Keywords

6.1 Vision and Reading

When people think about vision, especially in children, they tend to consider glasses or contact lenses as a first solution – images seem blurry, so better focus should help. Yet there are many reasons vision might not be optimal besides poor focus. Disease, accidents, and genetic factors can all affect the eyes and brain.

Binocularity is one particular aspect of how we process visual information – we have two eyes, each of which presents a slightly different image to the visual cortex, where perception begins. The eyes only “see” because they are connected to the brain. If the two eyes are not well coordinated – if the person’s ability to converge or diverge them in order to take in images from different depths in the world, for example, then perception can be inaccurate or misleading.

Figure 6.1 shows eye movement recordings [8] from two students with very different eye coordination skills. The lines of text being read are on the left; time goes downward. The left trace is from a 14-year-old student (GAR39 59) who exhibits poor vergence control, indicated by the lack of parallel tracking with constant vergence – the eyes drift together and apart. This student’s reading efficiency is that of a 3rd grader, even though she is in 8th grade.

Fig. 6.1
A set of 2 illustration of visa graph of two students eye. Both exhibit two zigzag vertical lines. The unequal gaps for third grade and equal gaps for twelfth grade between the two lines.

Visagraph [8] traces of two students’ eye movements while reading

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The trace on the right is from a different 14-year-old student (GAR28 48) in 8th grade whose reading efficiency is at 12th grade level. The recordings on the right illustrate excellent control, in that both eyes are moving across a line of text from left to right sides of the passage, and then resetting to the beginning of the next line in one smooth movement. The traces are parallel – meaning that the eyes are maintaining a relatively constant convergence and are well coordinated in their movements.

The trace on the left in Fig. 6.1 shows a student who reads 5 grade levels below norms for her grade level because of potentially correctable vision problems, not because of cognitive difficulties. The traced eye movements show they are not coordinated; there are large changes in convergence, which means that the two eyes are not seeing two matched images. At one point they even cross over each other.

One outcome of the kind of poor eye coordination shown on the left in Fig. 6.1 is blurring. When children complain of blurred images even after obtaining corrective lenses, the kind of binocular weakness as demonstrated here can be a cause. Powers and colleagues have shown, using quantitative optometric measures of vergence, accommodation (focusing with the two eyes together), and saccadic tracking [10, 21], that poor visual skills are associated with poor reading outcomes as measured in school-administered tests [22].

6.2 Diagnosing Binocular Vision Problems

In 2003, Borsting and colleagues [5] reported the development of a 15-item Convergence Insufficiency Symptom Survey (the “CISS”) intended for children between 9 and 18 years of age (Table 6.1). The items describing the symptoms are read to the subject, who indicates the frequency of occurrence on a scale of 0–4, with 0 representing “Never” and 4 being “Always.” Total scores can range from 0 to 60. Borsting et al. [5] established a statistical cutoff from their data, with a score of 16 or higher representing children who exhibited signs of convergence problems from optometric measurements. Those with a score of 15 or lower did not.

Table 6.1 Convergence insufficiency symptom survey item content
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Borsting’s group later repeated their study with the CISS instrument on adults, and found a higher score was more appropriate to distinguish those with and without convergence insufficiency [24]. Since that time, several groups have found that the survey can also identify accommodation issues (e.g., [15]) which relate to binocularity in that the eyes need to focus on the plane of the object being viewed to see it clearly, via accommodative movements of the intra-ocular lens.

In the field of outcome measurement, professional concern for patient satisfaction has given way to devising means to improve patient involvement [4]. Analysis of patient satisfaction surveys revealed that those who are more involved with their care have better outcomes. Thus, patient participation in and engagement with their care have become a focus of efforts in research and practice. In the context of our work, the student is the “patient,” so involvement of family member(s) becomes essential [6]. This concern will be taken up in subsequent research building out deepening engagement in relationships along the continuum from informing to consulting to involving to collaborating to empowering [7, 11, 13]. The state of practice concerning binocular deficiencies remains at the level of the need to ensure students and families are informed about their effects on learning outcomes. General public awareness of children’s difficulties with eye coordination remains low. Much more must be accomplished to boost knowledge and awareness before any true involvement can be designed or expected.

During a study on the relation between visual skills such as vergence, accommodation, and tracking ability and reading outcomes in Los Angeles Unified School District (LAUSD) the first author obtained a large dataset with symptom scores and optometric values on the same individual students in the age range specified by the CISS; some were longitudinal, before, during, and after an intervention designed to improve binocular function. The second author suggested this might be a rich dataset for beginning a search for a unified Functional Binocular Vision (FBV) variable – a potentially one-dimensional construct around which a more inclusive and comprehensive battery of vision, survey, and assessment instruments might be designed, with the aim of providing practitioners a better indication of how binocular vision issues affect their students or patients.

