The Abacus: Instruction by Teachers of Students with Visual Impairments

12 Pages·2013·0.79 MB·English

CEU Article
The Abacus: Instruction by
Teachers of Students with
Visual Impairments
Sheila Amato, Sunggye Hong, and L. Penny Rosenblum
Structured abstract: Introduction: This article, based on a study of 196 teachers
of students with visual impairments, reports on the experiences with and opin­
ions related to their decisions about instructing their students who are blind or
have low vision in the abacus. Methods: The participants completed an online
survey on how they decide which students should be taught abacus computation
skills and which skills they teach. Data were also gathered on those who reported
that they did not teach computation with the abacus. Results: The participants
resided in the United States and Canada and had various numbers of years of
teaching experience. More than two-thirds of those who reported that they taught
abacus computation skills indicated that they began instruction when their
students were between preschool and the second grade. When students were
provided with instruction in abacus computation, the most frequently taught
skills were the operations of addition and subtraction. More than two-thirds of
the participants reported that students were allowed to use an abacus on high-
stakes tests in their state or province. Discussion: Teachers of students with
visual impairments are teaching students to compute using the Cranmer abacus.
A small number of participants reported they did not teach computation with an
abacus to their students because of their own lack of knowledge. Implications for
practitioners: The abacus has a role in the toolbox of today’s students with visual
impairments. Among other implications for educational practice, further studies
are needed to examine more closely how teachers of students with visual
impairments are instructing their students in computation with an abacus. Topics
to examine include the frequency of instruction, the age at which instruction
begins, how instruction is provided to children with multiple disabilities, whether
instruction is provided in the general education classroom or via pullouts, the
role of math teachers and paraeducators in instruction, and how the abacus could
be used collaboratively with technology.
T
he expanded core curriculum (ECC), model of inclusive and high-quality edu­
initially conceptualized by Hatlen (1996), cation. Professionals in the field agree
is well accepted in the field of education that knowledge of math, identified as part
of children who are visually impaired as a of the compensatory access–academic
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skills area of the ECC, is essential for and Sticken (1997) noted that the abacus
children who are visually impaired. It is is useful because of its speed, accuracy,
well established that children who are vi­ portability, and flexibility. According to
sually impaired should learn math skills Kapperman, Heinze, and Sticken (2000),
at the same level as their sighted peers abacus users benefit from the ability to
(Tindell, 2006). Yet, the curricular area of manipulate the beads concretely, which
math for these students has received little ultimately leads to a greater understand­
research attention (DeMario, Lang, & Lian, ing of numbers than would be gained
1998; Lohmeier, 2008). A case in point is from use of a calculator. Whether a stu­
the fact that only two studies in the past dent receives or does not receive instruc­
decade, one by Wolffe and colleagues
tion in computation using an abacus is
(2002) and the other by Rule, Stefanich,
often dependent on the attitude of the
Boody, and Peiffer (2011), examined the
teacher of students with visual impair­
role of teachers of students with visual im­
ments. “A teacher’s competence and atti­
pairments in delivering services to their stu­
tude have a great impact on a student’s
dents. In neither study did the authors men­
potential for success with the Cranmer
tion the abacus as a tool used by students
Abacus. Therefore, a teacher must be
with visual impairments.
skilled in the use of the Cranmer Abacus,
Despite the dearth of studies in this
convey a positive attitude toward it, and
area, some professionals in the field be­
demonstrate its relevance to the student”
lieve in the value of the abacus for use by
(Kapperman et al., 2000, p. 385). Chil­
those with visual impairments. For exam­
dren must also be given opportunities to
ple, Millaway (2001, p. 1) stated: “The
use an abacus within the general educa­
Cranmer Abacus is generally regarded by
tion classroom (Culpepper, 2001) and be
special educators as the best all-around
taught in an educational environment in
computing device available to blind stu­
which the abacus is viewed positively
dents. Therefore, teachers of the visually
(Kapperman et al., 1997; Lohmeier,
impaired must be prepared to provide in­
2008).
struction to their students on the use of the
As part of a larger study, approved by
Cranmer Abacus.” Braille Mathematics
the Institutional Review Board at the Uni­
Standards (California Department of Ed­
versity of Arizona, data for this study
ucation, 2006) specifies graded-level math
were gathered about the experiences of
competencies that recognize the impor­
teachers of students with visual impair­
tance of the abacus for children with vi­
ments in teaching computation with an
sual impairments. Kapperman, Heinze,
abacus to their students. Topics for which
data were gathered included the age at
which instruction began, criteria for de­
termining if abacus instruction was ap­
EARN CEUS ONLINE
propriate for a student, and the abacus
by answering questions on this article.
