Executive Brain Mathematics: Domain-General and Domain-Specific

What is a key component of domain-specific skills in mathematical processing?

• Inhibition

• Procedural knowledge

• Shifting

• Processing speed

Answer explanation

Procedural knowledge involves knowing how to carry out mathematical operations effectively and efficiently. It is a domain-specific skill directly related to arithmetic strategies and operations.

Which of the following options primarily describes domain-general components involved in mathematical problem-solving?

• Short-term memory & working memory

• Procedural skills

• Executive function

• Processing speed

Answer explanation

Procedural skills are domain-specific because they involve step-by-step processes directly related to mathematical knowledge.

Which of the following options primarily describes domain-specific components involved in mathematical problem-solving?

• Procedural skills

• Factual knowledge

• Conceptual understanding

• Executive function

Answer explanation

Executive function is a domain-general component involving higher-order skills like inhibition, shifting, and updating, which support mathematical problem-solving indirectly.

Which domain-general component is primarily responsible for retaining and manipulating numerical information during a calculation?

• Procedural skills

• Working memory

• Conceptual understanding

• Factual knowledge

Answer explanation

Working memory is a domain-general component that holds and manipulates information for problem-solving tasks.

A student struggles with suppressing irrelevant information while solving a multi-step equation.

Which domain-general component is most likely involved?

• Working memory

• Inhibition

• Shifting

• Procedural knowledge

Answer explanation

Inhibition is a domain-general component—an executive function responsible for suppressing distractions and irrelevant information during problem-solving.

Which domain-specific component is demonstrated when a student applies the correct order of operations to solve (2+3) × 4 ?

• Conceptual understanding

• Factual knowledge

• Procedural skills

• Shifting

Answer explanation

Procedural skills involve accurately following ordered steps, such as the order of operations, to solve mathematical problems.

A student efficiently switches between addition and multiplication while solving a mathematical problem.

What domain-general component is primarily at work?

• Inhibition

• Shifting

• Conceptual understanding

• Factual knowledge

Answer explanation

Shifting is a domain-general skill—an executive function that enables flexible transitions between different operations or strategies.

Identify whether the given scenario involves a domain-general or domain-specific component.

Specify the type of component involved.

A student uses the commutative property to explain why 3+4= 4+3.

• Domain-specific: Factual knowledge

• Domain-specific: Conceptual understanding

• Domain-general: Working memory

• Domain-general: Inhibition

Answer explanation

Domain-specific: Conceptual understanding involves understanding the mathematical principle behind the commutative property, a core aspect of conceptual knowledge.

Classify the following as domain-general components:

• Retaining intermediate results in a multi-step calculation.

• Ignoring irrelevant numbers in a word problem.

• Switching strategies from addition to subtraction.

• Memorising multiplication tables.

Answer explanation

A. Retaining intermediate results in a multi-step calculation: true-working memory retains intermediate results.

B. Ignoring irrelevant numbers in a word problem: true-inhibition helps suppress irrelevant details.

C. Switching strategies from addition to subtraction: true-shifting allows flexible transitions between strategies.

D. Memorizing multiplication tables: false: Memorisation is a domain-specific skill—factual knowledge.

Evaluate whether the following are components of executive function as related to mathematical processing

• Inhibition

• Shifting

• Conceptual knowledge

• Updating

Answer explanation

• A. Inhibition: True – Inhibition is a core executive function, essential for suppressing irrelevant information during mathematical tasks.

• B. Shifting: True – Shifting allows flexible transitions between strategies or operations, a key executive function.

• C. Conceptual knowledge: False – Conceptual knowledge is a domain-specific component, not part of executive function.

• D. Updating: True – Updating, a component of working memory, monitors and manipulates information, making it part of executive function.