An examination of 40 years of mathematics education among Norwegian braille-reading students.
Article Type: Brief article
Subject: Disabled students (Research)
Disabled students (Analysis)
Disabled students (Education)
Mathematics (Study and teaching)
Mathematics (Research)
Mathematics (Analysis)
Vision disorders
Authors: Klingenberg, Oliv G.
Fosse, Per
Augestad, Liv Berit
Pub Date: 02/01/2012
Publication: Name: Journal of Visual Impairment & Blindness Publisher: American Foundation for the Blind Audience: Academic Format: Magazine/Journal Subject: Health Copyright: COPYRIGHT 2012 American Foundation for the Blind ISSN: 0145-482X
Issue: Date: Feb, 2012 Source Volume: 106 Source Issue: 2
Topic: Event Code: 310 Science & research
Geographic: Geographic Scope: Norway Geographic Code: 4EXNO Norway
Accession Number: 282068140
Full Text: Structured Abstract: Introduction: The study presented here estimated the occurrence of braille-reading students in Norway who were educated according to their grade-level progression in mathematics from 1967 to 2007. It also analyzed the association among these students' progression in mathematics and the causes of visual impairment, the age at which the diagnosis was established, the students' gender, and the students' use of reading media (braille as the sole, primary, or secondary literacy medium). Methods: A retrospective, population-based study design was used. All the students who had received braille education in the past four decades prior to the study were included. The following data were abstracted from each student's records: birth year, country of birth, gender, year diagnosed, diagnosis, type of reading media, and whether the student's education had followed their grade-level progression. Results: In total, 248 braille-reading students were identified. Of these students, 141 (57%) had been taught mathematics at grade level. In 19 of the 45 principal eye diagnoses that were registered, all the students were educated according to the normative grade progress in mathematics. There were no statistically significant associations between gender and the abstracted variables or between mathematics education and reading media. Discussion: During the four decades under study, there was some variation in the distribution of different diagnoses. Students with diagnoses related to the central nervous system had a comparatively higher risk of not attaining their normal grade level in mathematics. Implication for practitioners: Teachers may expect that a braille-reading student will follow his or her grade level in mathematics. It is essential, however, to gain information on the causes of visual impairment, in general, and in cases of the co-occurrence of visual impairment and learning disabilities, in particular. It is essential to document typical learning patterns among braille-reading students and intervention strategies for students with visual impairments and learning disabilities.

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Mathematics and mathematical terms are interwoven with activities of daily life and social situations, and fundamental mathematical concepts and skills are essential for entry into various vocational and educational programs. All students, whether sighted or visually impaired (that is, those who are blind or have low vision), should have an opportunity to obtain a level of competence in mathematics according to their abilities.

Mathematics may be assumed to be challenging for students who are visually impaired because many aspects of mathematics are understood to be visual in nature. A survey from the United States in 1988 supported this assumption to some extent because it reported that only 48% of the braille-reading students in Grades 9-12 were enrolled in a mathematics course (Rapp & Rapp, 1992).

The literature on children with visual impairments has often built on a "developmental lag" theory (Warren, 1994), which means that it is expected that children with severe vision loss acquire different abilities (cognitive, motoric, and social) at a later age than do sighted children. However, when a group of braille-reading students (hereafter referred to as "braille students" and "braillists") is compared to sighted norms, the variances within the group will not be apparent. A comparative approach obscures the fact that some braillists may progress at a normal or higher rate than their sighted peers (Besnoy, Manning, & Kames, 2005; Warren, 1994). Another criticism is that the conclusions of research are often drawn without considering important factors, such as the age at which vision loss occurred, the presence of any visual function, the cause of vision loss, and the presence of additional disabilities (Warren, 1994). Thus, there may be hidden factors in the research literature that may lead to expectations that are either too low or too high in terms of, for example, mathematics content to be learned in school. It is therefore relevant to gather more information about variations and patterns of variations in mathematics education within groups of braille students.

