This statement is not true. Proponents of reform know that teaching is a very complicated, complex activity. A teacher's traditional role as a dispenser of information imposes ways of doing mathematics and ways of thinking about mathematics that may not make sense to learners. Students are not empty vessels into which information is poured, but rather, they are products of experiences on which knowledge and skills are built. Although teachers are the content experts in the classroom, they learn about their students' insights and level of understanding by listening carefully to learners' interpretations and explanations.
Teachers use what they learn about students in planning for instruction.
Since not all textbooks are created equally, this statement is not true. A criterion for judging materials that purport to support reform in school mathematics is that the rigor, depth, and logic of mathematics are preserved while problem solving, communication, reasoning, and connections within and beyond mathematics are highlighted. Although authors and publishers of new textbooks and new curricula may claim to support the reform efforts, many are pseudo attempts at fulfilling the goals of reform. Textbooks that superficially treat mathematics in the interest of making connections with literature, history, and science do a disservice to students and to reform efforts. No research is available to support reform efforts.