Engagement and affect patterns in high school mathematics classrooms that exhibit spontaneous problem posing: an explora
- PDF / 1,151,176 Bytes
- 22 Pages / 439.37 x 666.142 pts Page_size
- 57 Downloads / 323 Views
Engagement and affect patterns in high school mathematics classrooms that exhibit spontaneous problem posing: an exploratory framework and study Lorna Headrick, et al. [full author details at the end of the article] Accepted: 2 October 2020/ Published online: 17 November 2020 # Springer Nature B.V. 2020
Abstract
Spontaneous problem posing (SPP) is presented as a phenomenon central to mathematical thinking, wherein learners generate problems without formal prompting, and where posed problems originate from the learner’s motivation to improve their knowledge. Because of this, they may serve as important markers of productive mathematical engagement—in particular, affective engagement—both for problem posers and their classroom communities (D’Mello & Graesser in Learning and Instruction, 22(2), 145–157, 2012). We report on a study which utilized mixed methods to examine SPP and associated affective engagement of students in four early high school mathematics classrooms in two geographic regions of the USA. For each classroom, we used observational and experience sampling methods to examine the patterns of affect problem posers and their peers experienced at individual and group levels, respectively, on a day with at least one instance of SPP observed compared with a day with no observed instances of SPP. Results show evidence of positive affect among problem posers, while their peers reported fewer negative emotions about mathematics tasks on days with SPP than on days without SPP. Moreover, a detailed analysis of two spontaneous problem posers revealed that they showed a desire to extend their own mathematical thinking, expressed dissatisfaction with their current knowledge, and directed their problems primarily towards the teacher. Results are discussed regarding the need to support students’ confidence in their original mathematical ideas in class, and for reducing negative emotional responses to mathematics tasks. Keywords Spontaneous problem posing . Mathematical problem . Affect in mathematics . Mathematical curiosity . Mathematical engagement . Early high school mathematics classes In the past three decades, the field of mathematics education has recognized problem posing as an important mathematical activity, both for promoting students’ conceptual understanding, and for engaging them in deep exploration of mathematical ideas, conjectures, and proofs (Brown & Walter, 2005; Cai et al., 2013; Cai, Hwang, Jiang, & Silber, 2015; Carillo & Cruz, This research was supported in part by a grant from the National Science Foundation (#1661180). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation
436
Headrick L. et al.
2016; Cunningham, 2004; Silver, 1994). Although previous research has provided considerable insight into how explicitly asking students to pose their own problems can enable them to articulate and develop their mathematical thinking (Cai, 2003; Cai et al., 2013; Kapur,
Data Loading...