The study presented here focused on educational progress in mathematics among braille students in Norway. The aims of the study were to estimate the occurrence of braille students who were educated according to their grade-level progression in mathematics from 1967 to 2007 and to analyze the association between progression in mathematics among braille students and the gender, reading media, and age of diagnoses of visual impairments among these students.

Methods

DESIGN AND SOURCES OF DATA

A retrospective study design of clinical data was used in that "existing data that [were] recorded for reasons other than research" (Hess, 2004, p. 1171) were used. The goal was to include all students who had received braille education in Norway between 1967 and 2007.

In Norway, attendance at school has been obligatory for children with visual impairments since 1881. At first, this requirement was for children aged 9-21 (Forsbak, 2008). Today Norwegian children start school at age 6, regardless of their physical or cognitive abilities. Attendance at elementary school and middle school (7 years plus 3 years) is obligatory, and students have the right to receive a high school education (3-5 years, depending on their personal needs). Compulsory education is free, and the net enrollment is close to 100% (Ministry of Education and Research, Norway, 2010). Experience data indicate that almost 100% of braille students attend high school, but not all of them take the academic examinations. Several braille students have an adapted education.

The data used in the study were gathered both from the period when there were residential schools and special classes in public schools for students with visual impairments (1967-1995) and from the period of inclusive education in public schools (1970-2007) (Forsbak, 2008). Following an examination and diagnosis by an ophthalmologist, children with severe visual impairments are referred to one of two national resource centers, Huseby or Tambartun, depending on their place of residence. The two centers were formerly residential schools for students with visual impairments, but since the early 1990s there has not been a residential school for students who are visually impaired in Norway.

For each student, records (a journal), consisting of educational and medical information, including visual status, are kept at his or her resource center for up to 10 years after the last contact (contact related to special educational guidance, courses arrangements, textbooks in braille, and so forth). After 10 years, all records are filed in the national government archive. Records related to students who were educated at special boarding schools are also filed in the national government archive. The probability of identifying all students who received braille education in Norway between 1967 and 2007 is thus high.

Braille for mathematics notation is determined by the Governmental Committee of Braille (Offentlig Utvalg for punktskrift). The braille is standard (that is, upper numbers and plain letters) and includes both 6-dot braille and 8-dot braille. There are rules and guidelines on how to render expressions in arithmetic, algebra, geometry, trigonometry, and calculus that are followed by the two national resource centers that produce textbooks in braille.

SUBJECTS

In total, 287 students who had been taught braille in Norway from 1967 to 2007 were identified (Augestad, Klingenberg, & Fosse, 2011). Of this number, 119 students who were born between 1957 and 1988 had a record related to residential schools, and 168 students who were born between 1970 and 2001 had a record from one of the two resource centers. Only students who had received a braille education were included in the study.

A total of 25 braille students who had been diagnosed with neuronal ceriod lipofuscinoses were excluded from the total group of subjects, since the development of this group of degenerative disorders affects cognitive processes that are vital for progress in mathematics. After the exclusion of cases with missing information related to diagnoses or mathematical achievement or both, the total number of subjects was 248 (119 girls, or 48%, and 129 boys, or 52%). The subjects were born between 1960 (started school in 1967) and 2001 (started school in 2007).

MEASUREMENTS

The following information was abstracted from each student's journal: year of birth, country of birth, gender, year diagnosed, neuro-ophthalmologic diagnoses, and use of braille (braille only, braille primarily and print, print primarily and braille). The diagnoses were classified into four nosological groups (nosological is a systematic classification of diseases): sequelae of brain disorders, congenital ocular anomalies, ocular dystrophies, and miscellaneous, according to Rosenberg et al. (1996).

In addition, the yes or no responses to the question of whether the student was taught according to the intended curriculum in mathematics were abstracted. The intended curriculum, curriculum standards, is a specification of mathematics that students are expected to learn for particular grade levels (Hirsch & Reys, 2009). In Norway, national standards are ensured through legislation and regulations. Education should be organized so every student is assigned to a grade (in a group of students of the same age), but instruction should be adapted to individual students' abilities and capabilities. Thus, a student in the fifth grade may, for example, be taught according to the mathematics curriculum for students in the third grade and use schoolbooks for the third grade, while his or her fellow students use schoolbooks for the fifth grade. The type of school attended and whether the student was taught in a group or class or individually in a group room were not specified.

