This process may be compared favorably to a cow chewing cud.

The digestion principle also has implications for school scheduling, namely, for why block scheduling in either form (alternate days or alternate semesters) is not productive, why it has been dropped by the fashion-oriented districts who tried it, and why it was never tried by the common-sense leaders.

For if a student studies science only on alternate days, the natural sleep processes that provide for recall and synthesis are not nearly as strongly involved as when the student studies science each day and sleeps on science each night.  Every-other-day routines may be fine for runners and body-builders, but the mind is NOT a muscle.

The Request Principle states that suggestions of many kinds are more influential than is generally believed, but that specific requests for attention are helpful in gaining even involuntary attention.  When a student hears a teacher say, “Eyes up here,” action is also involved, and as most people are highly visual, attention is further aroused.  Pointing, one of the first forms of communication learned by infants, is another effective request, as is any encouragement.

The Load Limit Principle asserts that attention can be overloaded and thus be made less available, much as a bridge might be labeled “Max Weight 2 Tons.”  Richly-informative reading material may incline a reader to pause for a brief nap or other kind of break now and then.

The Challenge Principle (involving creativity, problem solving, discovery) may arrest so much attention that the individual thus challenged can think of nothing else for a considerable period of time.  For this reason, a teacher may wisely postpone introduction of such stimulus until the end of the school day, or at least before lunch or recess.

The Emoting Principle encourages teachers to state dry material with vocal inflections as a pre-K teacher emotes when reading a story about baby chicks.

What distracts student attention?

• Skin, which is why a good dress code, and enforcement, is a good idea.
• Off-task speech.
• Students getting up out of seat for trash or pencil-sharpening.
• Other student faces, which is why theater-style seating arrangements are generally more productive that groupings around trapezoidal tables.  Principle:  Attention goes involuntarily to rich sources of information, such as human eyes and mouths.  “Knees under desktop, elbows at sides or forward.”

Experienced teachers plan for some kind of shift in classroom events for every 15 minutes or so.

Organized Schema Principle:

The Gordon Bower experiment

• Half of a lecture audience is given twenty-six words pertaining to minerals.
• The other half is given the same terms but in a schematized outline.
• The audience members look at the terms casually, with no one aware of what the other half has.
• The lists of terms are stowed; the lecture continues.
• A half hour or so later, audience members are asked to write down what mineral terms they recall.
• Much more is recalled by those with the organized list.  (Bower et al., 1969.)
• Recall is better for the first word (primacy) and the last word (recency).  The primacy and recency effects are temporary.

Schemas have great value for both initial learning and recall.

Most powerful routines for gaining involuntary attention in a classroom:

1. Familiarity principle:  Have review questions on display (overhead or board) when students enter classroom.
2. Schema (organization) principle:  Present new material in organized format – – outlines, symmetry.  (Connections)
3. Pointing, pointing (index) words:  Have schematized posters to point to.

 Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

II,  Preliminary: Development of Verbal and Visuo-Spatial Potential

Humans are born with innate potential for two abilities that must be developed.

* Verbal:  developed with much correctly spoken English (or…) in early years.  Without human language, child develops his/her own.

* Visuospatial sense: developed with origami, gross-motor sports, hand tool use. Defined:  Ability to look at a two-dimensional drawing of a three-dimensional object and correctly identify another view of the same object.

(Other  “intelligences” described by John Gardner are not confirmed.)

Innate Potential Perspective: All people are born with potential for these two important cognitive abilities.  Environmental development is needed, the earlier, the better.

Research: An Investigation of Effects of Origami and Ambiguous-Figure Drawing on Development of Visuo-Spatial Sense in Middle School Students

A study was conducted of visuospatial sense development, using two treatments (origami; drawing of ambiguous figures), involving ten teachers and 654 students; a pre-test/post-test 2 ´ 2 design involving factorial analysis, and tests for interaction with teacher, gender, grade-level, pre-test score, time of day, and ethnicity.  Significant gender-related gains were found.

Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

III.  Initial Learning
The content of learning involves

• Information,
• Skills,
• Processes, and
• Understanding

Initial learning is not the be-all and end-all as implied in teacher in-services and pre-service training.  What is implied is the idea that if initial learning is done “right”, forgetting and confusion will never happen.  FOLLY!  Recall of learning is where dramatic gains are made.

But!  There ARE issues – –

The First Draft (Bootstrapping) Principle states that less than 100% of the sensory input of a lesson or other situation is learned on the first day, and that 80% of what is learned is not recalled in 24 hours.

In the classroom, therefore, the teacher must provide for a brief re-hash of the previous day’s lesson/experience, and a bit on what was learned the day before that, considerably improving on that first-day draft.

The Whole-Part-Whole Principle involves a summary statement of a new lesson at the outset, followed by some detail about one aspect, followed by a review of the summary, followed by detail of a second aspect, etc.  A Russian educator called this pulsing.

