The Role of Representation(s) in Developing Mathematical Understanding

By Stephen J. Pape, Mourat Tchoshanov. 2001

354 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/23a3f0c5647c6cae9818f285efbf9da6dd34e4aa

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Citations in the corpus

Improving Students' Proportional Thinking Using Schema-Based Instruction (2011, background): “Schematic representations that can be used to interpret and elaborate on information in the problem lead to enhanced problem solving performance (Pape & Tchoshanov, 2001).”
Representational disfluency in algebra: evidence from student gestures and speech (2009, background): “One of the challenges of learning and using mathematical representations is grasping their meaning by recognizing or forging associations between them and other representations, or connecting them to objects and events in the world (e.g., Pape & Tschoshanov, 2001 ).”
The Influence of Spatial Visualization Training on Students’ Spatial Reasoning and Mathematics Performance (2019, background): “…to solving word problems, where a spatial representation might be created by the problem solver, decoding processes involved in tasks such as interpreting a bar graph or reading a map, involve knowing the conventions of a representation that one did not create oneself (Pape & Tchoshanov, 2001).”
The effects of the classroom flip on the learning environment: a comparison of learning activity in a traditional classroom and a flip classroom that used an intelligent tutoring system (2007, background): “In other words, teachers enter into many different types of conversations with individual students and groups of students, and it is through these conversations that representations are used to negotiate, refine, and explain mathematical concepts (Pape & Tchoshanov, 2001).”
Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment (2013, background): “…& Potter, 2006, p. 186), schematic representations allow students to look beyond surface features of word problems to interpret and elaborate on information, which may be especially important for ratio and proportion problems (Hegarty & Kozhevnikov, 1999; Marshall, 1995; Pape & Tchoshanov, 2001).”