-Algebra is generally considered as manipulating symbols, while algebraic thin king is about generalization. Patterns can be used for generalizat ion to develop early graders' algebraic thinking. In the generalization of pattern context, the purpose of this study is to investigate middle school students' reasoning and strategies at different grades when their algebraic thin king begin s to develop.First, 6 open-ended linear growth pattern problems as numeric, pictorial, and tabular representations were asked to 154 middle g rade students. Next, two students from each grade (6 th , 7 th , and 8 th grade) were interviewed to investigate how they interpret the relationship in different represented patterns, and which strategies they use. The findings of this study showed that students tended to use algebraic symbolis m as their grade level was increased. However, the students' conceptions about 'variable' we re troublesome.
Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the pre-service teachers' anticipation of students' misconceptions and difficulties for the given task. To conduct our analysis, we conducted interviews with three 5 th and three 6 th grade students, and eight preservice teachers. During the interviews we asked them to solve the question and explain their solution strategies. The findings of the study indicate that students and pre-service approach this problem in different ways. However, both groups have a tendency to think of decimals successively and indicate precise answers rather than specifying a range of possible values. We also observed the preservice teachers could only partially anticipate the misconceptions and difficulties faced by the students.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.