Application of whole-part-whole learning can occur in literature if the teacher is not rushing to finish any story or poem in one day.  The example here uses the classic Thorton Burgess story, “Spotty the Turtle Wins a Race” from Old Mother West Wind. 

If “Spotty” is done in thirds, the first day introduces the characters and sets up a race between Reddy Fox, Billy Mink, and Peter Rabbit – –  and, after some teasing, Spotty.  The first third ends when the race director (Grandfather Frog) says GO.

Whereupon the teacher can stop and ask the class some questions.

1. Have you heard of a story like this before? Describe it.
2. How is this story like the one you heard before?
3. How is this story different?
4. Will these differences affect the outcome of the race? (Who wins?)
5. Will these differences affect the rabbit’s attitude/behavior about the race?
6. What do you think will happen next?

The next day’s Spotty experience begins with a review of what happened in the first third, and of the class discussion that followed.  Then the second third is read.  Similar questions are discussed, such as, “What is the most important thing in the new part?”

The rest of this second day of Spotty is used for the last third of something else that was started two days ago, and for the first third of the next story or poem or whatever.

The third day of Spotty begins with a review of the first two days, and so on.  The ending is compared with class predictions.

Depth of Processing Principle.  Psychologists have determined that different modes of processing information have varying intensities.  The more intense the processing, the better the chances of recall and synthesis.

At the low end of processing are hearing and seeing, because these are passive.  The form of the information is not changed.

So when a student who is not taking notes is admonished to begin taking notes, that student will often respond with “I understand what you are teaching.”  The teacher may respond that such understanding goes in the eyes and out the ears, but when notes are taken, the information goes up the arm’s neurons and into the brain, and stays there.  Such is a bit silly, but a bit true also.

(Smelling, by the way, is permanent, and needs no additional processing for establishing familiarity and recall.)

1. Whenever there is sensory input, the mind attempts to form a representation.  This is the most basic information processing.
2. When the mind works to change the form of the representation, deeper processing occurs, particularly when the new form is the person’s own speech.  Recitation and choral reading are to be greatly valued.
3. When a person retrieves the input after attention has lapsed, deeper processing occurs also.
4. When this retrieval succeeds under stress, such as an exam or public recitation, or in a creative application, very deep processing occurs, as when the mind synthesizes several representations.

Speech is the most intensive thing we do voluntarily to our central nervous systems.  This is why peer tutoring helps both the tutored student and the student doing the tutoring.  Prerequisite: the student doing the tutoring must be proficient with what is being explained.  Veteran teachers often say that we never learn anything quite so well as when we learn to explain it to someone else.  (Even this is not cognitive “Super-Glue.”  There is no such thing.)

The Depth of Processing Principle has been twisted into useless simplicity by any number of sources, most popularly by Glass (after Dale) and by the fraudulent Chinese Proverb: “I hear, and I forget; I see, and I remember; I do, and I understand.”  All of which is nonsense.

By the Chunking Principle (Bower), information is absorbed (and recalled) more easily if learned or considered by categories.  For example, if asked to name as many kinds of flowers as possible, most people can list up to seven.  The limit is tied to the Load Limit Principle: once a few have been recalled (activated), those few keep popping back up into consciousness, crowding out the possibility of recalling more.

But if asked to name kinds of flowers in categories, such as “holiday” flowers, “garden” flowers, “woodland” flowers, “special someone” flowers, and so on, up to seven different kinds can now be recalled in each category.

The Separation From Context Principle was exemplified in one Kindergarten class in Wichita Falls, Texas, through use of three different arrangements of alphabet letters.  Each child had two file folders.  One folder had the alphabet letters in three rows with the apple-bat-cat drawings; the other folder had the alphabet letters and drawings in two columns – – a new context.  The alphabet strip atop the chalkboard contributed a third context.

By contrast, these students had only one number strip atop the chalkboard.  A practicum student would point at the numbers in order while the students chanted the names.  Several chanting students were observed looking elsewhere during this exercise, prompting this question of the practicum student: if the students were asked to identify the 14 without chanting the whole list in order, would they succeed?  When this was tried, the students failed.  They could not identify the numbers outside the context.

The suggestion was made to have the students do the list backwards, forwards and backwards, and, of course, with the pointer skipping around with no particular order.  Also suggested was

• using the calendar as a second context, which would change nearly every month.
• a chart of numbers in rows by tens, found in the typical classroom.
• a list of numbers from one to two hundred, in eight columns of 25.

The last suggestion was used by many classroom teachers with their own elementary students while said teachers were graduate students in evening courses.  Returning for the following evening class meeting, several teachers were asking, “Why did the columns-by-25’s work better than the others?”

The additional context was at work, not necessarily its particular nature.

Identification of alphabet letters and numbers need to be recalled apart from any particular context – – as does anything else.

