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The Numerical Brain

Module description

What do catching a bus and space travel have in common? They would not be possible without the human ability to represent and process numbers. This ability is crucial for functioning in the modern world. From basic tasks such as organising your daily schedule, cooking, or managing your finances and health, to complex tasks such as computer programming and mathematics, numbers are a central pillar of our daily lives. Through a combination of lectures, discussions, and student presentations, thismodule examines how numerical information is represented in the human brain, including nonsymbolic magnitudes (i.e., sets of objects) and symbolic numbers (i.e., Arabic digits). We will also examine the development of these representations and processes, and in particular, what goes wrong in individuals with mathematical learning disabilities (i.e., dyscalculia).

Module aims - intentions of the module

The aim of this module is to provide you with a broad understanding of the current knowledge regarding how the human brain represents and processes numerical information. You will be introduced to behavioural and neuroimaging research examining a range of topics including:

• Numerical abilities in the animal world
• Nonsymbolic numerical processing
• Symbolic numerical processing
• Typical and atypical development of numerical abilities (e.g., math learning disabilities)

You will develop the following skills, many of which are transferable to future employment:

• Problem solving (linking theory to practice, developing your own ideas with confidence, being able to respond to novel and unfamiliar problems)
• Managing structure (identifying key demands of the task, setting clearly defined goals, responding flexibly to changing priorities)
• Time management (managing time effectively individually and within a group)
• Collaboration (respecting the views and values of others, taking initiative and leading others, supporting others in their work, maintaining group cohesiveness and purpose), and
• Audience awareness (presenting ideas effectively in multiple formats, persuading others of the importance and relevance of your views, responding positively and effectively to questions).

Intended Learning Outcomes (ILOs)

ILO: Module-specific skills

On successfully completing the module you will be able to...

• 1. Provide an overview of the principal theories of numerical cognition
• 2. Provide an overview of the principal brain regions and networks supporting numerical cognition

ILO: Discipline-specific skills

On successfully completing the module you will be able to...

• 3. Review and analyse scientific articles at an advanced level, synthesising this literature to present logical, coherent and sustained arguments.
• 4. Engage in scientific debates, forming arguments from evidence in the literature

ILO: Personal and key skills

On successfully completing the module you will be able to...

• 5. Communicate complex scientific concepts in a concise and accessible way

Syllabus plan

Indicative topics that will be covered include:

• Do animals understand numbers?
• Foundations of numerical thinking.
• Nonsymbolic numerical processing: The Approximate Number System
• Symbolic Numerical Processing: The Symbol Grounding Problem
• How does the brain know a number is a number?
• Maths learning disabilities: Causes & Characteristics

Learning activities and teaching methods (given in hours of study time)

Details of learning activities and teaching methods

Formative assessment

Summative assessment (% of credit)

Details of summative assessment

Details of re-assessment (where required by referral or deferral)

Re-assessment notes

Two assessments are required for this module. Where you have been referred/deferred in the examination you will have the opportunity to take a second examination in the August/September re-assessment period. Where you have been referred/deferred in the essay you will be required to resubmit the essay. If you are successful on referral, your overall module mark will be capped at 40%; deferred marks are not capped.

Indicative learning resources - Basic reading

Basic reading will include a selection of scientific articles to prepare for each seminar, for example:

• Ferrigno et al (2017): Universal and uniquely human factors in spontaneous number perception. Nature Communications 8, 13968.
• Kersey, et al. (2019): Gender similarities in the brain during mathematics development. npj Science of Learning 4, 19.
• Pollack, & Price. (2019). Neurocognitive mechanisms of digit processing and their relationship with mathematics competence. NeuroImage 185, 245–254.
• Price, et al (2013): Why mental arithmetic counts: brain activation during single digit arithmetic predicts high school math scores. Journal of Neuroscience 33, 156–163.
• Iuculano, et al (2015): Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities. Nature Communications 6, 8453.

Indicative learning resources - Web based and electronic resources

• ELE – College to provide hyperlink to appropriate pages

Key words search

Psychology, brain imaging, cognition, numerical cognition, learning disabilities, fMRI, cognitive neuroscience