For more information, skills taught to the students. Data were
visit: �http://jvib.org/CEUs�. also gathered from teachers who reported
that they do not teach computation with
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CEU Article
an abacus to students with visual impair­ participants completed all the questions,
ments in an attempt to learn how and why so the number of participants who re­
these teachers decided not to provide this sponded to a specific question is reported
instruction. when the total number of respondents for
the question is not 196. Demographic data
Methods on the participants are reported in Rosen­
INSTRUMENT blum and colleagues (2013).
The survey gathered demographic data on
the participants through eight questions ABACUS INSTRUCTION FOR STUDENTS
(such as age, gender, and number of years WITH VISUAL IMPAIRMENTS
employed as a teacher of students with There were 122 participants who cur­
visual impairments). The participants rently or in the past taught abacus com­
were then asked to respond to an online putation to students with visual impair­
survey that was developed to gather data ments. The number of students in their
on how the participants were prepared to caseloads who were using an abacus in
use an abacus for computation; their atti­ their math classes during the 2011–12
tudes toward the effectiveness of the aba­ school year ranged from 0 to 10 as re­
cus as a computational tool for students ported by 148 participants. Fifty (33.8%)
who are visually impaired; whether they did not have a student who used an abacus
teach computation with an abacus to in a math class, 49 (33.1%) had 1 student,
their students; and, if so, which skills 26 (17.6%) had 2 students, and the other 23
they teach. Information on the first two (15.5%) had 3 to 10 students. A teacher of
areas of the survey is reported in Rosen­ students with visual impairments in an ele­
blum, Hong, and Amato (2013), which mentary school commented, “It is incredi­
contains a detailed description of the bly empowering, especially for younger
survey instrument. students who are just moving past sim­
ple addition. I think the abacus helps
RECRUITMENT them think of the math in a different
The study was advertised on national elec­ way: less memory and rote, more pro­
tronic bulletin boards in the field of visual cessing the numbers.”
impairment. We also contacted individuals
we knew who had completed their univer­ USE OF AN ABACUS ON HIGH-STAKES
sity preparation at one of the universities at TESTS
which we currently or previously taught A series of questions was posed to the
who might not be participants in national or participants about instructing their stu­
local professional online networks. dents in the use of an abacus. Of the 168
participants who responded, 121 (72%)
Results reported that students were allowed to
A total of 196 individuals completed the use an abacus on high-stakes tests in
survey. This section reports the data gath­ their state or province, 2 (1.2%) re­
ered from the participants about their ex­ ported that an abacus was not permitted,
periences teaching the abacus to students and 45 (26.8%) were unsure. Sixty-
who are visually impaired. Not all the three participants provided comments
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CEU Article
about high-stakes testing, including METHODS OF INSTRUCTION AND SKILLS
many who offered the analogy that the TAUGHT TO STUDENTS
abacus is like a pencil and paper for The participants were asked which methods
sighted students. “Its use should be per­ of instruction they used to teach their stu­
mitted any time a sighted student is dents to compute using an abacus. Multiple
allowed ‘scratch paper’ (or the test mar­ responses were allowed. A description of
gins) for working out problems.” “It is a the methods for computation is presented in
tool, equivalent to paper [or] pencil for Box 1. Of the 148 participants who re­
students who are [blind or visually im­ sponded, 71 (48.0%) used the counting
paired]. Students must know how to method, 57 (38.5%) used a combination of
add, subtract, multiply, and divide to methods, 51 (34.5%) used the logic-partner
use the abacus, so it is not equivalent method, 28 (18.9%) used the paper-
to a calculator.” Some teachers com­ compatible method, 21 (14.2%) used the
mented on their students’ preference for secrets method, 17 (11.5%) used the Hadley
using technology, especially in the School for the Blind method, 12 (8.1%) did
higher grades: “By the time my students not recall the name of the method they used,
are in high school, they would usually and 7 (4.7%) used a method they devel­
rather use the talking calculator than the oped. Several of the written comments sup­
abacus, so although it is listed as an ported the perceptions that some preservice
accommodation, I can’t remember any training programs did not provide the par­
students using their abacus past about ticipants with adequate exposure to a vari­
[the] 5th grade.” ety of computational methods on the aba­
cus. One participant noted, “I teach the way
ABACUS GOALS ON INDIVIDUALIZED I was taught, and I have had to switch a
EDUCATION PROGRAMS student because [he or she was] taught an­
When asked if their students had goals other method but could not compute accu­
related to the abacus on their Individu­ rately.” Yet an encouraging theme of the
alized Education Programs (IEPs) for comments revolved around the teaching
the 2011–12 school year, 147 partici­ strategy of using the abacus as a tool to
pants responded. Of the 147, 69 teach place value: “I love using the abacus
(46.9%) reported that their students did right away to help with understanding place
not have IEP goals for an abacus, 42 value. [It] makes it so easy to braille [or]
(28.6%) had 1 student with such goals, write the answers with the commas in the
18 (12.2%) had 2 students with such correct place by copying from the abacus.”
goals, and 18 (12.3%) had 3 to 6 stu­ The participants were asked at what
dents with such goals. One participant age they typically begin introducing the
observed, “Students who were allowed abacus to their students. Of the 137 who
to have abacus skills on their IEP often responded, 24 (17.5%) did so during pre­
enjoyed instruction. If the regular class­ school, 55 (40.1%) did so during kinder­
room teacher and/or classroom aide was garten, 36 (26.3%) did so during the first
able to learn with the student, things grade, 9 (6.6%) did so during the second
went very well.” grade, 6 (4.4%) did so during the third
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Descriptors of instructional methods
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 10 (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 (Livingston, 1997).
Secrets 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 (Davidow, 1988).
Counting method. This method has the student count each bead as it is added or sub­
tracted, 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 (Millaway, 2001).
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 (Willoughby & Duffy, 1989).
Hadley School for the Blind method. Hadley School for the Blind 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.
Box 1.
grade, 3 (2.2%) did so during the fourth The participants were given a list of
grade, 2 (1.5%) did so during middle factors to consider when determining
school, and 2 (1.5%) did so during high when to begin instruction in an abacus,
school. Some participants commented with multiple responses allowed. Of the
that the introduction of the abacus de­ 148 participants who responded, 105
pended on the developmental level and (70.9%) considered a student’s academic
the ability of a student to understand the abilities, 71 (48.0%) considered whether
basic concepts of the tool. Others intro­ a student is blind, 67 (45.3%) considered
duced the abacus when it made sense to a student’s fine motor abilities, 49 (33.1%)
do so in the academic curriculum. One considered a student’s grade in school, and
participant explained the rationale for the 24 (16.2%) each considered a student’s
choice: “When students’ peers are asked chronological age and whether the student
to count (e.g., in many preschools, chil­ has low vision. The participants taught stu­
dren count the days of the month, etc.), dents from kindergarten through high
we just count right along by moving school. Their comments covered the full
beads when counting.” range of grade placement and students’
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Table 1

The abacus skills that the 146 participants taught to students by educational setting (N;

% in parentheses).

