In the first video Patrick Honner, a teacher from NYC, shows examples from his classroom where students are working with spheres and construction paper to better understand surface area and volume. He explains how having open problems can lead students to finding creative solutions that are unexpected and highlight their thought process and views. He also points out issues that can occur during these types of lessons and explains where instructors will need to assist and direct students to keep them on task and moving towards a viable solution. He highlights how group work isn't like the traditional busy work given to students currently. The teacher facilitating engaging group work needs to be actively walking around the classroom and assessing the students work and process to given them informed and constructive feedback.
The second video discusses different types of mathematics and how critical thinking is an important skill in understanding and decoding problems that occur in the real world. Students need to understand that mathematics is also a language of patterns and relationships and that it can be used for more than solving for x. I feel that he shares some interesting ideas in this video for areas that we can explore in our mathematics classes to increase student engagement. Showing students different uses for math and how its applied can help students to understand the value and purpose of the information we are having them work through.
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