Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

The representations of the arithmetic operations include functional relationships.

J A Dixon1, J K Deets, A Bangert

  • 1Department of Psychology, College of William and Mary, Williamsburg, Virginia 23187-8795, USA. jadixo@wm.edu

Memory & Cognition
|June 16, 2001
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Measurement of the centrality dependence of the charged-particle pseudorapidity distribution in proton-lead collisions at [Formula: see text] TeV with the ATLAS detector.

The European physical journal. C, Particles and fields·2017
Same author

Jet energy measurement and its systematic uncertainty in proton-proton collisions at [Formula: see text] TeV with the ATLAS detector.

The European physical journal. C, Particles and fields·2015
Same author

Rash with DERMABOND PRINEO Skin Closure System Use in Bilateral Reduction Mammoplasty: A Case Series.

Case reports in medicine·2015
Same author

Measurement of the inclusive jet cross-section in <i>pp</i> collisions at [Formula: see text] and comparison to the inclusive jet cross-section at [Formula: see text] using the ATLAS detector.

The European physical journal. C, Particles and fields·2015
Same author

Measurement of the charge asymmetry in top quark pair production in <i>pp</i> collisions at [Formula: see text] using the ATLAS detector.

The European physical journal. C, Particles and fields·2015
Same author

Search for lepton flavour violation in the <i>eμ</i> continuum with the ATLAS detector in [Formula: see text]<i>pp</i> collisions at the LHC.

The European physical journal. C, Particles and fields·2015
Same journal

The properties of personal semantics.

Memory & cognition·2026
Same journal

Music enhances associative generalization: Evidence from a memory integration task.

Memory & cognition·2026
Same journal

Video, text, and memory: An emotional verbal overshadowing effect.

Memory & cognition·2026
Same journal

Limited protective effects of multilingualism against age-related cognitive decline.

Memory & cognition·2026
Same journal

Validation of illustrated texts: Can pictures raise awareness of inconsistencies?

Memory & cognition·2026
Same journal

I remember (and forget) your happy smiling face: Directed forgetting of emotionally expressive faces of in-group and out-group members.

Memory & cognition·2026
See all related articles

People mentally represent principles for arithmetic operations, with simpler operations like addition having more developed representations than complex ones like multiplication. These representations influence mathematical problem-solving strategies.

Area of Science:

  • Cognitive Psychology
  • Mathematics Education

Background:

  • Mathematical problem solving theories suggest structure mapping between problem and operation representations.
  • This structure-mapping hypothesis relies on analogous relations within these representations.
  • Prior research indicates problem representations involve functional relationships or principles.

Purpose of the Study:

  • To investigate if individuals represent analogous principles for fundamental arithmetic operations (addition, subtraction, multiplication, division).
  • To examine how the developmental history and frequency of mathematical operations influence the representation of their underlying principles.

Main Methods:

  • Participants (college and 8th grade) rated problem attempts based on adherence to operation-specific principles.
  • Experiment 3 involved rating statements for their consistency with principles of different operations.

Related Experiment Videos

  • Manipulated distance of answers from correct solutions and consistency of statements with principles.

    • Main Results:

    • Violations of operation principles were perceived as poorer attempts at solving problems.
    • Operations learned earlier (e.g., addition) exhibited more extensive principle representations than later-learned operations (e.g., multiplication).
    • Principles frequently encountered or with longer developmental histories showed stronger representations.

    Conclusions:

    • Findings support the hypothesis that individuals represent principles for arithmetic operations.
    • The depth of these principle representations correlates with the operation's learning order and frequency.
    • Results have implications for understanding mathematical problem solving through a structure-mapping framework.