Translations toward Connected Mathematics

Mark Applebaum, Roza Leikin

Research output: Contribution to journalArticlepeer-review


The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one particular problem as well as similar solutions to different problems. To encourage mathematics teachers to generate this type of discourse in their classrooms, professional development programs should integrate these topics. A translations-enabled problem-solving strategy can be effective, and, in many cases, solutions based on this approach are short and elegant. Using this strategy in solving problems can develop students' senses of mathematical efficiency and aesthetics. In this article, the authors present examples that highlight different uses of translations in problems from geometry, algebra, and calculus. For some of the problems, they provide solutions that are typically seen in the classroom. They show detailed solutions using translations for all the problems. They hope that teachers will find these examples useful and that they can begin in their own classrooms by applying these techniques to classic problems from the school mathematical curriculum; later they can present less typical geometry, algebra, and calculus problems. (Contains 7 figures.)
Original languageEnglish
Pages (from-to)562-569
Number of pages8
JournalThe Mathematics Teacher
Issue number8
StatePublished - 1 Apr 2010


  • Translation
  • Mathematics Teachers
  • Geometry
  • Calculus
  • Algebra
  • Mathematics Instruction
  • Problem Solving
  • Discussion (Teaching Technique)
  • Faculty Development
  • Teaching Methods
  • Secondary School Mathematics
  • High Schools
  • Mathematical Concepts
  • Correlation


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