The evidence from research suggests that students can achieve proficiency if mathematics is taught in a coherent, integrated way. For example, a large-scale study of 150 first-grade to sixth-grade classrooms serving low-income families demonstrated the advantages of teaching for mathematical proficiency. One set of classrooms used a conventional computation-oriented curriculum. Another set stressed conceptual understanding and expanded the range of mathematical topics included in the curriculum beyond arithmetic. In the latter classrooms, teachers used multiple representations of mathematical ideas to support understanding, focused on nonroutine problems to strengthen application of concepts, emphasized multiple solutions to problems to develop computing fluency, and held classroom discussions requiring logical reasoning that explored alternative solutions or meanings of mathematical procedures or results.

Students in the latter classrooms performed substantially better than those in the conventional classrooms. At the end of the two-year study, these students not only had a greater grasp of advanced skills but also had better computational skills. Similar results were found for reading and writing.

A commonly held myth in education is that students in high-poverty classrooms should not engage in academically challenging work until they have mastered the basic skills. This study dispels that myth. It shows that teaching that is organized around all the strands of mathematical proficiency is especially appropriate and effective with disadvantaged students.¹¹