# Case Study - Can Holding a Student Back a Grade be Beneficial or Hurt in the Long Run?

Case Study

Pertinent Information

Student 1 is a six-year-old, Caucasian male who comes from an upper-middle class family in Charlotte, North Carolina. He is the youngest of three boys in his family. Student 1 has just turned six, as the day of this clinical interview was also his birthday. His mother decided to hold Student 1 out of school last year, so he has just entered kindergarten this fall. The extra year in pre-school seems to have put Student 1 in a good position to excel in school this year, as he is quite intelligent and mature for his age and grade level. Student 1’s physical development is also above the mean for his age and gender, according to the National Center for Health Statistics and National Center for Chronic Disease (chart included). Student 1’s height (48 inches) places him within the 95th percentile; his weight (53 lbs.) places him within the 90th percentile. Overall, he seems to be a healthy, happy, well-adjusted kindergartner.

Cognitive Development

Task 1 – Conservation of Discontinuous Quantity

Student 1 easily identified the two rows of eight quarters I placed in front of him and told me that the quarters were “twenty-five cents each.” His initial response when I asked him to ascertain the equality of number of quarters in each row was that they were the indeed the same amount because they “were in the same line.” This initially led me to predict that Student 1 would be at the pre-operational level of cognitive operations, because his comment reflected “seeing is believing.” However, when I asked him to explain to me how he knew for sure that there was the same amount of quarters in each row, he proceeded to count each row accurately and told me, “there’s eight and eight is an even number!” showing his ability to quantify. Even after I spread out the quarters in one row, put them back to even, and then condensed the quarters in the other row, Student 1 was able to very surely state that each row still contained the same amount of quarters. I asked him how he knew this without physically counting the rows each time, and his response was that he saw me “switch them” but knew they were still the same amount. Student 1’s comments show reversibility in his logico-mathematical mental operations and that he could conserve a discontinuous quantity – despite the irrelevant perceptual changes in row length and spacing. His understanding of this task indicated that he is at the concrete operational stage of cognitive development.

Task 2 – Conservation of a Continuous Quantity

This task presented more of a challenge to Student 1 than the previous task. After each manipulation of the liquid in bottles, he would initially state what he saw – and then self-correct after further questioning. Student 1 initially had no difficulty determining the equality of liquid in two identical bottles because they water level was at the same part of the bottle in each. After watching me transfer the liquid from one of the bottles into a taller bottle of smaller circumference, Student 1 initially said the two bottles did not contain the same amount of liquid because the water level was higher in one. After further questioning, Student 1 corrected his assessment and compensated that they did still contain the same amount because the taller bottle was “skinnier” and had “lines” (referring to the indents that circled the bottle and displaced water) which made the water level appear higher. After returning the water to the identical bottle, then pouring it into four separate, smaller bottles, Student 1’s initial reaction was that they weren’t equal because the water level was lower in the smaller bottles. When I asked Student 1 to further compare the amount of water in the one larger bottle to the amount of water in the smaller bottles, he corrected himself. He concluded that they were in fact equal amounts because he had watched me pour it from the same identical sized bottle – demonstrating reversibility in his mental operations. I concluded that Student 1’s final responses to each of the manipulations indicate that he is in the concrete operational stage of cognitive development.