6.3 Defining Functional Binocular Vision (FBV)

The optometric variables numbered about 30, all recorded at school during specified testing sessions, after permission from parents was obtained. Examples of measurements taken are:

  1. 1.

    visual acuity measured in each eye separately with the Snellen eye chart placed 20 feet away from the student,

  2. 2.

    the ability to rapidly re-focus the eyes from distances across the room to a book,

  3. 3.

    near point of convergence,

  4. 4.

    vergence ranges and ability to change vergence,

  5. 5.

    tracking ability, and

  6. 6.

    resting eye alignment.

For purposes of analysis, there were 4 items concerning basic optometrics (measuring acuity and ocular balance; both static variables) 7 items addressing vergence (measuring different attributes of dynamic convergence and divergence ability), 4 items for accommodation (different attributes of focusing ability, also a dynamic variable), and the CISS’s 15 items concerning symptoms (measuring discomfort and visual symptoms while reading). Clinicians currently select a subset of these variables to determine whether a patient has binocular vision problems, doing so in the absence of any substantive model of the multidimensional phenomenon. We wanted to simplify that task, estimate the model parameters, and perhaps improve diagnostic accuracy, for clinicians and also for testing in schools. Frequencies of the optometric measures were used to assign arrays of ratings in accord with the clinical inferences typically made concerning FBV. Data were fit to a probabilistic model formulated separately for each of the two visual dimensions and one survey dimension measured.

6.4 Methods

After administering the CISS in four elementary schools in LAUSD to 1062 students ages 8 through 11, those with scores greater than 15 were identified for inclusion in the training vision skills study, as this is the criterion indicating convergence problems. Sample size was thus reduced to 418. An FBV scale of 13 items and an acuity scale of eight items were then organized from optometric variables measured for 312 cases overall. The 312 students’ repeated training sessions produced a grand total of 4064 individual measurements. Because students varied in the numbers of training sessions they experienced, data from the earliest available and latest available measurements were grouped for the comparisons shown here. In the end, statistical comparisons focused on 76 students with visual skill problems upon assessment who received visual skills training via computer over a period of several months.

Training sessions offered five computerized modules (listed in Table 6.2); the number administered to individual students ranged from one to five across as many as 50 sessions, though most had between 10 and 40. Modules were always administered in the same order. Ten total items were tracked across the five modules, with four to seven included in any given module (see Table 6.3). Time data were recorded in seconds, hit percentages as fractions to four decimal places, and as other kinds of computed scores occurring in various numeric ranges. Applying methods also used in the measurement of chronic disease conditions in clinical chemistry [9], each distribution was divided into eight ranges and 1–8 ratings were assigned, where 1 indicated the worst possible performance, and 8, the best. One item’s highest range was between 0.99990 and 1.00000; because scoring was limited to four decimal places and no distinctions could be made, these were scored 7.

Table 6.2 Module descriptions
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Table 6.3 Items by module
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Left and right visual acuity optometry measurements were each scored in four categories, with worst at 1 and best at 4. Another six dichotomous items indicated whether or not the student had ever had eye surgery, had ever been diagnosed as needing prescription lens glasses, owned prescription lens glasses, had them with them, wore them in class, was wearing them at this moment.

Individual response data from the reading assessments were not available, so reading scores were incorporated in comparisons as received, with no scaling model applied.

6.5 Measurement Models

The FBV, Acuity, and visual symptoms constructs were each modeled as independent structurally invariant dimensions [23, 27, 28]). The physical and psychological constructs are conceptualized within a common mathematical frame of reference as being measured in interval units offering the potential for metrologically traceable quality assurance standards [14, 16, 17]. The FBV, Acuity, and CISS instruments were then scaled separately, applying rating scale models [2, 3, 29] using the Winsteps software [12], and then were combined in a regression model to predict reading scores.

6.6 Overall Scaling Results

Table 6.4 shows the summary statistics from the separate scaling analyses of the ten-item FBV, eight-item acuity, and 15-item CISS scales for the total samples from which the 312 cases were drawn. The 76 cases in the contrasting Effective and Ineffective groups were then selected from that subset of 312.

