As discussed above, problems were chosen for each topic by the topic leader, four topics had a second group taught by a different member of staff using the same material. All those interviewed except Lecturer D had been the topic leader, and so chosen the material.
An immediate issue that presents itself in choosing a topic and problems to go with it is the level of abstraction, and the speed with which students can begin to work on problems themselves:
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[…] I think the students always respond better with something they perceive more directly so if it’s something where they can draw pictures or do something directly without too much difficulty on the computer to supplement their understanding then it tends to go much more quickly. I don’t think most of our students are comfortable with abstraction and so the topics that are more abstract are just more difficult for them and they go much more slowly. (A75)“
So this is why, for example, I’ve chosen Graph Theory. It may be a bit more suitable for this method. […] there is not so much background they need to know. (E44)Lecturer E used pre-existing Moore Method course notes from the Journal of Enquiry Based Learning in Mathematics (Clark, 2007):
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Yes, everyone got a copy because it’s free online and this was specifically designed for students, I printed it for everyone and then we just went through problems.(E76)
I didn’t know how to do most of the problems, although they are elementary, and […] so it was okay for me. I managed to solve all of them, or most of them, right.
So I didn’t need to go through Graph Theory books or whatever. (E62)
Lecturer D was happy to teach a topic with which he was not familiar:
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But I wasn’t very familiar with the more pure mathematical side of it that the material we had steered us along. In a way I didn’t think that was a bad thing because it put me in the same position as the students and I could see a bit of the difficulties they had and also I was less tempted to give them my already pre-thought-out answers. (D49)Instead of building a topic up, Lecturer F opted to give students a paper (Shannon et al., 1949), in the hope that they would be able to bridge the gaps in it:
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[…] every student was given the paper. It didn’t contradict to the whole purpose of the course because the paper’s written in such a way that every formulation is not rigorous enough, and the proofs are not rigorous enough either. So what we’ve done, okay the idea is there, and the outline of this theory is there, so my plan was “Okay, why don’t we build a Mathematical Theory of Communication?”using Shannon’s work as a background. And of course depending on the level of detail and the level of rigour, you can arrive at different goals. (F52)
This was less successful than planned, mainly because of the difference between the expectation and reality of students’ abilities:
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I wanted the idea of a hook, and so I gave them Shannon’s paper, but in fact it was a little bit too difficult for them to get through. (F107)Reflecting on this experience, he went on to comment:
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But problem classes must not be done like “Here is a set of problems, I’ll see what you do.” It must be really carefully planned and supervised. […] if the students are stuck for more than five minutes, then my experience suggests that you need to interfere, you need to step in and give a hint. […] you need to make sure they’re not sleeping so you need to keep their competitiveness up, their desire for mark up. Okay for deep learners you don’t need to stimulate them, they’ll do anything you ask, but the rest of the group need to be also stimulated somehow. (F132)Students were given the choice of which topic to sign up for; this was cited as being significant:
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I deliberately allowed them to sign up for what they wanted […] so where possible folks were with their friends so they were comfortable with the people they were talking to. I think that was important. (C37)“
I think it played a role for this group because they all signed up for the topic they wanted. They also signed up with peers whom they shared that interest with, so pairs and groups that signed up at the same time. […] I do think that was […] why the group work and the discussion groups went so well, because I had studentswho had chosen the topic that they wanted to and they were all sort of curious about it in some way. (B73)
Due to the limited space available, not all students managed to get on their first-choice course, however this did not necessarily devalue the experience they had.
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So I definitely had a student in my group who told me that he had tried to sign up for a different one, but he was gracious enough to say that he was quite pleased that he’d come to this one and that he’d learned something from it. (D113)The fundamental difference between New Investigations and its previous versions, the interconnectedness of the problems given to students, was seen as an important part of its success: