Show What You Know - Ch 6

The results presented in this chapter brought to light the reality that the traditional teaching methods employed by the mathematics teachers at Amber Hill proved to be of disservice to the students when the time came to show what they know.....which in fact was very little. Students demonstrated that they actually understood very little of what they had covered in math lessons and heavily relied on memory and on obscure cueing systems to help them to figure out the answers to both procedural and conceptual problems. When memory and cueing systems failed them students had no idea how to go about solving the problems, no idea how to make sense of it on their own, and in many cases couldn’t even make sense of what the question was asking.



On the flip side of this coin, students at Phoenix Park had been exposed to a dramatically different teaching method, one which relied heavily on students own understanding of topics and their own creation of knowledge. It may appear that some students were disadvantaged in that they hadn’t been exposed to some mathematical formulas or “rules” and many did not have calculators to complete the exam, however, they were prepared to face the exam with a much more powerful and useful tool than a calculator or list of disconnected and misunderstood rules. These students were prepared to approach problems without fear, they were willing to take risks, and they were willing to THINK! Phoenix Park students had experienced a type of mathematics in which the first answer wasn’t always the right answer, in which the right answer wasn’t necessarily one that could be found in 2 or 3 minutes. Though they may not have had “practiced” numerous examples in preparation for the GCSE’s, the problems they had worked on all year had provided them with practice in thinking, in understanding, in being creative and in finding a way to solve problems that makes sense to them. They had become more skilled at thinking about the math than in thinking about the answer.


How wonderful it would be if we could prepare our students to face exams such as Publics, common finals and CRT’s with the same approach as the teachers at Phoenix Park, if we could in effect stop teaching to the test and start teaching to the students. Meeting the students where they are instead of dragging them to where we want them to be, using their existing knowledge as the basis for future knowledge and having them really understand the math as opposed to sort of remembering it (because we know they don’t remember it for very long.) What would it take to get to this point? Time, resources and a willingness to step back and evaluate our own instructional methods, our own ideas about what good math teaching looks like, a willingness on our part to accept change and make change.


Melanie