Cognitive Development and Language Case Studies

Case Studies 94) Trip, a seventh-grader, is having difficulty learning principles of fractions, such as two out of five is 2/5, 3/5 is less than 2/3, and so on. While his classmates seem to follow most of the examples given in class and in the textbook, Trip feels overwhelmed and confused by them. He is good at other subjects (such as reading and social studies) but is falling behind rapidly in mathematics. Being familiar with Piaget's stages of development, you suspect that Trip is very concrete in his thinking about mathematical principles compared to many of his classmates. A) Based on the above assessment of Trip's situation, what teaching approaches would Piaget's ideas suggest for making the principles of fractions more understandable to Trip? Answer: The teacher will want to provide Trip with hands-on learning experiences. For example, the teacher could give Trip two apples to cut into pieces. Trip could cut one apple into five pieces and the other apple into three pieces. He could then compare the combined physical amount of two of the pieces from the five-piece cut apple to two of the pieces from the three-piece cut apple. B) If Trip is a concrete thinker in mathematics, is he likely to think in similar ways in other subjects? Explain using appropriate ideas from Piaget and Vygotsky. Answer: According to Piagetian theory, Trip is also likely to think in concrete ways in other subject areas. For example, he may struggle with comparing the human brain to a computer. Neo-Piagetians, however, believe Trip may show general patterns of concrete thinking and yet be able to use some more advanced schemas within a particular domain. Trip may reason differently about social situations and numerical concepts. From Vygotsky's perspective, the teacher would want to consider Trip's sociocultural factors, such as how language is used, rather than focusing on whether or not Trip had surpassed a specific stage. 95) Mason is another seventh grader who is having difficulty in math class. He stares blankly at the test paper asking him to compute fractions such as 5/7 and 9/12 as percentages. He can't remember at all how to determine whether 4/5 is larger or smaller than 5/8, so he makes a guess. He hopes that, with some luck, he might manage in the class. On the weekend, Mason is watching his favorite sport, basketball. He remarks to his sister, "Oh, this guy made eight out of 11 shots last week; he's close to an 80 percent shooter so he should be for these free throws." After the player makes both shots, Mason looks down at the statistics sheet he's been keeping on the local teams' shooting percentages, and updates the statistics. A) Is the inconsistency between Mason's performances on school test problems and in working with basketball statistics a problem for Piaget's stage theory? That is, if Mason is at a particular stage of reasoning, shouldn't he be able to deal with the school problems as successfully as the basketball ones? Explain. Answer: The inconsistency noted in this case study is not a problem for Piaget's theory. According to Piaget, experience and interest can affect the stage one can reach. Mason should be able to solve the school-based math problems equally as well as the basketball ones. The teacher may need to help Mason see the connection between the two situations. Also, Mason's interest is likely to be influenced by the extent to which the student can move beyond rote memorization of mathematical principles. The teacher may want to introduce a math game to facilitate interest. Also, it is important for the teacher to explain why it is important for students to have an understanding of fractions and percentages in our society. Page Ref: 41 B) How might Vygotsky explain the role of other people in shaping Mason's math skills in the two contexts? Explain. Answer: First, the teacher may want to look at the statistics sheet Mason created. This sheet is viewed as a cultural tool and it would be important to find out if Mason shares the sheet with any other persons. For instance, what do the headings on the columns for the data communicate to others? In addition, from Vygotsky's perspective it would be important to know if Mason typically watches basketball alone or with his brother who is four years older. It may be that his brother is providing scaffolding (cues, encouragement) to Mason as they watch the game together. Page Ref: 42-44, 46 C) Knowing Mason's behaviors, how might a teacher work with him to improve his performances on the fractions and percentages unit? Answer: The teacher may want to integrate a physical education unit on basketball with a mathematics lesson. Mason would get the concrete experience recommended by Piaget. He would also be involved in a highly social activity, which would be supported by both Piaget and Vygotsky's theories. The basketball team could be instructed to plan and monitor their basketball activities in order to solve the math problem. Page Ref: 37, 43, 48