Resource room Residential
Itinerant or self-contained or specialized
or travel classroom school
Skill Total (n � 111) (n � 16) (n � 19)
One-digit addition without synthesis or secrets 113 88 (77.9) 12 (10.6) 13 (11.5)
Addition of two or more digits without synthesis
or secrets 109 85 (78.0) 12 (11.0) 12 (11.0)
One-digit subtraction without synthesis or secrets 99 76 (76.8) 1 (11.1) 12 (12.1)
Subtraction of two or more digits without
synthesis or secrets 94 74 (78.8) 10 (10.6) 10 (10.6)
One digit as the multiplier (multiplication) 98 71 (72.4) 14 (14.3) 13 (13.3)
One-to-one correspondence 97 77 (79.4) 9 (9.3) 11 (11.3)
One-digit addition with synthesis or secrets 88 68 (77.3) 11 (12.5) 9 (10.2)
Addition of two or more digits with synthesis
or secrets 86 67 (77.9) 10 (11.6) 9 (10.5)
One-digit subtraction with synthesis or secrets 84 64 (76.2) 11 (13.1) 9 (10.7)
One digit as the divisor (division) 82 60 (73.2) 10 (12.2) 12 (14.6)
Subtraction of two or more digits with synthesis
or secrets 80 60 (75.0) 11 (13.8) 9 (11.2)
Two or more digits as the multiplier
(multiplication) 80 56 (70.0) 12 (15.0) 12 (15.0)
Decimals or money 67 53 (79.1) 8 (11.9) 6 (9.0)
Two or more digits as the divisor (division) 66 46 (69.6) 10 (15.2) 10 (15.2)
Record keeping (such as telephone numbers
and score keeping) 48 36 (75.0) 4 (8.3) 8 (16.7)
Fractions 43 32 (74.4) 5 (11.6) 6 (14.0)
How to couple two abaci together to perform
more lengthy computational tasks 27 19 (70.4) 3 (11.1) 5 (18.5)
Square roots 11 6 (54.5) 2 (18.2) 3 (27.3)
abilities. A participant who worked with they teach their students. Data are reported
young students echoed the sentiments of for the skills in Table 1 on the basis of the
many respondents: “I start them when other participants’ employment settings. Addition
children begin doing math, i.e., when they and subtraction were the two math opera­
enter school!” tions most often taught to the students.
The participants who reported teaching Higher-level math computation skills, such
abacus skills to students were given the as multiplication with multiple digits in
same list of skills found in Rosenblum and the multiplier or division, were taught less
colleagues (2013). In this study, the partic­ frequently. Few participants provided in­
ipants were asked to tell the level of profi­ struction on computing fractions or square
ciency they were expected to achieve and roots using an abacus.
the exposure they received for each identi­ The participants were also asked to ex­
fied skill within their university preparation. plain the reasons they did not teach certain
Using this list and thinking of their students skills to their students. Seventy-seven an­
with visual impairments, the participants swered this open-ended question. Their re­
were asked to indicate which of these skills sponses included that they did not believe
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that they were effective instructors of aba­ for the Blind course on abacus methods to
cus skills, lacked confidence to teach abacus be great resources. The video Hands-on Ex­
skills, did not know where to get updated perience with the Cranmer Abacus (Pester,
training, did not like using an abacus, or did n.d.) was also used, as were instructional
not have time to teach abacus skills. Other videos clips on YouTube (a video-sharing
responses were related to the lack of sup­ website). Some participants referred to
port, including the lack of a paraprofes­ course materials from their university prep­
sional to follow up on abacus skills with aration programs. Only a few identified ad­
students. Still other responses were related ditional resources for activities they use
to the lack of time: “There isn’t typically with their students to teach and practice
enough time in a regular elementary curric­ computational skills using an abacus.
ulum to do both the math curriculum well
and teach the abacus besides.” PARTICIPANTS WHO DID NOT PROVIDE
The participants listed reasons related INSTRUCTION IN AN ABACUS
to their students as justification for not Of the 196 participants, 32 reported that
providing instruction in abacus skills. they did not teach abacus skills to chil­
These reasons included their perceptions dren with visual impairments. These in­
that students used mental math; that the dividuals were given a list of reasons why
abacus was not an appropriate tool for they might not teach abacus skills and
specific students; that students who are were asked to check all that applied. Ten
infants, toddlers, or preschoolers are not (31.3%) chose “I do not have the knowl­
yet ready for instruction in abacus skills; edge or skills to be an effective abacus
that students have difficulty learning aba­ instructor for my students”; 10 (31.3%)
cus skills; and that students use technol­ chose “My students use mental math or
ogy for mathematics. One participant sup­ rote memorization to complete mathemat­
ported the increasing use of technology: ical computation”; 8 (25.0%) chose “I am
“By the time the students have the basic no longer confident in my abacus skills
math knowledge to effectively use the because I have not taught abacus in a long
abacus, they are using technology that time [or]ever”; 8 (25.0%) chose “I work
includes calculators.” with students who do not have the ability
to complete simple addition [and] sub­
RESOURCES USED BY THE PARTICIPANTS traction using objects, so the abacus is not
An open-ended question asked the partici­ an appropriate tool”; 7 (21.9%) chose “I
pants which resources (such as books, web- don’t know where to go to get updated
sites, and activities) they use when teaching training in abacus skills”; 5 (15.6%)
abacus skills to their students. The most chose “I work with students who are in­
commonly used books were Abacus Basic fants, toddlers, . . . or preschoolers who
Competency: A Counting Method (Milla­ are not yet developmentally ready to use
way, 2001), Use of the Cranmer Abacus the abacus”; 2 (6.3%) chose “I do not
(Livingston, 1997), and The Abacus Made have time to work 1:1 with a student to
Easy (Davidow, 1988). Several participants teach him [or] her the abacus”; and 2
reported that they considered the materials (6.3%) chose “I do not have a parapro­
they received through the Hadley School fessional or other staff member who can
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follow through on abacus instruction vide the field with a snapshot of how
when I am not with the student.” The teachers of students with visual impair­
participants provided additional reasons ments decide to teach computation with
why they did not provide instruction in an abacus, how to determine when in­
the abacus, including that their students struction should begin, which methods of
had low vision, used technology, and computation are being taught, and which
were not developmentally ready for in­ computational skills students learn with
struction in abacus skills. an abacus.
