"The Art of Problem Posing" -Reflection

In the book, “The Art of Problem Posing”, Brown and Walter stress the importance of posing the problems. In many articles that we have read for this class, we were told how important it is to use the quality problems to create effective learning environments for the students. As a result, I have been thinking only about how to select good problem sets and how to use those problems successfully. Thus, this new emphasis on creating the question came to me as a new area of mathematics. By following the authors’ examples, I realized that the questions that we usually ask our students are limited to the instrumental understanding. By giving the students the chance to freely come up with their own ideas, we help them to extend the idea of mathematics into their real life. Students can start to think from different perspectives and approach the topic in various ways, gaining a deeper understanding of the concept. One thing that I thought was very interesting was the question that can provoke the historical background of the mathematical concepts. I have never thought that the historical portion is important in Mathematics. However, by asking “what might have encouraged people to come up with some concepts?”, students seek to have a relational understanding of the concept. I think that the idea of posing abstract and challenging questions can be a very helpful tool in teaching mathematics and I hope to gain better insights into it through this book.