Bloom's 2 Sigma by Marietta Jones

1. Marietta Jones

2.  The following three conditions of learning were compared
in a study conducted by two University of Chicago doctoral
students:
 Conventional: Students learn the subject matter in a class with
about 30 students per teacher. Tests are given periodically for
marking the students.
 Mastery Learning: Students learn the subject matter in a class with
about 30 students per teacher. Formative tests (the same tests used
with the conventional group) are given for feedback followed by
corrective procedures and parallel formative tests to determine the
extent to which the students have mastered the subject matter.
 Tutoring: Students learn the subject matter with a good tutor for
each student (or for two or three students simultaneously). This
tutoring instruction is followed periodically by formative tests,
feedback-corrective procedures, and parallel formative tests .

3.  Using the standard deviation (sigma) of the control
(conventional) class, it was typically found that the
average student under tutoring was about two
standard deviations above the average of the control
class (the average tutored student was above 98% of
the students in the control class). The average student
under mastery learning was about one standard
deviation above the average of the control class (the
average mastery learning student was above 84% of
the students in the control class).

4.  90% of the tutored students and 70% of the mastery
learning students attained the level of summative
achievement reached by only the highest 20% of the
students under conventional instructional conditions.
 There were corresponding changes in students' time
on task in the classroom (65% under conventional
instruction, 75% under Mastery Learning, and 90+ %
under tutoring) and students' attitudes and interests
(least positive under conventional instruction and
most positive under tutoring).

5.  The most striking of the findings is that under the best
learning conditions they could devise (tutoring), the
average student is 2 sigma above the average control
student taught under conventional group methods of
instruction.
 The tutoring process demonstrates that most of the
students do have the potential to reach this high level
of learning.
 One – to – One Tutoring can be too costly for most
societies to bear.

6.  Can researchers and teachers devise teaching-learning
conditions that will enable the majority of students
under group instruction to attain levels of
achievement that can, at present, be reached only
under good tutoring conditions?

7.  Large numbers of teachers at every level of instruction
and in many countries can use the feedback-corrective
procedures to get the 1 sigma effect (the average ML
student is above 84% of the students under
conventional instruction-even with the same teacher
teaching both the ML and the conventional classes)
 Researchers have systematically tried other variables
which, in combination with ML, might approach the 2
sigma effect size. So far, they have not found any two
variable combination that has exceeded the 2 sigma
effect.

8.  Improving student processing of conventional instruction:
If students develop good study habits, devote more time to
the learning, improve their reading skills, and so on, they
will be better able to learn from a particular teacher and
course-even though neither the course nor the teacher has
undergone a change process.
 The major changes under the ML process are that more of
the students have the cognitive prerequisites for each new
learning task, they become more positive about their
ability to learn the subject, and they put in more active
learning time than do the control students.

9.  Help students develop a student support system in
which groups of two or three students study together,
help each other when they encounter difficulties in the
course, help each other review in advance of taking
tests, and review their learning periodically.
 There is evidence that students who take special
programs to improve their reading and/or their study
and learning methods tend to learn more effectively.
Ideally, such special programs should be available at
the beginning of each new school level.

10.  Improve Instructional Materials and Educational
Technology : the organizational aids can be built into new
textbooks and can be used by the students with a
minimum of emphasis by the teachers.
 Home Environment and the Peer Group: the most effective
method was the series of meetings between groups of
parents and the parent educator. The changes in the home
environment of this group were highly significant. If
parents continue to encourage and support each of their
children to learn well in school throughout the elementary
school years, this should greatly help the children during
the years they will attend schools and colleges.

11.  Improvement of Teaching: 20% of the students under
conventional instruction do about as well as the tutored
students, and about 80% of the students do relatively
poorly under conventional instruction. This is believed to
be in part from the unequal treatment of students within
most classrooms. Nordin found that the average student in
the enhanced cue and participation group was 1.5 sigma
higher than the average student in the control
(conventional instruction) classes. The tactic of providing
a "mirror" to the teacher of the ways in which he or she is
providing cues and explanations, appropriate
reinforcement, and securing overt as well as covert
participation of the students in the learning, seems to us to
be an excellent approach.

