Assessing the Difficulty of Mathematical Translations: Synthesizing the Literature and Novel Findings

Students perennially demonstrate difficulty in correctly performing mathematical translations between and among mathematical representations. This investigation considers the respective difficulty of various mathematical translations based on student activity (defining mathematical errors during the translation process, teacher beliefs and instructional practices, student interpretive and translation activities, and the use of transitional representations) and the nature of individual representations (fact gaps, confounding facts, and attribute density). These dimensions are synthesized into a more complete model through which to analyze student translation work and delineate which mathematical translations are more difficult than others.