From a research methodology perspective, there are problems associated with categorizing whether a student is educated according to grade level or not and categorizing the use of reading media. To deal with these difficulties, the following procedures were used. Progression in mathematics was categorized on the basis of the years reported in the student's records. The number of years taught at grade level (= yes) and not grade level (= no) were summarized, and the higher score was used. If the number of years taught at grade level were found to be equal, the report for the most recent year was used. Reading media were categorized into the three groups described earlier. The highest number of years associated with one of the three different groups determined the student's placement in a group. The counting started when braille was first introduced and applied.

Descriptive statistics were used to summarize the results. Because of missing data in some journals, it was not possible to gather all the informational variables for all the subjects. To compare the groups, chi square tests were used in the analysis of contingency tables. Statistical significance was defined as p = < .05. All the analyses were performed using the SPSS 17.0 statistical package.

The Helsinki Declaration on ethical principles for medical research involving human subjects was followed (World Medical Association, 2000). The Norwegian Regional Committee for Ethics in Medical Research and the Norwegian Ministry of Education and Research approved the study and gave permission for data from each student's journal to be used.

Results

BRAILLE STUDENTS AND MATHEMATICS

EDUCATION

Table 1 presents the characteristics of the subjects. Of the 248 students who had been taught to read braille in the study period, 223 (90%) were born in Norway, 14 (6%) were born in Asia, 5 were born in South America, 4 were born in other European countries, and 2 were born in the United States. With regard to the students' reading media (data on 246 students), 168 (68%) students used braille as their only reading medium, 22 (9%) used primarily braille but also print, and 56 (23%) used primarily print but also braille. The latter group (n = 35; 63%) was most often educated at the level appropriate for their age (grade) in mathematics. The corresponding percentages for the other two groups were 59% (n = 13) of the students who primarily read braille but also print, and 55% (n = 92) of the students who read braille only. No statistically significant associations were found between education in mathematics and reading medium (chi square = 1.07, df = 2, p = .59).

In total, 141 students (57%) were taught mathematics at the grade-level expectations for their age, and 107 students (43%) were taught below grade level (see Table 1). The data did not include any students who had initially been educated at a lower grade level than their age and later showed progress appropriate for their age. In mathematics, 69 girls (58%) and 72 boys (56%) were educated at the grade standards for their age, while 50 girls (42%) and 57 boys (44%) were educated at a lower grade level. Because no statistically significant associations were found between gender and individual characteristics, no further analyses related to gender were undertaken.

[FIGURE 1 OMITTED]

Figure 1 shows the number of braille students who were born between 1960 and 2001 and the distribution of students who were educated at grade level and below grade level in mathematics. The period in the figure is subdivided into 14 three-year spans. The number of braillists who were born in each three-year period was, respectively, 18, 25, 22, 16, 11, 25, 12, 16, 15, 18, 26, 21, 15, and 8. The eight students who were born between 1999 and 2001 were students in Grades 1, 2, and 3.

MATHEMATICS EDUCATION AND DIAGNOSES

The 45 principal eye-disorder diagnoses registered in the students' records are listed in Table 2 and presented for six--year periods. The percentage of students by nosological group who were educated according to grade level in mathematics was as follows: ocular dystrophies, 65% (n = 45); congenital ocular anomalies, 64% (n = 49); miscellaneous, 51% (n = 105); and sequelae of brain disorders, 30% (n = 26). Statistically significant associations were found between education in mathematics and the nosological groups (chi square = 11.20, df = 3, p = .01). Standardized residuals showed that the nosological group sequelae to brain disorders particularly contributed to the significant findings in that students in this group of diagnoses are not educated according to grade level in mathematics.

