MATH30340

In this module, you will gain experience as a Peer-Assisted Tutor (PAT) in a workshop-style tutorial for a first-year mathematics module. You will be encouraged to observe how students in your tutorial think about mathematics and then based on your interpretation of this, scaffold their thinking so they can make sense of the mathematics. You will be encourage to reflect on mathematical interactions you have with students, both by yourself and with peers, with a view to improving your skills of eliciting, attending to, interpreting, and responding to students’ mathematical thinking. Whatever career you wish to pursue, you should develop the transferable skills of supporting others in making sense of complex ideas and engaging in reflective practice - the latter being a skill that is essential in all walks of life where you want to learn from experience.

“Noticing” is a theme that runs through the module and there are two main types that you will engage in. The ultimate aim of the course is for you to develop your skills of eliciting and noticing students’ mathematical thinking in-the-moment in the first-year tutorial. This is the first form of noticing involved in the course and we will use Jacobs et al. (2010) theoretical framework where noticing students’ mathematical thinking is conceptualised as encompassing three inter-related skills: (1) Attending to their thinking; (2) Interpreting their thinking; and (3) Deciding how to respond based on this thinking. In order to support you in this endeavour, especially when it comes to “deciding how to respond”, you will use Mason et al.’s (1982) Thinking Mathematically framework. As you progress through the trimester, you will be challenged to improve your practice of noticing your students’ mathematical thinking, especially in-the-moment. This is where the second form of noticing comes in - the professional noticing of your own practice. You will engage in Mason’s (2002) Discipline of Noticing to do this. These involves writing brief-but-vivid (BBV) accounts of mathematical interactions you have with students in the tutorial that hold significance for you, and analysing them by yourself and with peers, in the form of task exercises. By identifying threads or themes in your accounts, and in the peer-group collection of accounts, you will use the Thinking Mathematically framework and your developing knowledge of student mathematical thinking to prepare for similar scenarios in the future. At the end of the course, you will be required to identify and describe how your skills of eliciting and noticing students’ mathematical thinking in-the-moment developed and reflect on how the practices you engaged in during the course contributed to this development. You will also be required to illustrate your knowledge of students’ mathematical thinking and their skills of responding to this by completing a lesson-script.

The module is organised as follows: You will be assigned as a peer-assisted tutor (PAT) to a first-year tutorial, usually in Calculus. These tutorials are usually “workshop style” meaning that students will be required to work on tasks with the senior tutor (a graduate student) and PATs on hand to provide support. You will not be by yourself in the tutorial - a graduate tutor will have ultimately responsibility and be there to assist you if required. The tutorials usually start in week 2 and end in week 12. In addition to the weekly tutorial, you will attend a weekly workshop as part of the course with the other PATs who are assigned to the same first-year module as you. This is where a significant amount of work for the module will take place. As they are interactive, attendance is necessary. In addition, for the first four weeks there will be a lecture each week to introduce you to the main theory and readings in the module.

This module is core for all BSc in Science, Mathematics and Education students. For any Mathematics or ACM student who wishes to take it as an option please email the module coordinator, Prof. Maria Meehan, at maria.meehan@ucd.ie by 24 August expressing your interest. This is to allow enough time to find placements for each student. Due to the placement element in the module, it may not be possible to accommodate everyone who applies but every effort will be made to do so.