The 32 participants were asked, “In Most U.S. states and Canadian prov­
the future do you plan to teach the aba­ inces have standards that require students
cus to students who are visually im­ to pass high-stakes tests to advance to the
paired for whom it would be an appro­ next grade or to graduate. More than one
priate tool?” Seventeen (53.1%) said in four participants did not know if an
that they were definitely unlikely or un­ abacus was permitted to be used on high-
likely to teach abacus skills, 10 (31.3%) stakes tests in their state or province. It is
were fairly certain that they would teach imperative that teachers of students with
abacus skills, and 5 (15.6%) had defi­ visual impairments be well versed in what
nite plans to teach abacus skills in the is and is not permissible for students to
future. The 32 participants were asked use on these tests. In addition, almost half
to share their level of agreement with the participants indicated that their stu­
the statement, “I believe the abacus is a dents do not have IEP goals related to
useful tool to teach students to perform using the abacus. When one considers
mathematical calculations” on a 4-point that sighted students are allowed to use
Likert scale from 1 � “definitely not scratch paper to compute, children with
likely” to 4 � “definitely likely.” The visual impairments who are abacus users
mean for this item for 32 participants should be allowed to use this tool.
was 2.85 (SD � 1.17), the median was We were surprised to note that not all
3.00, and the mode was 3. the participants who indicated that they
taught abacus computation skills used an
Discussion abacus to teach the concept of one-to-one
In this age of technology, the abacus is correspondence. It is possible that they
still being used and continues to have a use other math manipulatives to teach this
place in the toolbox of students with vi­ skill before they introduce the abacus.
sual impairments. Rosenblum and Smith Further examination of this aspect of aba­
(2012) found that computation with an cus instruction could be valuable. It is not
abacus was taught in 25 of 26 university surprising that higher-level math skills
preparation programs. University instruc­ (such as division with two-digit divisors
tors would not allocate precious time to or computing fractions and square roots)
teach preservice teachers of students with were taught to few students. It would be
visual impairments to use this device if valuable to determine if these skills are
they did not think it had a place in the not taught because teachers of students
toolbox of students. The data gathered in with visual impairments are not comfort­
this study are valuable, because they pro­ able with these skills, students are not
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developmentally ready for instruction in and organizing data, were not readily
these skills, or other tools (such as a cal­ identified. We acknowledge that the aba­
culator) are used. cus has distinctive roles for students
The role that technology plays in the whose learning needs are more concrete
decision-making processes of both teach­ and functional. Approximately one-third
ers of students with visual impairments of the participants taught record keeping
and students as to what strategies and using an abacus. They identified keeping
tools are used in math instruction and scores during games, tallying the number
how this technology influences a stu­ of items completed, and developing num­
dent’s choice to compute with an abacus ber concepts as ways to use an abacus that
or other devices, such as a talking calcu­ should be taught to students.
lator, would also be worth further explo­
ration. Both mental math and the use of LIMITATIONS
technology have their place in education.
