## Evidence based mathematics teaching

On Wednesday 18 March 2015 a meeting was held at Royal Holloway to share new ideas and approaches to mathematics teaching.

I posted a summary of the talks and discussion to my blog.

1.00 | Lara Alcock (Loughborough) |
How do people read mathematics? |

1.45 | Toby Bailey (Edinburgh) |
Mathematics lectures—a flipping good experience |

3.00 | Franco Vivaldi (QMUL) |
Writing mathematics |

There was a lively discussion session at 3.45pm, following the final talk.

The meeting was supported by a College Teaching Fellowship Award.

### Abstracts

**Lara Alcock.**
How do people read mathematics? And how can we help undergraduates to read mathematics effectively?
These questions are rarely articulated — students take notes and lecturers direct
them to other sources of written information, but we do not usually consider whether and how
they will make sense of these. This talk will report on a sequence of
empirical studies of this issue using both experimental and eye-tracking methods. It will include
information on
(a) a well-intentioned but unsuccessful attempt to support undergraduates
mathematical comprehension, (b) an expert-novice study that identified different reading behaviours in undergraduates and in mathematicians, and (c) a
successful attempt to support undergraduates in learning to read mathematics effectively.

*Resources.* The article on which this talk is based is due to appear in Notices AMS. Some slides from an earlier talk with some overlap (but missing the animation of the eye fixations) are here. The 'Self-explanation training' booklet can be downloaded using this form: since its under a Creative Commons License I've made a mirror of the pdf.

**Toby Bailey.**
Perhaps your mathematics lectures are different. When I have "chalked and talked" I have very often found myself talking to a passive group most of whom are wondering how long it is until I finish. There are not many sure things in pedagogy but there is very wide agreement that learning needs to be an active process to be successful: the traditional approach to mathematics lecturing rests in practice, it could be argued, on the hope that often passive time in lectures promotes enough active learning outside of class to achieve results.

There is considerable evidence from physics education research, and now from other subjects including mathematics, that courses taught by "interactive engagement" methods lead to better learning. These methods are examples of "flipped classrooms" whereby students are expected to engage with information outside of class so that most "lecture" time can be given over to working actively on problems.

In Edinburgh, we have been teaching Year 1 for four years using "Peer Instruction" and I will try and explain how that works. More recently we have tried a flipped classroom approach to a final year course and I will discuss the model for that also.

**Franco Vivaldi**. A
second year course on Mathematical Writing has been offered at Queen Mary
for several years, originally intended as a preparation for
(or a soft alternative to) final year projects. But teaching writing gives you a lot more:
it provides a vivid portrait of the students' struggle with exactness and abstraction, and new tools for dealing with it.