Designing Instruction
Phases of Mastery
Martin A. Kozloff
Copyright 2006
Review
We’ve been studying tools for designing instruction. Let’s review them.
1.
We find out what our state standard course of study requires us to
teach. We add skills and make the wording of standards concrete and
clear.
2.
We determine what KIND or form of knowledge the standard is: verbal
association, concept, rule relationship, cognitive routine. This is
important, because the way we communicate information (the way we
instruct) depends on the kind of information (form of knowledge) we are
trying to communicate. To teach concepts, we present examples. To
teach verbal associations, we do not present examples.
3.
Then we determine which phase of mastery we are teaching:
acquisition (new knowledge; aim for accuracy), fluency (aim for accuracy
plus speed), generalization (aim for application to new examples),
retention (aim to sustain skill over time). WHAT we teach, HOW we
teach, and how we ASSESS learning depends on the phase of mastery we
are working on.
4.
Now we determine exactly which skills students must learn in order to
achieve the curriculum standard. What does someone have to know to
DO long division? (a) Some of these are new skills that we will teach.
(b) And some of these are pre-skills that students need before we begin
the new instruction, so that they can understand and learn from the new
instruction. So, we do a TASK ANALYSIS of long division to find out the
pre-skills and the steps that we must teach and must review and firm up
before we start on long division.
5.
Next, we state clear and concrete OBJECTIVES. What will students DO
to show whether they have achieved the standard. The objective tells us
what students will DO, what we must TEACH, and what we must ASSESS
with respect to the phase of mastery.
6.
Finally, we select EXAMPLES that will clearly communicate the
information---the concept, rule-relationship, or cognitive routine.
7.
Now we know what to teach. So, we can plan the instructional
procedure that will effectively communicate the information students
need in order to achieve the objective and standard. [Please read that
sentence again.] Specifically, we plan how to review prior knowledge and
pre-skills; gain attention; how to frame (introduce) the task; how to tell
(model) the new information; how to lead students through the new
information; how to test/check whether students learned it; how to
correct errors, and so on.
The first tool we studied was curriculum standards [in “Designing
instruction: Curriculum standards”]. We saw how to use scientific research and
subject matter experts to add standards to a curriculum, and how to improve
poorly worded standards. Then we studied the different forms of knowledge
[“Designing instruction: Forms of knowledge”]. Here are the main points you
learned regarding forms of knowledge.
1.
Experience is of specific things and events. See a dog. Hear music. But
knowledge is general. Knowledge is general ideas about how specific
things are connected.
a. Verbal associations are knowledge of how specific words and things go
together. “The dog’s name is Rover.” (simple fact). “Sugar consists of
three elements: carbon, hydrogen, and oxygen.” (verbal chain)
b. Concepts are an idea (far, on, green, government) based on features
that are shared by a set of things. The common features are the
concept. The name of the concept (“canine”) is NOT the concept.
The name is just a way to communicate the concept.
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c. Rule-relationships are connections between sets of things. For
example, “All dogs are canines” is a rule that connects the set of
dogs with the set of canines.
d. Cognitive routines are sequences of steps (governed by rules) that
accomplish something.
2.
However, you cannot teach a general idea all by itself. For example,
you cannot teach the concept---blue---without SHOWING examples of
blue. You cannot teach the cognitive routine for decoding words without
using words that show the routine. Without EXAMPLES, instruction is
literally empty.
3.
You can’t learn a concept, rule-relationship, or cognitive routine by
seeing just one example. Because any one thing has many features. If a
teacher holds up a pencil and says, “This is a pencil,” WHAT is pencil?
Yellow? Point? Piece of wood? Something with an eraser? Something in
the teacher’s hand? In other words, one example does not give precise
enough information so that a learner can figure out what it is an example
OF. Students are likely to make the WRONG interpretation.
4.
Therefore, to learn concepts, rule-relationships, and cognitive routines,
the teacher presents several examples that are DIFFERENT in many
(unimportant) ways, but are the SAME in the most important way that
defines the concept, rule-relationship, or cognitive routine. For example,
the teacher holds up blue squares, blue circles, and blue triangles and
calls them all “blue.” Students learn (get, figure out) the general idea
(concept--blue) by comparing these examples. They see that they are
the same in only one way (color) and they are called the same ONE name
(“blue”). Therefore, logically, the one way they are the same (color)
MUST be what MAKES them “blue.”
Then the teacher juxtaposes examples of blue and nonexamples of
blue, and names them. A blue circle. [“This is blue.”] A yellow circle.
[“Not blue.”] By CONTRASTING the example and nonexample, the
students learn, get, figure out that the one way they are DIFFERENT
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(color) must logically be what MAKES them different things---“blue” vs.
“not blue.”
[Don’t worry if you quite don’t get this yet. We will examine how we learn
from examples a little later in the course. And you will get it!]
5.
Certain elements make it possible to communicate information (e.g.,
definitions, examples) clearly, so that students learn quickly, without
struggling and making lots of errors---which is a huge waste of precious
time. The elements include concrete and clear objectives; reviewing
background knowledge or pre-skills needed to learn new material; gaining
attention; framing the instruction; providing focused instruction
(instruction focused on the objective) using model, lead, and immediately
testing/checking to see if students learned from the model and lead; error
correction; presenting examples and nonexamples; delayed
testing/checking (at the end of the instruction) to see if students learned
ALL of the examples; and review of instruction. These are organized into
what we called a General Procedure for Teaching.
However, we add a few elements to the general procedure so that we
can effectively communicate each form of knowledge. For instance, to
teach concepts, rule-relationships, and cognitive routines, we use
examples and nonexamples; and to teach cognitive routines, we also
teach the steps. The document “Designing Instruction: Forms of
Knowledge,” showed you examples of how to teach each form of
knowledge.
This document focuses on the next tool for designing instruction---
namely, the phase of mastery we are working on. You see, the objective, the
instructional procedure, and the assessment all depend on whether we are
working on new knowledge (acquisition); whether we want students to use
their new knowledge fluently; whether we want students to generalize their
new knowledge; or whether we want students to retain what they learned
earlier. [Please read that sentence again.]
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Four Phases of Mastery
You can’t take mastery for granted. Merely going over material won’t do it.
You have to pay attention to students getting it right, becoming faster while
maintaining accuracy, applying knowledge to new examples, and retaining
knowledge over time. Students will not learn these without you. And students
with diverse learning needs will fail miserably. I know of cases where a
teacher used a reading curriculum with 165 lessons. The class was almost
finished. When the teacher tested to see how much students retained, she
learned that students had learned almost nothing after lesson 30. So, please
pay attention, and learn the simple methods to assess and teach the four
phases of mastery. [Please see the table at the end of this document. It
summarizes main points in this document.]
