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, 20122012 AER International Conference

Our Colleague Sheila Amato Couldn’t Join Us

Today…

We Had Some Questions...

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.

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.

Instrument Development 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 196 participants Of 191 participants

9 Canadian / remainder from 39 states in the US

Of 194 participants 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? 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 on-line videos From an individual of Asian descent

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.

Method Counting Logic/Partner SecretsPaper

CompatibleHadley

Taught method to

proficiency 45 38 26 9 8

Prepared to Use an

Abacus for

Calculation

3.60 3.74 3.46 3.11 4.38

Prepared to Teach

Abacus Skills 3.68 3.84 3.48 3.32 4.50

Method Counting Logic/Partner SecretsPaper

CompatibleHadley

Exposed to Method 21 22 24 15 9

Prepared to Use an

Abacus for

Calculation

3.05 3.32 3.33 2.87 3.44

Prepared to Teach

Abacus Skills 2.98 3.43 3.25 2.93 3.63

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 proficiencyExposed to the skillNo instruction or exposure to the skillDid not recall

Highest Ranked Skills Taught to Proficiency in

University Programs 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 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?

“More competent trainers are needed to teach VI teachers how to teach more than just basic skills on the abacus.”

“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?

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

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

What Method Do You Teach Your Students?

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

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?

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? 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…

“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.”

 “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:

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

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.

Five Statements with the Highest Ratings

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

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…

“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.”

“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

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

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

“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

“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

“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… “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.”

“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…

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… 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…

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????