It is clear from people’s general dislike of mathematics that there is some flaw in how it is taught. It is often seen as overly difficult and obtuse, orthogonal to anything you’d want to actually know. I believe this can be fixed through a focus on pedagogical methods. Many older methods of teaching involve students being trained in the correct procedures for solving a mathematics problem, without much room for gaining true understanding. However, I believe, in mathematics, learning just the way to solve one specific problem is creating unnecessary difficulty, as then you can’t adapt when a similar type of problem is thrown at you. Not even understanding why you’re doing what you're doing just compounds the problem. I do not believe this method of instruction to be ideal for mathematics, at least.

The problem is solved by allowing students to have understanding, and to believe in their own skills in mathematics. Inquiry-based instruction solves this problem as the students are able to derive the mathematics themselves, the way they would at the university level. Additionally, I believe that students learn best when the students discover what they’re learning themselves, both in terms of true understanding and even in terms of memorizing procedures. In terms of confidence in their own skills, teaching students to have a growth mindset has been shown to help; it’s worth it spending some time to tell them how they can become good at mathematics, even if they were bad at it before.

Lastly, collaborative group work, as modeled in Jo Boaler’s complex instruction theories, can be instrumental in increasing student’s confidence in mathematics and their ability. The important parts to me are assigning each student a different role that they can be competent in, so everyone gets to feel like they’re good at math, and emphasizing that it’s important for students to help each other, so students can cover for each other’s weaknesses. Lastly, I think the very concept of group work also helps student learning in general, as a lot of mathematics features logical leaps that are easier to make with more people involved. Learning solo is learning mathematics on hard mode: it’s a fundamentally collaborative field.

As for assessments, I believe in using formative assessments primarily, with summative assessments coming only after students are well-prepared to do well on them. The goal of a teacher is to help students learn, and formative assessments allow a teacher to adjust their lessons to help the students learn better, without much stress for the students. To this end, I’d prefer to assess students as they’re doing activities, and naturally work assessment into the lessons much of the time, including by using the common technique of having a pre- and post-assessment.

My teaching philosophy is based on increasing student understanding and confidence. To this end, the main techniques I’d want to use are group work and inquiry-based instruction. I believe these can equip students to do well in and enjoy their math classes.