This book was an interesting read. It really makes you think about both what you have been doing in your classroom as well as ways you can improve your teaching. I think it is important for students to have authorship in their own problem solving methods.
I do think that implementing this method would require a lot of work up front. If you teach the same topics every year, it is not the same level of work each school year. I do think that the level of work that has to be put in to implement this method could be a detractor for many teachers. It’s something that I definitely think should be implemented if you have a strong, collaborative PLC because you have both extra support and feedback.
This article discussed the importance of creating a classroom culture that supports students in persisting with mathematical tasks. The goal is to create an environment where students feel comfortable tackling more cognitively challenging problems and persisting in finding a solution.
The key components of successfully accomplishing this are:
1. The way the tasks are introduced. If students are given preliminary experience, they were more comfortable in engaging in the task and persisting with it.
2. Providing support to students. It is important to allow students time to struggle individually, followed by working collaboratively, as well as overcoming the tendency to give students “hints” and to use prompts that differentiate the task. The authors make the point that you can provide support for students without detracting their opportunity to understand the math.
3. Providing an extension task. It allows students who have finished to explore the topic with more depth and allows those students who are still working adequate time to work with the task to a conclusion.
4. The sharing of student solutions. The authors note that is important to observe students as they’re working and to thoughtfully choose students to contribute. This allows students to explain their strategies and see that they are making an important contribution to the classroom.
5. The method of assessment. Students who feel like they are being assessed competitively (compared to their peers) are less willing to participate. Using a criterion-based rubric encourages students to participate and persist, because they can see up front how they will be graded, as well as encouraged them to reflect on their learning.
Overall, the authors concluded that a positive classroom environment is not just rules and procedures, but ongoing and interactive support from the teacher.