In 19 of the 45 diagnoses, all the students were educated according to the normative grade-level progress in mathematics, but in 12 of the 19 diagnoses, only one student was registered. For ethical reasons, the results related to educational grade level in mathematics in groups comprised of only a few students are not presented. Table 3 shows the 12 most frequent principal eye-disorder diagnoses and how the students with these diagnoses were distributed in the two categories of mathematics education and reading media.

All 12 students who were diagnosed with retinoblastoma were educated according to grade level, as were 12 (86%) of the 14 students who were diagnosed with retinitis pigmentosa. The corresponding percentages of students who were diagnosed with Leber's congenital amaurosis, congenital cataracts, and retinopathy of prematurity were 70% (n = 19), 67% (n = 8), and 38% (n = 18), respectively.

Discussion

Our examination of the medical and educational records of Norwegian braille students found that during the 40-year period under study (1967-2007), 57% (n = 141) of the braille students had been educated in mathematics at the grade level appropriate for their age. In addition, students with retinoblastoma and retinitis pigmentosa most often had been taught according to the curriculum standards for their age (grade).

The distribution of braille students who were educated in mathematics at the standard grade level fluctuated during the study period, as is shown by the black solid line in Figure 1. The highest percentages were found among students who were born between 1960 and 1971, between 1978 and 1986, and in a short period in the mid-1990s. The lowest percentage was for students who were born in the latest years of the study period. Also, for some years in the mid-1970s the percentage of students who were educated according to set school standards was low. Because of the small sample, it is difficult to explain these findings, with the exception of the percentages of students who were educated at grade level in the 1990s, when there was a peak in the diagnosis of Leber's congenital amaurosis and as students with this diagnosis had often been taught according to grade level (70%).

Regarding variations related to etiology, all students with retinoblastoma-caused blindness had an age-related education in mathematics. The finding matches with clinical experiences and corresponds with results published in international publications that have reported that students with this diagnosis are doing well in relation to cognitive functioning (Ek, 2000; Tobin, Hill, & Hill, 2010; Warren, 1994).

The average percentage of braille students who were educated in mathematics at grade level in this study was higher than that found in similar published studies. Rapp and Rapp (1992) found that 48% (n = 19) of braille students in a region of the United States selected mathematics courses in secondary school. In contrast, Beal, Rosenblum, and Smith (2011) reported that only 36% (n = 9) of middle school braille students who were participating in an educational computer experiment for mathematics conducted in Arizona were taught at grade level in mathematics. However, because of methodological issues--for example, the Norwegian study included students who were attending elementary school--it is difficult to compare the three studies.

Our study showed that there were students with neurological vision loss in all four decades. This result is in accordance with findings presented by Gogate and Gilbert (2007), who stated that lesions of the central nervous system, often associated with prematurity, are among the major causes of blindness in children in affluent countries.

One interpretation is that students who are not educated in mathematics at the grade appropriate for their age have some kind of learning difficulties. "Because some visual disabilities have a neurological origin, and because learning disabilities and visual disabilities in children who were premature babies occur at a higher rate than normal, there are physiological reasons to expect a high rate of co-occurrence" (Erin & Koenig, 1997, p. 310). A Canadian study of 150 braille students (including some adults) estimated that 45% of braillists have learning difficulties (Troughton, 1992). The finding that 43% of braille students in our study were educated below grade level in mathematics is comparable, and the reason may be learning difficulties. However, not only do cerebral activities affect the development of mathematical thinking, but experience affects cerebral structures and functions (Magne, 2006). According to Magne, other explanations than learning difficulties need to be taken into consideration, since it is difficult to determine whether low achievement in the objectives of a curriculum is due mainly to students' predisposition, mathematical content, or inadequate teaching methods and materials.