You’ve probably seen ballroom dancers on TV. Flawless. Their routine
goes on for five minutes and they don’t miss a beat; they don’t miss a step.
They have mastered the dance. Now imagine they are learning a new one—the
bolero.
http://www.ballroomdancers.com/Dances/media.asp?Dance=BOL&StepNum=43
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http://www.ballroomdancing.com.au/photogallery/qldopen2001/index.htm
How will they master the bolero? Probably like this.
Acquisition Phase
First they will learn one step or position.
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Their teacher will model it for them.
They will do it with the teacher (lead).
Then they will try it on their own (immediate acquisition test/check).
Model. “Watch me…Like this.”
Lead. “Try it with me.”
Immediate Acquisition Test/check. “Your turn.”
If they make any errors, or if they are off a bit (for example, not holding their
arms just right), the teacher will correct them.
“Like this” (model)…
“Now you do it” (test/check)
They practice this step or position until they do it the right way—accurately--until they are FIRM. Then they begin to learn the next step in the routine.
Maybe the next step is a turn. Notice that the turn builds on the first thing
they learned—the starting position.
Strategic integration is part of the phase of acquisition. When the
dancers have mastered the first step or position, they learn another, and
another. Then they learn to assemble these separate steps and positions
(elements) into a longer ROUTINE. This is called “strategic integration.” For
example, they begin in the start position; then they move across the dance
floor turning a few times; then the female partner bends to the side; then she
straightens up and they twirl a few times. That is a little routine that is part of
their whole performance. The little routine integrates of the elementary
steps and positions that they learned. Just as when students are learning
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long division, sounding out words, or writing essays (routines consisting of
steps), the dancers practice the routine until they “have it down”---they don’t
make mistakes.
As the days go by, they learn more new steps and add them to the routine
sequence, until finally (through practice) they have integrated all the steps
into a five minute performance. This is the same as students learning to read
words, and then read sentences, and then read whole paragraphs.
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Independence. Independence is another aspect of acquisition of new
knowledge. At first, the dancers receive a lot of assistance from their
teacher—live, video, diagrams in a book. But as the dancers acquire the skills
(that is, as they become more accurate), the teacher FADES OUT the
assistance, until the dancers can perform (first, each step; then each little
routine; and finally the whole performance) by themselves.
In summary, in the phase of acquisition,
1.
The teacher may be teaching single skills or knowledge only (such as a
simple fact or a concept or a rule-relationship in history); or the teacher
may be teaching the ELEMENTS of what WILL BE a routine. For example,
she will teach students to strategically integrate the elementary facts,
concepts, and rule-relationships into an essay on an historical period. Just
as the routine for doing long division integrates elementary skills such as
estimation, multiplication, writing numbers, and subtracting, so the
routine for writing an essay integrates the facts, concepts, and rulerelationships students have learned. [Please read that sentence again]
2.
The goal is accuracy.
3.
Gradually, the teacher fades assistance as students become more
consistently accurate, to build independence.
Fluency
Let’s say the dancers are (1) learning a new step (acquisition phase for
the new step), or (2) working on strategically integrating steps INTO a
sequence---a routine. They practice, identify weak spots, firm up the weak
spots, and practice some more. The more they practice and firm up their
skills, the more automatic the step or routine becomes. They no longer have
to guide themselves with reminders (“Head high.) or by counting
“One..two…three…fast…fast…one…two…three…fast…fast.” Their steps and the
routine become more graceful—much like little kids reading more smoothly.
And they do the routine faster and faster because they no longer are slowed
down by errors and by thinking about what they are doing.
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Generalization
The dancers borrow from earlier steps and routines to do new steps and
routines. For example, the dancers use (apply) the first position they learned
to a later step in the routine.
This is called generalization, transfer, or application. The dancers apply
something they learned earlier to a new situation.
“Okay, in this new step we hold our heads and arms the same way we do
when we start.”
Likewise, when students know the routine for writing essays (learned from
performing three earlier examples of the essay-writing routine), they apply
(generalize) the routine to different topics.
Retention
Imagine that every time the dancers learn a new step or routine, they
forget or become sloppy with the earlier ones. By the end of their course of
instruction, the only thing they’d be able to do (remember) would be the last
thing they learned. This often happens in schools, especially with students who
have diverse learning needs. Why is there little retention of what was learned?
The answer is:
1.
The students’ knowledge wasn’t firm, but the teacher moved ahead to
new material. For instance, the teacher didn’t use an effective
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instructional procedure, such as the General Procedure for Teaching.
Therefore, some students had no idea what the teacher was talking about.
Other students “sort of” got it, but soon forgot it. And other students
“got it” but still made errors.
2.
Memory naturally decays as time goes by, especially if you don’t
regularly USE what you learned. The teacher did not schedule frequent
cumulative review and practice.
3.
New material interferes with remembering and properly using earlier
material. For example, if a teacher first teaches the sound that goes with
the letter d, and soon after teaches the sound that goes with the letter b,
some students will confuse the two.
Instruction is almost completely wasted if there is little retention. Are
students going to pay attention and try hard if they know they will soon forget
it all? Are teachers going to work hard if they know that students will forget it
all? Of course not. There are four ways to retain skill:
1.
Make sure students are firm (100% correct) in the phase of mastery when
learning a new verbal association, concept, rule-relationship, or cognitive
routine---before you teach something new. How do you know they are
firm? You assess their knowledge. You’ll see how in a minute.
2.
Schedule frequent cumulative review and practice.
3.
Have students apply or generalize their knowledge. This is another way to
practice it. For example, students will remember the definitions of
different figures of speech (metaphor, alliteration) if they USE these to
write poems.
4.
Separate instruction on material that could be confusing---metaphor and
simile, mitosis and meiosis.
Very important!! There are assessments for every phase of mastery.
Basically, what do students know before you begin instruction on that phase;
what are they learning during instruction on that phase; and what did they
learn by the end of instruction on that phase? You must USE assessment
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information to make decisions. Is the class overall (and especially your
diverse learners) “ready” to learn new material? Are some students weak on
pre-skills, or not making satisfactory progress? Is the whole class, or are
certain students, forgetting what you taught them? If students DON’T have
the pre-skills, or are not making adequate progress, or have not learned or
retained enough by the end of instruction (e.g., the end of a unit), then you
must determine whether:
1.
Your curriculum materials are not adequate. For example, they do not
teach a wide enough range of examples for students to learn concepts.
2.
Your instructional design is weak. For example, your objectives are not
clear enough that you know what to teach.
3.
Your instructional delivery is weak in spots. For example, you do not
correct errors immediately or well enough.
4.
