Understanding Emotions in Mathematical Thinking and Learning

Ulises Xolocotzin

• Publisher: Academic Press
• Year: 2017
• Print ISBN: 9780128022184
• eBook ISBN: 9780128024898
• Topic: Psychology
• Subtopic: Mathematics General
• Index: Psychology

Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. - Covers methodologies in studying emotion in mathematical knowledge - Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition - Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches - Explores the role of anxiety in mathematical learning - Synthesizes unifies the work of multiple sub-disciplines in one place

Section III

Emotions In the Learning and Teaching of Mathematics

Section IIIA

Learners In Different Educational Levels

Chapter 6

Students’ Emotional Experiences Learning Mathematics in Canadian Schools

Jo Towers*; Miwa A. Takeuchi*; Jennifer Hall^†,a; Lyndon C. Martin^{‡ *} University of Calgary, Calgary, AB, Canada
^† Monash University, Melbourne, VIC, Australia
^‡ York University, Toronto, ON, Canada
^a Research conducted while at the University of Calgary.

Abstract

In this chapter, we draw on Canadian Kindergarten to Grade 9 students’ autobiographical accounts of learning mathematics in schools and their drawings of their feelings about doing mathematics in order to explore students’ relationships with mathematics and the emotions associated with doing mathematics. Drawing on enactivist thought, we offer insight into the complex relationship between emotion and learning. Our analysis reveals a nuanced emotional landscape associated with learning mathematics, including positive, negative, and highly topic-dependent relationships with mathematics among this population, together with narratives of changing relationships that shed light on the kinds of pedagogies that support and detract from learning. Drawings of students’ heads feature widely in the data, prompting us to raise questions about the disembodied nature of mathematics learning in schools.

Keywords

Emotion; Affect; Mathematics learning; Mathematics autobiography; Drawings; Embodiment

Introduction

This chapter offers insight into the complex relationship between emotion and learning in the domain of mathematics education. To better understand this relationship, we designed a project to explore (1) students’ lived experiences of learning mathematics in Canadian schools; (2) the images of mathematics that students are developing in schools and how they persist over time; (3) the nature of students’ mathematical identities, including students’ emotional relationships with mathematics and the emotions experienced while doing mathematics; and (4) the role that teachers and schools play in shaping these identities, relationships, and emotions. The first phase of the research, on which we report here, concerned Kindergarten to Grade 9 students’ experiences while later phases addressed secondary and postsecondary students’ experiences, as well as those of members of the general public. Preliminary findings of Phase 1 of the study, dealing primarily with students’ images of mathematics, appear elsewhere (Hall & Towers, 2014; Hall, Towers, & Martin, 2015; Hall, Towers, Takeuchi, & Martin, 2015; Plosz, Towers, & Takeuchi, 2015; Takeuchi & Towers, 2015; Towers, Hall, & Martin, 2015; Towers, Takeuchi, Hall, & Martin, 2015). In this chapter, we draw on Kindergarten to Grade 9 students’ autobiographical accounts of learning mathematics in schools to explore, in particular, students’ relationships with mathematics and the emotions associated with doing mathematics.

Review of the Literature

Mathematics education research about affective factors has been conducted since the 1960s, with early studies focusing on mathematics anxiety and attitudes toward mathematics (Zan, Brown, Evans, & Hannula, 2006). Two instruments developed in the 1970s, the Mathematics Anxiety Rating Scale (Richardson & Suinn, 1972) and the Mathematics Attitude Scales (Fennema & Sherman, 1976), are still widely used, particularly as affect becomes an increasing focus in mathematics education research. This focus on affect has been attributed to two underlying arguments: (1) attitudes toward mathematics are related to achievement in mathematics and (2) attitudes toward mathematics are significant in their own right (Di Martino & Zan, 2011; Zan et al., 2006). George (2009) posits that “the nature of participation in mathematics impinges on the relationship/identity a person develops with the subject” (p. 207). In addition to research conducted by mathematics education researchers, cognitive psychologists have also investigated affective factors in mathematics education. However, this research tends to be more narrowly focused, both in terms of methodology (quantitative) and topic focus (negative topics, such as mathematics anxiety) (e.g., Ahmed, Minnaert, Kuyper, & van der Werf, 2012; Ashcraft & Kirk, 2001; Young, Wu, & Menon, 2012). Understanding a wider breadth of students’ emotional connections to mathematics is essential for designing mathematics instruction and learning environments that foster students’ positive dispositions for learning mathematics (Boaler, 2011).

