1. Improving mathematical writing skills of undergraduate students
Karen Hogeboom and Michael Page

2. Communication matters
All science students, including mathematics students, should be able to explain their methods and reasoning. It is important that our graduates are able to explain their mathematics to us (their teachers), to their peers, and also so it is accessible to readers with less knowledge of mathematics. Employers value these skills. The development of mathematical communication skills is one of the major parts of a student’s studies in mathematics.
All science students, including mathematics students should be able to explain their methods and reasoning. The development of mathematical communication skills is one of the major parts of a student’s studies in mathematics.
Employers value well-developed communication skills very highly.
It is important that our graduates are able to explain their mathematics to us (their teachers), to their peers, and also so it is accessible to readers with less knowledge of mathematics.

3. It is not unusual to see first-year students trying to answer problems without writing any words at all.
And yet it is not unusual to see first-year students trying to answer problems without writing any words at all – with the reader expected to follow somehow their reasoning without any explanation or reasons provided

4. Communication is a skill
Students will arrive at university with different standards, practices and expectations. Good communication and mathematical writing will need to be encouraged from the beginning. Writing mathematics in a clear, precise and logical way is a skill. And like any skill, it takes practice and repetition to master. To ensure that we communicate our expectations to students, we wanted to be ensure our guide is concise. (TL;DR)
As students will arrive at university with different standards, practices and expectations, good communication and mathematical writing will need to be encouraged from the beginning.
The development of mathematical communication skills is one of the major parts of a student’s studies in mathematics. Writing mathematics in a clear, precise and logical way is a communication skill. And like any skill, it takes practice and repetition to master.

5. Creating a guide for writing in mathematics.
Step 1: Collect and collate the miscellaneous resources that were being used within the School. Step 2: Share the first version of our guide within the whole school (not just teaching staff for first-year units). Step 3: The updated version was used by a number of teaching staff last year with their students. Step 4: Their feedback helped refine the guide. The current version is being used this semester.
We saw the need for a guide -To aid students (first years) in the development of their communication skills – that was consistent across the school.
Step 1: We started by collating the miscellaneous resources that were being used within the School. Some of our level-1 mathematics units offered quite different written guidance on mathematical writing for students, and others provided no expectations at all.
Step 2: We shared the first version of our guide within the whole school (not just teaching staff). And got some very useful feedback. Which helped shape the second version.
Step 3 This second version was used by a number of teaching staff last year with their students.
Step 4: And their feed back helped with the current version, which we have been using this semester.

6. The writing guides – student version
All the important points are on the first page.
A short explanation that writing mathematics is a skill that will need to be practised and mastered.
A list of what a good piece of mathematics should contain – with a hook about getting full marks.
And a summary list of writing tips.
To avoid TL;DR we made sure that all the important points about writing in mathematics were on the first page.
For students:
A short explanation that writing mathematics is a skill that will need to be practised and mastered.
A list of what a good piece of mathematics should contain – with a hook about getting full marks.
And a short list of writing tips

7. The writing guides – student version
Inside the guide
The writing tips in much more detail.
A small section of commonly used words.
A dot point outline of a math/stats report.
An appendix with 5 example answers with commentary on each.
A table of common notation.
Inside the guide we expanded the writing tips in much more detail.
A small section of commonly used words. A dot point outline of a math/stats report.
An appendix with 5 example answers for a very simple question. Each example has a commentary on its description of its reasoning and mathematics.
At the end we have a table of common notation. There was much discussion what to include in this table and what to leave out.

8. The writing guides – staff version
The staff version is primarily aimed at the sessional teaching staff (tutors).
A short explanation that writing mathematics is a skill that students need to practiced and master.
Reasons why we insist on proper mathematical writing and how it benefits both the student and tutor.
It helps with student learning
It helps with their teaching
It can help identify when students are copying each other
In the process of developing a writing guide for students we saw a need for a companion guide for staff - particularly for sessional staff. To explain why we thought communication important and what staff could do to encourage students to develop their writing skills.
From a teaching staff point of view, encouraging proper mathematical writing helps their teaching in two ways.
Firstly it helps student learning. Getting students into the habit of writing their mathematics properly helps them develop a framework for their learning in mathematics. This is particularly helpful for weaker students.
Secondly, it helps with teaching. An emphasis on mathematical writing will also make marking assignments easier and more pleasant as students’ work will have better structure and layout. It also enables “blindly” copied work to be spotted more easilyThe staff version is primarily aimed at the sessional teaching staff (tutors).
A short explanation that writing mathematics is a skill that students need to practised and master.
Reasons why we insist on proper mathematical writing and how it benefits both the student and tutor.
A list of ways tutors can promote writing in their classrooms.
A list of what a good piece of student work should contain.
A table guide to the major aspects of communication in mathematics and the characteristics of the best level. This table also aids tutors by helping with phrases they can use when giving feedback to their students.
An appendix with 5 example answers for a very simple question. Each example has a commentary on its description of its reasoning and mathematics. This time the commentary is aimed at tutors.

9. The writing guides – staff version
A list of ways tutors can promote writing in their classrooms.
A list of what a good piece of student work should contain.
A table guide to the major aspects of communication in mathematics and the characteristics of the best level.
An appendix with 5 example answers for a very simple question with commentary.

10. High take up in all first-year units.
Implementation
Implementation across the whole department is still a work in progress.
High take up in all first-year units.
High take up in units that already provided materials to students.
Encouraging all teaching staff to model good writing practices at every opportunity (and to highlight when they are using ‘shorthand’).
Encouraging lecturers to value communication by explicitly including it in their assessment marking schemes.
Implementation of the writing guide across the whole department still a work in progress.
High take up in all first year units and across units, so students in first year mathematics units have the same resource.
Also a high take up in units that already provided materials to students.
We are also encouraging all teaching staff (especially sessional staff) to model good writing practices. And encouraging lecturers to value communication by explicitly including it in their assessment marking schemes.

11. Some comments from staff
“[Student writing]..something that’s been frustrating me for quite a while!” “These guides look great! I think that it's great to have something like this for students. Students come in not knowing how to write mathematics, and it would be great for them to leave knowing how to do it better!” “ The appendix of a question with 5 example answers is a great idea… to present several distinct answers to a problem and critique them. This will be very useful for students and tutors alike” But “…answering the question asked is a topic quite separate from clear and coherent writing”

12. Questions and comments
Question time and an invitation to hear from other institutions about their own approaches and experiences.

13. Supported by a Monash University Faculty of Science Teaching Innovation Fund
Project leader: A/Prof Michael Page
Steering group: Dr Heiko Dietrich, Dr Jerome Droniou,
Mr John McCloughan, Mr Simon Teague
Project officer: Ms Karen Hogeboom