PhD-Logical Reasoning: Studying and Developing Mathematical Expertise
PhD @Loughborough University posted 14 hours agoJob Description
Project details
In everyday language, we interpret logical connectives like ‘if-then’ flexibly according to content and context. The conditional inferences below have identical structures; however, most people accept the first but reject the second.
If you mow the lawn, then I will give you $5.
You do not mow the lawn.
Therefore, I will not give you $5.
If it is a dog, then it is an animal.
It is not a dog.
Therefore, it is not an animal.
In mathematics, this is problematic because we distinguish true conditionals with false converses (‘if x < 2 then x < 5’ is true; ‘if x < 5 then x < 2’ is false) from true biconditionals (‘if x is even then 3x is even’ is true; ‘if 3x is even then x is even’ is true). Studying mathematics therefore requires attention to logic, and specialising in mathematics at 16-18 improves students’ abilities to identify invalid inferences. However, there are substantive individual differences, and evidence indicates that even professional mathematicians remain vulnerable to certain logical errors. Certainly, mathematicians use more than logic in their reasoning: they also develop deep conceptual understanding based on experience with examples.
This raises an educational possibility. If mathematicians do not adhere to standard logic – if they use and perhaps even favour example-based strategies – then perhaps it would be more effective to teach these strategies. This PhD project will address this possibility using mathematical versions of conditional inference and truth-table tasks, which are used widely in psychology. It will use reaction-time and eye-movement studies to investigate how mathematicians understand logic and what students need to learn; it will then design and test teaching interventions.
94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Supervisors
Primary supervisor: Lara Alcock
Entry requirements
Our entry requirements are listed using standard UK undergraduate degree classifications i.e. first-class honours, upper second-class honours and lower second-class honours.
Entry requirements for United Kingdom
Students should have, or expect to achieve, at least a 2:1 or equivalent in mathematics or psychology or a master’s in mathematics, mathematics education, psychology, research methods, or a related field (note that for psychology students, an A level or equivalent in mathematics will be an advantage). They will also be expected to meet the university’s English language criteria.
English language requirements
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Fees and funding
Tuition fees for 2024-25 entry
UK fee
£4,786 Full-time degree per annum
International fee
£21,500 Full-time degree per annum
Tuition fees for 2025-26 entry
UK fee
£5,006 Full-time degree per annum
International fee
£28,600 Full-time degree per annum
Fees for the 2024-25 academic year apply to projects starting in October 2024, January 2025, April 2025 and July 2025.Fees for the 2025-26 academic year apply to projects starting in October 2025, January 2026, April 2026 and July 2026.
Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Fees are reviewed annually and are likely to increase to take into account inflationary pressures.
How to apply
All applications should be made online. Under programme name, select Mathematics Education. Please quote the advertised reference number: ME/LA-SF1/2025 in your application.
To avoid delays in processing your application, please ensure that you submit a CV and the minimum supporting documents.
The following selection criteria will be used by academic schools to help them make a decision on your application. Please note that this criteria is used for both funded and self-funded projects.
Please note, applications for this project are considered on an ongoing basis once submitted and the project may be withdrawn prior to the application deadline, if a suitable candidate is chosen for the project.
