"A student-centered approach is characterized by a shared focus on student and teacher conversations, including interactions among students." This statement stood out to me in the introduction because of the relationship between it and the topics discussed during the rich tasks session at TMC17. The introduction revealed more similarities as it listed some characteristics of high quality tasks. A high quality task should:
- Align with relevant content standards
- Encourage the use of multiple representations
- Provide opportunities for students to develop and demonstrate the mathematical practices
- Involve students in an inquiry or exploratory approach
- Have a low threshold and a high ceiling
- Connect previous knowledge with new learning
- Allow for multiple solution approaches and strategies
- Ask students to explain the meaning of a result
- Have a relevant and interesting context
The introduction also offered some suggestions on how to incorporate more questioning techniques in the math classroom. This was very reminiscent of the question techniques described in the 5 Practices. Essential Understanding states that questions should be reversible, meaning they should have the ability to change a student's thinking. This might be a question in which students are given the answer and have to create a solution path. Questions should also have flexibility. This might take the form of asking students to compare/contrast problems or might ask students to solve a problem in more than one way. A third suggestion states that questions should encourage generalization. Examples of generalization include having students look at cases and make a conjecture(s) or creating an example given a rule.
It is worth noting that the early parts of the introduction discuss 7 types of knowledge bases that help determine how a teacher teaches. These seven bases include content knowledge, curriculum knowledge, and pedagogical content knowledge. The introduction describes in detail how each of these bases influences how we choose which topics to present, how to present those topics, and how to assess learning.