Are visual perceptual skills related to mathematics ability in second through sixth grade children?

Abstract

Controversy exists regarding the relation between visual perceptual ability and mathematics. The purpose of this study was to investigate whether or not poor mathematics achievement was related to performance on tests of visual discrimination and visual memory. A masked investigation of visual perception and academics in 171 second through sixth grade children (mean age = 10.08 years) from a middle class, primarily white, elementary school near Columbus, Ohio was performed. Visual perceptual skills were assessed using the VMI Supplemental Developmental Test of Visual Perception (VP) and a new test of Visual Memory. The California Achievement Test-5 (CAT) and the Test of Cognitive Skills-2 were administered by the school and the scores were used as measures of mathematics achievement and cognitive ability, respectively. Age and verbal ability were controlled in all regression analyses. Logistic regressions revealed that poor visual perceptual skill was significantly related to poor mathematics ability (Visual Memory (aOR = 0.855, p = 0.039) and Visual Perception (aOR = 0.971, p = 0.048)). However, a logistic analysis that included both visual perceptual areas, revealed a significant relation for only the new test of Visual Memory (p = 0.039). Poor visual perceptual ability should be considered to be amongst the skills significantly related to poor mathematics achievement.

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Introduction

Visual perception refers to the process of interpreting and organizing visual information (Kavale, 1982). Visual perceptual skill is often subdivided into areas such as visual discrimination and visual memory. Visual discrimination involves the ability to attend to and identify a figure's distinguishing features and details, such as shape, orientation, color and size. Visual memory refers to the ability to remember a visual image.

It is reasonable to think that a relation may exist between visual perceptual skill and mathematical ability. For example, good visual discrimination/analysis skills could assist children in discriminating between numbers, differentiating between arithmetic signs, and breaking down problems into manageable components. In addition, good visual discrimination and visual memory skills would be helpful when spatially organizing calculations or solving geometry and word problems. Furthermore, good visual memory skills could also be instrumental when learning multiplication tables, retaining what has been read in a word problem, and copying assignments from the board to the paper. In another light, while simultaneous visual processing skills should be helpful when solving geometry problems that must be solved by looking at the problem as a whole, sequential visual processing skills should be instrumental when solving word problems and organizing calculations that must be solved in a sequential fashion. In fact, a significant relationship between visual perceptual skill and mathematics abilities has been previously reported (Kulp, 1999; Solan, 1987). Furthermore, even authors who have expressed a difference of opinion have reported a difference in visual perceptual skill between good and poor readers (e.g., on a test which involved copying geometric figures, a "draw a bicycle" test (p < 0.0001), and the "draw a clock" test) (Helveston et al., 1985; Solan, 1988; Stolzberg, 1986). In addition, several studies have shown that deficits in visual perceptual skill can be remediated with therapy (Halliwell & Solan, 1972; Rosner & Rosner, 1986; Seiderman, 1980; Solan & Ciner, 1989; Streff, Poynter, Jinks, & Wolff, 1990). Unlike previous work, which has largely been correlational, the current study was designed to determine whether or not performance on tests of visual perception could predict the children with poor current achievement in mathematics.

Therefore, this was a masked investigation of the ability of visual discrimination and visual memory scores to predict currently reduced mathematics achievement. Controls for age and verbal cognitive ability were included in all regression analyses because the failure to control for cognitive ability has been a criticism of some literature investigating the relation between visual and academic skills.

Research Design and Methods

Subjects and Inclusion/Exclusion Criteria 

All children in 2nd, 4th and 6th grade (mean age = 10.08 years) from a middle class, primarily white, elementary school near Columbus, Ohio were invited to participate in the study. Children were administered a Modified Clinical Technique vision screening which includes an assessment of clarity of vision, refractive error (e.g. nearsightedness or farsightedness), ocular coordination (how the eyes work together as a team), and eye health. The Modified Clinical Technique and its associated referral criteria were chosen because of their high efficacy and efficiency (Blum, Peters, & Bettman, 1959). Informed consent was obtained prior to participation in the study.

Mathematics/Cognitive Ability

The school administered the California Achievement Test-5 (CAT) and the associated Test of Cognitive Skills-2 and the resultant scores were used as measures of mathematics achievement (total math) and cognitive ability, respectively.

Visual Perceptual Testing

Tests of visual discrimination/visual spatial skill and visual memory were administered by clinicians masked to the results of the achievement and cognitive testing. A new visual memory test was developed because no commercially available test possessed the desired characteristics.

