Mathematical Discussions & Formative Assessment

Orchestrating Mathematical Discussions

When encouraging rich discussion in a math classroom, the task being presented should be carefully selected. I believe that to encourage discussion the task needs to be of interest to students. In addition, students need to feel comfortable in sharing their responses or ideas.  This connects back to the concept of creating positive norms in a math class. 

Asking good questions is an important part of having math discussions. A higher-level question will require students to think and go beyond memorizing or following the steps exactly from a previous example. These types of questions or tasks involve students making connections and really thinking. There may be more than one way to solve the question, and/or the question may not explicitly be stated. Open-ended questions can be a great example of this.

The cognitive demand of low-level tasks can be increased by changing (or eliminating) some of the information in the question, by asking students to prove their answer, describe what their answer means, or by having students explain why another answer may be correct or incorrect.

Formative Assessment

Formative assessment can help in determining if students require the lesson or part of a lesson to be re-taught. Using different forms of assessment like exit cards and observation, a teacher can determine how much of a lesson should be re-taught. In my first teaching placement, I would often start off the class with a couple review questions from the previous day. This would provide me the opportunity to explain the concept again, ask questions and have students practice.  

When giving feedback to struggling students, I think it is important to take into consideration the feedback strategies of timing, amount, mode and audience discussed by Susan M. Brookhart. 

If a student is struggling, it will be important to provide them with feedback in a timely way in order to help their understanding of a concept. It is also important to decide on the amount of feedback to provide so that the student does not get discouraged. Ensuring that there is positive feedback about the students work is also an important aspect. Depending on the mistakes or gaps of understanding causing a student to struggle, the mode of feedback may need to be adjusted. If there was a major concept being misunderstood, it would be very difficult to express this through written feedback and would likely be more successful visually/through demonstration

Timing is very important for feedback. Within a unit, I think it is important for all students to have different forms of feedback before the completion of a unit task/test.