Student-Program
Alignment and
Teaching
to Mastery
Professor
Siegfried Engelmann
(
Paper
Presented at National Direct Instruction Conference
When
students are taught to mastery, they become
smarter,
acquire information faster, and develop
efficient
strategies for learning. Teachers must have an
understanding
of what mastery is and how to achieve it
in
their students. However, teachers cannot teach to
mastery
without referencing the performance of their
students.
In addition, teachers cannot teach to mastery
without
a program design that supports the approach.
Teaching
to mastery is built upon effective
student/program
alignment. This paper discusses the
features
of a program design that supports mastery,
properties
of mastery, criteria and procedures for
measuring
mastery, procedures for aligning program
placement
with student performance, and the benefits of
mastery.
Features
of a Program Design that Supports
Mastery
A
program design that supports mastery does not
present
great amounts of new information and skill
training
in each lesson. Rather, work is distributed so
new
parts in a lesson account for only 10 - 15 percent of
the
total lesson. The rest of the lesson firms and
reviews
material and skills presented earlier in the
program.
The program assumes that nothing is taught in
one
lesson. Instead, new concepts and skills are
presented
in two or three consecutive lessons to provide
students
with enough exposure to new material that they
are
able to use it in applications. So a lesson presents
material
that is new today; material that is being firmed,
having
been presented in the last two or three lessons;
and
material that was presented even earlier in the
sequence
and is assumed to be thoroughly mastered.
This
material often takes the form of problems or
applications
that require earlier-taught knowledge.
The
amount of new material is relatively small because
most
students are not capable of assimilating more. This
design
provides for some “overlearning”, but having the
program
err in the direction of providing too much
practice
is better than providing too little practice. Work
on
material presented in the preceding few lessons is
needed
to ensure that students are “automatic” with
information
or operations that were previously taught.
The
review of earlier material assures that students use
and
apply what they have learned. Reviews also prompt
students
toward an understanding that they expected to
retain
and use material learned - not just learn it for the
moment.
Basically, most things are taught in the
program
so they can be used in applications or problemsolving
settings.
Therefore, the program is constructed
so
students review and use what they have learned
according
to a systematic schedule. Because reviews
are
a regular feature of every lesson, the program
design
provides daily prompting that material presented
will
appear again. Also, applications that involve earlier taught
skills
provide the kind of practice that students
need
to keep from mixing up different things they are
learning.
If students partially learn things, new learning
is
easily confused with things that are similar. If
students
learn material well, less confusion results.
Mastering
a step at a time. A
program designed with
small
amounts of new material in each lesson is
something
like a stairway. Like a stairway, it needs
strong
support. That support is in the form of the
previously
taught skills and knowledge that are logical
underpinnings
for what is to come next in the program.
Also,
for the stairway to work well, the “steps” in this
series
should be about the same size. Certainly, they
can’t
be fashioned with the accuracy of a physical
stairway,
but they can be designed so they are close to
each
other in size.
If
we conceive of the program as being like a stairway
that
transports students to increasingly complex
performance,
we recognise the supreme importance of
mastery,
what it is, and how it relates to the curriculum.
The
following six points clarify the relationship between
mastery
and the stairway.
1.
The program will function as a stairway if
the
student reaches eve ry stair on
schedule. If students are firmly
on the fifth
stair
(which is analogous to the fifth lesson),
the
new learning that students must achieve
to
reach the sixth stair is manageable. The
students’
position on the fifth stair represents
a
foundation that places the sixth lesson
within
stepping distance. Because the
foundation
is in place, the sixth lesson does
not
overwhelm students with too much new
vocabulary,
unfamiliar or unpracticed
operations,
too much information, or too many
unknown
or unexplained details.
2.
The steps are levelers of individual
differences. Not all students who
stand on
the
fifth stair are the same age, learn at
precisely
the same rate, have equal
intelligence,
or exhibit the same “style” of
learning.
However, every student who is
firmly
on the fifth step is the same with
respect
to the program sequence. Each has
the
skill repertoire and knowledge needed to
take
the next step and reach that step within
30-45
minutes of instruction. Because
students
could not reach the fifth step without
specific
skill and knowledge, the stairway
structure
of a well-designed program serves
as
a leveller. All students with a particular
skill
profile are placed on the same stair.
Certainly,
the program design does not
guarantee
that all students will progress at
exactly
the same rate; however, greatest
individual
differences occur on the very
beginning
levels. On higher levels, after
students
have mastered a battery of skills and
knowledge,
the difference in rate of ascent
for
appropriately placed students is far less
because
all students tend to have enough skill
to
master the new material at around the
same
rate.
3.
The benefits of the design of the program
are
obliterated if a student falls below the
level
of a stair.
This fact holds for students
who
are “smart” as well as those who have a
history
of failure. If a student is below the
fifth
stair and tried to reach the sixth stair
with
one step (which means thoroughly
mastering
the sixth lesson in one period), the
student
must learn substantially more than
students
who are firmly on the fifth stair.
Furthermore,
the student must learn this
material
during the same amount of time
allotted
for students who are firmly on the
fifth
stair. Therefore, the student who is
below
the fifth stair must learn the material at
a
faster rate. The student on the fourth stair
must
learn material at twice the rate of
students
who are correctly placed. The
student
who is on the third stair must learn at
three
times the rate. For the typical student,
a
step that requires three times the amount of
new
learning is too great. Even if the student
is
able to perform acceptably on lesson 6
after
some repetition, the retention rate of the
student
on the subsequent lessons drops
dramatically.
4.
Just as the design of the program
“guarantees”
a successful future for
students
who are firmly based on a stair,
the
design suggests an unsuccessful
future
for a student who is greatly below
that
stair. The
systematic stairway design
does
not provide relief because skills and
knowledge
do not go away. Once introduced,
they
are used throughout the rest of the
program,
either as elements that are used
regularly
(such as a word type that is
learned),
as details that are embedded in
problems
and applications (such as the math
operation
of carrying), or as items that are
frequently
reviewed (such as identifying the
verb
in sentences). Because of this program
design,
once a student falls behind, the
student
will tend not to catch up. If the
student
is initially 3 steps below the lesson,
the
student will probably end up a little more
than
3 steps below the next lesson, a little
further
below the following lesson, and so
forth
until the student is not 3, but 4, steps
below
the level of the lesson, then 5 steps
below,
and so forth.
This
student is not able to benefit from the design of
the
problem, because although the program presents
small
increments of learning, this student must master
large
increments of learning to catch up. For this
student,
the program presents a poorly designed
sequence.
It requires too much new learning and
does
not provide adequate reviews.
5.
Because the program’s design benefits
are
transmitted only to students who are
on
the lesson stairs, student performance
must
match the level of performance
assumed
by each stair. This
goal is
achieved
if teachers teach to mastery.
Mastery
assures that everything that is
supposed
to be taught is taught thoroughly
and
at the time it is introduced in the program
(not
20 or 30 lessons later).
Note,
however, that DI programs are designed with
enough
redundancy that a student who is absent for
two
or three days will not be perfectly lost for the rest
of
the year. Also, if students do not master a new
skill
on the first day it is introduced, the following
lessons
provide at least one - possibly two - reviews
of
the introduction so that students will have sufficient
opportunity
to learn the skill before it is assumed to be
in
their skill repertoire and begins to appear in
applications.
The
problem occurs when students are not brought to
mastery
on skills that will be used later. For instance,
students
in Level 1 of Reading Mastery are
supposed
to be taught to follow the teacher’s
directions
about “touching words” before lesson 30.
The
tasks that the teacher presents require students
to
follow directions to “Touch the first word ... touch
the
next word ... touch the next word ...”
Often
students are not brought to mastery when this
series
of tasks is introduced. These students have
problems
in the lesson range of the 40s because now
they
are expected to first “touch the next word...” and
then
“sound it out.” If they are not firm on touching the
next
word on signal, the activity becomes very sloppy
and
students often become confused about what they
are
supposed to do. If students are taught on time,
however,
they have far less difficulty mastering the
mechanical
steps of touching the next word and then
touching
the individual letters as they sound it out. The
program
design provides for enough practice; however,
that
practice must not be mere exposure or practice with
a
very low standard of performance. The practice must
lead
to mastery.
6.
Most programs do not require teaching
to
mastery. Teaching
to mastery is a
foreign
practice to many experienced
teachers
because most programs do not
require
mastery. Instead of providing
continuous
skill development, these programs
present
topical or thematic units. Students
will
work on a particular unit for a few days
and
then it will be replaced by another unit
that
is not closely related to the first and that
does
not require application of the same skills
and
knowledge. This design, referred to as a
“spiral
curriculum”, is more comfortable for
the
program designers, teacher, and students;
however,
it is inferior for teaching skills and
knowledge.
It
is comfortable for the designers because the design
does
not have to be careful. The designers do not
have
to document that everything that is presented is
“teachable”;
the amount of new learning does not
have
to be carefully measured. The amount of time
required
for a “lesson” does not have to correspond
precisely
to a period, because the design assumes that
different
teachers will take different amounts of time
to
get through a particular “lesson” and “unit”. The
amount
of new material is not controlled. The
expectations
for student performance is low because
teachers
understand that students will not actually
master
the material. They will simply be exposed.
The
accountability of the teacher is therefore more
“comfortable”
because the teacher is not expected to
get
through the material in a specified period of time
or
bring students to mastery. The spiral curriculum is
more
comfortable for students because they are not
required
to learn, use, or apply the skills from one unit
to
the next unit. They quickly learn that even though
they
do not understand the details of a particular unit,
the
unit will soon disappear an be replaced by another
that
does not require application of skills and
knowledge
from the previous unit. The design clearly
reinforces
students for not learning or for learning
often
vague and inappropriate associations of
vocabulary
with a particular topic.
If
the systematic program is like a stairway, the spiral
curriculum
is like a series of random platforms
suspended
on different levels. Students are
mysteriously
transported from one platform to
another,
where they remain for a few days as they
are
exposed to information that is not greatly
prioritized.
Mastery is impractical with a spiral
curriculum
design because many students lack the
background
knowledge they need to stand on a
particular
“platform”. The poor design relieves the
program
designer of assuring that earlier-taught skills
and
knowledge are mastered and used. The poor
design
also relieves students of the responsibility of
learning
to mastery and it relieves the teacher of
teaching
to mastery. It therefore promotes poor
teaching
and poor learning.
In
summary, a program that teaches to mastery is like a
stairway.
Mastery is the guarantee that students are
able
to reach each stair without falling.
Properties
of Mastery
Clearly,
mastery is the handmaiden of a systematic
program.
Mastery is effective for a number of reasons.
The
most important reason is that mastery permits
teachers
to achieve steady reliable progress in student
learning.
When teachers teach to mastery, we can
make
predictions about student performance. We can
very
accurately project where students will be 100
school
days from now or 200 school days from now.
Such
projections are very powerful, but very foreign to
traditional
orientations about learning, which view the
students’
performance as a function of their ability to
learn
and motivation to learn. Therefore, to predict that
student
X will be accurately reading 30 words per
minute
by the end of the kindergarten year would be
something
of a contradiction because it assumes that the
teaching
somehow controls the student’s learning.
The
traditionalist hopes to reach and motivate the
student
and hopes that the student does not have some
type
of mysterious “learning disability” that interferes
with
learning to read. The traditionalist, however, is
unable
to predict who will read and who won’t.
Readiness
tests are tools that are supposed to predict
performance
according to what the student brings to
school.
Because they don’t take into account the kind
of
reading instruction the student will receive, readiness
tests
fail to predict accurately. In fact, the traditional
orientation
to reading has a classification for students
who
are predicted by readiness tests to succeed but who
fail
to learn to read on schedule - specific learning
disabilities.
Note that this label holds fast to the
assumption
that the student’s failure to learn to read has
to
do with a flaw in the student, not a flow in the
instruction.
The school or teacher does not have a
“disability”.
The student does. In other words, for the
traditionalist,
the performance of the student is not
clearly
linked to teaching. The more scientific
orientation
to teaching that by DI espouses assumes that
the
student who meets the entrance requirements for the
program
and who is taught appropriately (to mastery and
on
schedule) will respond in perfectly lawful ways and
will
be reading at a predicted skill level by the end of the
kindergarten
year.
Individualisation must occur from the
beginning.
Projections
are keyed to the performance of a student.
Not
all children entering kindergarten have the same
projections
because not all of them start at the same
place.
Those who enter with more skills have a
headstart and are expected to be farther after
nine
months
of instruction than the child who enters with a
lower
skill level. However, even if children begin as low
performers,
the prediction is that
they will master
beginning
reading skills in kindergarten and will be
reading
by the end of kindergarten. For the child who
enters
with a low skill level, the projected end-of-K-year
performance
may be lesson 120. The projection for the
higher
performer may be double that number.
The
fact that projections are met means that the DI
orientation
to teaching and mastery is correct. Students
will
learn if the teaching is appropriate. If they fail to
learn,
the reason lies not with their inability to learn but
with
the delivery system’s inability to teach.
The
concept of individualisation is closely related to
the
issue
of mastery and to projections about students’
performance.
The teacher cannot teach to mastery
without
referring to the performance of the students
being
taught. The teacher bases decisions about what
to
do next on samples of each student’s behaviour. This
sample
may come from tasks presented to the group,
tasks
presented to individual students, or worksheets and
similar
work samples. DI is designed so students’
thinking
is made overt. The teacher therefore receives
samples
of behaviour at a high rate on everything that
is
being taught. The teacher uses this information to
judge
what rate of presentation is appropriate. If
students
have already learned the skill or concept, the
teacher
is to move on. If the teacher determines that
some
students have not mastered what is being taught,
the
teacher corrects the mistakes and possibly repeats
parts
of the exercise. If quite a few students missed the
item,
the teacher may repeat the entire exercise with the
whole
group, which is more efficient than presenting it
to
some students individually.
In
summary, teaching to mastery is possible only if the
teacher
keys the amount and type of practice students
receive
to the performance of these children.
Criteria
and Procedures for Measuring Mastery
Teaching
to mastery is a difficult procedure for teachers
to
learn. They must learn to reference what to do next
according
to the students’ performance. They must
learn
high, but realistic, expectations for their students.
They
must also learn to coordinate mastery with fast
pacing
so that the lesson is neither a chore for students
nor
busy-work. The teacher uses efficient means of
checking
students’ work, of providing additional practice
and
firm-ups for students who do not achieve mastery
on
skills that were taught, and of providing
reinforcement
for trying hard and for succeeding.
First-time correct procedures. An important key to
teaching
to mastery is the use of first-time correct
procedures.
Procedures for inducing mastery require
the
teacher to interpret students’ performance. The
primary
indicator of mastery is how well students
perform
the first time a particular task or exercise is
presented
in the lesson. Each time a task is presented,
the
group either responds correctly (all students correct)
or
incorrectly (some students giving the wrong response
or
no response). First-time correct means all students
are
correct the first time a task is presented in a lesson.
Also
important is how well students perform on the task
or
exercise if the teacher presents it more than once. If
the
teacher corrects and repeats the task or exercise, it
is
important for students to perform correctly the second
time.
However, for diagnostic purposes, students’
responses
to the first time the task or exercise is
presented
provides the most critical information about
where
students are positioned on the stairway and
whether
they are appropriately placed in the program.
For
instance, the first time the teacher asks a question
such
as, “Do we multiply or divide to solve this
problem?”
or the first time students read a particular
word
list, their responses reveal information about the
mastery
level the students bring to the lesson.
The
students’ pattern of correct responses also provides
important
mastery information. If they are making too
many
mistakes, or if they are not firm on material that
had
been taught earlier and that is assumed to be firm,
they
are placed too far in the program and should be
moved
back. If students give solid indications that they
already
know what the lessons is teaching, the students
may
not be placed as far in the program as they might
be,
and the rate of lesson presentation should increase.
Finally,
the “correct-response” patterns of a group
indicate
whether all students belong in the group or
whether
some should be placed in other groups.
Four
criteria permit precise interpretation of the correct response
performance
for groups and individuals:
Criterion1.
Students should be at least 70% correct on
anything
that is being introduced for the first time.
Criterion
2. Students should be at least 90% correct
on
the parts of the lesson that deal with skills and
information
introduced earlier in the program
sequence.
Criterion
3. At the end of the lesson, all students be
virtually
100% firm on all tasks and activities.
Criterion
4. The rate of student errors should be low
enough
that the teacher is able to complete the lesson
in
the allotted time.
Again,
all the percentages are based on how students
perform
the first time a particular task is presented in
the
lesson. For material that is assumed to be mastered,
the
group should respond perfectly at least 9 out of 10
times.
As
noted above, students’ first-time performance shows
what
they have brought with them to the lesson. That is
the
material that is in their memory and skill repertoire.
The
performance of students after the teacher repeats
the
material indicates only what the students may retain
for
possibly less than 10 minutes. That time span does
not
measure mastery. When students master a skill they
know
it “as well as they know their own name.”
All
four criteria should be considered in evaluating the
mastery
of the group. If students meet the first three
criteria
but can’t seem to get through lessons in the
allotted
time, something is wrong. The following
sections
examine the four criteria in more detail.
Criterion
1. Students should be at least 70 percent
correct
on anything that is being introduced for the
first
time.
This percentage is based on the
understanding
that even the new skills or procedures
that
are being introduced are not composed entirely of
material
that is new. Much of it will be familiar.
Therefore,
the initial rate of correct responses should not
drop
below 70 percent. If students are at mastery on
the
preceding lessons, this outcome will occur in almost
all
cases.
If
students perform much below 70 percent, they are not
learning
the material. If they are only 50 percent
correct,
they may be at a chance level - guessing at the
answers
or the steps in the operation. Their responses
are
not generated by an overall understanding of what
they
are learning. At 70 percent correct, their responses
show
that they are much closer to understanding the
new
material than they are to taking blind stabs at
responding,
and therefore should be able to master the
new
material during the lesson.
Criterion
2. Students should be at least 90 percent
correct
on the parts of the lesson that deal with
skills
and information introduced earlier in the
program
sequence. Criterion
2 is based on the fact
that
students must be completely at mastery on earliertaught
material.
When earlier-taught material occurs in
later
lessons, no reteaching should be required. If
substantial
reteaching is needed, the amount of new
learning
that students must achieve to mater the lesson
becomes
too great. If students are consistently not at
the
90 percent correct level on material that had been
taught
earlier in the program, students need more
extensive
firming and more delayed tests. Possibly, the
teacher
should use a game format in which she asks
students
different questions at the end of the lesson.
Students
who respond correctly receive points. When
virtually
all students consistently earn points, they have
learned
good techniques for learning and retaining
information
presented in the lesson.
Criterion
3. At the end of the lesson, all students
should
be virtually 100 percent firm on all tasks
and
activities.
Criterion
4. The rate of student errors should be
low
enough that the teacher is able to complete the
lesson
in the allotted time. Criteria 3 and 4 go
together.
When the rate of errors for the overall lesson
is
low, the teacher does not need to spend great amounts
of
time firming students, and the teacher should be able
to
complete the lesson in the allotted time. If students
enter
the lesson with skills that permit them to attain 70
percent
correct on new material and 90 percent correct
on
material taught earlier, students should be able to
achieve
virtually 100 percent on all exercises presented
in
the lesson. Achieving this performance level may
require
a little additional firming, but it should not be
necessary
or excessive lesson after lesson. Therefore,
if
Criteria 1 and 2 are met, students should easily
achieve
Criterion 3 and the teacher should be able to
complete
the lesson during the allotted time.
Calculating percentages. Several different
procedures
are
effective for teachers to learn how to “estimate” or
calculate
the percentage of first-time-correct responses.
One
way is to place sticky tabs in the teacher
presentation
book after each task, or affix a sheet of
paper
to the page so the teacher can mark whether the
group
(or individual) correctly responded to each task.
After
the children have responded to ten tasks, the
teacher
simply counts the number of tasks that were
correct.
If seven were correct, the percentage is 70
percent.
(Note: if the teacher repeats a task, she would
not
mark the second-time performance the same way
she
would mark the first-time performance. She could
circle
the second-time performance, note the
performance
in a second column, or use another way to
separate
the first-time performance from performance
on
tasks or exercise that are repeated.)
After
using a procedure of actually counting the
responses
within each exercise, the teacher should try
to
make estimates in her head. One way is to “ball
park”
patterns in terms of whether students are
performing
closer to 50 percent or 100 percent. If they
seem
closer to 50 percent (missing a little less than half
of
what the teacher presents) their first-time percentage
is
too low. If they are clearly closer to 100 percent than
50
percent, their performance tends to be high and in the
ball
park.
For
some tasks, such as reading a passage, the
percentage
should be high, even on the first reading,
because
virtually all the words should be familiar.
Students
should not fall below 90 percent correct on the
first
reading of a passage. One the second reading,
students
should perform close to 100 percent.
Once
the teacher becomes facile at estimating the
percentage
of correct responses, she has learned to
respond
sensitively to students’ progress and problems.
The
teacher would apply this skill. If only some of the
students
in the group consistently make mistakes, they
should
probably be placed in another group.
Decisions
about mastery do not derive only from the
percentages
of first-time correct performance. The
teacher
also has information about in-program test
performance
and independent-work performance. The
value
of identifying the first-time-correct performance
is
that it affords the teacher the opportunity to correct
problems
of mastery when they first appear. This
opportunity
results in greater efficiency in teaching to
mastery.
Assessing mastery through delayed tests. Delayed tests
are
simply selected tasks from the lessons that are
presented
again later in the lesson. Because of the
“delay”
between the time students worked the task and
when
they work it again, the teacher is provided with a
good
indication of whether students have the information
in
their memory.
Presenting
delayed tests, either to the group or to
individuals,
is the best way to shape or improve students’
ability
to remember new information and to learn how to
organise it mentally so that they are able to
recall and
use
it. The tests work best when there is a contingency
attached
to them. If students know that they will be
tested
later on any exercise, skill, or problem type
presented
in the lesson, students will tend to learn the
material
far better than when no contingency exists. For
instance,
at the beginning of a reading lesson, the
teacher
indicates that at the end of the reading lesson,
“I’ll
call on individuals to read some of the harder words
in
the lesson. Let’s see if we can get a perfect score”.
After
the word attack, the teacher says, “Now you’re
going
to read some of those harder words. Remember,
if
you read all the words correctly when I call on you,
you
earn five bonus points. If everybody reads the hard
words,
everybody receives another three bonus points.”
This
procedure could be repeated at the end of the story
before
students begin independent work. Similar
routines
are effective for math and language lessons as
well.
To
further assure that students are at mastery, the
teacher
could present delayed tests at different times of
the
day. A good rule is that whenever students are lined
up
in the classroom, ask them questions about the newly
taught
material. Praise students who do well.
Remember,
the more students understand that they will
use
the information that they are learning, the more they
will
develop strategies that permit them to master new
material
quickly and efficiently. More importantly, by
providing
delayed tests, the teacher shows students what
is
important. If the teacher shows that their learning and
retention
of material are important - not simply within
the
time frame of the period during which the material
is
taught - the teacher models what they are to think
about,
mentally rehearse, and use. This message goes
a
long way to help students prioritize their thoughts and
goals.
Procedures
for Teaching to Mastery
One
of the most obvious questions about teaching to
mastery
is: If mastery teaching has so many benefits,
why
haven’t we seen the effects of mastery teaching on
lower
performers? The reason is simply that schools
typically
(and historically) have not been designed to
provide
for teaching to mastery. The schools have not
been
organized either to recognize mastery teaching as
important
or to address the technical details of achieving
it,
particularly with lower performers.
Three
basic components must be in place if a school is
to
achieve the transformations that are possible by
teaching
to mastery:
a)
programs in various subject areas that are
designed
to accommodate mastery teaching;
b)
teachers who scrupulously teach everything
to
mastery; and
c)
a system that provides for the grouping of
students
and the coordination that is required
to
achieve maximum acceleration of student
performance.
Until
very recently, no schools have incorporated these
three
components into a systematic plan that involves all
the
teachers and all the instruction. The following
sections
examine these three components in detail.
a)
Programs for teaching to mastery. The
requirements
for instructional sequences are very
different
from the requirements that states and districts
use
to adopt instructional material. All instructional
programs
must have two primary features to make
teaching
to mastery uniformly possible:
1)
The programs must be designed to present
instruction
for each skill and concept in a way that
permits
the teacher to teach it to mastery (given
that
the teacher follows program specifications).
2)
The programs must be coordinated from level to
level
so they are continuous and so the later level
builds
efficiently on what was taught in the earlier
level.
Program
design.
A slogan for a well-designed
program
is that it teaches everything that students will
need
for later applications, and it doesn’t teach anything
that
is not needed for future applications. This feature
sets
the stage for mastery. Students who are at mastery
in
the program know at least 70 percent of any new skill
or
operation that will be taught in the program.
Therefore,
their first-time percentage on new material
will
be in the acceptable range. Traditional programs do
not
have this structure and therefore do not permit
application
of the rules about first-time correct.
Although
traditional programs may work adequately with
higher
performers, they tend to be very ineffective with
the
lower end of the student population (those students
for
whom the material is unfamiliar).
The
small-step program has a ‘track’ structure, which
means
that more than one separate skill is taught during
each
lesson. What had been taught earlier is reviewed.
Traditional
lessons are often organized around single
topics,
rather than around a series of continuing tracks.
Also,
traditional programs are frequently based on loose
associations
of ideas, such as the various meanings of a
vocabulary
word like fine. Except in limited cases, the
well-designed
program would present only the meaning
that
will be used in upcoming applications.
Traditional
programs also do not provide the review
students
need. Advanced material presented in the
traditional
textbook is not actually designed to teach
content.
Rather, the text is a reference
book—something
like an encyclopedia organized around
different
topics. The teacher is expected to transfer this
information
to the students, but the manner in which this
transfer
is supposed to occur is not clear. What is clear
is
the fact that it doesn’t happen with many students.
A key element of the
effective program is that it is
designed so that it does
not generate possible misrules.
For
instance, if students are actually taught to guess at
the
word by figuring out the beginning sound and the
general
shape of the word, teaching students to mastery
will
simply guarantee later failure. This is a false rule.
If
applied, students will certainly confuse words like
slop,
shop, and stop. A program with spurious teaching
may
work when there is a small range of examples (only
the
word shop appearing in what students read). Later,
however,
the program will fail (when stop also appears
in
what they read).
Also, the program cannot
have false or spurious clues
that permit students to
give the right answer for the
wrong reason. If students always
recite number facts
in
the same order, they could learn a serious misrule,
which
is that the answers always follow the counting
order.
What’s 1+1? What’s 2+1? What’s 3+1?
What’s
18+1? Students who have always recited the
facts
in the counting order will respond to the last
question
by saying, “Five”. The sequence is seriously
flawed
and introduces a serious misrule.
Unless
the program is well designed for teaching to
mastery,
it will often not produce gains, but frustration,
both
for students and the teacher. The program must
provide
both for the rapid teaching of new skills and for
a
high rate of student responses. These responses let
the
teacher know whether or not students are at
mastery.
Level-to-level
coordination.
For mastery teaching to
be
possible, programs must be thoroughly coordinated
from
level to level. Different levels of traditional
instructional
programs present the same topics and the
same
examples. For instance, over 75% of a sixthgrade
math
program may be presented in the
corresponding
fifth-grade program. Obviously, this
sequence
makes no assumption that students have
mastered
anything that was taught in the fifth grade. In
fact,
math assessments regularly disclose that students
have
not mastered any of the content that is new to the
current
level of the program. Rather, students know
only
what had been taught 1 to 2 levels earlier. This
relationship
confirms that students have not received
consistent
experiences in learning what teachers and
textbooks
teach. They tend to learn the material much
later,
through experimentation and trial and error.
b)
Teachers who teach everything to mastery.
This
criterion is necessary, but very difficult to attain.
Teaching
to mastery is the most difficult skill for
teachers
to learn. One problem is that teachers have a
strong
tradition of simply exposing students to material,
rather
than assuring that they master it. What often
occurs,
even in schools that are supposed to be full immersion
DI
schools and that do well with the DI
subjects,
is that teachers tend to have split teaching
philosophies.
When presenting DI lessons, they teach to
mastery,
but when they present other
instruction—social-studies
units, art, vocabulary
information—they
don’t. Instead of constructing
variations
of routines that they have used in DI
sequences,
they simply expose students and don’t
consider
the effects of their instruction on how students’
knowledge
base and attitudes.
For
example, we recently observed a good DI teacher
presenting
a “unit” on
grade.
These children had completed
3; yet, when the teacher
presented the unit, she did not
refer
to anything they had learned in
present
the information about
way,
and did not provide any tests to determine whether
the
students had mastered the new information about
contained
a map of
questions.
She read the facts, briefly discussed some of
the
customs, told the students about several other things
that
characterize
to
write answers to the questions and color the map.
At
this point, we asked students a series of questions to
determine
whether they knew the new information and
knew
how to fit it into what they already knew about the
world.
Here are some of the questions.
“It
says that
live
in that country? . . . What’s the name of the country
you
live in? . . . Can you find
Can
you show me where
Have
you read about any other countries in
..”
We asked about several of the vocabulary words
that
appeared on the worksheet. The students failed
nearly
all of these items.
It
would not have taken the teacher more than five
minutes
to teach students to mastery on all the
information
they would have needed to fit the worksheet
material
into the framework of knowledge they already
possessed.
They had read about Herman the fly, who
flew
around the world, landing in
able
to locate
point
for going north to
from
the
size
and its relation to places they already knew. That
was
the purpose of teaching the global information in
Reading
3 - to provide them with “stepping stones” upon
which
to build new facts and operations.
The
teacher, however, did not know how easy it was to
teach
to mastery on things that were not in the DI
curriculum
or how important it was. Her approach was
very
ill advised because it promoted
compartmentalization
of information and discontinuous
learning
strategies. When doing the social studies, the
students
had a dabbling attitude. Some of the material
was
so strange to the students that they apparently
didn’t
even know what sort of questions they should ask
to
make sense of it. They didn’t even try to understand
it.
In the case of
where
it was, what it was, or how it related in any way
to
the things they had learned.
During
the direct-instruction periods, in contrast, the
students
had strategies that permitted them to learn to
mastery.
The net result of the unit on
the
teacher lost lots of opportunities to build on what
students
already knew. Furthermore, she lost
opportunities
to help accelerate the intellectual growth of
her
students.
