Chapter 7 - Exploring the Differences......

What stuck with me the most from this chapter was the false sense of success the Amber Hill students must have experienced in mathematics, particularly those in the higher sets. Students worked through the classroom assignments and textbook work with little difficulty, if they followed the steps and memorized the rules then surely they could do well in maths. However, when the time came for the GCSE’s and the questions were posed in an unfamiliar way, when cuing systems were removed and the math had to be applied as opposed to memorized the Amber Hill students found they were ill-prepared for the test. They realized that when their memory failed them they had little else to turn to; they had no real understanding of the math.

On the flip side of this coin we have the Phoenix Park students, while they may not have been prepared for the test entirely in that there were some topics that they had not encountered or been taught through their project work, these students still fared better in the GCSE’s because they could think about the math. These students could make the connections between mathematics and its real world applications. They did not rely on the cuing systems which Amber Hill students struggled without. They were more willing to try questions when the answer or method wasn’t instantly apparent.

Towards which end of this spectrum are our own students lying? Are they prepared for new and challenging tasks? Are they willing to take risks in mathematics to increase their understanding or are they reliant on us as teachers to provide them with the answers to “difficult questions”?

How often do we hear our colleagues talking about classes that just don’t “get it”, classes that don’t “know their basic facts”? Why is it that year after year we hear these same questions, even though we know that we have taught these skills and ideas? Amber Hill’s teachers were especially concerned with their students’ success, so much so that they provided all sorts of “helpful hints” to get them through the math, all sorts of rules that they “just had to remember” and we can see in the end how these students fared. Let’s set things up differently for our students, let’s encourage them to think, to make sense on their own and to truly understand the mathematics we are “teaching”.