Table 6.4 FBV, Acuity, and CISS scale student measurement summary statistics
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Table 6.5 shows the summary item statistics for each scale. The original five categories for CISS ratings were reduced to three by combining Infrequently with Sometimes, and Often with Always, in order to align higher ratings with higher measurements. After this rescoring, measurements were associated with the expected Never, Infrequently/Sometimes, and Often/Always categories for 75%, 56%, and 67% of the responses, respectively, and the observed categories were associated with the expected measurement ranges for 63%, 77%, and 25%, respectively.

Table 6.5 FBV, Acuity, and CISS scale calibration summary statistics
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Figure 6.2 gives the sample sizes for training sessions completed by our subjects. Note that each module is reported separately. Modules addressed: (1) accommodation facility, (2) smooth tracking, (3) saccadic tracking, (4) convergence, and (5) divergence. The numbers of computerized training sessions were aggregated into 1–7, 8–12, 13–19, and 20 or more for the purposes of later regression analysis. The number of measures summarized ranged from about 150 to 260, with about 750 to 1250 measures within a session group.

Fig. 6.2
A bar graph of count versus module. Values are estimated for session 1 through 7, sessions 8 through 12, sessions 13 through 19, and sessions 20 plus. The bar is high for session 20 plus in 1 module.

Sample sizes by number of sessions per module

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6.7 Changes in FBV with Intervention

The purpose of the study Powers [10, 18, 21, 22] conducted in the Los Angeles schools was to see whether reading fluency scores would improve with systematic intervention by a visual skills training procedure in class. Thus, the data set also contained multiple measurements of all variables repeated several times during the intervention. Though the number of students for whom data were available was limited (N = 76), the trends are encouraging [19, 20].

For about half of the students, training was defined as “Effective,” meaning that they had become proficient in at least four of the five visual skill training modules offered (n = 37). For the remainder (n = 39), training was “Ineffective,” meaning that they did not attain proficiency.

Figure 6.3 shows paired t-test results for three measures: symptoms (earlier to later CISS scores), scaled optometric variables (items like vergence, accommodation, and tracking) and visual acuity (from eye chart measurements) after the third measurement, comparing the Effective treatment vs Ineffective treatment groups. Results for Ineffective Training (top three rows in Fig. 6.3), where students did not complete training or did not attain a level of competency, demonstrate no significant improvements; in fact, both optometric values and acuity got worse. In contrast, the results for Effective Treatment (bottom three rows in Fig. 6.3), categorized by completion of the program with high levels of skill achieved, did show improvement. Training improved both symptom scores and optometric scores, while not affecting acuity.

Fig. 6.3
A tabular format of paired sample tests. The columns are mean, S D, S E mean, 95 percent C I upper and lower, d f, s i g. The rows are an ineffective and effective treatment.

Paired t- test results of differences between measures earlier vs. later in visual skill training

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We were interested in how FBV-related variables changed over time as well as any changes in acuity. Eyechart acuity was not expected to change with an intervention that did not attempt to address acuity. The computer program only presented easily detectable targets, well above acuity thresholds, and emphasized the ability to use visual skills like vergence and accommodation- not acuity.

Figure 6.4 is a graph of the data in Fig. 6.3, showing how the mean changed with training for Effective and Ineffective groups. It shows that CISS measurements – where lower is better – declined after intervention. The optometric variables related to binocularity improved after intervention, and visual acuity showed no change- and perhaps worsened over the time period reported.

Fig. 6.4
A bar graph of mean versus effective and ineffective treatment. Bars of Optom and V A change 03 lie under ineffective treatment and of C I S S, Optom, and V A change 03 under effective treatment.

Summary results of Fig. 6.3, showing marked improvement in symptoms (fewer after Effective training) and optometric values (better after training)

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We concluded at this point that:

  • FBV is a uniform variable construct.

  • Interventions designed to affect FBV do indeed improve the targeted optometric and symptom responses, but not visual acuity, which was not targeted.

  • Scaling variables that have been measured accurately so they can be compared on a common scale allows insights into relationship and mechanisms that would otherwise remain obscure.

6.8 Relationship of FBV to Reading in School Children

One of the goals of our collaboration is to produce a measure of binocular function that relates to reading in school children. FBV appears to do so, at least for this dataset.

The eye movement tracings in Fig. 6.1 are similar to the post-training measurements shown in Table 6.6. Comparing the two, we see that student GAR20 48 had a better outcome in the training measure than student GAR39 59. Similarly, the FBV measure was higher for the good eye movement trace. Students with poor traces scored lower on the reading measure and higher on the symptom measure, but did not differ on the acuity measure from students with good traces.

