Curriculum Alignment and Problem-Solving Instruction in Mathematics: Evaluating Azerbaijani Textbooks in Light of Modern Pedagogical Demands

Abstract

This article examines the extent to which mathematics textbooks align with modern curriculum demands for problem-solving instruction. A review of literature shows that problem solving has become a central objective of mathematics curricula worldwide, framed as both a goal and a method of teaching. Effective problem-solving instruction requires aligning curriculum standards, textbook content, and classroom practices to emphasize higher-order thinking and real-world application. We discuss the concept of curriculum alignment and its importance, drawing on studies of alignment between learning objectives and educational materials. An analysis of mathematics textbooks – including a case example from recent curriculum reforms in Azerbaijan – highlights common misalignments: problem-solving tasks are sometimes superficially included or pitched at inappropriate difficulty levels, and cognitive demands in textbooks may not fully reflect those in curriculum standards. We identify challenges such as inconsistent integration of problem-solving across topics, insufficient guidance for complex real-life problems, and a tendency to focus on rote procedures over strategy development. Recommendations are offered for improving alignment, including designing textbook tasks that foster deep understanding and inquiry, ensuring a progression of problem-solving experiences, and supporting teachers’ pedagogical content knowledge. Aligning textbooks with modern problem-solving demands is critical for developing students’ analytical skills and for the overall coherence of reform-oriented mathematics education.