How do you balance scaffolding and student autonomy in math instruction?

. Educators who are cognizant of these aspirations can align scaffolding efforts with the overarching goals of students, providing a sense of purpose and direction. This alignment not only enhances the effectiveness of scaffolding but also nurtures a sense of autonomy as students perceive the relevance of their learning to their future endeavors. Also in this line, they can also deploy scaffolding techniques to provide the necessary support, gradually diminishing the impact of weaknesses

Based on my experience, scaffolding is not a technique I would use with any students whom I have not known for enough time. Usually, it would take up to 4 meetings for me to understand the scaffolding my students need. That involves not only knowing what basic mathematical skills they have mastered or what specific topics they need more help on, but also their learning style of mathematics, which is sometimes overlooked. As a math olympiad coach, my go-to is to provide a wide range of practice problems, from algebra, geometry, combinatorics, and number theory, and check on the ability of the students on different topics. I would use class discussions, too, as it helps me understand the students' thinking process, which is often unwritten.

Based on my experience, balancing scaffolding and student autonomy is crucial. Every task and context requires a different approach, which is why I adjust my support according to my students' progress. Sometimes verbal, visual, or written support is more appropriate, while other times, I leverage digital tools. My primary goal is to provide enough support to help my students without hindering their autonomy, empowering them to learn and grow independently.

Building student autonomy takes time and it’s much hard to develop the older the students get. Students need to be comfortable with failure before they are ready to embrace autonomy. Unfortunately our current outcome driven system does not support this mindset. For this reason it is important as maths educators to be persistent in this. Learning maths can be messy and we can support our students by embracing that messiness ourselves as teachers.

In the math olympiad, it is always crucial for students to not only be able to solve the problems but also understand the thinking process behind them. My type of scaffolding, which was usually called "hints" during the classes, is always related to the thinking process.?Thinking-process-based scaffolding will help the students much more than just the concept-based one. It provides them with some ideas on how to solve a problem without taking away the creativity in their approaches. It also triggers the students to be able to solve questions by themselves based on their experience solving similar questions in the past, which makes it easier for me to fade the scaffolding whenever I need to.

As I fade the scaffolding, I ask my students about their thinking process and solutions to the problems they solve. There are three purposes: 1) I am able to understand how they think; 2) I evaluate the scaffolding I provided earlier; and 3) I encourage my students to reflect on their own methods. There are various math olympiad problems out there, so my students knowing whether they use the correct and most efficient method is key. It provides them with ideas on how to solve similar problems in the future. It also stimulates them to ask questions, such as whether there is a more proper method, whether there is a different concept to consider, etc.