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Attitudes, Beliefs, Motivation and Identity in Mathematics Education: An Overview of the Field and Future Directions

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.

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Attitudes, Beliefs, Motivation, and Identity in Mathematics Education

This experiment explored the effects of ability and effort attributional feedback given during subtraction competency development on children's perceived self-efficacy and achievement. Children who were deficient in subtraction skills received training on subtraction operations and engaged in problem solving, during which they periodically received ability attributional feedback for their progress, effort feedback, ability + effort feedback, or no attributional feedback. Children given only ability feedback demonstrated the highest subtraction skill and self-efficacy; the effort and ability + effort conditions did not differ, but each outperformed the no-feedback condition. Future research should examine in greater detail how children process attributional information and its effects on achievement outcomes.

Ability versus effort atributional feedback : Deferential effects on self-efficacy and achievement

It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as “relational” rather than “Instrumental” understanding. More recently, Kilpatrick, Swafford and Findell (2001) proposed five “intertwining strands” of mathematical proficiency, namely Conceptual Understanding, Procedural Fluency, Strategic Competence, Adaptive Reasoning, and Productive Disposition. In Australia, the new Australian Curriculum: Mathematics (F–10), which will be implemented from 2013, has adapted and adopted the first four of these proficiency strands to emphasise the breadth of mathematical capabilities that students need to acquire through their study of the various content strands. This paper addresses the question of what types of classroom practice can provide opportunities for the development of these capabilities in elementary schools. It draws on data from a number of projects, as well as the literature, to provide illustrative examples. Finally, the paper argues that developing the full set of capabilities requires complex changes in teachers’ pedagogy.

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Developing Mathematical Proficiency.

The series of adaptive reasoning and strategic competencies represent the five components of mathematical proficiency to describe the students’ mathematics learning success. Gender contribute to the problem-solving process. This qualitative research approach investigated the adaptive reasoning and strategic competence aspects of a male student and a female student when they solved mathematical problem. They were in the eleventh grade of high school in Makassar. Both also had similar mathematics ability and were in the highest category. The researcher as the main instrument used secondary instrument to obtain the appropriate subject and to investigate the aspects of adaptive reasoning and strategic competence. Test of mathematical ability was used to locate the subjects with similar mathematical ability. The unstructured guideline interview was used to investigate aspects of adaptive reasoning and strategic competence when the subject completed the task of mathematical problem. The task of mathematical problem involves several concepts as the right solution, such as the circle concept, triangle concept, trigonometry concept, and Pythagoras concept. The results showed that male and female subjects differed in applying a strategy to understand, formulate and represent the problem situation. Furthermore, both also differed in explaining the strategy used and the relationship between concepts and problem situations.

Investigating adaptive reasoning and strategic competence: Difference male and female

Mathematics education research has documented several classroom practices that might influence student self-regulation. We know little, however, about the ways these classroom practices could be structured in real classroom settings. In this exploratory case study, we purposefully selected a sixth-grade mathematics teacher who had participated in a professional development program focussed on NCTM standards and SRL in the mathematics classroom for extensive classroom observation. The purpose was to explore how and to what extend she structured classroom practices to support strategic competence in her students. Four features of classroom practices were found as evidence for how strategic competence was potentially supported in this classroom: (a) allowing autonomy and shared responsibility during the early stages of learning, (b) focusing on student understanding, (c) creating contexts for students to learn about strategic learning and to exercise strategic behaviour, and (d) helping students to personalise strategies by recognising their ideas and strategic behaviours.

Supporting students’ strategic competence: a case of a sixth-grade mathematics classroom

Research and theory suggest several instructional practices that could enhance student self-efficacy. However, little is known about the ways these instructional practices interact with individual students to create opportunities or challenges for developing adaptive self-efficacy. In this study, we focused on two sources of efficacy, mastery experiences, and social persuasion, and examined how these sources were structured for three students with different levels of mathematics achievement and self-efficacy within a sixth-grade mathematics classroom. Analyses within each case showed that each student experienced success and received social persuasion differently. On the other hand, analyses across the cases suggest that not only the amount but also the form (i.e., with and without assistance) of successful experiences and the type of performances (e.g., stating definitions, explaining solution procedures, sharing problem-solving strategies, and making comments on others' ideas) through which the student experienced mastery may have played important role in developing self-efficacy. Consistently, the amount and form of teacher feedback was different for each focal student. Examining these differences provide insight into each student's self-efficacy assessed over the course of the study as well as the kind of support each student needed to develop adaptive self-efficacy.

I. Elif Yetkin Özdemir

Papers

Supporting students’ strategic competence: a case of a sixth-grade mathematics classroom

The Role of Interactions Between Student and Classroom Context in Developing Adaptive Self‐Efficacy in One Sixth‐Grade Mathematics Classroom