A taxonomy of high school students' levels of understanding in solving algebraic problems.

This article focuses on developing a six-level taxonomy to classify grade 11 students' levels of understanding in algebraic problem-solving tasks, based on data collected from Ontario high schools in Canada. The taxonomy, derived from analysis of students' written responses and interviews, spans from minimal to abstract evaluative understanding across four algebraic areas: variables, expressions, equations, and word problems. Levels 1 to 3 reflect lower-level cognitive skills with limited or partial connectivity to the problem context, while levels 4 to 6 involve higher-order thinking, including full comprehension, inductive evaluation using concrete examples, and deductive evaluation employing abstract algebraic reasoning. The taxonomy aims to assist teachers in both assessing students' conceptual understanding and designing instructional activities that scaffold learners toward deeper algebraic thinking, addressing a noted gap in research on grade 11 algebra learning and supporting progression to advanced mathematics courses.