Abacus Instruction by
Teachers of Students
with Visual Impairments
Sunggye Hong, Ph.D.
San Francisco State University
L. Penny Rosenblum, Ph.D.
University of Arizona
July 21, 2012
2012 AER International Conference
Our Colleague Sheila Amato
Couldn’t Join Us Today…
We Had Some Questions...
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Are university programs adequately preparing
future TVIs in abacus computation and
instruction? What methods are they teaching?
Is an abacus still regarded as an important tool for
the math toolbox for students with VI?
What resources do TVIs use to support abacus
instruction?
When do TVIs begin abacus instruction and what
factors influence this decision?
What are the personal beliefs of TVIs with regard
to the abacus and its use by youth with VI?
After all, the Abacus HAS Been
Around for Many Years
Important Points
from the Literature
Steinbrenner and Becker (1982) reported
that universities were ineffective in their
preparation of TVIs to teach abacus to
students who are blind.
 Rapp and Rapp (1992) suggested that
university personnel preparation programs
should teach abacus to future TVIs and
assist in the updating of skills of practicing
TVIs.
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Important Points from
the Literature
Smith and Kelly (2007) reported that
teacher preparation programs teach the
abacus at different technology-awareness
levels; 27% teach at the "awareness" level,
33% teach at the "proficient" level, and
40% teach at the "advanced level.
 Kapperman, Heinze, and Sticken (1997)
noted that the abacus is useful because of
its speed, accuracy, portability, and
flexibility.
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Instrument Development
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Generated questions from our own work both
as individuals who prepare TVIs and as TVIs.
Used DatStat Illume® to put the questionnaire
on-line.
Field tested with 7 individuals for accessibility,
item appropriateness, clarity of questions and
instructions, and overall coherence of the survey
tool.
Demographic Data
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196 participants
Of 191 participants
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Of 194 participants
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9 Canadian / remainder from 39 states in the US
14 male / 180 female
14 participants reported that they had a VI
38 used an abacus for their daily tasks
122 participants responded that they, in the
past or currently, teach abacus skills
64 reported that they have not taught abacus skills
How Did Participants Learn to
Compute Using an Abacus?
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University preparation program (n=112)
Self-study (n=92)
Instruction by a colleague (n=26)
Distance education school (i.e., Hadley School for
the Blind) (n=18)
Other ways participants listed included:
From a student with VI
 As a child from own TVI
 As an adult through a VI rehab program through online videos
 From an individual of Asian descent
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Methods of Computation
Counting Method: This method has
the student count each bead as it is
added or subtracted, moving from the
unit beads to the 5 beads (but counting
only 1 for all beads). There are also
specific rules regarding certain numbers
and operations, but fewer than the full
set of secrets. (S. Millaway)
Methods of Computation
Logic or Partner Method: This method
focuses on understanding the “what” and
“why” of the steps in solving a problem on
the abacus. It requires that the student know
the partners or complements of the numbers
up to ten (5=2+3, 5=1+4). This method
uses synthesis when beads cannot be set
directly. Verbalizing the steps and the
reasons for each movement made on the
abacus is an important feature of this
approach. (R. Livingston)
Methods of Computation
Secret Method: This method focuses on the
process of moving the abacus beads in a particular
sequence, following a specific set of rules for
different numbers and operations. It does not
emphasize the understanding of that process,
rather the rote memory of the bead movements.
(M. Davidow)
Methods of Computation
Paper Compatible Method: The paper
compatible method has the user
complete problems in the same way an
individual completes them using paper
and pencil. The standard math facts are
used, not the secrets or a series of
questions. (D. Willoughby)
Methods of Computation
Hadley School for the Blind: This method uses
the indirect method to teach the abacus. The
indirect method combines both the logic or
partner method and the secrets method.
Complements are explained and students are
expected to use that understanding to follow a
specific set of rules for adding and subtracting.
Paper
Method
Counting
Logic/Partner
Secrets
Hadley
Compatible
Taught method to
45
38
26
9
8
3.60
3.74
3.46
3.11
4.38
3.68
3.84
3.48
3.32
4.50
proficiency
Prepared to Use an
Abacus for
Calculation
Prepared to Teach
Abacus Skills
Paper
Method
Counting
Logic/Partner
Secrets
Hadley
Compatible
Exposed to Method
21
22
24
15
9
3.05
3.32
3.33
2.87
3.44
2.98
3.43
3.25
2.93
3.63
Prepared to Use an
Abacus for
Calculation
Prepared to Teach
Abacus Skills
Skills Taught in Personnel
Preparation Programs
A
list of abacus skills were provided to
the 112 participants who reported they
learned to use an abacus as part of
their university preparation program.
