This paper describes the difficulties faced by a group of middle school students (13- to 15-year-olds) attempting to translate algebraic statements written in verbal language into symbolic language and vice versa. The data used were drawn from their replies to a written quiz and semi-structured interviews. In the former, students were confronted…

Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students' difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students' proof reasoning in one-on-one task-based interviews, we analyzed students' oral…

This study aimed to describe 1-year changes in students' vocabulary in written narratives. Secondary aims included examination of accuracy and the relationship between lexical diversity and achievement. Participants included 749 students in first through eighth grades. Within-subjects 1-year change in diversity, productivity, and accuracy was…

Based on third language acquisition theories (Flynn, Foley, & Vinnitskaya, 2004; Marx & Hufeisen, 2004; Rothman, 2010, 2015) and cross-linguistic influence (Sharwood Smith & Kellerman, 1986), this study explored the written production errors of L3 English acquisition of word order in the affirmative and interrogative structures by L1…

The educational welfare of children of native and minority groups in continental United States and its outlying parts involves instructional procedures which in recent years are becoming more and more recognized as constituting specialized problems in education. Bilingualism is generally recognized as offering serious instructional difficulties…