Response to "Thinking Mathematically", chapter 3 (Mason, Burton, & Stacey, 2010)

Two "stops" that I had while reading chapter 3:

• "[T]he headlong rush to get to an answer is a primary cause of becoming truly STUCK!" (p.47): I can deeply relate to this. Rushing through math challenges often leads me to give up prematurely, especially in today's environment where the Internet and AI offer quick hints or solutions at the click of a button. This instant accessibility creates a strong temptation, especially when time feels limited. It makes me wonder how we can cultivate a healthier approach to math challenges for students—one that encourages them to engage with problems at their own pace, fostering comfort and motivation in the process. How do we create opportunities for exploration and encourage them to engage with the challenge itself rather than focus solely on finding a quick solution? How can we help students develop patience and perseverance in problem-solving, especially when the "rush" to finish can hinder their progress? Incorporating exploration practices without inducing feelings of frustration or urgency seems crucial for fostering deeper engagement and resilience. This should definitely be considered when designing exams and testing environments.

• "Not knowing that the questions were supposed to be difficult made it possible for him to work on the questions without bias. He was not put off by any sense of lack of confidence." (p.52): This taps into the Imposter Syndrome or the lack of confidence that many students experience with math. When we label a problem as difficult or "classic," it often leads to a self-fulfilling prophecy—students may feel it's beyond their ability before even attempting it. This raises an important question: why do we develop such low self-confidence around math? Perhaps it's because we don't see ourselves represented among renowned mathematicians, or maybe it's rooted in past experiences with math challenges. A potential strategy to combat this is introducing classic math problems without framing them as difficult. By allowing students to approach these problems with a fresh perspective, they might surprise themselves with their ability to solve them before discovering the problem’s historical or intellectual context. This approach could help reduce bias and boost confidence.