The concept of a fraction is particularly difficult, and too often made uselessly “easy” by context-bound situations.  Four distinct concepts of a fraction exist; many differing written and pictorial representations are used to help develop these concepts.  None done in isolation are helpful.

• Among the pictorial representations, drawings of circles are preferred for implying one whole.
• Time on a standard clock face provides an important context for fractions, and allows a child’s participation in telling time.
• Ruler literacy is also important in its own right, and allows another reinforcing context for fractions.  Students may experience a progression of teacher-supplied paper rulers that have, at first, only whole and half-inch markers.  Later, paper rulers that also have quarter-inch, and then with eighth-inch marks also, are introduced
• Music, especially piano music, provides several kinds of context for fractions, including time signatures; half-notes, quarter-notes, etc., and rests; dotted half-notes and half-rests, etc.  Inexpensive keyboards make possible a program for in-school piano-music literacy.
• United States coins commonly used for making change provide another context for fractions.
• Sports statistics provide opportunity for understanding changing form, from common fraction to decimal fraction to per cent.

Comfort with the concept of fraction takes many years, many representations, and many contexts.

Initial Learning: General

• It really doesn’t matter HOW students learn. What matters is whether students recall and synthesize.
• Direct Instruction is the most efficient and reliable avenue to student learning.
• “Discovery” is more desirable for student enthusiasm if the discovering can be done with certainty and efficiency. Group discussion helps application later.
• After learning has occurred, group discussion provides
  • new context,
  • speech for deep processing, and
  • viewpoints for understanding and applying ideas.
• The Matthew Effect (paralleling St. Matthew, Ch 13, v 12) states that much prior learning eases acquisition of new learning. Proper application of principles of cognition will minimize this advantage.

Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

IV.  Recall memory and Synthesis

Dramatic gains in student achievement most often follow implementation of innovations in recall strategies.  A brief summary of the inevitable need for such changes follows on pages 11-18.

The issue of recall is often confused with memory, memorize, and remember.  Memory is always there in the brain, but cannot always be accessed consciously.  Recall is the correct term, because recall involves voluntary and ready access to memory.

Without voluntary and ready access to memory, learning is relatively useless.  It is argued here that useful learning only exists if it can be voluntarily and readily recalled.

Cognitive psychologists measure strength of recall in terms of speed and accuracy.  Taken together, speed and accuracy constitute automaticity.

Automaticity (rapid and strong recall) is given a bad reputation by some because it evokes unthinking memorization.  One needs only to consider the alphabet song to realize that accurate recall of otherwise unrelated information can still be useful.

Automaticity of arithmetic facts or algorithms does not cancel out ability to justify a result, in spite of common assertions otherwise.  This false accusation against automaticity also ignores the usefulness of fact automaticity when a common denominator or common multiple is needed when working with fractions.

So automaticity is not only harmless – – it is critical to discovery and understanding in many situations.  The checkerboard problem that follows in the application section illustrates the value of automaticity to problem solving.

Fluency makes use easier, and means less taxation on attention load limits.  Language fluency is aided by work with a memorized sight vocabulary, intensive phonics, cursive writing, and spelling.  Good grammar and general language fluency are attained more easily.

Arithmetic facts are easily learned with daily reading of fact charts – –  not tables – – with timed tests (student against self), games, and flash cards providing other contexts.

The key here is review (not “repetition”).  Review involves reactivation after deactivation, sleep being the most powerful kind of deactivation.  “Repetition” can mean drill, which involves no deactivation/reactivation and is thus useless.

Along with review, association is a powerful (while less available) aid for developing recall power.  Outlines, charts, and other visual schemas provide parallel and hierarchical associations that aid in recall (and understanding).

Other forms and examples are

1.  Songs and stories, with helpful self-referencing cues for recall
2. Word and picture pairings
   1. For word recall, associate a picture.
   2. For picture recall, give the picture a name.
3. Visualization in general
4. Schemas such as HOMES (names of the Great Lakes), Roy G. Biv (ordered colors of the visible spectrum) and M. Vem J. Sun, with P or X (ordered planets of our solar system.  PEMDAS is a faulty attempt at a schema for learning the arithmetic order of operations.

Review routines for recall and synthesis

In the 1980’s, teams of teachers in the Oklahoma City Public Schools created year-long programs of carefully-sequenced ongoing review exercise sets for arithmetic.  Called DARES for Daily Assorted Review Exercise Set, each day’s work consisted of one addition, one subtraction, one multiplication, and one division exercise, along with one or two exercises concerning time, money, place value, or distance measure.  (See sample on last page.)

Teachers had a DARES on the display at the start of school, or after recess or lunch.  The basic familiarity of this routine captured involuntary attention.  After students had the chance to try the set, the teacher would do each exercise at teacher speed, speaking and writing.  Then the usual class routine would begin.

Achievement scores for the OCPS students significantly improved from below to above the national average for mathematics on the California Achievement Test, across all grades.  Results continued to snowball in subsequent years.

