Amber Hill

After reading this chapter, I had the general thought that how these students were being taught is how I was taught, however, because of my learning style and personality (desire to succeed and persistent), I was successful.
I imagine that most classrooms still teach ion this fashion. We are beginning to move toward more exploration and explanation. For example, in my mathematics classes, one would regularly see students performing investigations (often with the aid of manipulatives) in an attempt to have students discover some mathematical concept. Also classroom discussions involve various students explaining how they arrived at an answer or concept in an attempt to have students realize that there is more than one way to arrive at an answer and also allowing students’ time to develop reasoning and communication skills.
Having said all of this, I still feel that if I were to ask my math students their views about the nature of mathematics, I am fairly certain that most of them would have the same basic beliefs as the students at Amber Hill:
- That math is about following rules
- That math is not about understanding and making sense
- That all math problems can be solved in a few short minutes

Also, to add to this, I have witnessed my students use cue-based behavior. They are not confident enough in themselves and in their understanding of mathematics. For example, when a student answered a question in class, I responded to the answer by simply saying “ok!” (I neither approved the answer nor disapproved the answer). The student immediately changed her answer, she was now unsure of the answer. The student was correct, however like most students, she fears being wrong and lacks confidence in math.
I think that these common beliefs in the nature of mathematics, that were evident in the Amber Hill students as well as my own students, are a result of the environment in which mathematics is taught and the way the mathematics is taught. Even with the minor changes that exist in some math classes today.