Your students merely need to have errors corrected, or they need “partfirming” (basically, reteaching a chunk of a task), or they need
reteaching, or they need intensive instruction.
All of this is discussed in the document, “Four level procedure for
remediation.”
Let’s look at each phase of mastery. What it is. How to teach it. How to
assess it.
Acquisition Phase
Definition of Acquisition
In acquisition, the student learns (figures out, induces) a new verbal
association, concept, rule-relationship, or cognitive routine from the set of
examples---called an acquisition set (and perhaps nonexamples) presented and
described. Instruction must focus precisely on the objective. Communication
(examples, descriptions) must clearly reveal the verbal association, concept,
rule-relationship, or steps in the cognitive routine. The General Procedure for
Teaching (e.g., reviewing pre-skills, gaining attention, framing the new task,
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modeling the information, etc.) is one way of delivering focused and effective
instruction.
Objectives or Aims for Acquisition
What does it look like when students “get” or learn a new verbal
association, concept, rule-relationship, or cognitive routine? They USE IT
ACCURATELY, or CORRECTLY. The percentage of correct responses is close
to 100. For example, the teacher holds up cards. Each one has a letter on it
whose sound the teacher taught during the lesson. The teacher says “What
sound?” Almost every student gets every one right. The 100% correct rule is
crucial! If students are not FIRM on what you have just taught, how can you
go on to next things to teach—especially if the next things require skill at the
earlier? For example, how can students learn the next skill---sounding out the
new words sun, fun, and run---if students are not 100 percent accurate at
saying sss when they see s, fff when they see f, rrr when they see r, and uhhh
when they see u? How can they sound out words if they are not firm on
what the letters say? How can students multiply two-digit numbers if they
are not firm on one-digit multiplication? How can they analyze an historical
document if they don’t know what the words in it mean? What happens when
you add another layer of bricks to a wall whose lower layers are weak?
Assessment of Acquisition
Assessment happens at three different times: before (pre-instruction),
during instruction (progress monitoring), and at the end of instruction on new
material (post-instruction or outcome). Let’s say acquisition instruction is on
two-digit multiplication. The teacher will use an acquisition set of examples of
two-digit multiplication to reveal the common steps in the routine.
Pre-instruction Assessment
Do students know the pre-skills or elements of two-digit multiplication:
counting, writing numbers, renaming, multiplication facts?
If so, they
are ready to learn two-digit multiplication. If not, the teacher must firm
up or even reteach these elements. [This is discussed in the document,
“Four level procedure for remediation.”]
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Progress monitoring or During-instruction Assessment
When the teacher models and then leads students through each
example of two-digit multiplication, the teacher immediately has
students do it on their own. This is an immediate acquisition test. If they
make an error, she corrects it by modeling it again, leading them through
it, and testing. If and when they do the example correctly, the teacher
goes on to the next example.
Post-instruction or Outcome Assessment
Post-instruction or outcome assessment can be (1) at the end of a lesson;
(2) at the end of a unit (series of lessons on the same topic and with
the same objective); or better (3) both.
Lesson 1 and Test
Lesson 2 and Test
Lesson 3 and Test
Lesson 4, end of unit, and Comprehensive Test.
By the end of a lesson the teacher has modeled, led students
through, and tested/checked to see whether students can do each
example problem on their own. Now the teacher presents ALL of the
SAME problems to see if students can do them all, on their own. This is
a delayed acquisition test. If any student makes an error, the teacher
immediately corrects it (directing the correction to the whole class) with
the model, lead, test/check procedure. The teacher knows that she must
review these problems before the next lesson. And perhaps she must
provide reteaching to some students.
It is also post-instruction or outcome assessment if the teacher
tests/checks learning after a number of lessons (e.g., a unit) that
focused on a objective. For example,
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1. Students might write an essay describing the main disputes in the
writing of the U.S. Constitution, in which they use all of the concepts,
dates, political philosophies, persons, and events they were taught.
2. The teacher makes up an exam that asks questions about the concepts,
dates, political philosophies, persons, and events they were taught.
Most assessment should be connected directly to what you are
teaching. That is, you assess students on what you will teach, what you are
teaching, and what you just finished teaching. Sometimes this is called
“curriculum based measurement” or CBM. Here is an excerpt from
Curriculum-based measurement: A manual for teachers, at
http://www.jimwrightonline.com/pdfdocs/cbaManual.pdf [Italics added for
emphasis.]
Curriculum-based measurement, or CBM, is a method of monitoring
student educational progress through direct assessment of academic
skills. CBM can be used to measure basic skills in reading, mathematics,
spelling, and written expression. It can also be used to monitor
readiness skills. When using CBM, the instructor gives the student
brief, timed samples, or "probes," made up of academic material
taken from the child's school curriculum. These CBM probes are given
under standardized conditions. For example, the instructor will read the
same directions every time that he or she gives a certain type of CBM
probe. CBM probes are timed and may last from 1 to 5 minutes,
depending on the skill being measured. The child's performance on a
CBM probe is scored for speed, or fluency, and for accuracy of
performance. Since CBM probes are quick to administer and simple to
score, they can be given repeatedly (for example, twice per week). The
results are then charted to offer the instructor a visual record of a
targeted child's rate of academic progress.
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Assessment of students’ acquisition of knowledge can also be provided by
validated, standardized instruments. However, these do not measure students’
proficiency with the same examples that you used during instruction. They
measure the more general skill. You can find examples of reading assessments
here
http://idea.uoregon.edu/assessment/analysis_results/assess_results_by_test.html
Let’s look at examples of the pre-instruction, during-instruction, and postinstruction assessment during acquisition.
Pre-instruction assessment. Pre-instruction assessment tells you what
students already know or do not know so you can plan instruction; for
example, which letter-sounds to start with; how much to review. You can also
use pre-instruction assessment to create temporary homogeneous groups so
that students who are at the same spot in a curriculum are taught exactly what
they are ready to learn.
Let’s say you are a first grade teacher. It’s the first week of school.
Your state and district standard course of study tells you to begin teaching
students to sound out words.
Decoding and Word Recognition
1.10 Generate the sounds from all the letters and letter patterns [lettersound correspondence. f says fff], including consonant blends and longand short-vowel patterns (i.e., phonograms), and blend those sounds
into recognizable words.
http://www.cde.ca.gov/be/st/ss/enggrade1.asp
However, students can’t sound out (blend sounds into) words if they are not
firm on letter-sound correspondence, because letter-sound correspondence is
an element or part or pre-skill of sounding out. Therefore, you give a preinstruction assessment of letter-sound knowledge. For example, you have
cards. Each card has a letter (a , s, m, i, t) or a blend (br, st, fl). You also
have a sheet of paper that lists all the sounds and blends, and has three
columns to score students’ responses. You hold up each card, and say, “Boys
and girls, what sound?” You mark the sheet after each sound or blend. When
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you are finished, you know that a few students need extra practice (firming up)
on certain letter-sounds. You also know which sounds and blends require more
than extra practice (firming up), but need beginning instruction (on
acquisition).