[FIGURE 1 OMITTED]

Visual Memory

The Visual Memory figure test contains figures selected for their difficulty to be verbalized in order to promote the use of visual rather than auditory memory to recall the figure (See Figure 1). Demonstration items are administered prior to beginning the test to ensure the child's understanding of the task. The test includes 27 items, from two to nine figures in length. The basal item is three figures in length. The child is asked to look at the figures and try to remember the order in which they are presented. Each item is presented to the child for five seconds and then removed. The child is then given chips with the figures printed on them and asked to place the chips in the correct order. Children are presented the chips in a uniform manner. Children are given a second attempt on each sequence if needed. Two points are scored for a correct response on the first attempt and one point is scored for a correct response on the second attempt. Testing is discontinued after four consecutive errors. Reliability of the new test will be discussed in a future publication.

Visual Discrimination/Visual Analysis

Visual Discrimination/Visual Analysis ability was evaluated with the Beery-Buktenica Supplemental Test of Visual Perception because it is a standardized, motor-reduced test of visual spatial/visual discrimination skill. The VMI has an objective scoring system and has been shown to be valid and reliable (Demsky, Carone, Burns, & Sellers, 2000; Wesson & Kispert, 1986; Spreen & Strauss, 1998; Beery, 1997; Preda, 1997).

Statistical Analysis

Statistical analyses were performed using SPSS base 10.0. Descriptive data were determined for performances on each visual perceptual test. One-way ANOVA was performed to determined whether a significant age effect was present. Two sample t-tests were performed to determine whether or not any significant difference was present in the mean performances on visual perceptual or mathematics testing of children who passed or failed the Modified Clinical Technique (MCT) vision screening. Two sample t-tests were also performed to investigate whether or not any differences in visual perceptual ability existed between males and females. Because the test of visual memory was a newly developed test, its validity as a test of nonverbal ability was assessed by performing a multiple linear regression controlling for age and verbal ability to determine whether it was significantly predictive of nonverbal ability (as measured by the Cognitive Skills test).

Multiple linear regressions were also performed to determine the relation between mathematics achievement and visual perceptual ability. In order to determine whether or not visual perception was predictive of reduced mathematics ability, logistic analysis was performed. The dependent variable was based upon total math percentile on the California Achievement Test, with scores below the thirty-fifth percentile classified as reduced performance (the scores in the lowest 8 percent of this population). Independent variables in these analyses included Cognitive Skills test verbal ability percentile score, age and the tests of visual perceptual skills. Adjusted odds ratios (aOR) are reported for each visual perceptual test. After performing analyses of the ability of each test to predict achievement in mathematics alone, a multivariable model was employed to understand how the two measures of visual perceptual skills performed as a set. Controls for age and verbal cognitive ability were included in all regression analyses. A significance level of 0.05 was used for all analyses.

Results

One hundred seventy-one children participated in the study. All of the children were able to complete all of the testing (MCT vision screening and visual perceptual testing). Forty-seven children were found to have a vision problem or a potential vision problem on the vision screening (e.g. nearsightedness). Independent sample t-tests revealed no significant difference in the mean mathematics or visual perceptual test scores of children according to performance on the MCT (i.e., pass vs. fail) (mathematics: p = 0.782; visual memory: p = 0.191; visual perception: p = 0.901). Therefore, all children were included in the analysis. Descriptive data were calculated for each test of visual perception (see Table 1).

No significant difference in visual perception was found between males and females (visual memory: p = 0.157: visual perception: p = 0.598).

ANOVA was performed to determine whether a significant age effect was present for performance on the tests of Visual Memory and Visual Perception. Analysis revealed that scores significantly increased with age on each test (Visual Memory: p < 0.001; Visual Perception: p < 0.001).

Linear regressions controlling for age and verbal ability revealed that the new test of visual memory was significantly related to nonverbal ability (p < 0.001) which supports its validity.

Linear regressions controlling for age and verbal ability also revealed a significant relation between mathematics achievement and visual perception and visual memory (p = 0.011 and 0.001, respectively). Logistic analyses were performed to determine whether visual perceptual ability was predictive of poor current achievement in mathematics. Thirteen children were classified as having reduced achievement in mathematics (children in the lowest 8 percent of this population, mean score [+ or -] standard division = 20th percentile [+ or -] 12). Logistic regressions controlling for age and verbal ability showed that each additional point on the visual memory test decreased the odds of reduced mathematics performance by 15% (aOR = 0.85, p = 0.039, 1-0.85 = .15). In addition, it was found that each additional percentile point on the Visual Perception Test decreased the odds of reduced mathematics performance by 3% (aOR = 0.97, p = 0.048, 1-0.97 = 0.03) (See Table 2).