Feelings About Mathematics

As noted, a great deal of research has investigated students’ affective relationships with mathematics. Much of this research involves the use of quantitative questionnaires (i.e., those involving closed question types, such as Likert scales), including the Mathematics Anxiety Rating Scale (Richardson & Suinn, 1972) and the Mathematics Attitude Scales (Fennema & Sherman, 1976), though affect has also attracted the attention of researchers who draw on qualitative approaches. For example, in Hall’s (2013) research, most participants expressed that they liked mathematics, felt confident in their mathematics abilities, and recognized the importance of mathematics. While Hall did not find any gender differences in these views, the younger participants (Grade 4 students) in her study expressed more positive views than did the older participants (Grade 8 students). This lack of gender difference stands in contrast to other research, which typically reports that boys feel more confident in their mathematics abilities and like mathematics more than do girls, while the age-related differences in views are consistent with other research (e.g., Hall, 2012; Lubienski, Robinson, Crane, & Ganley, 2013; Lupart, Cannon, & Telfer, 2004). Other aspects of students’ identities, including racialized identities, can also impact students’ relationships with mathematics. Berry, Thunder, and McClain’s (2011) research involved gathering mathematics autobiographies from Black boys in Grades 5–7 in the United States who were top achievers in mathematics. In these reflective pieces, the boys shared that their relationships with mathematics were highly influenced by external recognition (e.g., praise from parents and teachers), and their identities as Black boys, both from a racialized and gendered standpoint, caused them to feel a sense of “otherness” as mathematically proficient students.

Images of Mathematics

An important emerging strand of research concerns students’ views about the nature of mathematics and mathematical practices. Perkkilä and Aarnos (2009) addressed this topic and explored the views of Finnish children, aged 6–8, by asking them to draw themselves in the “land of mathematics.” The drawings tended to show the students alone, working on arithmetic or number facts, in a nature-based setting. These findings indicate that students view mathematics as a solitary pursuit involving only certain types of mathematics. Other researchers have also investigated students’ views about the nature of mathematics, though typically without including drawing as a data collection tool. For example, research conducted in New Zealand (Young-Loveridge, Taylor, Sharma, & Hawera, 2006), involving interviews with elementary students, found that students tended to view mathematics as being related to number and/or operations, as opposed to other mathematical topics, a finding that is consistent with our own research and that we have described elsewhere (e.g., Plosz et al., 2015; Towers, Hall, et al., 2015). Similarly narrow views of mathematics were also found in Hall’s (2013) research with elementary school students in Canada. Students in Hall’s (2013) research, which involved questionnaires, drawings of mathematicians, and focus group interviews with media prompts, tended to conceptualize mathematics as comprising either number sense and numeration concepts, particularly arithmetic, or financial mathematics. Hall suggested that these narrow views were influenced by the students’ interactions with their teachers, parents, and popular media.

Suggestions to Improve Students’ Emotional Relationships with Mathematics

Recently, researchers have started to examine the conditions and instructional contexts in which students’ emotional reactions to mathematics can be altered (Evans, Morgan, & Tsatsaroni, 2006; Hannula, 2002; Vandecandelaere, Speybroeck, Vanlaar, De Fraine, & Van Damme, 2012). Various suggestions have been made for classroom practices that may help to better engage students in mathematics and consequently improve their emotional relationships with the subject area. In some examples, the suggestions relate to classroom practices of teaching mathematics (with the implication that improved teaching will lead to improved student experience and emotional relationships with mathematics), whereas other examples suggest addressing students’ emotional relationships with mathematics directly. As an instance of the former, recent Canadian research in a Grade 10 classroom (Liljedahl, 2014) found that using random groupings durin...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Contributors
• Preface
• Section I: Introduction: An Overview of the Field
• Section II: Cognition and Emotion In Mathematical Activity
• Section III: Emotions In the Learning and Teaching of Mathematics
• Section IV: Theoretical Advances
• Index