Pre-instruction Assessment of Letter-sound Correspondence
All students
were correct
a
m
s
t
Only a few
students
made errors
Many students Preparation
made errors
x
x
x
x
e
x
d
x
i
x
f
x
Review
Review
Review
Teach these
students
Teach these
students
Teach the
whole class
Teach the
whole class
Teach the
whole class
You could also test each student individually, using the same method.
This would enable you to track the progress of each student, by giving the same
assessment every few weeks.
You should conduct pre-instruction assessments in almost every
subject you teach. For instance,
1.
Before teaching long division, pre-test students on the elements or preskills of long division: estimation (27 goes into 110 how many times?);
multiplication; addition. This tells you which skills are firm; which skills
need a bit of review and firming; and which skills (or which students) need
reteaching or initial instruction (acquisition). [Please skim the document
“Four-level procedure for remediation.”]
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2.
Before beginning the first chapter in a second semester algebra course,
pre-assess students to determine what they have retained (or forgotten)
from the first semester. Again, this tells you which skills are firm; which
skills need a bit of review and firming; and which skills (or which students)
need reteaching or initial instruction (acquisition).
3,
Before second semester Spanish, pre-assess students on what they have
retained (or forgotten) from the first semester: pronunciation, grammar,
vocabulary. Again, this tells you which skills are firm; which skills need a
bit of review and firming; and which skills (or which students) need
reteaching or initial instruction (acquisition).
4.
Before starting material in physics, pre-assess students on the math preskills they will need. Again, this tells you which skills are firm; which
skills need a bit of review and firming; and which skills (or which students)
need reteaching or initial instruction (acquisition).
5.
Before starting second semester U.S. history, pre-assess students on
concepts (federalism, representative democracy, checks and balances,
manifest destiny), events, persons, and processes (e.g., elections,
industrialization, how bills become law), that are needed to learn the new
material. This tells you which skills are firm; which skills need a bit of
review and firming; and which skills (or which students) need reteaching
or initial instruction (acquisition).
During-instruction, or progress assessment. During-instruction (or
progress-monitoring) assessment tells you how much students are learning as
you teach. You don’t want to keep going if they aren’t getting it! For
example, you just told (modeled) the verbal definition of the concept mitosis
(cell division).
Teacher.
http://www.accessexcellence.org/RC/VL/GG/mitosis.html
“Boys and girls. New concept.” [writes mitosis on the
board.]
“Spell mitosis.”
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Class.
“m i t o s i s”
Teacher.
“Yes, mitosis.”
Teacher.
“Get ready to write the definition on your note cards.
Mitosis is a process of cell division which results in the
production of two daughter cells from a single parent cell.
The daughter cells are identical to one another and to the
parent cell.” [Model]
[Teacher repeats the definition.]
Teacher.
“Say the definition of mitosis with me…” [Lead]
Teacher/
“Mitosis is a process of cell division which results in the
Class
production of two daughter cells from a single parent cell.
The daughter cells are identical to one another and to the
parent cell.”
Now you give an immediate acquisition test/check (to monitor progress) to
see if students learned (and correctly wrote) the definition.
Teacher.
“Your turn. Define mitosis.”
Class.
“Mitosis is a process of cell division which results in the
production of two daughter cells from a single parent cell.”
This progress assessment (immediate acquisition test/check) tells you
(1) whether students are firm on the definition, and so you can go on to the
next task (e.g., identifying the phases of mitosis); or (2) whether students are
not firm, and so you should go back and reteach the definition.
Post-instruction, or outcome assessment. Post-instruction, or
outcome, assessment tells you how much of the new material students learned
in a lesson. Therefore, it tells you whether they achieved the curriculum
standard or instructional objective. Let’s start with a simple example of postinstruction, or outcome assessment---a delayed acquisition test.
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Outcome assessment of sounding out new words.
You taught students to sound our six new words. fun sun run ran man
fan. Here is the procedure you used.
Teacher.
ma n
o-------->
“Listen. mmaann
Teacher/
man.” [Model]
“Read it with me. mmmaaannn. man.” [Lead]
Class.
Teacher.
“Your turn.” [Immediate acquisition or progressmonitoring test]
Class.
“mmmaaannn man.”
Teacher.
“Yes, man!” [Verification]
At the end of the lesson, point to each word and have students READ THEM
ALL. This is the delayed acquisition test---outcome or post-instruction
assessment.
1.
Put all the words on the board (or on cards).
2.
Point to each word.
3.
Say, “What word?”
4.
Correct any errors with the model, lead, test, verification procedure.
“That word is man.”
“Say it with me.” man
“What word?”
man
“Yes, man.”
5.
This tells you which words you need to firm up or even reteach. [See the
document, “Four level procedure for remediation.]
Outcome assessment of learning a new concept.
Here’s another example. You have taught students the definition of
granite---both the verbal definition and examples/nonexamples. How do you
test the outcome of instruction? Simple, give a delayed acquisition test.
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1.
Show the examples and the nonexamples one by one.
2.
Ask, “Is this granite?”
3.
When students answer, ask a follow up question. “How do you know?”
This requires them to use the definition.
4.
Correct any errors.
Outcome assessment of learning several new concepts.
Let’s say you taught five new vocabulary words (concepts) during today’s
history lesson.
Federalism. http://plato.stanford.edu/entries/federalism/
Federalist. http://www.u-s-history.com/pages/h375.html
Anti-federalist. http://www.u-s-history.com/pages/h374.html
Representative democracy.
http://en.wikipedia.org/wiki/Representative_democracy
Tyranny. http://dictionary.laborlawtalk.com/tyranny
You taught these definitions using the General Procedure for Teaching.
[Please review the procedure for teaching higher-order concepts in the
document, “Designing Instruction: Forms of Knowledge,” before you go on.]
Teacher.
“Boys and girls. New concept. Tyranny. [Write tyranny on
the board.] Spell tyranny.”
Class.
“t y r a n n y”
Teacher.
“Yes, tyranny. Get ready to write the definition of tyranny
on your note cards.” [Check to see if ready.]
Teacher.
“Tyranny is a form of government in which the ruler is an
absolute dictator not restricted by a constitution or laws
or opposition.”
“Got that?” [Repeat definition.]
Teacher.
“Say it with me.” [If the class is now skilled at
listening, writing, and remembering, the teacher can TRY
to fade out the Lead step.]
