Session 1
In the first online session we dove into the problems with mathematical discussions in the classroom, or more accurately the lack there of. The article Orchestrating Productive mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell provides a great set of practises to apply to the classroom. These are:
- Anticipating likely student responses to cognitively demanding mathematical tasks
- Monitoring students' responses to the tasks during the explore phase
- Selecting particular students to present their mathematical responses during the discuss-and-summarize phase
- Purposefully sequencing student responses that will be displayed
- Helping the class make mathematical connections between different students' responses and between students' responses and the key ideas.
Using these strategies will help develop a classroom community that encourages and thrives from mathematical discussion. The one practice that really resonated with me is the first one. As a teacher, being able to anticipate students' responses - even the more abstract responses - will prepare you for a more in depth discussion. Furthermore, this will push your classroom into thinking about the problem through a variety of lenses and ultimately gaining a deeper, richer understanding of the problem.
Another aspect of this first online session that I found very important was the idea of developing mathematical curiosity. If we, as educators, can foster a curiosity in the minds of our students they will inevitably be much more driven to resolve problems. Finding creative, effective ways to do this is fundamentally important for the ever-changing classrooms we face. We are well aware of how individually different our students are, for that reason finding a wide variety of ways to spike the interest of students is ever so important.
Session 2
In this session we looked into formative assessment and more specifically into providing feedback as learning. One issue that continually arises in the classroom is the student who has not yet reached the correct solution to the problem. Often they will have taken a few of the correct steps but then somewhere, along the way, misstepped and arrived at an incorrect or incomplete answer. When assessing work it is important for teachers to address this issue in an effective way. Looking back to the first online section and the five practices; practice one will help greatly with this. As a teacher we must attempt to follow the students path of work and see where there was a discourse. From here we need to develop feedback to help the student realize the problem and ultimately correct it. This is a lot easier said than done.
As an educator it is important to keep a few things in mind when providing feedback. It should be positive, help the student diagnose their problem and provide direction. If formative feedback can follow these important features students who are on the cusp of a correct answer will surely self-correct and achieve their potential.
In conclusion, these two online sessions have helped me gain a deeper understanding how to foster mathematical discussions in a classroom as well as provide beneficial formative feedback. Furthermore, it has shown me the incredible importance of being effective at both of these skills.
Cheers,
Mike Studenny
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