To
make sure that they really learned the information on
part
of her daily routine—the openers—which consist of
a
series of questions the children are to answer. The
new
items would relate to
the
country you live in? . . . Is that country in
.
. . Name some countries in
big
as the
globe.
Tell me the name of the country I touch. . .”
“Compartmentalized”
teaching is far more common than
teaching
designed to build on what students already
know.
The general guideline for a teacher who wants
to
accelerate intellectual growth is: If you teach
anything,
teach it to mastery.
To
do that, the teacher figures out how the new material
is
related to what students already know and makes this
relationship
explicit and part of the mastery teaching.
Before
teachers are able to teach everything to mastery,
they
must be trained and they must receive extensive
models
about how to do it.
c)
A system that supports mastery and
acceleration. Because students will
not be seriously
accelerated
unless they receive possibly three or more
years
of undiluted immersion in mastery teaching, the
school
must have a system that requires teaching to
mastery.
A system is necessary because immersing
students
in mastery instruction involves more than one
teacher.
In fact, if mastery-teaching immersion is to
occur
for all students, it must involve all teachers, all
subjects
and virtually all aspects of the school day.
This
system meets seven primary requirements:
1.
All students must be appropriately placed in
each
instructional program.
All placements are
based
on first-time-correct performance. Mastery is not
possible
unless students are placed according to the
criteria
for first-time-correct performance.
2.
All groups must be homogeneous with respect
to
the performance level of all students in the
group. This requirement is an
extension of the firsttime-
correct
requirements. Unless all students in the
group
are appropriately placed, the teacher will not be
able
to bring the group to mastery in a reasonable
amount
of time. The teacher will have to spend time
providing
additional practice to students who should not
be
in the group. This additional practice tends not to
serve
students who need it nor the other students, who
waste
time while the teacher works on firming skills that
they
have already mastered.
3.
There are actually three critical scheduling
issues. The first is that
adequate time must be
scheduled
on a daily basis for teaching each group each
subject.
The second is that the schedules must be
coordinated
to permit relatively easy movement of
students
from one instructional group to another, based
on
their performance. If two students should be in a
math
group that is 55 lessons earlier in the program, the
transfer
is relatively easy if the group that is to receive
these
students is teaching math at the same time as the
group
in which the students are currently placed. The
third
issue is that movement of students from one
instructional
group to another should occur frequently
throughout
the year. A general rule for grades K-3 is
that
major regrouping should occur at least three times
during
the year. This regrouping assures that
instructional
groups remain homogeneous in
performance.
Note that regrouping is generally not
required
as frequently in the upper grades after the
implementation
is stabilized. However, periodic changes
may
have to occur in math and language. All schedules
must
be coordinated across classrooms and grades so
that
cross-class grouping and regrouping is possible.
This
need is met only if specified classrooms teach the
same
subjects at the same time.
4.
Schedules must provide adequate time for each
subject
and each instructional group, and teachers
must
faithfully follow schedules. The schedules must
include
time for workchecks, so that students receive
timely
feedback on any mistakes they made, and so
teachers
receive information about any skills or items
that
need additional firming. The worksheets and
possible
firming periods are particularly important during
the
first several years of the implementation.
Many
problems of scheduling periods occur in the
beginning
grades. Sometimes, schedules provide
adequate
time for two of three groups in a subject, but
not
for the third. Sometimes, the schedule is different on
different
days, which means that students may not
receive
instruction in some subjects on some days.
Sometimes,
the time allotted for the teaching of a subject
is
not adequate. All these problems must be corrected
if
adequate mastery is to be attained.
5.
A group’s progress in mastering new material
must
be continuous throughout the year. If the
group
completes level 3 reading in the middle of
February,
students must begin level 4 within no more
than
two or three school days. Level 4 should not be
delayed
until the beginning of the next school year.
6.
All teachers must enforce the same set of
schoolwide management rules and
practices for
celebrating
academic achievements.
There should
be
rules for how students are to behave in the class, so
that
if students misbehave, they understand both the rule
that
they broke and the consequence. The system of
rules
should be designed so students receive
reinforcement
for complying with rules. The schoolwide
celebration
of students’ achievement should be the
centerpiece
of the school’s ceremonies. Students who
achieve
well should be recognized in a way that leaves
no
doubt about how important the school feels mastery
accomplishments
are.
7.
The performance of students must be regularly
monitored. The school must have
systems for
regularly
monitoring students’ progress. The monitoring
information
may consist of weekly summaries of
progress
in each subject, summarises of student
performance
on in-program tests, and reports on daily
independent
work. The purpose of the monitoring is to
guarantee
that no students fall through the cracks and
that
all receive the best instruction that the school is able
to
deliver.
This
full set of seven requirements is rarely met. Each,
however,
is necessary if the school is to achieve
maximum
acceleration of student performance.
Four
rules for teaching to mastery. One of the
reasons
that mastery instruction is difficult for teachers
to
learn is that facts about mastery soundly contradict
beliefs
that teachers have about individual differences
and
how children learn. Note however that the
teachers’
misconceptions are perfectly consistent with
their
experiences. The teachers’ beliefs are based on
exactly
what they have observed. The problem is that
they
usually never observed students who have received
extensive
mastery instruction. To engage in mastery
instruction,
teachers must adhere to four basic rules that
contradict
conventional wisdom and the beliefs that
many
teachers hold.
Rule
1: Hold the same standard for high
performers
and low performers. This
rule is based
on
the fact that students of all performance levels exhibit
the
same learning patterns if they have the same
foundation
in information and skills. The false belief that
characterises the conventional wisdom
about teaching is
that
lower performers learn in generically different ways
from
higher performers and should be held to a lower or
looser
standard. Evidence of this belief is that teachers
frequently
have different “expectations” for higher and
lower
performers. They expect higher performers to
learn
the material; they excuse lower performers from
achieving
the same standard of performance. Many
teachers
believe that lower performers are something
like
crippled children. They can walk the same route
that
the higher performers walk, but they need more
help
in walking.
These
teachers often drag students through the lesson
and
provide a lot of additional prompting. They have to
drag
students because the students are making a very
high
percentage of first-time errors. In fact, the
students
make so many mistakes that it is very clear that
they
are not placed appropriately in the sequence and
could
not achieve mastery on the material in a
reasonable
amount of time. The teachers may correct
the
mistakes, and may even repeat some parts that had
errors;
however, at the end of the exercise, the students
are
clearly not near 100% firm on anything.
Furthermore,
the teacher most probably does not provide
delayed
tests to assess the extent to which these
students
have retained what had been presented earlier.
The
information these teachers receive about low
performers
is that they do not retain information, that
they
need lots and lots of practice, and that they don’t
seem
to have strategies for learning new material.
Ironically,
however, all these outcomes are predictable
for
students who receive the kind of instruction thes e
students
have received. High performers receiving
instruction
of the same relative difficulty or unfamiliarity
would
perform the same way. Let’s say the lower
performers
typically have a first-time-correct
percentage
of 40%. If higher performers were placed
in
material that resulted in a 40% first-time-correct
performance,
their behaviour would be like that of lower
performers.
They would fail to retain the material, rely
on
the teacher for help, not exhibit self-confidence, and
continue
to make the same sorts of mistakes again.
If
students are placed according to their first-time correct
percentages,
they tend to learn and behave the
same
way, whether they are “lower performers” or
“higher
performers.” In Project Follow Through, we
mapped
the progress of students of different IQ ranges.
The results showed that
regardless of students entering
IQ, the rate of progress
was quite similar across all
children and across
different subjects. Lower
performers learned as
fast as higher performers. They
simply started at a
different place,
with material that
higher
performers had long since mastered. Note that
this
conclusion may be somewhat biased because we
paid
particular attention to the instruction for the lower
performers.