20
Teacher/
“Tyranny is a form of government in which the ruler is an
Class.
absolute dictator not restricted by a constitution or laws
or opposition.”
Teacher.
“Your turn. What is the definition of tyranny?” [Immediate
acquisition test/check. Progress-monitoring.]
[Now---to illustrate the verbal definition---you present examples and
nonexamples of tyranny one after another and label each one. “This is
tyranny…. Notice its features from the definition….. This is NOT
tyranny. Notice the features it does NOT have.” Teach each new
concept the same way.]
After you have taught all the new concepts, you give a delayed
acquisition test to assess the outcome of the instruction. Use the SAME
examples and nonexamples that you used during instruction.
Teacher.
“Class. Let’s review all of our new concepts.”
“Representative democracy. What is the verbal
definition?”
Class.
“Representative democracy is a form of democracy
founded on the exercise of popular sovereignty by the
people's representatives.”
Teacher.
“Excellent stating the definition of representative
democracy.
Teacher.
Okay, here’s a political system. You tell me if it is a
representative democracy. Ancient Sparta. At the top was
a dual monarchy: two kings. Below the monarchy was a
council composed of the two kings and twenty-eight nobles
who created laws and foreign policy. There was also an
assembly of all the high ranking males, called the
Spartiate. They elected the council and approved or
vetoed proposals from the council. But above them all was
a group of five men who led the council, military,
educational system, and could veto anything from the
21
council or assembly of Spartiates—the ephores. They could
even depose the king.”
[Adapted from
http://www.wsu.edu/~dee/GREECE/SPARTA.HTM]
Class.
“It has some features of representative democracy--the
Spartiate assembly. But it is also a monarchy.”
Teacher.
“Good use of the definition. Ancient Sparta was not a
representative democracy. It was a mixed type of
government.”
[The teacher than tests all of the other new concepts—democracy,
tyranny, federalism, etc.]
Note. This delayed acquisition test/check, outcome assessment, or postinstruction assessment uses the same examples and nonexamples that
were presented during acquisition instruction. If you use different
examples, you are not testing exactly what you taught. You are testing
generalization of knowledge to new examples.
Instruction During the Phase of Acquisition. It’s essential that
instruction during the phase of acquisition is effective. All students must learn
the material to 100% accuracy. How do you design and deliver instruction
during the phase of acquisition to ensure that all students learn to the point of
100% accuracy? The answer is, Use the General Procedure for Teaching.
Please review examples of the General Procedure in the document, “Designing
instruction: Forms of Knowledge.” Notice how the General Procedure
(modified slightly depending on whether you are teaching a verbal association,
concept, rule-relationship, or cognitive routine) pays attention to every
detail: students are attending to the right thing; students know what to
expect; the set of examples clearly reveals the essential information (e.g., the
minerals in granite); students are shown again and again, and led through the
examples; every error is corrected; everything taught is checked to see if
students learned it.
22
Fluency
Definition of Fluency
A person whose skill is fluent no longer has to think about what he or she
is doing.
67
x23
“Let’s see. First I multiply the numbers in the ones column. That’s 7 and
3. 7 times 3 is 21. I write 1 and carry the 2….”
When a person is fluent, knowledge (of a verbal association, concept, rulerelationship, or cognitive routine) is internalized, or covertized; it is
automatic. The time between steps is shorter; the person makes fewer errors;
therefore, the person applies the knowledge faster and more smoothly. For
example, students read word lists, read connected text, define concepts, solve
math problems, conduct lab experiments, and analyze poems accurately (they
do it right) and quickly.
Objectives or Aims for Fluency
The objective or aim for the phase of fluency is accurate (or correct)
plus quick and smooth (no gaps and hesitations) performance. Research has
determined useful fluency aims or benchmarks for different reading skills. For
example,
23
http://reading.uoregon.edu/flu/flu_cm_1.php
http://reading.uoregon.edu/flu/flu_cm_2.php
http://reading.uoregon.edu/flu/flu_cm_3.php
So, the benchmark fluency objectives for word reading are: end of grade 1, 60
words correct per minute; end of grade 2, 90-100 words correct per minute;
and end of grade 3, 120 words correct per minute.
Assessment of Fluency
As with acquisition, you should assess fluency before, during, and at the
end of fluency instruction on a certain skill. Here are some examples of the
skills whose fluency you would want to increase:
24
1.
Saying the sounds that go with letters. “What sound?”… rrr.
2.
Reading words from a list.
3.
Reading connected text: sentences in paragraphs.
4.
Writing letters of the alphabet.
5.
Identifying and correcting spelling errors in a prepared text.
6.
Writing numbers.
7.
Addition, subtraction, and multiplication facts.
6
26
7
+3
-12
x4
8.
Multi-digit multiplication.
9.
Long division.
10. Operations with fractions and percentages.
11. Algebra operations.
(12 + 2) (16 -5)
Calculating slope
Solving equations.
12. Determining distances on a map.
13. Finding locations on a map, given latitude and longitude.
14. Circling examples of metaphors, given examples of different figures of
speech.
15. Sorting or identifying samples: rocks, fungi, trees.
16. Anything else you are teaching that students ought to do more
quickly.
Building fluency for a particular skill takes time. One way to assess
fluency over time—from pre-instruction on fluency, through progress on
fluency, to outcome of fluency instruction—is with a graph. Each student has
his or her own graph for the fluency target. You can even establish an
outcome fluency aim with the students. For example, 60 words correct per
minute by the end of the year with your first graders. (See the table above.)
The class has just learned how to read connected text in story books
(acquisition phase of this skill).
25
The cat ran and ran. It ran fast. The cat can see a rat. The rat can see
the cat. The rat was sad.
Students read the above text accurately, but they read slowly—stopping
between words, and sounding out some of the words. You continue teaching
new words and sentences, AND you teach them to read the above story more
fluently. Here’s how you might assess fluency.
1.
Assess each student’s rate and accuracy before you begin fluency
instruction. Use a story whose words they can accurately decode.
2.
Have each student read for one minute.
3.
Mark on your copy of the story each time a student makes an error--reads
a word incorrectly or adds a word that isn’t there. Count the same word
error (e.g., rans) only once.
4.
Count how many words the student read correctly in a minute. And
count how many total errors the student made.
5.
Plot these numbers on the student’s graph, and help the student to do
this.
6.
Every week, repeat the assessment (progress assessment), and plot the
number correct and the number of errors on the graph. Naturally,
students will be reading new stories; so, draw a vertical line on the
graph.
7.
At the end of the year, assess the student’s outcome fluency. Of course,
each next story will have new and longer words. It might look like this.
