Attitude

Research on mathematics-related affect is varied in theories and concepts. In this survey we record the state of the art in this research through short sections from leading experts in different areas. We describe the historical development of the concept of attitude and different ways it is defined. Research on student self-efficacy beliefs in mathematics is summarized. There is reflection on the dialectic relation- ship between teacher beliefs and practice as well as on how their beliefs change. One section records the emerging research on student and teacher mathematical identities over the last two decades. Finally, mathematical motivation is explored from the perspectives of engagement structures, social behaviors, and the relation- ship between individual factors and social norms

Attitudes in Mathematics Education

Attitudes towards mathematics has a long history in mathematics education research. Over the time, research on attitudes and, more in general, on affective aspects developed a wide range of methodologies and perspectives in mathematics education, playing a growing role in the field. In this chapter, I will describe the development of the research about attitude in mathematics education, discussing the main issues emerged in this field. In particular, I will discuss the definition problem, that is the emergence of the need for a clear definition of the construct, and the ground for the development of our (TMA) three-dimensional model of attitude (Di Martino and Zan, 2010). In the last part of the chapter, some fields of application of the TMA model will also be discussed

Teachers and standardized assessments in mathematics: an affective perspective

Standardized assessments in mathematics have an increasing relevance in the educational debate and, often, they heavily affect educational policies. Specifically, the framework and the items of standardized assessments suggest what is considered relevant as an outcome of mathematics education at a certain school level. The strength and the quality of the educational impact of standardized assessments seem to depend heavily on teachers’ affective reactions to standardized assessment; however, studies focused on this issue are very rare: what are teachers’ attitudes towards the standardized assessments and their effects? In this frame, we carried out a large qualitative research to investigate teachers’ attitudes in the Italian context

Where does fear of maths come from? Beyond the purely emotional

Fear of mathematics is a widespread emotion that has many negative consequences in students: it is a possible factor of local failure (since it prevents the best use of one’s competence and knowledge) but also a possible factor of global failure (since it might lead to students giving up any engagement with mathematics). Investigating the cognitive origin of this emotion is fundamental to prevent it and to overcome its negative consequences. In this study we try to understand this origin giving voice to the students, analysing students’ narratives about their relationship with mathematics

“Think about your math teachers”: a narrative bridge between future primary teachers’ identity and their school experience

Pre-service teachers approach their professional learning in mathematics with a complex set of needs and wants. These needs and wants are strongly affected by the tension deriving from the realisation of the gap between what an individual wants to become as a mathematics teacher (his/her ideal of mathematics teacher) and what he/she believes to be at present. Professional identity as a mathematics teacher can be seen as a continuous development arising from this gap. For these reason, both as researchers and as teacher educators, it appears significant to study what ideals of positive and negative mathematics teachers the future teachers have

The role of affect in failure in mathematics at the university level: the tertiary crisis

The tertiary transition between secondary school and university appears to be an insurmountable struggle for many students. This is also the case, surprisingly, in a certain sense, of students enrolled in Mathematics degree courses, and therefore students considered “gifted” with respect to mathematics. This case seems particularly interesting from an affective point of view: these students often live failure in mathematics as a tragedy, and – above all – initially they are not able to interpret their failure. For these reasons, it appears crucial to investigate which role is played by emotions in the emergence and management of this crisis, and how the students’ view of mathematics and their self-perception develop in the tertiary crisis period

The first-time phenomenon: successful students' mathematical crisis in secondary-tertiary transition

The huge difficulties related to the transition from secondary to tertiary mathematics are documented by several official data. The analysis of these difficulties is a main issue in educational research at undergraduate level. It is of particular interest the case of the students who choose mathematics as a major. In fact, for the most part, they are students considered excellent in mathematics during secondary school, they seem to have the cognitive resources to succeed, but, in many cases, they encounter several difficulties during their university experience. Therefore, it appears particularly interesting to study also the affective sources and consequences of these difficulties. With this aim, we developed a qualitative and narrative study focused on students’ reflec- tions about their mathematical difficulties in the university experience

Students’ suspension of sense making in problem solving

Research on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the pres- ence of words and expressions having many and sometimes opposite meanings. Significant examples are the terms ‘realistic’ and ‘modeling’ associated with word problems in school. Understanding how these terms are used is important in research, because this issue relates to the design of several studies and to the interpretation of a large number of phenomena, such as the well-known phenomenon of students’ suspension of sense making when they solve mathematical problems. In order to deepen our understanding of this phenomenon, we describe a large empirical and qualitative study focused on the effects of variations in the presentation (text, picture, format) of word problems on students’ approaches to these problems. The results of our study show that the phenomenon of suspension of sense making is more precisely a phenomenon of activa- tion of alternative kinds of sense making: the different kinds of active sense making appear to be strongly affected by the presentation of the word problem

Tales from three countries: reflections during COVID-19 for mathematical education in the future

How can school mathematics prepare citizens for a democratic society? Answers to this question are not static; they change as society and its problems change. The SARS-CoV-2 pandemic with its corresponding disease COVID-19 presents such a problem: what is needed to navigate this complex situation that involves, among other things, mathematics? Using the essay genre, we use three narratives from three countries—Italy, the USA (California), and Germany—to reflect on the goals of teaching mathematics during this crisis and examine aspects of each country’s standards for mathematics education. These three stories are framed by the authors’ backgrounds, experiences, interests, their country’s situation, and response to the pandemic. We first present the three narratives and then examine common issues across them that might provide insights beyond this current crisis, for preparing students to become active citizens. In particular, we focus on three issues: (1) developing a positive mindset toward mathematics to engage with and reflect on real-world problems, (2) improving interdisciplinary connections to the sciences to better understand how science professional practices and insights are similar or different from everyday practices, and (3) considering interpersonal and collective matters beyond the individual

Mathematical induction at the tertiary level: looking behind appearences

The relevance of inductive proofs in Mathematics is beyond question and the research in Mathematics Education has widely documented the students’ difficulties in under- standing and applying mathematical induction, both at secondary school level and at university level. In this paper, we present a qualitative study involving third year Mathematics degree students aimed at investigating the solidity/fragility of mathe- matical induction comprehension. The results highlight that mathematical induction is a very hard topic also in this context, in which are involved mathematical competent students. We argue the need to design non-standard activities able to get the miscon- ceptions emerge, in order to support a deep understanding of the topic