They tended to have better teachers and
their
instruction tended to be monitored very closely. In
any
case, they learned at a very healthy rate, one that
paralleled
that of students with IQS 40 points higher.
The
typical practices of placing and teaching students
are
completely opposed to appropriate placement and
teaching
procedures. At the
place
teaching-practice students in special-ed
classrooms
that use direct-instruction programs. During
the
years that we first offered these practica, we
typically
worked with teachers who were teaching DI
but
had not generally received much training. Before
we
arranged for a placement with a new supervising
teacher,
therefore, we made sure that the classroom
was
“appropriate” for our students, which means that
the
children the practicum students were to work with
were
placed appropriately and that the teacher was
using
and modelling appropriate practices. As part of
the
review of the new classrooms that were candidates
for
receiving practicum students, we checked the
program
placement of the students and changed their
placement
if necessary.
Our
estimate is that in the first 40 or more classrooms
we
used, the children were moved back in DI reading
programs
an average of 100 lessons - sometimes 120
lessons.
The children, in other words, were placed
about
3/4 of a school year or more beyond the optimum
first-time-correct
percentages. Nearly all teachers had
children
that were seriously misplaced. Furthermore, I
don’t
recall a single classroom in which children’s
percentages
required us to move children ahead in the
programs.
Children were always “over their heads”.
Coincidental
with the inappropriate placement was
inappropriate
expectations. Often, teachers were good
technicians
- acting positively, exhibiting good pacing and
other
mechanical skills, and correcting mistakes in a
timely
and apparently appropriate manner. They often
had
noble motives for placing the students where they
were,
so that students would be closer to the appropriate
placement
for their age. Their error, however, was that
this
placement made mastery impossible. Without
achieving
steady and predictable mastery, children could
not
gain at a healthy rate.
An
almost inevitable conclusion that teachers derive
from
observations based on inappropriate placement of
children
is that these children are different. For many
teachers
the difference suggests that the children need
a
“different approach.” We have seen many teachers
who
have asserted that “that group has been through the
program
two times, and it just doesn’t work with them.”
The
teacher is not actually blaming the children for not
learning,
but rather suggesting that they may be able to
learn
more easily with some kind of approach that
matches
their different way of learning.
In
about 12 cases, we were able to test the children
who,
according to the teachers’ reports, had gone
through
the program and not mastered the material. In
every case, it was very
apparent that they had never
been through the program
at anything approximating
mastery. In some cases, the
appropriate placement
(based
on first-time-correct [percentages) was the
beginning
of a lower level of the series - about 300
lessons
from the end of the level the teachers said the
children
had completed two times. Furthermore, when
children
were placed appropriately and actually taught
to
a high standard of performance, they learned at a
predictable
rate, and they indeed mastered the material.
Rule
2: At the beginning of the school year, place
continuing
students who have been taught to
mastery
no more than 5 lessons from their last
lesson
of the preceding year. If something is
thoroughly
learned and applied, it will be retained by
lower
performers as well as by higher performers.
The
conventional wisdom, in contrast, holds that lower
performers
“have it one day and forget it the next.”
And
whatever they have, “they completely lose over the
summer.”
Again, this expectation results largely from
the
kind of instruction students have received. Even
after
teachers have learned to teach students to
mastery,
however, they often retain their expectations
about
how much lower performers will retain. In the
first
ASAP schools we worked with in Utah, teachers
routinely
placed continuing students at the beginning of
the
school year 80 to 100 lessons behind the last lesson
they
had completed the preceding spring.
Teachers
had been told the ASAP policy for placing
students
at the beginning of the school year: Go back no
more
than five lessons in the program sequence and
bring
students to a high level of mastery on the material.
This
firming is to take no more than five school days.
After
the review, students should be well prepared to
pick
up in the program where they had finished in the
spring.
The
teachers were openly sceptical about this
procedure,
and they ignored it. They argued that, over
the
summer, students forget much of what they had
learned.
We told them that learning didn’t work that
way.
We pointed out that there is a lot of literature on
learning
and retention that shows that even if something
that
had been thoroughly learned and had not been
practised for years, there would be great “savings”
in
the
amount of time needed to reteach this material to
mastery.
Therefore, if appropriate placement for
students
in the fall (based on error performance) is 80
lessons
behind where they finished in the spring, the only
possible
conclusion is that they had never learned the
material
in the spring.
For
several years, the teachers resisted following the
fall-placement
rules and continued to use their traditional
practices.
To correct this situation, we documented the
mastery
of all students several weeks before the end of
the
school year. We staged “show off” lessons that
were
observed. The observations confirmed what
students
did know, and in some cases, identified some
things
they had not adequately mastered. Before the
end
of the school year, students were placed according
to
the rules about first-time-correct percentages so they
were
firm in everything that had been presented in the
program
sequence.
At
the beginning of the next school year, we controlled
the
placement of students to make sure that teachers
were
placing students no more than 5 lessons behind
where
they had left off in the spring. Students
performed
as predicted. After possibly one or two
lessons,
they clearly performed as well as they had in
the
spring.
The
response of the teachers was overwhelmingly one
of
disbelief and revelation. Most of them said something
like,
“I’m amazed. They actually retained what they
had
learned.”
The
magnitude of their surprise suggests how strong the
belief
was that students could not possibly retain the
information
over the summer. This strong belief had
been
supported by what they had observed in the past,
which
was based on spring placements that were far
beyond
what students had actually mastered.
Rule
3: Always place students appropriately for
more
rapid mastery progress. This fact contradicts
the
belief that students are placed appropriately in a
sequence
if they have to struggle - scratch their head,
make
false starts, sign, frown, gut it out. According to
one
version of this belief, if there are no signs of hard
work
there is no evidence of learning. This belief does
not
place emphasis on the program and the teachers to
make
learning manageable but on the grit of the student
to
meet the “challenge.” In the traditional interpretation,
much
of the “homework” assigned to students (and their
families)
is motivated by this belief. The assumption
seems
to be that students will be strengthened if they
are
“challenged.”
This
belief is flatly wrong. If students are
placed
appropriately, the work
is relatively easy.
Students tend
to
learn it without as much “struggle.” They tend to
retain
it better and they tend to apply it better, if they
learn
it with fewer mistakes.
The
prevalence of this misconception about “effort” was
illustrated
by the field tryouts of the Spelling Mastery
programs.
Over half of the tryout teachers who field
tested
the first and second levels of Spelling Mastery
with
lower performers indicated on their summary forms
that
they thought the program was too easy for the
children.
Note that most of these teachers were not DI
teachers
and had never taught DI programs before.
When
asked about whether they had ever used a
program
that induced more skills in the same amount of
time,
all responded, “No.” Nearly all agreed that the
lower
performers had learned substantially more than
similar
children had in the past. When asked if students
were
bored with the program, all responded, “No”.
What
led the teachers to believe that the programs were
too
easy? All cited the same evidence: students didn’t
have
to struggle. For them, it wasn’t appropriate
instruction
if it wasn’t difficult for the lower performers.
Often,
good DI teachers place students who are behind
as
close as possible to their age-appropriate placement.
Their
rationale is that if students can make good
progress
at this placement, they will be farther ahead.
Placing
students at the edge of their ability to perform,
however,
mans placing them where the students are
“working
very hard” and where they will make a high
percentage
of mistakes. This placement effectively
negates
good teaching.
One
teacher we observed would have scored a 10 on
the
teaching behaviours that good teachers are supposed
to
exhibit. She was working with fourth graders who
were
placed far beyond where they should have been
placed
in the Corrective Reading program. In trying to
read
one of the longer sentences, the students missed
five
words. The teacher corrected each mistakes with
alacrity.
