TY - JOUR

T1 - Engagement and affect patterns in high school mathematics classrooms that exhibit spontaneous problem posing

T2 - an exploratory framework and study

AU - Headrick, Lorna

AU - Wiezel, Adi

AU - Tarr, Gabriel

AU - Zhang, Xiaoxue

AU - Cullicott, Catherine E.

AU - Middleton, James A.

AU - Jansen, Amanda

N1 - Funding Information:
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
Publisher Copyright:
© 2020, Springer Nature B.V.

PY - 2020/11

Y1 - 2020/11

N2 - 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.

AB - 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.

KW - Affect in mathematics

KW - Early high school mathematics classes

KW - Mathematical curiosity

KW - Mathematical engagement

KW - Mathematical problem

KW - Spontaneous problem posing

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U2 - 10.1007/s10649-020-09996-7

DO - 10.1007/s10649-020-09996-7

M3 - Article

AN - SCOPUS:85096072057

SN - 0013-1954

VL - 105

SP - 435

EP - 456

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

IS - 3

ER -