Chapter 2: Cognitive Development and Language

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.

1. 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?

2. 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’s and Vygotsky’s theories.

3. How might Vygotsky explain the role of other people in Trip’s learning of math? Explain using the concepts of “scaffolding” and “zone of proximal development”.

4. How did your reflections on this case study prepare you to become more responsibly engaged in the world?