The study revealed that students who read primarily print but also braille were most often educated in mathematics at a grade level appropriate for their age. The result was not statistically significant, but may support the notion that students with total vision loss experience a greater number of mathematical problems. However, the finding may also be related to other factors, such as teaching methods, teachers' competence, and the quality and the type of textbooks. Because braille textbooks in mathematics, braille transcriptions of symbols that underpin mathematics, and calculation rules in braille are all considered more challenging than printed books, printed symbol systems, and printed calculation rules (Kapperman, Heinze, & Sticken, 2000; Rosenblum & Amato, 2004), one may assume that the students who read primarily print were taught mathematics on the basis of the use of their residual vision.

Children with visual experiences for one year or more in early childhood have considerable advantages not only in looking at and perceiving shapes, but in reaching for and trying to grasp objects (Millar, 2008). They will have started to interact in a physical world, since "the world seeks infants who can see, but infants who cannot see must learn to seek the world" (Foulke & Hatlen, 1992, p. 47). In contrast, according to the literature, by the end of the first year of life, a child who is congenitally blind is at risk of developing passivity (Martinsen, 1994). In the study, at least three of the six students who were congenitally blind because of bilateral congenital unilateral anophthalmos had been educated at grade level in

mathematics (note that information is lacking for three other students with this diagnosis of the absence of one or both eyes). Despite the low number of students with this diagnosis, the findings revealed that the students with no visual experience were capable of standard mathematical progression. Rather than focus on the lack of vision itself as the main causal factor related to the ability to engage in mathematical thinking, it is more appropriate to look for other factors, such as adaption of the physical environment and the importance of being physically active, as prerequisites to spatial understanding and mathematical thinking. The strength of the study is that the data included the number of Norwegian students receiving a braille education and the underlying causes of their visual impairments.

LIMITATIONS

The study had some limitations. First, data related to whether a student was educated at grade level or below grade level in mathematics can be used only to generate a rough assessment of mathematics achievement. In addition, when a student was educated for some years at grade level and some years below level, the coded data were not exact. Second, the study focused only on eye-disorder diagnoses, and consequently information related to additional diagnoses was insufficient or missing. The third disadvantage is related to the retrospective study design because it relied on the accuracy of the written records (Hess, 2004). Since the records in the study covered four decades, the way of writing pedagogical reports and using diagnoses may have changed. In addition, some data, such as precise documentation of how many years each student attended school, were not available. Furthermore, there was a lack of information related to the multitude of decisions and actions taken to filter and select students for assignment to either grade level or below grade level.

Conclusion

Basic competence in mathematics may be essential for functional participation in society. To educate each student with realistic and positive expectations, teachers need information on the causes of visual impairment, as well as on the functional consequences of the visual impairment on learning. Braille students need to receive comprehensive and appropriate assessments and appropriate services from specialists whose expertise may provide the multidimensional interventions required by each student.

There is every reason to expect that a braille student who has no brain disorder will learn the mathematics outlined in the curriculum. The challenge is to improve teaching methods and learning materials that draw on research on how braille students learn. In addition, professionals in the field of visual impairments should discuss and search for a natural progression of mathematics curricula that are fitting for students with severe vision loss. On the basis that mathematics learning is regarded as a function of biological and social factors, it is also vital to continue to research how young children with visual impairments join society and interact with different physical environments and how their initiative can be stimulated.

IMPLICATIONS FOR PRACTICE

The principal finding of the study was that vision is not a prerequisite for following grade-level education in mathematics. The evidence that most braille-reading students in Norway are taught at grade level should be a source of considerable support for parents, teachers, counselors, and students. No braille-reading student should have to encounter such attitudes as Abraham Nemeth (quoted in Navy, 1991) did: "I always liked math. But various counselors told me that I couldn't have a career in math because I was blind. I heard this from so many counselors that I believed it."

The second main implication is that parents and teachers of braille students should know whether medical disorders that lead to visual impairments may also lead to learning disabilities that are due, for instance, to neurological disorders. Thus, there is a need for a multidisciplinary team to discern whether a student has a learning disability. A student with a visual impairment in combination with a learning disability has needs additional to those that are provided for by traditional approaches to braille instruction. Educational programs must reflect appropriate interventions in both areas.