Teachers using Daily Oral Language (DOL) noticed the same power of ongoing review for recall and synthesis.  Each DOL set consisted of two sentences daily for spelling, grammar (all editing).  Examples (grade 7):

         jake dont want to watch national geographic presents at his uncles house

         father has tore the editorial from the new york times but he cant make no sense of it

Teachers wrote their own DARES for other subjects, with exciting results.  Following are steps teachers may use to write Daily Assorted Review Exercise Sets for themselves for any subject.

1. Get a spiral notebook
2. List 5-6 basic review objectives inside front cover
3. On first notebook page, write one review exercise for each review objective.
4. Make four similar sets of review exercises for same objectives – a week’s supply.
5. Give first set to class, on display or copied on paper. Students work without help; teacher does housekeeping.
6. Teacher does exercises (writing & talking) on display once students have had chance to try. Minimize interaction.
7. Go on to new lesson. The DARES routine should take 5-6 min.

Quizzes, oral/choral or written, and exams should be cumulative, reflecting current class work and material from the DARES routine.

To fully appreciate the power of ongoing review routines on classroom learning, one might peek in at band practice or practice for any sport.  Note that both band and athletes must perform well in public, or someone responsible will need to go.  Basketball is the example used here – –

Imagine your basketball coach saying, “OK, team,

• Monday night’s practice will be only dribbling.
• Tuesday will be only free throws — no dribbling.
• Wednesday will be only three-point shots — no dribbling or free throws.
• Thursday’s practice will be only in-bounds plays.
• Then you’ll put it all together in Friday’s game.”

RIDICULOUS.

No successful coach of athletics or director of music or theater would do anything so silly.

With good coaching, directing, or teaching, each day’s practice is mostly cumulative review, with some time set aside for moving some aspect to a new level.  Students see daily growth and enjoy the learning, which is one reason why most band members prefer band to any other school experience.

Yet the ridiculous, fragmented approach is how most people in the United States learned mathematics, and, consequently, why we have such national illiteracy and phobia regarding mathematics.

DOL  (Daily Oral Language) and DARES (Daily Assorted Review Exercise Sets ) (etc.) succeed because they imitate successful practice structure used by successful coaches of athletics, or directors of music or theater.

DARES: Historic results may be found on the web site given at the top of this post.

Arithmetic Facts:  Choral Reading

In the 1930’s, first grade students read multiplication facts aloud in unison each day at St. Patrick’s school in Paola, KS.  At the end of first grade, every student knew the multiplication facts, along with the meaning of multiplication and many of the patterns that are routinely discovered with such daily review.  Applications to real-world situations are likewise discovered with such a knowledge base.

Kindergarten and first-graders might do daily recitation to master the addition facts. The multiplication fact chart recitation could then begin, perhaps by the first of November of first grade.

 

1 + 1 = 2 1 + 2 = 3 1 + 3 = 4 1 + 4 = 5 1 + 5 = 6 1 + 6 = 7 1 + 7 = 8 1 + 8 = 9 1 + 9 = 10	2 + 1 = 3 2 + 2 = 4 2 + 3 = 5 2 + 4 = 6 2 + 5 = 7 2 + 6 = 8 2 + 7 = 9 2 + 8 = 10 2 + 9 = 11		3 + 1 = 4 3 + 2 = 5 3 + 3 = 6 3 + 4 = 7 3 + 5 = 8 3 + 6 = 9 3 + 7 = 10 3 + 8 = 11 3 + 9 = 12		4 + 1 = 5 4 + 2 = 6 4 + 3 = 7 4 + 4 = 8 4 + 5 = 9 4 + 6 = 10 4 + 7 = 11 4 + 8 = 12 4 + 9 = 13		5 + 1 = 6 5 + 2 = 7 5 + 3 = 8 5 + 4 = 9 5 + 5 = 10 5 + 6 = 11 5 + 7 = 12 5 + 8 = 13 5 + 9 = 14
6 + 1 = 7 6 + 2 = 8 6 + 3 = 9 6 + 4 = 10 6 + 5 = 11 6 + 6 = 12 6 + 7 = 13 6 + 8 = 14 6 + 9 = 15		7 + 1 = 8 7 + 2 = 9 7 + 3 = 10 7 + 4 = 11 7 + 5 = 12 7 + 6 = 13 7 + 7 = 14 7 + 8 = 15 7 + 9 = 16		8 + 1 = 9 8 + 2 = 10 8 + 3 = 11 8 + 4 = 12 8 + 5 = 13 8 + 6 = 14 8 + 7 = 15 8 + 8 = 16 8 + 9 = 17		9 + 1 = 10 9 + 2 = 11 9 + 3 = 12 9 + 4 = 13 9 + 5 = 14 9 + 6 = 15 9 + 7 = 16 9 + 8 = 17 9 + 9 = 18

Why is work on recall so helpful?  Is the quest for the magical “forever learned” explanation really a fantasy?  YES.  Is there no cognitive Super-Glue?  NONE.

