Dave Hewitt's classroom teachings

Student-driven learning has always been something that I have struggled with understanding as I have never experienced it firsthand. Throughout most of my education, it has always been the teacher with the teacher as the driving force of my classes. Of the few chances that it was "student-driven," it was self-learning, which is different from how Dave Hewitt taught his class. Rather than giving the students a prompt to learn independently, Hewitt approached it by guiding them to discover something themselves. Throughout the lesson, Hewitt never told the students any facts; instead, he asked if they recognized any patterns. During the algebra lesson, it was clear that Hewitt was trying to elicit a specific answer from the students on how they solved the number. However, the students were clearly struggling, so he intervened with more guidance to get them to realize the pattern. Once the pattern was discovered, Hewitt did a few more examples with the students and got them to repeat the steps a couple more times. Then he went with a question that was more difficult than usual and required the need to write on the chalkboard. Hewitt seamlessly transitioned from a discussion to some chalkboard work.

While reading "Arbitrary and Necessary," I struggled with understanding how to make my teachings fit under necessary content and not give students the answers. However, this video on Hewitt teaching has brought to my attention how to guide students to develop their understanding of the content. Some of the techniques that Hewitt demonstrated while he encouraged students to understand algebra would be something that I would like to try and adapt during my practicum. While my experience teaching students math is a novice skill, these exciting techniques, which encourage authentic student-driven learning, are things I would love to explore and adapt into my teaching arsenal.

_______________ Nov 14 edit after seeing the post ____________________

Stop 1) How Hewitt leads the class to be "student-driven," where he tries to guide their exploration by providing hints and activities.

Stop 2) When students approach a roadblock or a hump that stops their exploration, Hewitt provides hints at varying levels of support to guide the students.

Stop 3) Hewitt transformed their exploration into something tangible on the chalkboard.

Stop 4) The paintbrush and the pencil introduction as I had to think, wait a moment, what am I supposed to say?

I believe that Hewitt created the fraction problems to encourage students to explore equivalent fractions in a way that does not require too much interaction with students, as this was during the peak of COVID lockdowns. The exploration had to be self-sufficient; thus, the student's chance of getting stuck must be minimal as the teacher could not help guide exploration. While these teacher-created math problem does not solve any particular problem, it gives the students a chance to be introduced to the idea without doing drill from a textbook. 

Hewitt likes to encourage students to explore their understanding of a topic, similar to how Peter Liljedahl wants students to think about it rather than copy the steps provided by the teacher. Because of all the self-sufficient learning students will do, students, in theory, can better understand how they learn and the concepts they just provided. So far, I am interested in how to encourage student-led learning while I am there to help students guide their knowledge to a correct understanding.