I A Theory of Affect for Mathematical Problem Solving.- 1 Affect and Learning: Causes and Consequences of Emotional Interactions.- 2 The Role of Affect in Mathematical Problem Solving.- 3 Describing the Affective Domain: Saying What We Mean.- II Studies of Learning.- 4 Affect in Schema Knowledge: Source and Impact.- 5 Aesthetic Influences on Expert Mathematical Problem Solving.- 6 Self-Confidence, Interest, Beliefs, and Metacognition: Key Influences on Problem-Solving Behavior.- 7 Information Technologies and Affect in Mathematical Experiences.- 8 Searching for Affect in the Solution of Story Problems in Mathematics.- III Studies of Teaching.- 9 Young Children's Emotional Acts While Engaged in Mathematical Problem Solving.- 10 Teaching Practices and Student Affect in Problem-Solving Lessons of Select Junior-High Mathematics Teachers.- 11 Affect and Problem Solving in an Elementary School Mathematics Classroom.- 12 Affective Factors and Computational Estimation Ability.- 13 Affective Issues in Teaching Problem Solving: A Teacher's Perspective.- IV Responses to the Theory.- 14 The Study of Affect and Mathematics: A Proposed Generic Model for Research.- 15 Psychological Conceptions of Mathematics and Emotion.- V Looking Back.- 16 Affect and Learning: Reflections and Prospects.- 17 Beliefs, Attitudes, and Emotions: New Views of Affect in Mathematics Education.- Author Index.

Affect + Cognition = Mathematical Problem Solving@@@Affect and Mathematical Problem Solving: A New Perspective

This paper will review theoretical approaches for research on mathematics-related affect from the 1990s until today. In order to organise this field, a metatheory of the affective domain is developed, based on distinctions along three dimensions: 1) cognitive, motivational and emotional aspects of affect; 2) rapidly changing affective states versus relatively stable affective traits; and 3) the social, psychological and physiological nature of affect. Using ideas from enactivism and other system theories, the third dimension is elaborated. The embodied perspective brings forth on the one hand the evolutionary basis of human affect, and on the other the individual developmental perspective. Classroom microculture and cross-cutting social variables (e.g., gender and ethnicity) are identified as two different ways of theorising the social dimension of mathematics-related affect.

Exploring new dimensions of mathematics-related affect: embodied and social theories

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest, value and self-efficacy were assessed before and after a ten-lesson teaching unit promoting modelling competency related to the topics “Pythagoras’ theorem” and “linear functions”. The study aimed to answer the following research questions: (1) Do students’ enjoyment, value, interest and self-efficacy expectations differ depending on the type of task? (2) Does the treatment of modelling problems in classroom instruction influence these variables? (3) Are there any differential effects for different ways of teaching modelling problems, including a “directive”, teacher-centred instruction and an “operative-strategic”, more student-centred instruction emphasising group work and strategic scaffolding by the teacher? The findings show that there were no differences in students’ enjoyment, interest, value and self-efficacy between the three types of tasks. However, teaching oriented towards modelling problems had positive effects on some of the student variables, with the student-centred teaching method producing the most beneficial effects.

Teaching methods for modelling problems and students’ task-specific enjoyment, value, interest and self-efficacy expectations

This paper offers an outline and a characterisation of the didactics of mathematics, alias the science of mathematics education, as a scientific and scholarly discipline, and discusses why its endeavours should be of interest to research mathematicians (and other mathematics professionals). It further presents and discusses a number of major, rather aggregate findings in the discipline, including the astonishing complexity of mathematical learning, the key role of domain specificity, obstacles produced by the process-object duality, students' alienation from proof and proving, and the marvels and pitfalls of information technology in mathematics education.

Aspects of the nature and state of research in mathematics education

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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

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Affect and mathematical thinking : Exploring developments, trends, and future directions

The first working group on affect was organized in CERME 3 in 2003. This was the fourth affect working group and like the previous three, it was an energizing and inspiring event. We had 18 participants and 17 papers were submitted to our working group. One of the papers was cancelled, and the peer review process led to rejection of one paper before the conference. Several papers were revised and all except one of these were accepted for publication in the proceedings, leading to 14 published papers.

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CERME 6 - WORKING GROUP 1 Multimethod approaches to the multidimensional affect in mathematics education

The quantitative data about the participation to TWG08 at CERME9 highlights the growing interest toward affective issues in the field of Mathematics Education. 40 manuscripts were submitted to the group, 34 were accepted for the discussion, and finally in these proceedings 29 papers and 4 posters are included. 
Although we have seen a general upward trend in the number of countries represented within this TWG, CERME9 set a new record in this regard with 16 countries present, representing four different continents. This meant that we had more papers both submitted and presented than ever before. 40 manuscripts were submitted to the group, 34 were accepted for the discussion, and finally in these proceedings 29 papers and 4 posters are included.

https://hal.archives-ouvertes.fr/hal-01287327/document

Marilena Pantziara

Papers

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

Attitudes, Beliefs, Motivation, and Identity in Mathematics Education

Affect and mathematical thinking : Exploring developments, trends, and future directions

CERME 6 - WORKING GROUP 1 Multimethod approaches to the multidimensional affect in mathematics education

Introduction to the papers of TWG08: Affect and mathematical thinking