The challenge posed by algebra story problems creates a significant hurdle for many students, transcending both the mathematical content of the problem and the specific instructional background received. This study offers a distinctive contribution to the existing literature by focusing on the cognitive conditions essential for comprehension in…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

The purpose of this research was to determine if recognizable error types exist in the work of preservice teachers required to create story problems for specific fraction operations. Students were given a particular single-operation fraction expression and asked to do the calculation and then create a story problem that would require the use of…

This study examined Advanced Placement Calculus students' mathematical understanding of rate of change, after studying four years of college preparatory (integrated or single-subject) mathematics. Students completed the Precalculus Concept Assessment (PCA) and two open-ended tasks with questions about rates of change. After adjusting for prior…

Teaching is an interactive process in which teachers gather information, analyze the results, and construct a response based on this diagnosis (Cooney, 1988). Considering alternatives in constructing a response, that is, making an instructional decision, is of great importance in teaching. How might mathematics teacher educators provide…

Discusses errors made by remedial intermediate algebra students in factoring polynomials in light of student definitions of factoring. Found certain beliefs about factoring to logically imply many of the errors made. Suggests that belief-based teaching can be successful in teaching factoring. (16 references) (Author/MKR)

Illustrates, categorizes, and analyzes typical mathematical errors in algebra and trigonometry made by high school and lower division college students. (16 references) (Author/MKR)