The teacher faithfully returned to the beginning
of
the sentence and directed the reading again. At last,
the
students read the sentence without error, and the
teacher
praised them. They smiled and apparently felt
good
about their achievement. Later, we tested the
students
individually on the sentence. No student made
less
than 3 errors in reading the sentence. The
teacher’s
expectations for these students were simply
unrealistic,
and although the teacher had superior
teaching
skills, all were effectively negated by the
placement
of the students. When asked why she placed
the
students where she did, she expressed her concern
with
their future if they didn’t catch up to grade level.
She
wanted them to learn as much as possible in the
available
time, and she assumed that the closer they
were
to working on forth-grade material, the greater
their
chances of achieving this goal sooner.
In
working with the ASAP schools in
several
demonstrations that tested this formula. During
the
first two years of the project, these schools had
great
concern over the math place of fifth - and sixth grade
students.
Very few sixth graders placed in the
sixth
level or oven the fifth level fo Connecting Math
Concepts. Some barely passed the
placement test for
the
fourth level of the program - Level D. This level
assumes
that students have mastery of a wide range of
math
facts and operations. Therefore, we were
reluctant
to place new students in D unless they had a
strong
performance on the placement test. The schools,
like
the teacher in the example above, assumed that the
fastest
way to get sixth graders into sixth-grade material
was
to start them as close to that material as possible.
On
three occasions, we had the opportunity to split
groups
that were fairly homogeneous in performance
and
to place half the group at the beginning of D and the
other
half at the beginning of C, where they would learn
the
facts and operations that are assumed by Level D.
The
strategy for these students was to make sure they
performed
according to the ideal percentages of first time
performance
and to move as quickly as possible.
If
students were clearly firm on something, we would
either
direct the teacher to skip it in half the lessons or
present
the problems as independent work. As soon as
the
percentages started to drop, we would return to
presenting
full lessons and continue at that pace until it
was
clar that the students could be safely accelerated.
(Note:
We tend not to skip material when we accelerate
students.
We simply go through the material faster.
We’ve
discovered that when teachers start skipping
material,
they often skip too much or skip material that
should
not be skipped even if students perform at
acceptable
percentages).
In
all cases, groups that started in C performed much
better
and actually passed up groups that started in D.
In
two cases, this occurred before the end of the first
year.
For the last case, it occurred in the middle of the
second
year. The student who stated in D tended not to
perform
near the ideal first-time percentages. They
often
failed the ten-lesson tests, and teachers had to
spend
a great deal of time reviewing and reteaching
things
the students were expected to have learned. In
contrast,
the student who had been placed in C were
able
to do more than one lesson a day (until they
reached
about lesson 30 in DS) and had a very high rate
of
passing the ten-lesson tests. For these students, the
sequence
of the program was congruous with their skill
level,
and the steps in the program were small; for the
students
who started in D, the program steps were too
large
and the climb too steep. The overall effect was
that
the D-starting students didn’t like match as much as
the
other students did and had far less confidence about
their
ability to learn math. We later adopted the practice
of
starting all students with marginal understanding in
Level
C, not D.
Rule
4: Move students as quickly and as
reinforcingly as their performance
permits. This
rule
opposes the notion that teaching to mastery is
somehow
synonymous with having picky or punishing
standards.
For instance, I recently observed a teacher
who
seemed to confuse teaching to mastery with being
a
“taskmaster.” She was teaching reading to a group of
10
first graders. Students were attempting to read a
sentence
in unison. After the second word, the teacher
stopped
the group because of the students did not have
both
feet on the floor. On the second trial, one of the
students
did not point to a word on time. The third time,
one
of the students did not clearly respond to the last
word
in the sentence. On the fourth trial, three students
did
not read the second word, etc.
This
teacher, and many others who attempt to teach to
mastery,
confuse form with function. The goal is to give
the
children the information and practice they need as
quickly
and efficiently as possible, secure evidence that
they
have mas tered the
material, and move on. While
military
precision may indicate mastery for some things,
effective
tests should be used to determine mastery.
After
observing the teaching of the reading lesson for a
while,
I pointed to a student who had unwittingly been
responsible
for the group going back to the beginning of
the
sentence at least twice and asked the teacher,
“Does
he know all the words in this sentence?”
She
said, “I don’t know.”
I
asked, “If you presented an individual turn to him,
would
he know all the words?”
She
said, “I’m not sure”.
Her
responses indicated that she had been largely
looking
at the wrong things. The student was at
mastery,
but his performance was being judged
according
to standards that were simply barriers - not
indicators
of mastery. The teacher was trying to teach
to
mastery without actually evaluating what was
happening.
She was being a taskmaster, not an
evaluator.
The teacher’s behaviour showed the students
that
they were failing, even though they were actually
quite
firm on the material. And it wasn’t apparent to
them
what they should do to please her. It seemed
inevitable
that they would have to read each sentence
many
times, regardless of what they did.
Although
these students were placed properly in the
instructional
sequence, the teacher’s method of firming
preempted
her from being able to meet the criterion of
getting
through the lesson in a reasonable amount of
time.
That fact should have been a signal that
something
was wrong.
I
told her to use a different format for presenting to this
group.
She would tell students that they would read the
sentence
only one time. If they made a mistake, the
teacher
would tell them the correct word and then they
would
move on. After the group read the sentence one
time,
the teacher would call on two or possibly three
students
to read the sentence individually. L If they all
read
it correctly, everybody in the group would receive
a
point for the sentence. (Also, when students read the
sentence,
they were permitted one, but only one, re-read
or
self-correct of a word).
Although
this format is not appropriate in all situations,
it
was good for this teacher because it helped her
separate
the mechanical details from the substance of
what
is being learned and helped her present in a way
that
gave students a chance both to achieve mastery and
to
feel good about their success. When she was able to
observe
the performance of individual students, she was
able
to see more clearly whether they were at mastery.
She
was also able to increase the pace of the lesson so
that
it was far more enjoyable for her.
Benefits
of Immersing Students in Mastery
Teaching
to mastery has benefits for students, teachers,
and
the school system. Students benefit by becoming
much
more competent and by gaining options for their
futures
they otherwise would not have. Teachers
benefit
because students who are taught to mastery tend
to
succeed; therefore, teaching becomes easier.
Schools
benefit because students are much easier to
teach
in the upper grades if they have a solid mastery
foundation
starting in kindergarten. In the upper grades,
students
are able to learn new material at a good rate,
and
the bottom end of the student population performs
more
like traditionally taught students.
Two
types of performance change occur in students.
The
most obvious is that students learn more material
during
a specified time period. The second change is in
their
ability to learn new material. There is a simple
relationship
between the amount of material they master
and
their overall facility to learn new material. The
more
success students have with a particular type of
material,
the better they become at it.
Teaching
to mastery also installs self-confidence in
students
because they learn they are capable of learning
whatever
new skills or material the teacher presents.
Their
positive attitude is firmly grounded in experience.
Because
students have learned everything the teacher
has
taught, students understandably have confidence
that
it will happen the same way for future instruction.
What
governs these changes in student performance
and
self-confidence? The degree to which students
benefit
from being taught to mastery depends on the
extent
of the mastery teaching and on the number of
areas
in which students experience mastery.
Early
work in the Direct Instruction Preschool provided
many
examples of the acceleration achieved in specific
areas
of knowledge by teaching to mastery. One of the
cleanest
demonstrations came from the teaching of
classification
concepts - vehicles, clothing, food, animals,
etc.
- to four-year-olds. For this demonstration, the
order
of introduction for the classes differed from one
group
of children to another. (One group started with
food,
another with clothing, etc. and learned the classes
in
different orders).
Children
learned one class to mastery, then learned the
next
in their sequence. Children were considered to be
at
mastery if they could name members of a class and
correctly
respond to inference games that asked about
the
larger class and the smaller class. For instance,
after
children had learned about clothing, the teacher
would
say, for instance, “I’m thinking of something that
is
clothing. Is it a shoe?” The answer is “Maybe”, or
“We
don’t know”.