26
Stories
80
First | New 2
| New 3
| New 4
| Final New |
75
|
|
|
|
|
70
|
|
|
|
|
65
|
|
|
Objective
*
60
Words
55
|
|
|
Correct
50
|
|
|
Per
45
|
|
Minute
40
|
|
(* *)
35
|
30
* |
Total
25
Errors
20
(+ +)
15
10
**
+
|
|
|
|*
|
|
|
|
|
|
|
|*
|
|
|
|
|
|
|
|
|
| + +
|
|
|
|
* *
+ + |+ +
| + +
+ +
4 5 6 7
*
*
|*
++ |
123
|
|
|
*
|
*
*
|*
*
* *
* |
|+ +
+ +
|
+ +
8 9 10 11 12 13 14 15 16 17 18 19
Weeks
The graph shows that each time you added a new story, the student’s accuracy
and/or speed decreased, but with repeated reading (one way to build fluency),
errors decreased and speed increased. Was your fluency-building instruction
effective? Yes. The student reached the outcome aim or objective. If
students are NOT making adequate progress (for example, the errors do not
decrease, or speed does not increase) you have to look closely at HOW they are
reading? Are they weak on letter-sound correspondence? If so, reteach this.
Are they weak on reading whole words (e.g., they are still sounding them out
27
rather than saying them fast)? Then firm this skill through practice sessions.
[See the document entitled, “Four level procedure for remediation.”]
You can do the same thing in other subjects. How many math problems,
spelling errors corrected, numbers written, letters written, concepts defined,
rocks correctly sorted per minute? Sometimes these fluency assessments are
part of fluency instruction itself. For example, students do short “speed
drills” (for instance, using math worksheets) to build fluency, and you and the
students count and graph the number correct per minute and the number of
errors.
Instruction During the Phase of Fluency Building
There are several ways to build fluency: modeling, special cues, and
practice.
1.
Modeling. The teacher demonstrates what fluent (quicker and smoother,
and accurate) performance look like, and then gives students a chance
to do it. Sometimes, the teacher adds little rules or reminders as she
does this. Here are examples.
[This is a phonemic awareness skill.]
Teacher.
“Boys and girls. Listen. foot…ball. I can say it fast.
football.”
Teacher.
“Listen. foot…ball. Say it fast!!”
Class.
“football!!”
[This is an alphabetic principle, or phonics, skill.]
Teacher.
“Boys and girls. First I’ll sound out a word. Then I’ll say it
fast. Here I go.
run
o------->
[Teacher moves her finger slowly under each letter.]
“rrrruuunnn.”
“I can say it fast.”
[Teacher moves her finger quickly under the word.]
28
“run”
Teacher.
“Your turn. First you’ll sound it out. Then you’ll say it
fast. Get ready.”
run
o------->
[Teacher moves her finger slowly under each letter.]
Class.
“rrruuunnn”
Teacher.
“Say it fast!”
run
o------->
[Teacher moves her finger quickly under the word.]
Class.
“run!”
Likewise, the teacher can model how to perform the routine for
multiplication and division, reading sentences, calculating the slope, and other
skills more quickly, and then have students do it.
2.
Special Cues. The faster the conductor waves the baton, the faster the
orchestra plays. Likewise, the teacher can use special cues that provide a
tempo for the students’ performance. For example, there is a list of
words on the board.
run
runs
buns
sock
socks
docks
flocks
flip
slip
slips
slipped
29
The teacher says, “”Let’s read all these words the fast way. Try not to
make mistakes. The error limit is two.” The teacher points to the top
word…
Teacher.
“First word. What word?”
Class.
“run.”
Teacher .
(moves down and points to runs.) “Next word. What
word?”
Class.
“runs.”
Teacher.
(moves down and points to buns) “Next word. What
word?”
Class.
“buns.” Etc.
Teacher.
“Oh, you are such fast readers. But we can do it
EVEN faster. Here we go.”
Next, the teacher moves down the list faster. She barely stops
between words. Also, the teacher shortens the signal. Instead of “Next
word. What word?” the teacher simply moves her finger down to the next
word and says “Word?” With practice every day, students will become
very fast readers of word lists.
The teacher can also use special cues to help students become fluent at
reading connected text. For example, students have already learned
to track under each word and then say it. The question is how to move
them from one word to the next faster. The teacher does this by clapping
before each word.
Teacher.
“When I clap, you say the word. Then move your finger to
the next word. Get ready.”
Class.
“The…cat…ran…and…ran…She…was…a…fast…cat.”
[When students are skilled at following the teacher’s cue or
signal, the teacher speeds it up.]
“The.cat.ran.and.ran…She.was.a.fast.cat.”
30
3.
Practice. We already spoke of practice.
Repetition. One kind of practice is simply repetition. For example,
students read a passage once (and the teacher corrects every error). They
read it again (the teacher corrects every error). And once more (the
teacher corrects every error). Or, students conjugate a French verb once,
twice, and one more time. Or they say all the phases of mitosis once,
again, and once more. Or the teacher says the number of the
amendment in the Bill of Rights (“First Amendment.”) and students say
the rights that are protected (speech, religion, assembly, petition).
http://www.law.cornell.edu/constitution/constitution.billofrights.html
The class does this again. And one last time.
Speed drills. Practice can also be in the form of short speed drills or
sprints. These should only be for 1 to 3 minutes. Here are examples.
“Okay, here’s a page with 15 misspelled words. Circle each misspelled
word and correct it. I want you to get at least 12. Get ready? GO!”
[Afterwards, the class goes over the page and checks work. If done every
few days, students will become fluent at spelling and at checking.]
“Here’s a math worksheet. There are 30 multiplication facts. Do them
quickly but try not to make errors. Think. Check your answer. You have
two minutes. GO!” [Afterwards, the class checks work. The teacher
notes which students made more than a few accidental errors. These
students may need more practice on accuracy.]
Remember that students can also have their own graphs of fluency drills
on, for example, math problems correctly solved per minute and words
read correctly per minute. Aside from the teacher working with each
student, students can do this in pairs. One student reads and the partner
follows along and marks errors on his or her own copy of the text. Then
the partners review the text and correct errors. Then the partners graph
31
the number of words correctly read and the number of errors. And then
they switch roles of reader and checker.
Generalization
Definition of Generalization
Let’s say that during the phase of acquisition you used five examples of
conifers to reveal the features that define the general idea (concept) of
conifer.
Giant
Sequoia
Juniper
Red
Cedar
Spruce
Fir
And let’s say that during the phase of acquisition you used five examples of
poems so that students learned the steps in the general cognitive routine for
analyzing poems.