 For each skill they indicated if they:
 Learned
the skill to proficiency
 Exposed to the skill
 No instruction or exposure to the skill
 Did not recall
Highest Ranked Skills Taught to
Proficiency in
University Programs
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One digit addition without synthesis/secrets
One digit subtraction without synthesis/secrets
Two or more digits addition without
synthesis/secrets
One-to-one correspondence
One digit addition with synthesis/secrets
Two or more digit subtraction without
synthesis/secrets
Lowest Ranked Skills Taught to
Proficiency in
University Programs
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Decimals/money
Record keeping (e.g., telephone number, score
keeping)
Fractions
How to couple 2 abaci together to perform more
lengthy computation tasks
Square roots
Are Universities Doing
Their Job Well?
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“More competent trainers are needed to teach
VI teachers how to teach more than just basic
skills on the abacus.”
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“I hope prep[aration] improves for abacus
training for TVIs and that AER or other
continuing ed. for TVIs offer classes/sessions
on improving skills in abacus.”
Can Students Use an Abacus on
High Stakes Tests?
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121 (72%) reported “yes”
2 (1.2%) reported “no”
45 (26.8%) were unsure
During 2011-2012 Did You
Have a Student Using an
Abacus in Math Class?
50 (33.8%) did not
 49 (33.1%) had 1 student
 26 (17.6%) had 2 students
 23 (15.5%) had between 3
and 10 students
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A Participant Shares…
“I've taught visually impaired students for many
years and have seen the desire to include abacus
instruction both increase and decrease throughout
those years. Abacus instruction is vital for a
visually impaired student.”
During 2011-2012 Did You Have a
Student with Abacus IEP Goals?
69 (46.9%) reported none
 42 (28.6%) had 1 student
 18 (12.2%) had 2 students
 18 (12.3%) had 3 to 6
students
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What Method Do You
Teach Your Students?
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71 (48.0%) taught the counting method
57 (38.5%) taught a combination of methods
51 (34.5%) taught the logic/partner method
28 (18.9%) taught the paper compatible method
21 (14.2%) taught the secrets method
17 (11.5%) taught the Hadley School for the Blind
method
12 (8.1%) didn’t recall the name of the method they
used
7 (4.7%) taught a method they developed
themselves
Most Frequent Skills
TVIs Teach to Students
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One digit addition without synthesis/secrets
Two or more digits addition without
synthesis/secrets
One digit subtraction without synthesis/secrets
Two or more digit subtraction without
synthesis/secrets
One digit as the multiplier multiplication
One-to-one correspondence
At What Age Do You Begin
Abacus Instruction?
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24 (17.5%) preschool
55 (40.1%) kindergarten
36 (26.3%) 1st grade
9 (6.6%) 2nd grade
6 (4.4%) 3rd grade
3 (2.2%) 4th grade
2 (1.5%) middle school
2 (1.5%) high school
A Participant Shared…
“I just start early in kindergarten with all of my
students who have severe enough visual limitations
so that they can participate in circle time when
there is any counting going on so that they are
exposed to the abacus, hold it correctly, work on
fine motor skills, etc.”
What Factors Do You Consider
When Determining When to
Begin Abacus Instruction?
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105 (70.9%) academic abilities
71 (48.0%) if the student is blind
67 (45.3%) fine motor abilities
49 (33.1%) grade in school
24 (16.2%) chronological age
24 (16.2%) if the student has low vision
Participants Shared…
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“Mostly I think, ‘What does this kid need to
know?’ or ‘What is preventing this kid from
moving on with his classmates in math skills?’
and if the answer is something that the abacus
can make concrete for him/her, I go with it.”
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“I teach abacus to any child who cannot easily
access scrap paper.”
Why Don’t You Teach Abacus
Skills to Your Students?
TVI RELATED RESPONSES FELL INTO THESE
CATEGORIES:
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The TVI didn’t believe he/she was an effective
instructor in his/her abacus skills.
The TVI lacked confidence to teach abacus skills.
The TVI didn’t know where to get updated
training.
The TVI didn’t have time to teach abacus skills.
The TVI didn’t have a paraprofessional to follow
up on abacus skills with students.
The TVI didn’t like the abacus himself/herself.
A Participant Shares…
“The abacus fills a role
no other tool serves for
students who are braille
readers. All TVIs
should be proficient in
using the abacus, so that
they can pull it out of
THEIR toolbox, when
it is appropriate.”
Why Don’t You Teach Abacus
Skills to Your Students?
STUDENT RELATED RESPONSES FELL
INTO THESE CATEGORIES
 Students use mental math.
 The abacus is not an appropriate tool for the
student.
 Chronologically the students are not ready for
the abacus (e.g., infants, preschoolers).
 Students have difficulty learning abacus skills.
 Students utilize technology for computation.
What Resources Do You Use?
Abacus Basic Competency: A Counting Method
(Millaway, 2001)
 Use of the Cranmer Abacus (Livingston, 1997)
 Abacus Made Easy (Davidow 1988)
 Materials from Hadley School for the
Blind’s abacus course
 The video: Hands-on Experience with the
Cranmer Abacus (Pester, n.d.)
 YouTube
 Materials from university preparation
courses
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Your Attitude as a TVI Impacts
What You Teach and the
Message You Give Your Students
“A teacher's competence and attitude have
a great impact on a student's potential for
success with the Cranmer Abacus.
Therefore, a teacher must be skilled in the
use of the Cranmer Abacus, convey a
positive attitude toward it, and
demonstrate its relevance to the student.”
Kapperman, Heinze & Sticken, 2000, p. 385
TVIs Beliefs About the Abacus
146 participants completed this section
 15 statements were provided
 Participants rated each statement from
strongly disagree to strongly agree using a
5-point Likert scale.
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Five Statements with the
Highest Ratings
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Whenever a test taker is allowed to use a paper
and pencil for working calculations, an abacus
should be considered an equivalent substitution
for a student who is visually impaired.
(M = 4.46)
An abacus provides a student who is visually
impaired an easily accessible, portable,
inexpensive tool. (M = 4.35)
Five Statements with the
Highest Ratings
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The abacus is analogous to pencil and scratch
paper for sighted individuals. (M = 4.23)
An abacus is a vital component of the
“blindness specific” tools for a student’s
academic toolbox. (M = 4.09)
The abacus is a valuable tool for students who
are visually impaired. (M = 4.07)
Abacus “Believers” Share…
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“I believe the abacus is not obsolete and a
critical [tool] for students with vision
impairments to know in order to make informed
decisions about appropriate math tools.”
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“I think the abacus is an extremely valuable tool
and should not be discounted. Our students
need many ways of completing math tasks (just
as sighted students have many ways of
completing math tasks.”
Five Statements with the
Lowest Ratings
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There are more efficient tools (e.g., talking
calculator, portable notetakers) than an abacus.
(M = 2.76)
The time spent teaching abacus is better spent
teaching a student other skills specific to his/her
visual impairment (e.g., braille, assistive
technology). (M = 2.08)
Five Statements with the
Lowest Ratings
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Because of my own perceived lack of expertise
with abacus skills, I am not comfortable
teaching students who are visually impaired to
use the abacus. (M = 1.93)
The abacus is obsolete. (M = 1.74)
Students who are visually impaired can do math
computation in their heads or through rote
memorization and do not need to learn the
abacus. (M = 1.71)
Why Participants Don’t
Teach Abacus Skills
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“I do not have the knowledge or skills to be an
effective abacus instructor for my students.”
(n=10, 31.3%)
“My students use mental math or rote
memorization to complete mathematical
computation.” (n=10, 31.3%)
“I am no longer confident in my abacus skills
because I have not taught abacus in a long
time/ever.” (n=8, 25.0%)
Why Participants Don’t
Teach Abacus Skills
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“I work with students who do not have the ability
to complete simple addition/subtraction using
objects so the abacus is not an appropriate tool.”
(n=8, 25.0%)
“I don’t know where to go to get updated training
in abacus skills.” (n=7, 21.9%)
“I work with students who are infants, toddlers
and/or preschoolers who are not yet
developmentally ready to use the abacus.”
(n=5, 15.6%)
“I do not have time to work 1:1 with a student to
teach him/her the abacus.” (n=2, 6.3%)
Why Participants Don’t
Teach Abacus Skills
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“I do not have a paraprofessional or other staff
member who can follow through on abacus
instruction when I am not with the student.”
(n=2, 6.3%)
Other reasons stated:
 Students have low vision.
 Students use technology such as calculators.
 Students are not developmentally ready for
abacus skills instruction.
Participants Share…
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“Although I would be the one to teach abacus
skills, the curriculum needs of the student and
accessibility of electronic technology, makes it
an ineffective tool in the 21st century.”
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“It's a hard sell to get the student to buy into the
value of knowing how to use an abacus because
they're so used to relying on a calculator. It's also
difficult to explain to educators why the abacus
is important.”
In Summary…
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The Counting and Logic/Partner methods are
most frequently taught in university programs.
Those prepared at the university level report
proficiency with addition and subtraction at a
higher rate than with other operations/skills.
The abacus is still viewed as an efficient tool that
provides students with visual impairment access
to mathematics computation.
We Couldn’t Agree More…
“I believe in Alan Koenig's
‘toolbox’. The Cranmer
Abacus is a tool that
should be in the toolbox
of any academic student
for whom pencil and paper
isn't convenient. If THEY
choose not to use it, that is
their choice.”
In Many Ways We Have More
Questions Than Answers…
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Are universities providing adequate preparation
in a variety of computation methods?
Do TVIs value the abacus and make instruction
in abacus computation a priority?
What is the role of the abacus in the age of
technology?
Is there a need to develop up-to-date interactive
resources?
An Abacus is a Tool in the
Toolbox…It Can’t Do It All!
Where We’re Headed…
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Look for two upcoming articles in JVIB
Development of an abacus app by Dr.
Rosenblum
Consideration of a study with youth to evaluate
their skills and beliefs related to the abacus
YOUR IDEAS????