Elementary school students often exhibit a variety of conceptions associated with algebraic thinking that their teachers fail to recognize or understand. It is crucial that elementary school teachers possess knowledge of the variety of student conceptions and also have abilities to address varying states of conceptions. Otherwise, students who are…

We investigated language variation and score variation in the testing of English language learners, native Spanish speakers. We gave students the same set of National Assessment of Educational Progress mathematics items in both their first language and their second language. We examined the amount of score variation due to the main and interaction…

Developed a framework for examining cognitive validity claims and used it to evaluate the validity of a "connected understanding" interpretation of three concept mapping techniques used by two teachers and six high school students. Results show that the three mapping techniques provide different pictures of student knowledge and suggest that…