One of the most refreshing things about the presentation was that Kristy gave us ideas for activities that really turned on an inquiry mindset and were accessible to all learners. In my placement I really struggled with differentiating for students of all levels, though this was partially due to the fact that it was a very 'traditional' classroom. This meant that activities and worksheets had a very narrow focus, checking off specific expectations one or two at a time, and differentiation was a matter of having an entire catalog of materials at the ready for every lesson.
While worksheets were the norm in my classroom, I spent a large amount of time modeling and deriving equations and relationships with my students. This was an idea that Kristy touched upon with respect to geometry. When teaching my fractions unit I emphasized the understanding of the core concepts of fractions---what the numerator and denominator represented, and the different ways to represent this---and not equations. My students were all rather unenthusiastic when they heard we were going to start the fractions unit, and I found that this was due to their tenuous understanding of the foundations. My students all knew how to add, subtract, multiply, and divide, so I always asked them to apply their knowledge of these concepts to fractions. My lessons were always executed using a stream of questions (e.g. What is a half plus a half? One whole or two quarters?) and I found the students were very receptive to working things out in this manner, whether as a class or individually. On the occasions when I used direct instruction for a concept, I found my students had more trouble digesting the idea and generally made more mistakes than with other concepts. So even though I wasn't calling my teaching inquiry at the time, my lessons often incorporated that element of questioning, and I saw firsthand how effective this was for the class as a whole.
Most resources related to inquiry that I have encountered thus far put a strong emphasis on modeling activities and questioning for a class. In a project for my cohort class I investigated teaching strategies for ELL students in mathematics. I consolidated my research by having students complete a survey about what methods and aspects of my lessons they found helpful. While modeling was emphasized in the literature for ELL students, my survey indicated that all students found a combination of modeling and discussion to be the best way for them to learn. This means that students will benefit greatly from an inquiry-based approach because they will have that exposure to modeled thinking and behaviour in order to draw deeper connections and understanding.
