Pietro Di Martino

The Construct of Attitude in Mathematics Education

This chapter addresses a number of crucial theoretical issues about research on attitude towards mathematics, a field that has a very long tradition in mathematics education, with early studies on attitude being published more than 60 years ago. Over time, research on attitude in mathematics education has developed a range of perspectives and methodologies, dealing with a variety of questions concerning the construct of attitude: discussion and development of tools for measuring/assessing/observing it; analysis of the relationship with other affective constructs and with cognition; investigation of the relationship with achievement; critique of the lack of a suitable theoretical framework. The chapter traces the ‘story’ of the construct of attitude, providing a theoretical discussion of the issues mentioned above that are crucial to understanding the mosaic of relationships and interactions within the affect field. Through the theoretical debate, the aim of the chapter is to highlight new directions for research on attitude in mathematics education.

Pupils’ view of problems: the evolution from kindergarten to the end of primary school

Educators and several national standards highlight the role that problem solving should play in students’ mathematics education: problem solving is recognized as one of the most significant activities of doing mathematics. From the research point of view, nowadays, it is well established that cognitive and affective factors come into play in problem solving activities, but some affective issues remain unexplored. In particular, we want to study pupils’ attitudes towards (mathematical) problems, analyzing their evolution from kindergarten (where the word ‘mathematics’ is rarely explicitly mentioned) to primary school. In a well-defined affective theoretical framework, where attitude is a three-dimensional construct including beliefs and emotions, we carried out a qualitative and narrative study involving 284 students of seven different Italian schools: 121 from kindergarten and grade 1 and 163 from grade 3 to 5. Analyzing the qualitative data collected, we described primary students’ attitudes towards problems and we compared these with those developed in kindergarten, where the word ‘mathematics’ is not explicitly mentioned.

Attitudes, Beliefs, Motivation, and Identity in Mathematics Education

Research on mathematics-related affect is varied in theories and concepts. Here, we record the state-of-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 students’ self-efficacy beliefs in mathematics is summarized. There is reflection on the dialectic relationship between teachers’ beliefs and practice as well as on how their beliefs change. One section records the emerging research on students’ and teachers’ mathematical identities over the last two decades. Finally, mathematical motivation is elaborated from the perspectives of engagement structures, social behaviors, and the relationship between individual factors and social norms.

The ELTP project: from multiple choice test to individualized learning paths

In previous studies we highlighted the role that metacognitive deficiencies and negative attitudes play in students’ difficulties in mathematics during the transition from secondary to tertiary level. This work served as a theoretical basis for an elearning project - ELTP (E-Learning Transition Project) - aimed at assisting students to self-assess and consolidate their mathematic knowledge as they face tertiary transition. In this paper we describe the goals and choices underlying this learning path, which also addressed metacognitive deficiencies and negative attitudes towards mathematics and its study. The aim is to help university students approach mathematics in a more productive way so that they can become autonomous learners.