Here’s why.  Two enemies of existing learning have been a part of common sense since at least Bible times, and were part of educational psychology textbooks in the 1950’s in the USA.

• First, time causes forgetting. Though I taught Simon & Garfunkel’s song, “Sounds of Silence”, over several years in the 1970’s, I struggle now to recall those lyrics.  Time causes forgetting.
• Second, further learning causes confusion. Learning the next Simon and Garfunkel song meant more practice on the “Sounds of Silence”; else, I would get the songs confused.  Further learning causes confusion.

In the early days of psychology, forgetting was called extinction, and confusion was called interference.  Today’s “ed psych” courses ignore these issues, and thus also ignore how to help students vanquish these enemies.

Can these enemies of learning be vanquished?  Yes!  The heroic practice of ONGOING REVIEW makes friends out of the enemies of learning.

Time causes forgetting?  Further learning causes confusion?

• Ongoing review turns forgetting into recall ability.  The first days of use of DARES or DOL take more time because recall ability is being nurtured.  After the first week or two, recall ability becomes obvious, and use in applications (such as word problems) is expedited.
• Ongoing review turns confusion into synthesis.  Without DARES, students can only subtract after a few days in the subtraction chapter, and subtraction ability notably weakens a month later.  Subtraction, and all other topics, are bound by context.

After a few weeks of DARES, a student will be able to subtract underwater, at midnight, hanging upside down, with one hand tied behind his or her back.  True learning is not bound by the context of an isolated two-week unit of study.

Association routines for recall and synthesis

Thinking Approach to Problem-Solving (TAPS)

For arithmetic word problems, are there two or more numbers to – –

Combine?  Then – –

Groups equal? Multiply

Groups unequal? Add

Separate?  Then – –

Groups equal? Divide

Groups unequal? Subtract

Compare?

To find a ratio? Divide

To find a difference? Subtract

Without TAPS organization (or…) and student practice on its features, students don’t have a helpful decision system for arithmetic applications.

The TAPS organization chart as outlined above should hang on a poster in the classroom, and be reviewed daily and be the subject of informal and formal quizzes.   [Generally, classroom posters are successful in the same way that highway billboards work, and they do work.  Outdoor advertising is a billion-dollar industry.]

One universal schema for organization key ideas in nearly any discipline involves classification and relationship . Classification involves one thing at a time.  Relationship involves two things at a time.

Schemas emerge that can, for example, take the enormous pile of important geometry vocabulary and make it all accessible to understanding and recall.  (See last page.)  The sciences all involve vocabulary with similar distinctions; “predator” is classification for one species; “predator-prey” is a relationship involving two species.

 

Stress in benevolent doses for recall and synthesis

Along with review and association, stress in proper doses is a powerful (while less available) aid for developing recall power.  Exam and quiz questions are recalled more readily than lesson and assignment examples, because of the stress involved.

Stress can be overdone, of course, doing more harm than good.  So exams and quizzes must be well-previewed.  An effective and comfort-inducing routine is to begin a class with a quiz preview, perhaps including the DARES, with a closely-related quiz at the end of the class.

Students who volunteer for simple recitation or at the board (or other display) are also within the zone of personal comfort.

Especially when the exam or volunteering are successful, the processing of the information involved is very deep.  In short, processing is deep and positive when public performance is successful.

Following is a geometry example of quiz-preview/quiz for a single class meeting.

 

Quiz Preview

Geometry Quiz 11     10/13/09

Dr. Stan Hartzler  ACHS                       Name___________________________per___

Set up, but do not prove:

1. All right angles are congruent    2.  Corresponding angles are congruent.

 

3. Draw and label the following, with no two coincident:

 

radius          diameter      chord        secant         tangent

 

4. State the Pythagorean Theorem.

 

Given ____________________________________, then ____________.

 

5. Show whether or not these are Pythagorean triples.

{ 40, 42, 56 }                                                { 33, 56, 65 }

 

6. Set up and prove the theorem about all right angles.

 

In the age of word processing, quiz-previews and matching quizzes are easy to generate.  In this example, questions 1, 2, and 5 have been changed from the forgoing preview with minimal effort.

 

Related Quiz

Geometry Quiz 11     10/13/09

Dr. Stan Hartzler  ACHS                        Name___________________________per___

 

Set up, but do not prove:

1. Vertical angles are congruent. 2. Alternate exterior angles are congruent.

 

3. Draw and label the following, with no two coincident:

 

radius             diameter       chord      secant       tangent

 

 

4. State the Pythagorean Theorem.

 

Given ____________________________________, then ____________.

 

5. Show whether or not these are Pythagorean triples.

{ 15, 36, 39 }                                                 { 44, 117, 127 }

 

6. Set up and prove the theorem about all right angles.

 

Synthesis is the blending together of information or other ideas from two or more lessons.