The point of using examples is not ONLY that students learn these
examples (e.g., what a Giant Sequoia looks like), but that they learn the
general idea (concept, cognitive routine) revealed by the examples, so that
that they can apply the knowledge gained from the examples to new
examples. Generalization is the application or transfer of knowledge to new
examples.
Objectives or Aims for Generalization
The objectives or aims are straightforward. Once students have learned
a concept, rule-relationship, or cognitive routine, they properly apply this
knowledge to examples they have not seen. They sound out new words,
analyze new poems, multiply new two-digit numbers, identify new conifers.
32
Assessment of Generalization. There are three parts to assessment of
generalization.
1.
Pre-instruction assessment of generalization. It makes no sense to
teach students to generalize knowledge to new examples if their
knowledge (from instruction during acquisition) is not firm. So, you
should review the knowledge you want students to generalize. Review a
set of two-digit multiplication problems that students have done before.
Correct any errors in the steps (e.g., multiplication or addition facts,
lining up the numbers below the line). When they do these problems
without errors, then give new examples to which they can generalize the
prior---and firm---knowledge.
Review words students have been taught to sound out. Correct any
errors. When they read the words without errors, then give new
examples.
2.
During-instruction, or progress-monitoring assessment of
generalization. Give new examples (for generalization) in a set—a
generalization set. These new examples must be similar to earlier
examples that students learned. For example, you taught the sounding
out routine with this acquisition set.
am
ram
ma
sun
run
man
What new words can you make using the same letters? sam, ran, sum, san
(pseudo-word), rum. These are the generalization set.
If you use unsimilar new examples, students are likely to be confused or
not to see them as basically the same as earlier examples, and they won’t
generalize or try their earlier skills.
33
“I can’t read THESE words!”
Present these new examples one at a time, and note how well students
sound them out.
“Boys and girls. Here are some new words. You can sound them out.
Don’t let them fool you just because they are new. When I touch under a
sound, you say the sound. Don’t stop between sounds.”
s u m
o--------->
Did every student do it correctly? THAT is the progress assessment.
Repeat it with each next word in the generalization set. Correct any
errors. Note any weak knowledge and firm it up. For example, a few
students have forgotten the sound that goes with n; a few other students
stopped between sounds.
3.
Post-instruction, or outcome assessment of generalization. You have
seen this several times now. Simply present the whole generalization set.
Correct any errors. Note any weak knowledge and firm it up.
Instruction on Generalization
The examples in the generalization set must be similar enough to
examples in the acquisition set that students know all they need to do the
generalization examples. [Please read that sentence again.] If the acquisition
set of words does not contain the letter l, then you can’t expect students to
sound out new words that have the letter l.
1.
Prepare students for generalization by reviewing background knowledge.
2.
Tell them they will be applying knowledge to new examples.
3.
Assure them that they can do it.
4.
Give them reminders. “Don’t stop between the sounds.” “Multiply
numbers in the ones column first.”
5.
Provide students with a list of steps or a visual guide (e.g., what the
solution to a multiplication problem looks like) so that students can guide
themselves and check their own work.
34
6.
Correct errors.
7.
Identify week spots. Firm these at the end of the lesson and before the
next lesson.
8.
In future lessons, teach new knowledge (for example, new letter-sounds,
new figures of speech, new examples of symbolism, new rhyme schemes).
Then create a new generalization set (words to sound out, poems to
analyze) that enables students to apply the new knowledge.
Retention
Definition of Retention
Retention means that knowledge remains firm (accurate, fluent) despite
the passage of time and despite acquiring new and possibly interfering
knowledge. What’s the point of education if students forget everything but a
few facts? No point. There are three enemies of retention.
1.
Students were not firm on the knowledge taught during acquisition.
[Maybe the teacher did not do progress monitoring or outcome
assessment.] Therefore, there is nothing for students to retain. The
solution is simple. Do not go on until students are 100% accurate on
new material.
2.
Time goes by and students are not using what they learned earlier. So,
memory decays. The solution is simple.
a. Schedule distributed practice on a sample of things taught earlierto-recently.
b. Give students many opportunities to generalize/apply (practice) earlier
knowledge.
3.
New knowledge interferes with earlier knowledge. This is often because
the new knowledge looks similar to the earlier (so students treat it as the
same), but isn’t. The solution is simple. Separate instruction on similar
looking (but actually different) items. Make sure students are firm on
the earlier before you teach the later, similar looking items.
35
Objectives or Aims of Retention
The objective is that when you present a retention set (a sample of
earlier items worked on), students get most of them right. They are still
accurate and fast.
Assessment and Instruction on Retention
You are teaching many things at once. In elementary school, you are
teaching letter-sound correspondence (r says rrr), sounding out words (run --->
“rrruuunn” ---> “run”), spelling, handwriting, addition, subtraction, concepts
in science, facts in social studies, and many more. Are you aware of what you
are teaching?
“Of course! I am teaching new letter-sounds. e, d, f. I have already
taught students the sounding out routine with am, ram, ma, sun, run,
man. As soon as they know the sounds that go with e, d, and f, I will
teach them to sound out new words----seed, feed, seem, fan, and fun. I
have already taught students to write all the letters. Now we are working
on fluency…”
Since you know what you are working on and what you have worked on,
it’s no big problem to schedule review and practice to build and assess
retention. Every day, before each lesson on a particular subject, review
(assess) and have students practice a small sample of what you have
already worked on in that subject---cumulative review. For example,
students practice translating some Spanish vocabulary words worked on during
the week before you teach them new ones during the lesson. This sample is
your retention set.
In addition, schedule longer sessions for cumulative review---the
retention set should draw on material relevant to the new subject, going back
a month or so---very early as well as recent items. For example,
1.
Before you teach vocabulary found in a new historical document,
review/assess earlier vocabulary.
2.
Before you teach new letter-sounds, review/assess earlier ones.
36
3.
Before you teach new figures of speech (synecdoche, oxymoron),
review/assess earlier ones (metaphor, simile, alliteration).
http://www.nipissingu.ca/faculty/williams/figofspe.htm
4.
Before you teach the phases of meiosis
http://www.biology.arizona.edu/CELL_BIO/tutorials/meiosis/page3.html
review/assess the phases of mitosis.
http://www.accessexcellence.org/RC/VL/GG/mitosis.html
5.
Before you teach new examples of simple addition, review/assess earlier
examples.
6.
Before you teach conjugation of re verbs in French, review/assess er
verbs.
7.
Before you teach long division, review/assess estimation, multiplication,
and subtraction.
In addition to review and practice, make sure that you separate
instruction on items that may be confusing. For example, do not teach
metaphor and simile near one another. They differ only by the words “like” or
“as.” Do not teach mitosis and meiosis near one another or at the same time.