When both measures of visual perceptual skill were included in a multivariable model, Visual Perception was no longer significantly associated with mathematics performance (p = 0.122).

Discussion

Logistic regressions controlling for age and verbal ability showed that increasing visual perceptual scores were significantly associated with lower odds of poor current achievement in mathematics (Visual Memory (aOR = 0.855, p = 0.039) and Visual Perception (aOR = 0.971, p = 0.048)). Therefore, this study supports previous reports of a significant relation between visual perceptual and mathematical ability (Kulp, 1999; Solan, 1987). In addition, although it has been argued that reports of a relation between visual perception and achievement are merely due to the confounding effects of cognitive ability/intelligence, this study supports previous research showing that these associations are maintained after controlling for verbal cognitive ability/intelligence (Kulp, 1999). Therefore, the significant relation between visual perception and achievement is not merely due to the fact that children who are more intelligent do better on tests in general.

When both visual perceptual scores were entered into one model, only performance on visual memory remained significant. This suggests that visual memory is the visual perceptual skill that is more foretelling of mathematics achievement in this age group. The test of Visual Memory requires children to view a sequence of figures and then reproduce it from memory. Therefore, children must process and retain spatial and sequential information. A required sub-skill for this task is the ability to attend to and identify each figure's distinguishing features and details. Thus, strong abilities in this area could be useful in discriminating between numbers, differentiating between arithmetic signs, breaking down problems into manageable components, spatially organizing calculations, solving geometry and word problems, and learning multiplication tables. The failure of the significant predictive value of the Visual Perception test to be maintained in the final model may be because some degree of visual discrimination skill is prerequisite to good visual memory skill.

This study also supports previous work that has shown no difference in visual perceptual ability between males and females in elementary school-aged children (Lord & Nicely, 1997). Furthermore, this study may offer an explanation for the finding that children who perform better on spatial perception also prefer learning about math (Lord & Nicely, 1997). Specifically, it could be theorized that children with better visual perceptual skills may be attracted to and prefer learning about math because good visual perceptual skills facilitate better performance in math.

Conclusion

Poor visual perceptual ability is significantly related to poor achievement in mathematics, even when controlling for verbal cognitive ability. Therefore, visual perceptual ability, and particularly visual memory, should be considered to be amongst the skills that are significantly related to mathematics achievement. Consequently, visual perceptual ability, and particularly visual memory skill, should be assessed in children with poor achievement in mathematics. Further research is needed to explore whether or not this relation is maintained across racial/ethnic/social economic status groups. Further research is also needed to determine the effect of the teacher's visual spatial/visual memory ability on instruction. Finally, further research is needed to explore the effects of combining instruction in visual perception (visual discrimination/visual spatial ability/visual memory) with direct instruction in mathematics.

Table 1 Descriptive Data for Visual Perceptual Test Results

                                         Maximum
                              Standard   Score
Test               N    Mean  Deviation  for Test

Visual Perception
  Grade 2           62  22.2  2.83
  Grade 4           56  23.9  2.34       27
  Grade 6           53  25.3  1.38
  Total Group      171  23.7  2.63
Visual Memory
  Grade 2           62  18.0  5.88
  Grade 4           56  23.4  6.45       54
  Grade 6           53  28.0  6.73
  Total Group      171  22.9  7.53

Table 2 Predictors of Mathematics Achievement Controlling for Age and
Verbal Ability

                                             95% CI for Odds Ratio
                                 Adjusted    lower  upper
Visual Perceptual Area  p value  Odds Ratio  bound  bound

Visual Memory           0.039    0.855       0.737  0.992
Visual Perception       0.048    0.971       0.942  1.000

Acknowledgements

The support of COVD, T35-EY07151, OLERF, EF Wildermuth Foundation grants, and NIH/NHLBI grant #K30 HL04162 is gratefully acknowledged.

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Marjean Taylor Kulp, Michael J. Earley, G. Lynn Mitchell, Lisa M. Timmerman, Cara S. Frasco, Meghan E. Geiger

The Ohio State University College of Optometry