Table 6.6 Post-training measurements associated with the Fig. 6.1 eye movement recordings
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6.8.1 FBV Measurements Predict Reading Outcomes

Figure 6.5 shows the regression of sustained oral reading scores on FBV measures for a subset of the data in the larger study. The result yields an adjusted R2 of 0.61, which is highly significant. We can thus conclude that the measures selected to represent FBV (symptoms and optometric measures) are significantly related to this reading outcome measure.

Fig. 6.5
A scatterplot of reading fluency 1 b in logits versus regression standardized predicted value. A regression line arises at 1.75 and passes through point A N N 2918. The line reads R square equals 0.680.

Linear regression of scaled reading fluency (1-min sustained test a grade level) against the FBV symptoms and optometrics variables was significant: R = .825, R2 = .68, adj R2 = .61. SE = .6, F change = 9.56, 4 df1, 18 df2, p < .0001. Each point is a subject, N = 23

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Figure 6.6 shows what happened when visual acuity measurements – which did not change significantly with the intervention – were entered into the regression equation along with FBV measures. Although the regression is still significant, the fit is not better: adjusted R2 is 0.44, with p = 0.032. Thus, visual acuity (a measure of how clear the image appears in each eye individually) contributes less to the change in reading than FBV measures.

Fig. 6.6
A scatterplot titled the dependent variable, reading fluency 1 b plots reading fluency 1 b versus regression standardized predicted value. A regression line passes through point A N N 1267.

Regression is not as predictive of reading fluency when acuity enters the equation. Plotted are the same FBV variables plus changes in visual acuity. The result is barely significant at the p < .05 level, but the relationship is weaker with acuity included: R = .767, R2 = .589, adj. R2 = .44; SE = .74, F change = 3.94, 4 df1, 11 df2, p = .032. N for this comparison is 16 because not all students had complete data

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Thus, even though testing visual acuity is important for determining referrals for eye disease or optical needs, it cannot identify problems of eye coordination. This is illustrated in the multidimensional framework sketched in the association of Fig. 6.1 and Table 6.6.

6.9 Limitations

There are some caveats to the interpretation of our results. First among these is that none of the instruments involved were designed with the intention of calibrating interval measurements of FBV. The analyses reported are intended only to provide a basis for learning from the existing data so as to proceed toward improved research designs in the future.

More specifically, the original study was not designed to define FBV in terms of mathematical modeling, so there was no intention to try to gauge the effect of changes in the FBV construct on reading performance. The data were collected during a study designed to see whether training in visual skills such as vergence could improve reading. The individual variables, time points measured, and completeness of each students’ data set are limited, therefore, in ways that would not have been allowed in an intentionally designed calibration study.

Also, the N in the regression with acuity is smaller than the N in the regression without acuity. Part of the loss of significance can thus probably be attributed to a loss of power. The fact that acuity did not change when the other measures did, as expected, is probably also relevant.

6.10 Conclusions and Future Directions

  1. 1.

    Functional Binocular Vision (FBV) is a unidimensional construct made up of several measures, including a symptom survey and optometric measurements. It appears to be valid and measurable.

  2. 2.

    More work is needed to determine FBV’s reliability and its most meaningful components. However our findings with predicting reading scores suggest that acuity is not related to FBV or on its effects on measures of sustained reading fluency.

  3. 3.

    FBV components are symptoms and optometric measures such as ability to rapidly re-focus the eyes and move them toward and away from the nose in vergence movements. These abilities are reflected in eye movement recordings for good and poor readers, but FBV’s demonstrated relationship to fluency suggests other, less invasive measures may help us develop more meaningful testing of vision in our schools.

  4. 4.

    The rating scale models applied in this study can in principle be expanded to incorporate all four constructs in a multidimensional model [1] that leverage the information in the cross-dimensional correlations to improve uncertainty estimation. We are working toward a user-friendly multidimensional tool for evaluating functional vision. This tool would account for the various aspects of functional binocular vision represented by optometric physics, diagnostic survey data, and reading performance assessments.

This kind of modeling appears to offer a viable approach to establishing person-centered standards for FBV measures, like those that currently exist for acuity. The Snellen [25] eye chart and its derivatives are the gold standard for measuring subjective acuity, which relates to the need for glasses but says nothing as to how well the eyes move. Our goal is to create a model that assesses visual skills with sensitivity and specificity as fit for the purposes of diagnosis and treatment of FBV issues as the Snellen eye chart is for acuity [26]. Such a model and associated measurement standards could be used in conjunction with acuity standards to provide better, more comprehensive, and useful vision testing in children and adults.