Finding Out What They Could Do

This chapter in the book I found very interesting and to say the least, certain facts left me speechless. The fact the the amount of material that was retained after just 6 months, by Amber Hill students, was a mere 9%, was astonishing! Yet, having said that, I have had many situations where I will be in class and ask the students to recall information that has been previously taught to them, and an astonishing number of students will respond with, "we never learned that before miss!", yet I know they have, since I was the one who apparently taught them.

What this chapter seemed to present in a very clear and concise matter was that Amber Hill students, who were instructed in a traditional mathematics classroom, were pressured and driven by the GCSE, responded to questions in a cue-behaviour manner, had poor problem solving skills and used little to no thought process in answer questions, all of which lead to poor GCSE results and more importantly, little understanding and retention of mathematics. Again and again Jo Boaler makes the comment that the Amber Hill students had learned appropriate mathematics methods, but did not have the ability or skill necessary to apply the correct methods. This is something that I can relate to. Too often my students know their "mathematics", but do not know how to apply the mathematics to a given complex problem or real life situation. And this, the application of mathematics, is the most important and relevant function of teaching mathematics. If a person cannot apply the knowledge that they have acquired, then the knowledge is out of reach and for the most part, unless!

The Phoenix Park students, on the other hand, seem to be much better problem solvers, and seem to have the ability to apply the knowledge that they have acquired to novel situations. Also, the teaching and learning fashion of Phoenix Park, was not driven by the GCSE's. This seem to result in the students being better test takers! As contradictory as this may seem, considering that Amber Hill students should be use to taking test and should thus be accustomed to such environments as the GCSE's, unlike Phoenix Park students, the Phoenix Park students did not seem to get as frustrated and stressed out as the Amber Hill students if they faced a challenging or novel question. This I strongly believe is largely do to the fact that the GCSE's were not focused on and were not a huge deal for the Phoenix Park students. Thus, the stakes did not seem that high. This is the complete opposite situation for Amber Hill students. The other major factor in this, is that Phoenix Park students were use to dealing with novel problems, working through the problems themselves and use to applying all their math skills to any given situation, which the Amber Hill students were not. The Amber Hill students were not exposed to the connection and network of mathematics topics.

A few question that arose in my mind while reading through this chapter was, if the Phoenix Park students were being taught in a fashion (open-ended, reform) that the school and mathematics department thought was the best method to develop mathematical students, then why would they revert back to the traditional method of teaching mathematics the last few weeks before the GCSE in an attempt to fully and finally prepare the students for the exams???

Finally, a closing thought; The purpose of the GCSE is "to acquire skills, that they [students] are going to be able to use and apply in the rest of their lives, rather than to get some kind of body of knowledge", which to me seems to be in direct opposition of what the GCSE is actually testing! ............. Just a thought!
-