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.
more »
« less
Student-created math walks in informal learning spaces
Math walks are a form of inquiry learning where students can observe and create mathematical meaning from their everyday surroundings. Here we report on a study of 5th and 6th graders in an informal learning setting where they create and present their own math walks covering concepts of ratio, scale, and proportion. The students may have developed more positive attitudes towards math and were able to meaningfully engage with powerful math ideas.
more »
« less
- Award ID(s):
- 2115393
- NSF-PAR ID:
- 10336464
- Editor(s):
- Chinn, C.
- Date Published:
- Journal Name:
- .) Proceedings of the 16th International Conference of the Learning Sciences – ICLS 2022
- Page Range / eLocation ID:
- 2006-2007
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Math walks are informal learning activities where students create mathematical meaning from their everyday surroundings. In this qualitative study, we observed 5th–8th-grade students (N = 52) across three urban informal learning sites (a community center, a zoo, and an aviation museum) as they created their own math walks exploring geometric concepts. In a post-survey questionnaire, students described their attitudes toward math using affective language motivated by three psychological factors: autonomy, competence, and relatedness. Implications for informal math learning are discussed.more » « less
-
This qualitative study examines the use of math walks with middle grade students and adult facilitators at a local zoo. Drawing on situated learning and participation frameworks, we used interaction and stance analysis to compare two contrasting cases: In the first case, the adult chaperone asked more questions and evaluated student responses. In the second case, the adult chaperone intervened less frequently, leaving more room for student discourse. Findings support efforts to design informal math learning activities which amplify student voices, towards increased mathematical interest and learning.more » « less
-
more » « less
Abstract Artificial intelligence (AI) can enhance teachers' capabilities by sharing control over different parts of learning activities. This is especially true for complex learning activities, such as dynamic learning transitions where students move between individual and collaborative learning in un‐planned ways, as the need arises. Yet, few initiatives have emerged considering how shared responsibility between teachers and AI can support learning and how teachers' voices might be included to inform design decisions. The goal of our article is twofold. First, we describe a secondary analysis of our co‐design process comprising six design methods to understand how teachers conceptualise sharing control with an AI co‐orchestration tool, called
Pair‐Up . We worked with 76 middle school math teachers, each taking part in one to three methods, to create a co‐orchestration tool that supports dynamic combinations of individual and collaborative learning using two AI‐based tutoring systems. We leveraged qualitative content analysis to examine teachers' views about sharing control withPair‐Up , and we describe high‐level insights about the human‐AI interaction, including control, trust, responsibility, efficiency, and accuracy. Secondly, we use our results as an example showcasing how human‐centred learning analytics can be applied to the design of human‐AI technologies and share reflections for human‐AI technology designers regarding the methods that might be fruitful to elicit teacher feedback and ideas. Our findings illustrate the design of a novel co‐orchestration tool to facilitate the transitions between individual and collaborative learning and highlight considerations and reflections for designers of similar systems.Practitioner notes What is already known about this topic:
Artificial Intelligence (AI) can help teachers facilitate complex classroom activities, such as having students move between individual and collaborative learning in unplanned ways.
Designers should use human‐centred design approaches to give teachers a voice in deciding what AI might do in the classroom and if or how they want to share control with it.
What this paper adds:
Presents teacher views about how they want to share control with AI to support students moving between individual and collaborative learning.
Describes how we adapted six design methods to design AI features.
Illustrates a complete, iterative process to create human‐AI interactions to support teachers as they facilitate students moving from individual to collaborative learning.
Implications for practice:
We share five implications for designers that teachers highlighted as necessary when designing AI‐features, including control, trust, responsibility, efficiency and accuracy.
Our work also includes a reflection on our design process and implications for future design processes.
-
Mathematics is an important tool in engineering practice, as mathematical rules govern many designed systems (e.g., Nathan et al., 2013; Nathan et al., 2017). Investigations of structural engineers suggest that mathematical modelling is ubiquitous in their work, but the nature of the tasks they confront is not well-represented in the K-12 classroom (e.g., Gainsburg, 2006). This follows a larger literature base suggesting that school mathematics is often inauthentic and does represent how mathematics is used in practice. At the same time, algebra is a persistent gatekeeper to careers in engineering (e.g., Harackiewicz et al., 2012; Olson & Riordan, 2012). In the present study, we interviewed 12 engineers, asking them a series of questions about how they use specific kinds of algebraic function (e.g., linear, exponential, quadratic) in their work. The purpose of these interviews was to use the responses to create mathematical scenarios for College Algebra activities that would be personalized to community college students’ career interests. This curriculum would represent how algebra is used in practice by STEM professionals. However, our results were not what we expected. In this paper, we discuss three major themes that arose from qualitative analyses of the interviews. First, we found that engineers resoundingly endorsed the importance of College Algebra concepts for their day-to-day work, and uniformly stated that math was vital to engineering. However, the second theme was that the engineers struggled to describe how they used functions more complex than linear (i.e., y=mx+b) in their work. Students typically learn about linear functions prior to College Algebra, and in College Algebra explore more complex functions like polynomial, logarithmic, and exponential. Third, we found that engineers rarely use the explicit algebraic form of an algebraic function (e.g., y=3x+5), and instead rely on tables, graphs, informal arithmetic, and computerized computation systems where the equation is invisible. This was surprising, given that the bulk of the College Algebra course involves learning how to use and manipulate these formal expressions, learning skills like factoring, simplifying, solving, and interpreting parameters. We also found that these trends for engineers followed trends we saw in our larger sample where we interviewed professionals from across STEM fields. This study calls into question the gatekeeping role of formal algebraic courses like College Algebra for STEM careers. If engineers don’t actually use 75% of the content in these courses, why are they required? One reason might be that the courses are simply outdated, or arguments might be made that learning mathematics builds more general modelling and problem-solving skills. However, research from educational psychology on the difficulty of transfer would strongly refute this point – people tend to learn things that are very specific. Another reason to consider is that formal mathematics courses like advanced algebra have emerged as a very convenient mechanism to filter people by race, gender, and socioeconomic background, and to promote the maintenance of the “status quo” inequality in STEM fields. This is a critical issue to investigate for the future of the field of engineering as a whole.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
