My philosophy of teaching math is continually being refined through experience and reflection. I think that we often push students to learn algorithms and ideas that are abstract without taking time to formalize foundational concepts, which results in low self-image and a sense of being bad at math.
I am a huge fan of visual models and solid questioning strategies, and I will typically question a student through a struggle when I can. At the same time, I recognize the value of repetition for developing procedural fluency with basic skills and observe that many students with learning disabilities face their greatest challenges in knowing how to tap into correct steps to deal with the basics. It's a dance between helping them to remember the how tos and understanding the reasoning behind those how tos. I'm not talking about drill and kill repetition where students face tons of intricate problems in a single assignment. I'm talking about repeated exposure to a common set of problems such that my students become confident enough to then face similar problems. Students typically provide feedback stating that I present things so that they understand. Ironically, many of the adults who sit in on my classes as paraprofessionals also indicate that they learn while in my class.
My students are very often those who struggle with concepts that are not concrete. I am often pressured to move ahead because of the pacing required to cover it all, and yet, I find that moving too quickly deprives my strugglers of the opportunity to get a better handle on their understanding. It's always a balancing act.
My resources focus on areas and design that will support students who struggle. Strugglers often need graphic organizers, slower pacing, chunking, and a lot of repetition. They often state that Algebra looks like gibberish, so I create resources with fewer problems and more space on a page. Fancy writing throws them off, so I keep my fonts simple. Self-guided and self-correcting activities are excellent as these will allow students to immediately know if they are on track or not.
I'm a lifetime learner, and I'm always learning from my students! I also learn about what works and what does not so that I can refine my practice.