Translation errors and conceptual misunderstandings made by students translating among graphical, tabular, and symbolic representations of linear functions were examined. The study situated student errors in the context of the “Translation‐Verification Model” developed specifically for the purpose of explaining student behavior during the process of translating relationships from one mathematical representation to another. Three distinct error types were identified to explain student performance. An examination of the error types revealed that specific translation errors tend to occur at different stages of the translation process. Translation errors are also related to “attribute density,” the amount of information inherently encoded in a given representation. The findings of the study have implications for teaching linear relationships—student weaknesses and strengths are identified.

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This study applies the Mathematics Acquisition Framework (MAF) (Bossé, Ringler, Bayaga, Fountain, & Young, 2018) to investigate fifth-through seventh-grade students' comprehension of fractions and decimals and examines how students build understanding of mathematical principles and concepts regarding fractions and decimals. Based on case studies and discourse analysis, the results revealed students in different stages of the MAF with some students employing informal/social language in their mathematical communication and others using formal/academic language. Additionally, mathematically erroneous student communication was more positively interpreted through the lens of the MAF, which interpreted student errors, misunderstandings, and miscommunications as natural components to learning.

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