The
teacher would also present tasks that referred to
things
in the class of clothing. “I’m thinking of
something
that is a shirt. Is it clothing?” The answer is
“Yes”.
Also, “I’ll name some things. Tell me if they
are
clothing or not clothing. Truck ... glass ... hat ....
etc.”
The
number of trials required for the children to learn
different
classes followed a predictable trend regardless
of
which class they learned first and which they learned
fourth
or fifth. The class that required the largest
number
of trials was the first class or second class in
their
sequence. The fourth or fifth class in the sequence
required
less than half the number of trials required for
the
children to learn the first class.
One
of the reasons for this accelerated learning is that
the
children did not have to learn as much to master the
fifth
class as they had to learn to master the first. In
learning
the first class, they had to learn the names of
higher-order
class (vehicles, for instance) and some
members
of this class (boat, train, bus , etc.). Children
also
had to learn the relationship between the higher
order
class and the members of the class. They had to
learn
basically that all trucks are vehicles, but that all
vehicles
are not necessarily trucks. This relationship is
tricky
and requires practice.
All
the classes have this same structure. Children who
learn
the structure for the first class do not have to
relearn
it for each of the other classes. They still have
to
learn the name for the new higher order class and the
names
for the various members. But the children do not
have
to relearn the structure or relationship of higherorder
class
to members. Therefore, the children do not
have
to learn as much to master later examples.
Consequently,
children are able to master these classes
faster,
in fewer trials and with less learning. Note,
however,
that these children could not benefit from the
savings
in how much learning is required unless the
children
thoroughly learned the structure of at least one
class.
If the children “sort of” learned the earlier
classes,
there wold not be a dramatic change in the
number
of trials or amount of practice the children
needed
to “sort of” learn later classes. These children
could
not “transfer” the structure from one class to
another
because the children did not thoroughly
understand
the structure.
Because
they had more experience learning to mastery,
they
developed more effective strategies for
categorizing
new information or operations in a way that
permits
them to recall land use this information. In other
words,
they are better at learning how to learn,
simply
because they have had more successful
practice
in thoroughly learning new information and
skills. This practice permits
them to learn new material
faster
than students who don’t experience mastery.
The
same benefits that occur in this example apply to all
bodies
of related knowledge. If students learn one
particular
subject, such as match, to mastery, but don’t
learn
spelling, reading, handwriting, language, and other
skills
to mastery, the students gain an advantage in math.
Students
develop the facility needed to learn new math
concepts
and applications faster. However, the benefits
of
the mastery instruction would not be greatly evident
in
other content areas. Not a great deal of “transfer”
would
be expected to affect the students’ reading
performance
or writing performance.
Students
who are immersed in mastery, in all subjects
for
at least three years, will become much smarter than
comparable
students taught in a traditional manner.
Mastery-taught
students will not only know more - these
students
will be far more proficient and faster at learning
new
academic material of any kind. Because these
students
have been immersed in mastery, the students
have
thoroughly learned everything taught and have
developed
generalised mastery-learning skills that permit
them
to achieve mas tery quickly
with any academic
content.
In other words, if students experience mastery
instruction
in all subjects for a substantial period of time,
they
are changed. They become smarter. They learn
faster.
They retain new information better.
Students
who are taught mastery in all subjects for only
a
short period of time (a school year or less) will benefit,
but
not as much as those who receive mastery
instruction
for a much longer period. They tend to learn
more
skills during a given time period than students of
the
same initial performance level who are not taught to
mastery.
But these mastery-taught students will not
receive
the extent of learning to mastery needed to
greatly
change their rate of learning new material. If a
student
who starts at 7 years old has had no previous
experience
in being taught to mas tery,
the student’s
new-learning
performance will probably not be greatly
different
than it was before this instruction.
What
this means is that mastery teaching provided for
several
years has the power to take students who enter
school
performing at a relatively low level and transform
them
into students who are much smarter, as measured
by
any method we might choose to assess intelligence
and
skill. Through mastery teaching for several years,
the
school has the power to change lower-performing
students
into higher-performing students. In many Title
I,
full-school DI implementations, the lowest performing
fourth
graders complete Level 4 in reading, math, and
language
programs. Furthermore, the higher performers
in
fourth grade frequently complete Level 6 of these
programs.
Mastery learning is the only vehicle that is
capable
of achieving this transformation.
Results
of Not Teaching to Mastery
Just
as reading to mastery has a positive effect on
students’
self-image because it provides students with
evidence
that they are learning, failing to teach to
mastery
promotes a negative self-image. The student
who
is consistently incapable of performing correctly on
the
material presented is quite aware of this failure rate.
In
time, the student comes to the unfortunate conclusion,
“I
am a failure”.
This
attitude is dangerous because students who know
they
fail are quick to give up after experiencing
evidence
of failure. Failure is punishing; they
understandably
do not want to engage in punishing
activities.
Therefore, they often avoid the kind of
practice
that would actually help them become
successful.
Reteaching students who have learned inappropriate
strategies
and negative attitudes requires great amounts
of
time. When students are not taught to mastery, they
often
mislearn the skills and concepts the teacher
attempts
to teach. For instance, they may learn to guess
at
words in sentences. Reteaching them requires many
more
trials and much more work than that required to
teach
them to mastery initially. Initial teaching may
require
only 10 or fewer trials on some skills.
Reteaching the same skill after students have mislearned
it
and have practised inappropriate strategies for years
may
require several hundred trials. Even with careful
remedial
instruction, however, the student leaves the
school
with unnecessary scars of failure. The student
has
experienced unnecessary pain and has drawn
unfortunate
negative conclusions about self and school.
These
conclusions could have been avoided by teaching
to
mastery.
Summary
Teaching
to mastery represents the most effective use
of
available instructional time. It accelerates students’
performance,
provides students with demonstrations of
success
rather than failure, and reduces the total amount
of
work that must be done to transmit a given body of
skill
and knowledge to students. If students are
immersed
in mastery, they become smarter because
they
acquire information faster, and they develop
efficient
strategies for learning and retaining new
material
of any type.
For
mastery to occur, the program design must be like
a
stairway, distributing new learning in small amounts
and
providing for mastery of each step before moving on
to
a new step. After being introduced, new learning is
firmed
for several days, then systematically reviewed
across
time. Students learn that once something is
learned,
it must be remembered and used again and
again.
In
addition, the teacher and the system must have
provisions
that permit continuity, appropriate placement
of
students according to their performance, close
coordination
of schedules within the school, ample
models
of what students are to do, and provisions for
celebrating
academic achievements of students.
Teachers
must be able to make predictions about
student
performance.
Teaching
to mastery is difficult for schools to
orchestrate
because of the various details that must be
coordinated
and difficult for teachers to learn because
the
implications of teaching to mastery often contradict
conventional
wisdom about hot to teach, place, and
challenge
students.
Mastery
is difficult for teachers for three reasons:
1.
It is contrary to their practices and expectations about
how
students will perform.
2.
It therefore forces the teacher to view students and
instruction
in a way that hinders success.
3.
Schools do not have good models of doing it the right
way.
At
the core of teaching to mastery is information about
student
performance, which is expressed as the
percentage
of first-time-correct responses for material
that
is introduced the first time and for material that is
assumed
to be at mastery.
Students
taught with a mastery approach will change in
three
ways:
1.
They will be able to learn new material that has the
same
structure in fewer trials.
2.
They will know more information and more
operations.
3.
They will have more skill in applying what they have
learned.
Students
taught to mastery have learned how to learn.
They
have developed generalised mastery-learning skills
they
can apply to all subjects. When done properly,
mastery
is able to change the lives of children and
provide
them with a far brighter future than they would
have
in the absence of mastery.