Four aspects of fraction are introduced one at a time in early grades.  As the second aspect is learned, the first should be reviewed, and this pairing should be reviewed daily for weeks.  Synthesis begins.

• As the third and fourth aspects of fractions are introduced, the previously-learned aspects are reviewed.
• Diagramming sentences provides synthesis and elaboration on parts of speech.
• Habitat provides synthesis of the characteristics and needs of living things.
• Two or three varied arithmetic word problems are needed daily for TAPS to instill recall and synthesis in students.

Do manipulative experiences aid recall?  Yes and no.

A popular hands-on group activity allows discovery of the approximate value of π with use of round lids and masking tape.

• Tape and lids of varied diameters are given to pair of students, one lid per pair.
• Imitating the teacher, students wrap a piece of masking tape around the edge of the round lid, exactly once. Extra tape is discarded carefully.
• This “perimeter tape” is removed from lid and laid out flat on table or desk.
• Lid diameters are marked off sequentially across the tape.
• Diameters marked on the tape are counted.
• Discussion results leads to the conclusion that no matter what the size of the lid, the perimeter is three diameters and a little more.
• Applications are posed and answered. How big is the perimeter if the diameter is 10?

The lesson is hailed as a great example of how a lesson should be conducted.  What student could possible forget?  Has cognitive Super-Glue been found?

But when the students are asked the next day, “Who recalls what we did yesterday?”, all is lost, even for college students, without prompts.  No glue.

Moral: manipulatives provide an important new context, but activity and links between activity and its purpose must be reviewed in subsequent days.  Eventually, the experience can become the substance of quizzes and exams.

 

Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

 

V.  Application – – Pinnacle Experiences

Routine applications such as word problems in science or mathematics are often the limit of student experiences and teacher applications.  Slightly better are uses of mathematics and science in cooking, tailoring, agriculture, construction, and so on.

Truer and more educational applications are more extensive.  A commonly-accepted list of independent pinnacle experiences follows.

• Discovery in science – – independent investigations from the student’s curiosity, with minimal coaching from a teacher.
• Critical thinking and understanding in social sciences
• Creativity in language arts and fine arts: new analogies
• Problem-solving in mathematics – – beyond the level of instruction, of interest to the student, using non-essential content, and developed away from class time.

Student interest is often sparked by a teacher modeling such a project.  A science teacher should have some kind of personal investigation project as a kind of hobby, and share this hobby with students.

Likewise, teachers in other courses should likewise be involved personally with pinnacle projects pertaining to their subjects – – problem solving, digging local history, creative writing  – – as Mr. Holland had his opus.

The challenge of such projects should be sufficient to sustain student efforts beyond a day or two.  In the real world of problem-solving, efforts are made that fail; the project is set aside and then revisited.  Eventually, an “Aha!” moment transpires.

Investigators often find that a failed effort is more informative than successful attempts.  Tavern Puzzles such as the “Unlucky Horseshoes” are great models for the following discussion.

Caution: such problems must be shown to students at the end of a day or of a class period.  How many squares (of any size) are in a standard checkerboard?

The student will typically attempt to solve and then given up, or ask to be told how to remove the ring.  The teacher must resolutely refuse to help.  The teacher may show that the ring can be removed by turning away while solving.  But the student can only sleep on it and try again the next day.

As with any problem-solving or other kind of pinnacle experience, the solver’s mind eventually learns to ignore or see beyond the distractions, to see what is needed.  When successful, the student is almost always glad that no one showed him or her how to do it.  Another challenge is then sought and found, to be enjoyed similarly.

 

Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

 

 

VI.  Associative Networks

Definition:   Associative networks are neurological connections between interrelated ideas in the brain.  Such connections are helpful for meaning, understanding,and application.  Meaning is often defined in terms of these connections.

Associative networks are naturally developed with ongoing review.  The key points of TAPS are rediscovered and reinforced with DARES for arithmetic.

Spreading activation is a phenomenon linked to associative networks.  A struggle to recall a name of a person or place may prompt, “It’ll come to me in a second…” as the brain begins an off-line search.  Minutes or hours or days later, the name is recalled.

          Dog and cat are associated in most adult minds in our culture, as both are common pets, are featured in popular advertisements, and are linked by such expressions as “It’s raining cats and dogs” and “Well, dog my cats.”

An experiment demonstrating the associative network between dog and cat involves the time needed to start spelling dog, for example.  Subjects in the control group would simply be asked to spell dog.  The time between the request and the start of the spelling is measured.

          For the experimental subjects, and prior to the request to spell dog, the experimenter would have a brief, casual chat with the subject, and the word cat would be mentioned.  Then the subject is asked to spell dog.  The time needed to start spelling is significantly less, because the word dog has been activated through the network associating the two words.

Other networks can be taught.  The distinction between its and it’s can be tied to the contrast between other possessive pronouns, such as his and hers, vs. contractions such as he’s and she’s.

