“What counts as algebra in the eyes of preservice elementary teachers?” is the title of an article written by Ana C. Stephens for the Journal of Mathematical Behavior. The abstract describes an interesting article, and is enclosed below:

This study examined conceptions of algebra held by 30 preservice
elementary teachers. In addition to exploring participants’ general
“definitions” of algebra, this study examined, in particular, their
analyses of tasks designed to engage students in relational thinking or
a deep understanding of the equal sign as well as student work on these tasks. Findings from this study suggest that preservice elementary
teachers’ conceptions of algebra as subject matter are rather narrow.
Most preservice teachers equated algebra with the manipulation of
symbols. Very few identified other forms of reasoning – in particular,
relational thinking – with the algebra label. Several participants made comments implying that student strategies that demonstrate traditional
symbol manipulation might be valued more than those that demonstrate
relational thinking, suggesting that what is viewed as algebra is what
will be valued in the classroom. This possibility, along with
implications for mathematics teacher education, will be discussed.