1Y is a Module Outside the Main Discipline (MOMD), optional modules that students choose to meet the credit requirements to progress to the following year. In the first year in the School of Mathematics undergraduate students take 100 credits of prescribed modules and are free to take 20 credits of a MOMD, which need not be mathematics.
The 1st year module descriptions booklet describes 1Y as follows:
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By engaging with interesting elementary problems and by reflecting on the expe-rience, students will learn certain specific techniques and will gain insight into the nature of mathematics in the context of elementary material. Mathematical reasoning skill will be developed through an extended period of directed student centred learning in which students are expected to work through a list of problems, present solutions on the board to class mates, and to comment on their own work and the work of others. To succeed in this module students will need to be able to the work independently outside class hours, without the use of reference materials.The module began in 2004/05, covering naïve set theory and being taught by Dr. Good.
From 2006/07–2010/11 it was a geometry module taught by Dr. Sangwin. In 2011/12 it was taught to two distinct groups, one covering set theory (again taught by Dr. Good), one covering geometry (Dr. Sangwin). Each of the module leaders uses their own problems, that are designed
to form a complete (though limited) part of their topic. There is very limited exposition in the module material.
Example 6.2.1 is the first problem that the geometry class has to answer. It is originally taken from Lines and Curves (Gutenmakher et al., 2004), a book that was previously used as the original source of problems in the geometry module, until 2009/10:
▾Example 6.2.1— Cat on a Ladder.
A ladder standing on a smooth floor against a wall slides down to the floor. Along what curve does a cat sitting in the middle of the ladder move? Along what curve does the cat move if it does not sit in the middle of the ladder?
Most modules in the School have the same structure: two lectures weekly and a fortnightly tutorial each lasting 50 minutes, continuing for the whole of the 11 week term. While 1Y nominally has the same format, in practice there is no distinction made between the lectures and tutorials, and student participation is expected at all 27 class meetings.
6.2.1 Teaching and Examination
The module is taught using a close approximation to the original Moore Method. Students begin with a set of ‘axioms’, a list of assumed results that can be taken for granted and used to solve the problems in the module. In the geometry group, this is presented as a sheet titled Some Facts from School Geometry, of which Example 6.2.2 is one:
▾Example 6.2.2— Fact B.1.4.
A theorem on proportional segments in a circle. If two chords AB and CD of a circle intersect at the point E, then
|AE|.|BE| = |DE|.|CE|.
The first week of lessons are then used to discuss these results, with students demonstrating their meaning on the board without having the pressure of presenting their own work to the class. This also gives students enough time to begin working on problems outside of class, so time is not wasted.
Once students begin working on the problem sheets, the class takes on a format that it maintains for the rest of the term: a student will present a solution at the board and the rest of the class ask questions or make comments about the solution, and decide whether it is correct and complete. The module leader also participates in discussions, though their role is to act as chairperson, and clarify the objections of others. They are responsible for keeping discussion focused and at a professional level. It is always the aim that the teacher is the last to speak, so that all students have the opportunity to contribute to the discussion first. If the class has agreed on an incorrect solution, it is the job of the teacher subtly to direct them in recognising the issue.
Problems are solved in order and students are chosen by the module leader in an ostensibly random order to present solutions to the class. If a student fails to offer a solution to a number
of problems in a row the module leader will likely ask them, sometimes descreetly, to work on a few particular problems for the following class.
When a correct solution is reached it may be tided up and the whole of the class makes notes to enable them to submit written solutions later. Students are required to submit solutions to all problems, not just those that they solved themselves, and they may resubmit solutions as many times as they like on receiving feedback for them.
For purely administrative reasons, 1Y is bound to another module, 1X, titled “The Impact of Mathematics”, which shares its final mark equally with 1Y; departmental regulations previously limited the amount of coursework that can be used in the examination of a module. Until the academic year 2011/2012 the module mark consisted of the following:
• Quality of two best presentations to the class (26%)
• Individual written solutions to all problems (24%)
• Written examination (50%)
From 2011/12 the written examination was dropped and the marks distributed equally between students’ two best presentations and their written solutions to problems.
6.2.2 Self Selection
There is an element of self selection in 1Y participation. As a set theory course, 1Y was limited to students who scored the equivalent of an A in A-Level mathematics, however from 2006/07 this restriction was lifted. The number of students in the department who did not meet this
requirement has been small and decreasing, to the extent that the 2009/10 and later cohorts consist entirely of grade A students. As 1Y was optional, it was usual that a number of students drop out in the first few weeks in favour of a different MOMD.
From 2011/12, the module became expected of students enrolled on the Mathematics MSci programme, G103. This requirement was put in place to reflect the difference in offers to BSc and MSci students (AAA/AAB for BSc and A*AA for MSci). MSci students who wish to study a foreign language are encouraged to do so, and BSc students wanting to take 1Y are still welcome on the module, space permitting. While this means that the group is less self-selecting, it is more clearly distinct from the rest of the cohort. Before 2011/12, MSci students made up a similar proportion of 1Y students as in the cohort as a whole.