This study had several limitations. First,
Like all students, students with visual im­
we did not gather data about specific
pairments should be expected to be pro­
children to whom abacus instruction
ficient in these skills. Seeley (2005) sug­
was provided, nor did we evaluate the
gested that there are two major functions
quality of the instruction that the par­
of mental math. Traditional means of
ticipants provided. Second, all the data
computation may be considered the pri­
we gathered were from self-reports, and
mary role, but the extended function of
we did not verify them. Third, the topic
mental math includes conceptual under­
of preparation and instruction in an aba­
standing and problem solving. Therefore,
cus may have been one that did not
we must be cautious in not sacrificing
interest some potential participants be­
students’ understanding of concepts, such
cause they do not believe in the value
as place value and the ability to compute
of the tool, do not have experience
without using technology. The abacus is
teaching abacus computation, or for any
not a tool that is exclusively replacing
other unspecified reason. Therefore,
technology, but is a device that can com­
these individuals may not have partici­
plement mental math and technology op­
pated in the study, which may have
tions for mathematics. A well-balanced
skewed the data gathered from the re­
instructional program that combines the
goals of the general education curriculum ported experiences and interest levels of
and the ECC (Hatlen, 1996) is necessary the participants. Fourth, not all the par­
for students with visual impairments. ticipants responded to all the questions.
It is interesting to observe that the par­ Finally, the study was advertised on
ticipants did not view the presence of an national electronic bulletin boards, and
additional disability as a determining fac­ we sent information to teachers of stu­
tor in whether to provide instruction in dents with visual impairments whom we
using an abacus. Although a significant knew. Thus, this convenience sample
number of participants rated academic may not represent the population of
ability as a determining factor, functional teachers of students with visual impair­
use of the abacus, such as keeping records ments in the United States and Canada.
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Implications for practitioners core state standards that define the knowl­
edge and skills that students should have
The abacus is used with students who
during their K–12 education. These stan­
are visually impaired to teach computa­
dards focus on preparation for future edu­
tion. We recognize that the role of
cational and vocational goals and include
teachers of students with visual impair­
STEM (science, technology, engineering,
ments is multifaceted, as Spungin and
and math) standards.
Ferrell (2007) described. Teachers of
Future studies are needed to examine
students with visual impairments must
closely how teachers of students with
be well prepared to meet the diverse
visual impairments are providing in­
needs of their students. Although some
struction to students in using an abacus.
participants indicated that they did not
Questions to guide this research include
teach computation with an abacus to
these: At what age is it best to introduce
their students because of their own lack
the abacus to children? What method of
of knowledge, other participants re­
computation is best to use with specific
ported that this was not the case. Since
types of learners? Where should abacus
Rosenblum and Smith (2012) reported
instruction be provided (in a general ed­
that 25 out of 26 university preparation
ucation classroom or in a resource room)?
programs provide instruction to future
For students who have additional disabil­
teachers of students with visual impair­
ities, what criteria should be used to de­
ments in computation with an abacus, a
termine whether an abacus is an appro­
logical conclusion is that the vast ma­
priate learning tool, and what methods
jority of future teachers of students with
should be used to teach the students to use
visual impairments should have re­
an abacus in a meaningful way on the
ceived instruction in this area. If they
basis of their learning needs and future
have not received such instruction, or if
goals? Last, what is the role of an abacus
their instruction was so long ago that
for students who are using both assistive
they are “rusty,” resources are available
and mainstream technology?
to support their abacus computation
skills. These resources include instruc­ References
tional books, videos, and courses from
California Department of Education. (2006).
the Hadley School for the Blind. L. Braille mathematics standards adopted by
Penny Rosenblum, at the University of the California State Board of Education.
Arizona, is working on an iDevice app Retrieved from http://www.cde.ca.gov/sp/
se/sr/documents/braillemathstand.pdf
that will allow one to practice abacus
Culpepper, M. (2001). Teachers of the visually
computation skills for addition and sub­
impaired: Roles, rights, and responsibilities.
traction using the method developed by Future Reflections, 20(1). Retrieved from
Livingston (1997). If she is successful https://nfb.org/images/nfb/publications/fr/
in developing and distributing this app, fr20/issue1/f200108.htm
Davidow, M. E. (1988). The abacus made
she plans to add other math operations
easy. Louisville, KY: American Printing
and computation methods.
House for the Blind.
Abacus instruction for students who are
DeMario, N., Lang, S., & Lian, M. (1998).
visually impaired supports the common Teachers’ self-assessed competence and
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©2013 AFB, All Rights Reserved Journal of Visual Impairment & Blindness, July-August 2013