Mathematical Discussions and their Importance:
Online session 1, dealt with the importance of Mathematical discussions in the classroom and ways that we can go about orchestrating them to create collaboration between students and the teacher. I believe that one-dimensional questions with only one answer or method to solving them does not promote mathematical discussions in the classroom. It is important that the math questions designed are well thought-out and are held at a higher-level of thinking. This will prevent students from simply memorizing a formula or memorizing a method to answer the problem. Making the questions open-ended essentially allows the problem to be solved in various ways. For example, in a classroom, you could have several students employ different methods of how they achieved the final answer. This collaboration and multiple methods of solving the problem will promote mathematical discussions between the students. These types of questions make the students use their critical thinking skills which overall has them make connections and truly think about the problem. We as a class did an example of calculating the number of patio tiles in the pattern given. We were told to answer the question in three different ways and it really made me look at the question and think about different approaches to solve it. Sure, the first and obvious way of solving it was easy but the other two ways did take some time and careful critical thinking. Once we completed the question we opened up the discussion to fellow peers so we could compare and contrast our results. This was a very relevant lesson and I can use the idea of open-ended questions in the classroom to promote mathematical discussions which results in greater cognitive development for the students.
Importance of Formative Assessments and Feedback
Formative assessment is important in the mathematical classroom but this does not always mean it has to be written tests or quizzes for grades. Formative assessments is still a form of feedback and can be portrayed in manner forms such as; exit cards, math interviews, observations etc. They all serve the same purpose as they help the teacher gauge where their students are at with the lessons and content. If a teacher notices (through formative assessments) that their class has been struggling with a concept or lesson they are then able to go back and review the material with their students. Essentially, formative assessments are important because it gives students a better understanding and helps clarify any possible questions that they may have had about the previous lesson or content.
Feedback is important for students in a math classroom as it helps them improve their skills and their mental thinking about approaching a problem. The way the teacher demonstrates or provides the feedback is essential for student's learning as too much feedback may be overwhelming but too little may leave the student feeling confused. Individualizing feedback and finding an appropriate balance is a great way to provide solid feedback to all students. Moreover, Feedback is extremely important for students who may be struggling in the class. For example, if a student is struggling, you wouldn't want to just write a big red x on their test question as this may continue to discourage the student from the class. Instead, you may want to write one positive comment such as: "you were on the right track but...." and then provide some feedback on the question. Completing the feedback in a timely manner is also important as it gives the students enough time to digest the information and truly learn from their own work.
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