Such contrasts must be reviewed daily for some time, like anything else.

An associative network involving noun and pronoun issues might include study and application of an outline such as this:

	CASE
GENDER	nominative	objective	possessive
male	he	him	his
female	she	her	hers
neutral	they	them	their, theirs
common	it	that	its

 

	NUMBER
PERSON	singular	plural
first	I	we
second	you	you
third	he she it	they

The varied forms and interpretations of fractions can be associated into a most powerful network over time, provided that ongoing review is at work.  One eighth-grade mathematics book with thirty problems in each assignment featured 18 exercises in several consecutive lessons that required students to shift between common fraction, decimal fraction, per cent, word interpretation, mixed forms, reducing, and the four operations, to include complex fractions.

Students with such power for recall and synthesis had awesome associative networks for fractions and much more.  An inventory of fraction issues might include these:

• Common fractions, decimal fractions, per cent
• Reducing: common factor, improper fraction
• Operations: add, subtract, multiply, divide; complex fractions
• Form conversions
• Mixed forms
• Percent basics: per cent of base = percentage from fractional part of whole = fraction

The earlier fraction list involved concept development.  The list of issues above is about use and performance.  An associative network for fractions is priceless for such application.

Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

VII.  Generalization/Discrimination

Definition:   Generalization/discrimination refers to ability to examine instances, perceive commonalities and distinctions, and to describe and apply these with confidence.

Generalization/discrimination follows natural impulses – – impulse to sort, and to rank order.  If left alone with a pile of gravel, a person will eventually tend to begin sorting the rocks per some criteria, and then decide which kind is favored.

This natural compulsion to sort and rank leads easily to over-generalizing, to make classifications where none really matter.  Recognizable manifestations include racism, sexism, age stereotypes, etc.

Over-generalizing often occurs in classrooms.  The long a in ray is not a long a in cat, for example.

To make curriculum materials (especially textbooks) more marketable, publishers often sort varieties of exercises so completely that student generalization is made nearly impossible.  The topic of whole-number rounding off is typically fragmented as is shown here:

Day One:  Round off to the nearest ten:

55      64      38      29          92   ..  143     177      8166

Day Two:  Round off to the nearest hundred:

255      764      238      529      4443      2877     8166

Day Three:  Round off to the nearest thousand:

2345     8642      3749      66441     49701    227733

Per such a fragmented setup, generalizing to the concept or idea of rounding off is difficult to grasp.  If tested on rounding to the nearest hundred a week later, a student might try to remember what day it was when that particular variety was practiced.

Such is not education.  An assortment is needed each day for generalization.   Each day, students should round off to the nearest ten for a few examples, then to the nearest hundred for a few more, then to the nearest thousand for a few more, then do a review mix.

Each night, they sleep on the mix.  During sleep, the mind synthesizes to form a comfortable concept.  This will transfer fairly easily to decimal-fraction rounding in time.

Overgeneralizing is also an issue.  The different pronunciations of the a in  ray   cat   gate   watt   need to be practiced together.

Arithmetic word problems have been sorted in some textbooks beyond all hope of providing learning.  Across the top of a page, one may find “Using Addition to Solve Problems.”

On such a page, no decisions need to be made.  The problems do not need to be read.  Students find the numbers and add them.

The assortment each day as described with TAPS gives much promise that useful thought processes and decision systems will develop.  Students will learn to use their natural generalization and discrimination tendencies productively for arithmetic word problems.

Decimal Division Sorted (bad):  Standard textbook sort of decimal division will feature no decimal point moves the first day.  Placement of the decimal point in the quotient is the only new aspect.

On the second day, one-place moves occur.  There is no review of the first day.  The third day dwells on two-place moves, with no review of prior days.  Correct generalization cannot occur.

Assortment is needed each day for correct generalization

The dangers of sorting or fragmenting topics include the realization that students must make correct decisions.  Sorting or fragmenting topics removes decision-making, leading to zero learning.

 

Cognitive Psychology Themes

•  Attention  (involuntary)
•  Development of verbal & visuospatial potential
•  Initial Learning
•  Recall and Synthesis
•  Application
•  Associative networks
•  Generalization and discrimination
•  Affective goals

VIII.  Affective goals

• Confidence – – acquired when each child teaches himself or herself to talk (very difficult), using observation and God-given problem solving skills.
• Curiosity – – when learning happens, so does pleasure, and with pleasure comes desire to learn more.
• Persistence – – must be encouraged. Students can be urged to rest when needed, but not to quit.
• Self-esteem – – natural feeling of worth from meeting other learning goals and making useful contributions as a result.

In typical classrooms, where pie-in-the-sky “forever” explanations, drill, and ineffective approaches are expected to help students recall, students ask, “What’s wrong with me that I can’t remember what we learn?”  The desired affective goals are not met, and are made to seem unattainable.