Do not teach the sounds that go with b and d near each other. Instead, make
sure students are firm and automatic on the early item before you teach the
later.
Another way to assist retention is to provide students with written
routines or diagrams that they can use to guide and check themselves. For
example, the list of steps in analyzing poems.
Summary
You have learned another tool for designing instruction---phases of mastery.
Too often, teachers work only on the first phase---acquisition of new
knowledge. The result is that students forget most of it. What a waste! When
students are firm on new knowledge learning during the phase of acquisition,
you
37
1.
Build fluency, by modeling faster performance, adding special tempo
cues, practice, and speed drills.
2.
Work on generalization, by modeling how to transfer earlier knowledge to
new---similar---examples, in a generalization set.
3.
Increase retention, with cumulative review and practice (of a retention
set of examples) and by frequent opportunities for generalization.
Each phase has objectives or aims, and each phase has its own kind of preinstruction assessment; during instruction or progress monitoring assessment
(immediate acquisition tests; speed drills and charting rates); and postinstruction or outcome assessment (delayed acquisition tests; retention tests).
Use this information to evaluate and to improve your curriculum materials,
instructional designs, delivery of instruction, and your students’ skills.
We have used the words pre-skills and background knowledge many
times. We’ve said that you have to assess and firm up students’ pre-skills
before you teach something new that REQUIRES the pre-skills. For example, it
makes no sense to teach students tw-digit multiplication if they can’t do (or if
you don’t KNOW if they can do) single-digit multiplication. But how do you
know what the pre-skills are that you should assess and firm up? Task analysis
tells you. Task analysis is our next tool for designing instruction.
Useful Readings
Binder, C. (1996). Behavioral fluency: Evolution of a new paradigm. The
Behavior Analyst, 19, 163-197.
Brophy, J.E., & Good, T.L. (1986). Teacher behavior and student achievement.
In M.C. Witrock (Ed.), Third handbook of research on teaching (pp. 328375). New York: McMillan.
Dougherty, K.M., & Johnston, J.M. (1996). Overlearning, fluency, and
automaticity. The Behavior Analyst, 19, 289-292.
Haring, N.G., White, O.R., & Liberty, K.A. (1978). An investigation of phases
of learning and facilitating instructional events for the severely
38
handicapped. An annual progress report, 1977-78. Bureau of Education of
the Handicapped, Project No. 443CH70564. Seattle: University of
Washington, College of Education.
Horner, R.H., Dunlap, G., & Koegel, R.L. (Eds.) (1988). Generalization and
maintenance: Life-style changes in applied settings. Baltimore: Paul H.
Brookes.
Kame’enui, E.J., & Simmons, D.C. (1990). Designing instructional strategies: The
prevention of academic learning problems. Columbus, OH: Merrill.
Rosenshine, B. (1986). Synthesis of research on explicit teaching. Educational
Leadership, 43, 60-69.
39
Summary of Phases of Mastery
Definition
Relevant
Instructional
Objectives or Aims
Relevant
Instructional
Procedures
Acquisition of Verbal
Associations,
Concepts, or Rulerelationships.
The student learns a
new verbal
association, concept,
rule-relationship, or
cognitive routine
from the examples
(and perhaps
nonexamples)
presented and
described---the
acquisition set.
Accuracy. 100%
correct.
Fluency
Generalization
Retention
Accurate, rapid,
smooth (nearly
automatic)
performance.
The accurate
application or
transfer of knowledge
to new examples--called a
generalization set.
Knowledge remains
firm (accurate and
fluent) despite the
passage of time and
despite acquiring new
and possibly
interfering
knowledge.
Accuracy plus speed
(rate), usually with
respect to a
benchmark.
When presented with
a generalization set
(new but similar
examples) students
respond accurately
and quickly.
Focused instruction:
clear and concrete
objective; gain
attention; frame;
model, lead,
immediate
acquisition test;
examples and
nonexamples; error
correction; delayed
acquisition test;
Modeling fluent
performance
1. Review and firm
up knowledge to be
generalized.
When presented with
a retention set (a
sample of earlier
items worked on),
students respond
accurately and
quickly.
1. Every day, before
each lesson on a
particular subject,
review (assess) a
sample of what you
have already
worked on in that
subject.
Special cues; e.g., for
tempo.
Repetition (practice)
Speed drills
(practice)
2. Use a
generalization set
(new examples)
that are similar to
earlier examples
that students
learned.
2. Separate
instruction on items
review. Examples
and nonexamples are
selected from an
acquisition set.
Work on fluency
should at first be
with familiar
materials—text to
read, math problems
to solve. Why?
3. Model how to
examine new
examples to
determine of they
are the same kind
as earlier-taught
examples, and
therefore can be
treated the same
way.
If you use NEW
examples, you are
really working on
generalization.
Therefore, if students
do poorly on fluency
assessments, you
won’t know if they
just can’t generalize
or whether they were
never firm to begin
with.
Assess pre-skills or
background
knowledge essential
to the new material.
Measure rate (correct
and errors) before
instruction on fluency
During-instruction,
or progressmonitoring
assessment
Immediate
acquisition
test/check after the
model (“This letter
makes the sound
ffff”) and the lead
(“Say it with me.”).
Frequent (e.g., daily)
measure of rate
(correct and errors)
during instruction on
fluency, in relation to
a fluency aim or
benchmark
3. Provide written
routines or
diagrams that
students can use to
guide and check
themselves
4. Assure students
they can do it.
5. Provide reminders
of rules and
definitions.
6. Correct errors,
and reteach as
needed.
Review/test
knowledge you want
students to
generalize.
Pre-instruction
assessment
that may be
confusing; e.g.,
simile and
metaphor.
Add new examples to
the growing
generalization set.
Have students work
them.
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Review/test
knowledge you want
students to retain.
This would probably
be the most current
delayed acquisition
test—after a lesson or
unit.
Add examples from
the most recent
lessons and rotate
examples from
earlier lessons, to
form a retention set.
Post-instruction, or
outcome assessment
The immediate
acquisition
test/check is, for
example, “Your turn.
(What sound?” “Is
this granite?” “Now,
you solve the
problem.”)
Delayed acquisition
test using all of the
new material.
“Read these words.
First word. What
word?...Next word.
What word?”
Do this every time to
assess retention.
Rate (correct and
errors) at the end of
instruction on
fluency, in relation to
a fluency aim or
benchmark.
If students have
responded accurately
to past generalization
sets, the latest one
given is the outcome
assessment.
Or, “Is this an
example of tyranny?
[Yes] How do you
know?... Is this an
example of a
republic? [No] How
do you know?”
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If students have
responded accurately
to past retention
sets, the latest one
given is the outcome
assessment.
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