ABSTRACT

Background: We explore how school-based mathematical experiences shape out-of-school mathematical experiences, developing the idea that learners hybridize norms and practices around authority and evaluation across these two contexts. To situate our study, we build on constructs of participatory identity and framing.

Methods: Drawing from a large corpus of video records capturing children’s point-of-view, we present a case study of hybridization with two purposively sampled 12-year-old friends—Aimee and Dia—interacting in an out-of-school mathematics playspace. We use interaction analysis to articulate grounded theories of hybridization.

Findings: We present a thick description of how children hybridize their activity in out-of-school spaces and how such hybridization is consequential for engagement. Dia’s case illustrates how traditional norms and practices around authority and evaluation can lead to uncertainty and dissatisfaction, while Aimee’s illustrates how playful norms and practices can lead to exploration and pleasure in making. We argue that their school-based mathematics experiences and identities influenced these differences.

Contribution: This report strengthens theoretical and methodological tools for understanding how activity and identity development in one context become relevant and shape activity in another by connecting analytic constructs of identity, framing, and hybridizing.

摘要

背景：我们探索以学校为基础的数学经验如何塑造校外数学经验，发展这样一种理念，即学习者在这两种背景下围绕权威和评估混合规范和实践。为了定位我们的研究，我们建立在参与性身份和框架的结构上。

方法：从捕捉儿童观点的大量视频记录中提取，我们提出了一个杂交案例研究，两个有目的地抽样的 12 岁朋友——Aimee 和 Dia——在校外数学游戏空间互动. 我们使用相互作用分析来阐明杂交的基础理论。

发现：我们详细描述了儿童如何在校外空间中混合他们的活动，以及这种混合如何对参与产生影响。Dia 的案例说明了围绕权威和评估的传统规范和实践如何导致不确定性和不满，而 Aimee 的案例说明了有趣的规范和实践如何导致探索和制作乐趣。我们认为，他们在学校的数学经历和身份影响了这些差异。

贡献：本报告通过连接身份、框架和混合的分析结构，加强了理论和方法工具，以了解在一种情况下的活动和身份发展如何变得相关并塑造另一种情况下的活动。