Some learning issues that have been settled by cognitive psychologists, and that defy the compartments given above, are these:

• It’s nurture, not nature.  Nearly everyone is born with great potential for learning anything.  From age one (beginning speech), the child’s environment is the only real issue.
• Nearly everyone is more of a visual learner than any other kind.
• Music is still an unsettled mystery to cognitive psychologists.  Good!  But!  We recall songs even when we don’t want to…(alphabet song; Jimmy Driftwood / Johnny Horton’s Battle of New Orleans and Sink the Bismarck).

What school board members and school administrators can do…

• Inform your educators that there ARE reliable principles of learning that apply to nearly everyone at any age and for any discipline.  It’s not a matter of opinion or theory.  It is science.
• Compensate for the popular teacher training programs and administrative functions that never touch on these principles; and
• Share these principles and related examples with your leaders and teachers – – handouts and website.

Also settled are the falsehoods preached by these familiar mantras:

“The teacher is more important than the textbook.”

“Everything’s changed!”

“There are no quick fixes.”

“I hear and I forget.  I see and I remember.  I do and I understand.”    (Falsely ascribed to a Chinese Proverb.)

“Books are obsolete.”

“You can’t teach a pig to sing.”

“You can’t get blood from a stone (or turnip).”

“It’s a Catch-22.”  (Read the book.  It’s about loving the army.)

“Calculators are here to stay.”

“Everything is relative.”

“Less is more.”

“Individual differences”

“Brain hemispheres”

“The problem?  Rote! (rote learning, memorizing).”

“The problem?  Worksheets!”

“Drill and kill.”

“Only 5-7% of people are going to be __________.”

(choose: scientists, leaders, decision-makers).

“Cognitive approaches”,  “cognitive development”,

“cognitive constructivism”,   “cognitive behavior modification”

 

Quiz!

This week’s spelling list begins with “table, review, monitor, repetition…”

(A) Should the students write “table” ten times, then “review” ten times, and so on?  or

(B) Should students write the whole list once, and then the whole list again, and so on?

DEFEND YOUR ANSWER.

 

Responses of graduate students who are also classroom teachers:  “This makes so much sense.  Why didn’t we hear any of this before we started teaching?”

 Administrator response:  Not much response, unless the administrators were coaches once, and then there is favor.  Otherwise, since it’s not required by law nor popular with other administrators, it’s ignored – – understandably, given the huge volume of school law that administrators must attend to.

WISDOM   The forgoing is knowledge of how people learn, recall, and apply.

What follows is what the writer regards as wisdom.

School boards have the power.  Should that power be used to divide our communities into privileged segments against deprived dependents?  Should that power be used to serve the interests of those selling a snake-oil remedy for the latest contrived panic?  Or…

* Sam Houston said, “The benefits of education — generally diffused — are essential to the preservation of a free government.”

*The Supreme Court of the United States stated that “Education in public schools is a right which must be made available to all on equal terms.”  Brown vs. Board of Education

* Give a man a fish, and he eats for a day.  Teach a man to fish, and he eats for a lifetime.

* Jesus said, “Inasmuch as ye have done it unto the least of these, My brethren, ye have done it unto Me.”  “  …naked, and you clothed me; hungry, and you fed me”   In the present culture:  Discouraged, deprived, and degraded, and you gave me a way up and out, to stand on my own feet and be inspired.

* We must not “cause the little ones to stumble.”

Our prayer: that the Lord’s will be done – – in our lives, in the lives of the educators who work for us, and in the lives of the students we work for.

References at www.classappcogpsych.com

 

Geometric Classification & Relationship

Classification: categorizing one at a time.   Relationship: connection between two things.

ENTITY	CLASSIFICATION	RELATIONSHIP	H   O   M   O   G   E   N   E   O   U   S
SETS of POINTS in one dimension	line, ray, segment	coincident, congruent
LINES or CURVES	plane, simple, closed, simple-closed, polygon	intersecting, skew, perpendicular, parallel, coincident
ANGLES	acute, right, obtuse   straight, reflex	vertical, adjacent, corresponding, alternate interior, alternate exterior, supplementary, complementary   congruent
POLYGONS	concave, convex	congruent, similar
CONVEX Polygons	regular, irregular	congruent, similar
SOLIDS	polyhedra prism, pyramid other sphere, cone, cylinder, solids of revolution	congruent similar
TRIANGLES	sides:      equilateral, isosceles, scalene angles:    acute, right, obtuse, equiangular	congruent similar
QUADRILATERALS	square, rectangle, parallelogram, kite, rhombus, trapezoid	congruent, similar
LINES-SEGMENTS in or about a circle	radius, diameter, chord, tangent, secant	H  E  T  E  R  O –   G  E  N  E O  U  S
ANGLES in a circle	central, inscribed
Lines, Rays, Segments in a triangle	perpendicular bisector, altitude, median, angle bisector
ATTRIBUTES	length, area, volume;    velocity, mass, momentum, magnetic flux, luster, electrical charge, age, temperature