MATH30340 Peer-Assisted Tutoring

Academic Year 2022/2023

The aim of this module is to provide you with the opportunity, the practices, and the support, to notice students' mathematical thinking in a first-year mathematics module. In the first week of the trimester you will be assigned to a module as a tutor, and for the duration of the trimester you will act as a peer-tutor in one tutorial or workshop per week.

As well as acting as a peer-tutor for one hour per week, there will be lecture sessions (some face-to-face and some online) where you will be introduced to mathematics education research in three broad areas: mathematical knowledge required for teaching; professional noticing of students' mathematical thinking; and, in-the-moment decision making in the classroom and the factors that impact the decisions made. For mathematical knowledge for teaching (MKT) we examine the classic paper by Shulman (1986), before moving on to the categories of MKT proposed by Ball, Thames, and Phelps (2008). The complexities of teacher noticing in the classroom is a growing area of research and we will specifically examine what is involved in the professional noticing of students' mathematical thinking. Specifically we will examine the skills involved as proposed by Jacobs, Lamb, and Philipp (2010). Closely linked to noticing are the in-the-moment decisions that an educator must make while in the classroom. Schoenfeld (2011) proposes that the decisions made in the moment are a function of one's resources/knowledge, orientations/beliefs, and goals. A study by Rowland, Thwaites, and Jared (2015) describes moments when one has to think on one's feet as contingent moments and examines the triggers for these in the classroom.

You will be required to keep a weekly journal. A key aim of the journal entires will be to encourage you to link the research theory to your tutoring practice. Another aim will be to enable you to start to develop the skill of a reflective practitioner. Your weekly journal reflections will be assessed and you will also be asked to write a reflective essay based on your reflections that aims to trace the development of your knowledge and/or skills for teaching mathematics as you progress through the trimester. Some of the knowledge or skills that you work on must be grounded in the research discussed. You will also be asked to undertake a group project with other PATs in the same module as you, that will be focused on some aspect of MKT or noticing of students' mathematical thinking or in-the-moment decision making. Your team will be asked to make a group presentation.

This module is core for Stage 3 students taking a BSc in Science, Mathematics and Education. For all other students interested in taking the module, you should contact Assoc. Prof. Maria Meehan at before end August 2022 expressing your interest in taking part as places on the module are strictly limited due to the placement component. If necessary places on the module will be awarded based on GPA.

Show/hide contentOpenClose All

Curricular information is subject to change

Learning Outcomes:

On completion of this module, students will be enabled to:

Present, discuss, and critique the assigned readings from the mathematics research literature related to the following three broad areas: mathematical knowledge for teaching; professional noticing of students' mathematical thinking; and, in-the-moment decision making;

Identify, describe, and analyse ways in which their mathematical knowledge for teaching, noticing of students' mathematical thinking, and in-the-moment decision making has developed over the course of the trimester, and in doing so, link theory with practice;

Use mathematics education research as a lens with which to examine, and reflect on, practice;

Describe the sections of a "typical" maths education research paper;

Communicate and present findings on theory in practice to a mathematics and mathematics education audience;

Appreciate the role research and critical reflection play in developing as a professional teacher;

Apply APA referencing precisely.

Indicative Module Content:

Pedagogical content knowledge

Mathematical knowledge for teaching

Noticing students' mathematical thinking

In-the-moment decision making and resources, orientations and goals

Contingent moments in teaching, and their triggers

Student Effort Hours: 
Student Effort Type Hours
Seminar (or Webinar)




Specified Learning Activities


Autonomous Student Learning




Approaches to Teaching and Learning:
Online lectures on mathematics education articles and APA referencing. Face-to-face small group discussion classes - topics from online lectures and tutorials will be discussed. Student presentations at the end of the trimester. Engaging in reflective and critical writing. Examine practice as tutor in reflections and discussing with peers. 
Requirements, Exclusions and Recommendations
Learning Requirements:

Students should preferably be in Stage 3 or 4 and have completed a significant number of mathematics modules in Stages 1 and 2.

Module Requisites and Incompatibles
Additional Information:
Students should be in Stage 3 or Stage 4 and have studied a significant number of modules in Mathematics, Applied Mathematics and/or Statistics in Stages 1 and 2.

Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Presentation: Group presentation with PATs tutoring the same module, that examines theory in practice in the module Coursework (End of Trimester) n/a Graded No


Continuous Assessment: Individual written weekly reflections and/or accounts Throughout the Trimester n/a Graded No


Essay: Individual essay on skills and knowledge development while tutoring as a PAT Coursework (End of Trimester) n/a Graded No


Carry forward of passed components
Resit In Terminal Exam
Spring No
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, on an activity or draft prior to summative assessment
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Peer review activities
• Self-assessment activities

How will my Feedback be Delivered?

Feedback on reflections/accounts will be given individually online and/or in class. There will be a self-assessment activity on a first draft of the skills and knowledge essay. Formative feedback will be given on a trial presentation.