The third implication concerns educational reports and journal records. This retrospective study identified the need for significant descriptions of braille-reading students' competences in mathematics, for the purposes not only of daily and future planning, but for research. There is a need to provide detailed information on braille-reading students, as well as on teaching methods that are most successful in promoting effective learning. It is important to document typical learning patterns among braille-reading students and intervention strategies for students with visual impairments and learning disabilities.

References

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Rosenblum, L. P., & Amato, S. (2004). Preparation in and use of the Nemeth braille code for mathematics by teachers of students with visual impairments. Journal of Visual Impairment & Blindness, 98, 484-495.

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Oily G. Klingenberg, M.Ed., Ph.D. candidate, Department of Education, Faculty of Social Sciences and Technology Management, Norwegian University for Technology and Science, Matematikksenteret, NTNU, N0-7491 Trondheim, Norway; e-mail: . Per Fosse, Dr.Philos., senior advisor, Tambartun National Resource Centre for the Visually Impaired, NO7224 Melhus, Norway; e-mail: . Liv Berit Augestad, Dr.Polit., professor, Department of Human Movement Science, Norwegian University for Technology and Science, NTNU, Dragvol, N0-7491, Trondheim, Norway; e-mail: .
Table 1
Characteristics of the study subjects.

                                                Gender

                                          Girls           Boys
                                         n = 119        n = 129

Characteristic            n (%)          (48%) n        (52%) n

Reading medium
  Braille only          168 (68.3)        79 (47.0)    89 (53.0)
  Braille and print,
   priority
   braille               22 (8.9)           8(36.4)    14 (63.6)
  Braille and print,
   priority print       56 (22.8)         31 (55.4)    25 (44.6)
Total numbers (a)       246 (100)        118 (48.0)    128 (52.0)

                                      chi square = 2.47, of = 2,
                                                p=0.29

Nosological groups
  Sequelae to brain
   disorders             23 (9.3)          9 (39.1)    14 (60.9)
  Congenital ocular
   anomalies            77 (31.0)         37 (48.1)    40 (51.9)
  Ocular dystrophies    69 (27.8)         32 (46.4)    37 (53.6)
  Miscellaneous         79 (31.9)         41 (51.9)    38 (48.1)
Total number            248 (100)        119 (48.0)    129 (52.0)

                                       chi square = 1.28, of = 3,
                                                  p=0.73

Age at diagnoses (b)
Less than 1 year        142 (64.0)        72 (50.7)    70 (49.3)
1-5 years               54 (24.3)         25 (46.3)    29 (53.7)
6-13 years              23 (10.4)         11 (47.8)    12 (52.2)
14-18 years               3 (1.4)          1 (33.3)     2 (66.7)
Total number (c)        222 (100)        109 (49.1)    113 (50.9)

                                       chi square = 0.63, df = 3,
                                                 p=0.89

                        Education in mathematics

                                        Below grade
                        Grade-level        level

Characteristic          = 141 (57%)    n = 107 (43%)

Reading medium
  Braille only            92 (54.8)       76 (45.2)
  Braille and print,
   priority
   braille                13 (59.1)        9 (40.9)
  Braille and print,
   priority print         35 (62.5)       21 (37.5)
Total numbers (a)        140 (56.9)      106 (43.1)

                        chi square = 1.07, of = 2,
                                  p=0.59

Nosological groups
  Sequelae to brain
   disorders               7 (30.4)       16 (69.6)
  Congenital ocular
   anomalies              49 (63.6)       28 (36.4)
  Ocular dystrophies      45 (65.2)       24 (34.8)
  Miscellaneous           40 (50.6)       39 (49.4)
Total number             141 (56.9)      107 (43.1)

                        chi square = 11.20, of = 3,
                                     p=0.01

Age at diagnoses (b)
Less than 1 year          76 (53.5)       66 (46.5)
1-5 years                 36 (66.7)       18 (33.3)
6-13 years                  8(34.8)       15 (65.2)
14-18 years                1 (33.3)        2 (66.7)
Total number (c)         121 (54.5)      101 (45.5)

                        chi square = 7.43, of = 3,
                                   p=0.06

(a) Missing reading medium for one girl and one boy.

