• Roza LeikinEmail author
  • Mark Leikin
  • Ilana Waisman
  • Shelley Shaul


This study explores the effects of the presence of external representations of a mathematical object (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric figures. Performance was evaluated according to the reaction time (RT) required for solving the problem and the accuracy of the answer. Thirty high school students studying at high and regular levels of instruction in mathematics (HL and RL) were asked to solve half of the problems with ERs and half of the problems without ERs. Each task was solved by half of the students with ERs and by half of the students without ERs. We found main effects of the representation mode with particular effect on the RT and the main effects of the level of mathematical instruction and mathematical subject with particular influence on the accuracy of students’ responses. We explain our findings using the cognitive load theory and hypothesize that these findings are associated with the different cognitive processes related to geometry and algebra.

Key words

accuracy external representations internal representations level of instruction reaction time solving mathematical problems split attention effect 


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Copyright information

© National Science Council, Taiwan 2013

Authors and Affiliations

  • Roza Leikin
    • 1
    Email author
  • Mark Leikin
    • 1
  • Ilana Waisman
    • 1
  • Shelley Shaul
    • 1
  1. 1.Faculty of Education Interdisciplinary Center for Research and Advancement of Giftedness and Excellence (RANGE)University of HaifaHaifaIsrael

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