12.  Improvement of Teaching of the Higher Mental Processes:
In different countries (e.g., Israel, Malaysia, South Korea)
there is great emphasis on problem-solving, application of
principles, analytical skills, and creativity. Such higher
mental processes are emphasized because these centers
believe that they enable the student to relate his or her
learning to the many problems he or she encounters in day-
to-day living. In contrast, teachers in the United States
typically make use of textbooks that rarely pose real
problems. Attempts to improve higher mental processes
included group instruction emphasizing higher mental
processes and feedback-corrective processes, which also
emphasized higher mental processes.

13.  “Even being at U of M, when a student transition from a high school of
30 students in a class to a seminar of 150 students. It takes less and less
concentration on each student. One on one tutoring would be more
effective, because that teacher is focus on making sure that one student
is on right track.”
 “There was one teaching method that was a solution to the 2 sigma
problem that stood out a lot to me. It was the combination of ML and
initial enhancement of cognitive prerequisites. I believe this
combination would have really helped me in school, specifically for
math and foreign language classes.”
 “Peer groups are said to help student’s learning . If students see their
friends doing well then the more likely they will follow.”
 “Personally, I'm one of those students who study better by themselves.
So, it could be a consideration that many students learn differently as
individuals.”
 “smaller classes where the teacher is able to know each student name
and know their faces will allow for the students and teacher to make a
personal connection and will aid in the students to learn effectively. ”

14.  “While there may not be enough resources to provide each student
with a tutor, placing them in smaller groups with their peers will force
them to interact with one another and work together to understand the
materials. ”
 “The importance of the one on one, or the personal aspect of learning,
has without a doubt been proven here, especially when compared to
results of conventional learning.”
 “Oddly the student's peer group has the strongest influence (negatively
and positively) on the student's learning. I found this interesting
because it explains why the student learns better in one to one
tutoring.”
 “I find it very interesting that so many other places around the world
teach in a way that has ‘great emphasis on problem-solving, application
of principles, analytical skills, and creativity.’”
 “I had tutoring once and it helped out a lot but I think if I would found
two other people to tutor with me I would’ve understood the subject
better. I would have had the privilege of having two other people
opinions and how they understood it.”


15.  “One on one tutoring or small group tutoring tends to be much more
intensive - which is good, but can also require more time in order to
properly comprehend what is being taught, whereas conventional and
master learning(to a lesser extent) streamline the learning process so a
given quantity of material is covered in a given time period.”
 “I do not feel like there is any one method of group instruction that is
as effective as one-to-one tutoring but rather a combination of
instruction between the classroom, students, and home (parents). ”
 “I think often when students struggle it is viewed as they are
uncommitted or not capable of doing the work. The Sigma Problem
proposes the exact opposite in that it may be the approaches of the
teacher or an absence of positive learning environment that is the
actual culprit of a student's learning challenges.”
 “One on one learning gives a student undivided attention and more
opportunities to learn the lesson. The other methods give the student
have to learn the lesson within a given time whether they understand
or not.”
 “The (areas) that I think need the most improvement is involvement of
all students in the classroom, the way the information is being taught,
and a healthy home life.”

16.  “Tutoring allows us to read and tune studies to the students needs at the time,
which is very difficult to do with 30 students at a time. Is it possible to tune
studies per student in a class of 30 in a realistic fashion? If it were possible,
would it be better to have shorter classes with fewer students?”
 “I think that they are referring to the standard deviations but I do not
understand what it means by 2 sigma an why that determines the
effectiveness?”
 “A home environment that is routine with homework being a big part,
academic support and help from parents, stimulation like providing
opportunities to learn by exploring maybe a trip to the local museum, using
correct language in the home will help students to use it at school, and
academic expectations and standards that are set by parents and praised for
doing well are said to help.”
 “If more measures could be taken to prevent the slipping of students behavior
and grades, there may be less of a problem with failure and group instruction
will become as effective as one-to-one tutoring.”