1. How these ideas interact with your own hopes and concerns about taking up the profession of teaching.
When teaching this previous year, I was sometimes nervous to take students outdoors, play sports with them, or do unconventional activities. I wasn't sure if the principal or admins would allow that due to safety policies etc. However, reading the article has given me a sense of optimism and excitement that these activities are actually good practices for students, and help with student concentration and engagement. It allows them to explore mathematics in the real world, making the subject more enjoyable.
2. What images and metaphors you take away from the reading.
The metaphor "dancing teachers into being with a garden" from the title really resonates with me. I think it is a pretty cool metaphor and symbolizes a more creative, playful, adaptable, and less rigid approach to teaching. As prospective math teachers who used to be students, we often see math class as standard, with the teacher teaching the content and then students working on practice problems. This metaphor suggests that we can deviate from that and suggests that we explore more creative ways to teach in the classroom.
3. Things you agree and disagree with, wonder about and/or can extend to other ideas about teaching in a fast-changing and uncertain world.
Overall, I agree with the article's main point, in the sense that math teachers need to practice more creativity and need to be less rigid in the classroom. The stereotype that math class is doing problems and chugging numbers at a desk in the classroom needs to change.
On the other hand, I believe that there are certainly restrictions on what a teacher should and shouldn't do in a math class. The article mentions napping, dreaming, and sewing as some possible activities for students in class. Perhaps it may be something to consider for an elementary classroom, but in the secondary curriculum, mathematics is more rigorous and there is more content to cover. That being said, class should be a good use of time and should be relevant and working toward completion of both the course content and curricular competencies. Personally, I would not force activities into the curriculum or lesson plan which I don't seem fit or that I feel is not sufficiently relevant and helpful.