examination is a three-hour, traditional test made up of short mathematics questions. Despite the difference in each school’s approach, the students’ last-minute preparation for the examination was fairly similar as both schools gave students past examination papers to work through and practice. At Phoenix Park the teachers stopped the project work a few weeks before the examination and focused upon teaching any standard methods that students may not have met. They spent more time lecturing from the board, and classrooms looked similar (briefly) to those at Amber Hill.
Many people expected the Amber Hill students to do well on the examinations, as their approach was meant to be examination oriented, but it was the Phoenix Park students who achieved significantly higher examination grades. The Phoenix Park students also achieved higher grades than the national average, despite having started their school at significantly lower levels than the national average. The examination success of the students at Phoenix Park surprised people in England and the research study was reported in all of the national newspapers. People believed that a project-based approach would result in great problem solvers, but they had not thought that an approach that was relaxed and project based with no “drill and practice” could also result in higher examination grades.
These were not quite the headlines I would have chosen, but the approach was gaining rightful attention.
The Amber Hill students faced many difficulties in the examination, which they were not expecting, as they had worked so hard in lessons. In class the Amber Hill students had always been shown methods and then practiced them. In the examination they needed to choose methods to use and many of them found that difficult. As Alan explained to me: “It’s stupid really, ’cause when you’re in the lesson, when you’re doing work—even when it’s hard—you get the odd one or two wrong, but most of them you get right and you think, ‘Well, when I go into the exam, I’m gonna get most of them right,’ ’cause you get all your chapters right. But you don’t.” Even in the examination questions when it was obvious which methods to use, the Amber Hill students would frequently confuse the steps they had learned. For example, when the Amber Hill students answered a question on simultaneous equations, they attempted to use the standard procedure they had been taught, but only 26percent of the students used the procedure correctly. The rest of the students used a confused and jumbled version of the procedure and received no credit for the question.
The Phoenix Park students had not met all of the methods they needed in the examination, but they had been taught to solve problems and they approached the examination questions in the same flexible way as they approached their projects—choosing, adapting, and applying the methods they had learned. I asked Angus whether he thought there were things in the exam that they hadn’t seen before. He thought for a while and said: “Well, sometimes I suppose they put it in a way which throws you. But if there’s stuff I actually haven’t done before, I’ll try and make as much sense of it as I can, try to understand it, and answer it as best as I can, and if it’s wrong, it’s wrong.”
The Phoenix Park students didn’t only do better on the examinations. As part of my research, I investigated the usefulness of the approach to students’ lives. One way I measured this was by giving a range of assessments to students over the three years that were designed to assess students’ use of mathematics in real-world situations. In the “architectural activity,” for example, students had to measure a model house, use a scale plan, estimate, and decide upon appropriate house dimensions. The Phoenix Park students outperformed the Amber Hill students on all of the different assessments. By the time I was completing the research,
Many people expected the Amber Hill students to do well on the examinations, as their approach was meant to be examination oriented, but it was the Phoenix Park students who achieved significantly higher examination grades. The Phoenix Park students also achieved higher grades than the national average, despite having started their school at significantly lower levels than the national average. The examination success of the students at Phoenix Park surprised people in England and the research study was reported in all of the national newspapers. People believed that a project-based approach would result in great problem solvers, but they had not thought that an approach that was relaxed and project based with no “drill and practice” could also result in higher examination grades.
These were not quite the headlines I would have chosen, but the approach was gaining rightful attention.
The Amber Hill students faced many difficulties in the examination, which they were not expecting, as they had worked so hard in lessons. In class the Amber Hill students had always been shown methods and then practiced them. In the examination they needed to choose methods to use and many of them found that difficult. As Alan explained to me: “It’s stupid really, ’cause when you’re in the lesson, when you’re doing work—even when it’s hard—you get the odd one or two wrong, but most of them you get right and you think, ‘Well, when I go into the exam, I’m gonna get most of them right,’ ’cause you get all your chapters right. But you don’t.” Even in the examination questions when it was obvious which methods to use, the Amber Hill students would frequently confuse the steps they had learned. For example, when the Amber Hill students answered a question on simultaneous equations, they attempted to use the standard procedure they had been taught, but only 26percent of the students used the procedure correctly. The rest of the students used a confused and jumbled version of the procedure and received no credit for the question.
The Phoenix Park students had not met all of the methods they needed in the examination, but they had been taught to solve problems and they approached the examination questions in the same flexible way as they approached their projects—choosing, adapting, and applying the methods they had learned. I asked Angus whether he thought there were things in the exam that they hadn’t seen before. He thought for a while and said: “Well, sometimes I suppose they put it in a way which throws you. But if there’s stuff I actually haven’t done before, I’ll try and make as much sense of it as I can, try to understand it, and answer it as best as I can, and if it’s wrong, it’s wrong.”
The Phoenix Park students didn’t only do better on the examinations. As part of my research, I investigated the usefulness of the approach to students’ lives. One way I measured this was by giving a range of assessments to students over the three years that were designed to assess students’ use of mathematics in real-world situations. In the “architectural activity,” for example, students had to measure a model house, use a scale plan, estimate, and decide upon appropriate house dimensions. The Phoenix Park students outperformed the Amber Hill students on all of the different assessments. By the time I was completing the research,
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