Investigating problem-posing during math walks in informal learning spaces

Informal mathematics learning has been far less studied than informal science learning - but youth can experience and learn about mathematics in their homes and communities. "Math walks" where students learn about how mathematics appears in the world around them, and have the opportunity to create their own math walk stops in their communities, can be a particularly powerful approach to informal mathematics learning. This study implemented an explanatory sequential mixed-method research design to investigate the impact of problem-posing activities in the math walks program on high school students' mathematical outcomes. The program was implemented during the pandemic and was modified to an online program where students met with instructors via online meetings. The researchers analyzed students' problem-posing work, surveyed students' interest in mathematics before and after the program, and compared the complexity of self-generated problems in pre- and post-assessments and different learning activities in the program. The results of the study suggest that students posed more complex problems in free problem-posing activities than in semi-structured problem-posing. Students also posed more complex problems in the post-survey than in the pre-survey. Students' mathematical dispositions did not significantly change from the pre-survey to post-survey, but the qualitative analysis showed that they began thinking more deeply, asking questions, and connecting school content to real-world scenarios. This study provides evidence that the math walks program is an effective approach to informal mathematics learning. The program was successful in helping students develop problem-posing skills and connect mathematical concepts to the world around them. Overall, "math walks" provide a powerful opportunity for informal mathematics learning.