(b) Earliest documentation in records of severe vision loss.

(c) Missing age at diagnoses for 26 students.

Table 2
Braille students distributed according to nosological groups,
principal ophthalmic diagnoses,  and year of birth (6-year
periods)

Diagnoses                         N    60-65   66-71   72-77   78-83

Sequelae to brain disorders
  Anomaly of the brain            2      1
   (unspecified)
  Brain tumor                     8      1       2
  Sequelae to brain disorders
   (unspecified)                 13      2       1       4       1
Congenital ocular anomalies
  Albinism (unspecified)          1      1
  Coloboma of uvea                3
  Congenital anomaly              2              1
  Congenital anophthalmos         9      3       1               1
  Congenital cataract (a)        16      5       5       3
  Congenital glaucoma            12      3       3       1       1
  Congenital maculapathy          1
  Congenital nystagmus            1      1
  Cong. progressive cone          1      1
   dystrophy
  Congenital ptosis               1                      1
  Congenital retinal              2              1
   degeneration
  Congenital retina dysplasia     2
  Congenital unspecified          3      2       1
  Optic nerve hypoplasia         13      1       1               2
  Microphthalmos                  8      4               1       1
  Peter's anomaly                 2                              1
Ocular dystrophies
  Optic nerve atrophy            10      2       3               2
  Corneal dystrophy               1      1
  Corneal keratoconus             1      1
  Corneal opacity                 1                              1
  Deformity of orbit              1
  Hypermetrophi, blue cone
   monochromatism                 1
  Leber's congenital amaurosis   27      1       6       3       2
  Macular corneal dystrophy       1
  Retinal dystrophy               2                      2
  Retinal detachment              1
  Retinopathy                     4                      1       1
  Retinitis pigmentosa (b)       16      3               3       2
  Septo-optic dysplasia           3                      1
Miscellaneous
  Eye trauma                      5      1       1       1
  Following cardio-               1
   respiratory arrest
  Following leukemia treatment    1
  Following meningitis
   (optic nerve dystrophy)        1                      1
  Genetic: LMBB syndrome          5      1                       1
  Malignant, eye--other           1                      1
  Neoplasms: Haemangioma of       1              1
   the retina
  Neurofibromatosis               2      1
  Optic nerve glioma              1
  Progressive, degenerative
   disorders (unspecified)        1                      1
  Retinoblastoma                 12      5       2               2
  Retinopathy of prematurity     47      1       9      12      10
  Toxic epidermoid necrolysis     1      1
                                 248    43      38      36      28

Diagnoses                        84-89   90-95   96-01

Sequelae to brain disorders
  Anomaly of the brain             1
   (unspecified)
  Brain tumor                      1       2       2
  Sequelae to brain disorders
   (unspecified)                   1       3       1
Congenital ocular anomalies
  Albinism (unspecified)
  Coloboma of uvea                 2               1
  Congenital anomaly               1
  Congenital anophthalmos          3       1
  Congenital cataract (a)          2       1
  Congenital glaucoma                      4
  Congenital maculapathy                   1
  Congenital nystagmus
  Cong. progressive cone
   dystrophy
  Congenital ptosis
  Congenital retinal               1
   degeneration
  Congenital retina dysplasia      2
  Congenital unspecified
  Optic nerve hypoplasia           3       4       2
  Microphthalmos                           1       1
  Peter's anomaly                          1
Ocular dystrophies
  Optic nerve atrophy              2       1
  Corneal dystrophy
  Corneal keratoconus
  Corneal opacity
  Deformity of orbit                       1
  Hypermetrophi, blue cone
   monochromatism                          1
  Leber's congenital amaurosis     1      11       3
  Macular corneal dystrophy                1
  Retinal dystrophy
  Retinal detachment               1
  Retinopathy                              1       1
  Retinitis pigmentosa (b)         3       5
  Septo-optic dysplasia                            2
Miscellaneous
  Eye trauma                               1       1
  Following cardio-                        1
   respiratory arrest
  Following leukemia treatment                     1
  Following meningitis
   (optic nerve dystrophy)
  Genetic: LMBB syndrome           3
  Malignant, eye--other
  Neoplasms: Haemangioma of
   the retina
  Neurofibromatosis                                1
  Optic nerve glioma                       1
  Progressive, degenerative
   disorders (unspecified)
  Retinoblastoma                           1       2
  Retinopathy of prematurity       6       4       5
  Toxic epidermoid necrolysis
                                  33      47      23

Note: The nosological groups model is based on Rosenberg et al. (1996).
(a) Including cataract and lens anomalies and cataract and glaucoma.
(b) Including retinitis pigmentosa and Sensenbrenner's syndrome.

Table 3
Distribution of reading media and education in mathematics
according to the 12 most frequent principal ophthalmic diagnoses

                                             Reading media
                                             Braille only

                                                        Below age
                                          Age level     level in
Diagnoses                           N     in math n      math n

Retinopathy of prematurity          47        14        26 (a)
Leber's congenital amaurosis        27        15        8
Retinitis pigmentosa                14         1        0
Optic nerve hypoplasia              13         4        4
Sequelae to brain disorders         13         0        10
Congenital cataract                 12         4        0
Congenital glaucoma                 12         6        3
Retinoblastoma                      12        11        0
Optic nerve atrophy                 10         3        2
Congenital anophthalmos              9         5        4
Brain tumor                          8         3        2
Microphthalmos                       8         3        2
Total                              185        69        61 (a)

                                       Reading media

                                      Braille and print
                                      Priority braille

                                                Below age
                                Age level       level in
Diagnoses                       in math n        math n

Retinopathy of prematurity          1               1
Leber's congenital amaurosis        3               0
Retinitis pigmentosa                2               0
Optic nerve hypoplasia              0               1
Sequelae to brain disorders         0               1
Congenital cataract                 2               1
Congenital glaucoma                 0               1
Retinoblastoma                      0               0
Optic nerve atrophy                 1               1
Congenital anophthalmos             0               0
Brain tumor                         1               1
Microphthalmos                      1               0
Total                               11              7

                                    Reading media

                                  Braille and print
                                   Priority print

                                                Below age
                                Age level       level in
Diagnoses                       in math n        math n

Retinopathy of prematurity          3               1
Leber's congenital amaurosis        1               0
Retinitis pigmentosa                9               2
Optic nerve hypoplasia              3               1
Sequelae to brain disorders         0               2
Congenital cataract                 2               3
Congenital glaucoma                 1               1
Retinoblastoma                      1               0
Optic nerve atrophy                 0               3
Congenital anophthalmos             0               0
Brain tumor                         1               0
Microphthalmos                      2               0
Total                               23             13

                                     Reading media

                               Education in mathematics

                                Age level       Below age
                                 in math        level in
Diagnoses                         n (%)        math n (%)

Retinopathy of prematurity      18 (38.3)       29 (61.7)
Leber's congenital amaurosis    19 (70.4)        8 (29.6)
Retinitis pigmentosa            12 (85.7)        2 (14.3)
Optic nerve hypoplasia           7 (53.8)        6 (46.2)
Sequelae to brain disorders      0              13 (100)
Congenital cataract              8 (66.7)        4 (33.3)
Congenital glaucoma              7 (58.3)        5 (41.7)
Retinoblastoma                  12 (100)         0
Optic nerve atrophy              4 (40.0)        6 (60.0)
Congenital anophthalmos          5 (55.6)        4 (44.4)
Brain tumor                      5 (62.5)        3 (37.5)
Microphthalmos                   6 (75.0)        2 (25.0)
Total                          103 (55.7)       82 (44.3)

(a) Missing data for reading media for one student who was
diagnosed with retinopathy of prematurity and did not follow the
age level in mathematics.
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